hydraulic-fracturing-fundamentals-and-advancements compress

Hydraulic Fracturing
Fundamentals and Advancements
Jennifer L. Miskimins, Editor-in-Chief
MONOGRAPH SERIES
Hydraulic Fracturing: Fundamentals
and Advancements
Hydraulic Fracturing: Fundamentals
and Advancements
Society of Petroleum Engineers
Richardson, Texas, USA
© Copyright 2019 Society of Petroleum Engineers
All rights reserved. No portion of this book may be reproduced in any form or by any means, including electronic storage and retrieval
systems, except by explicit, prior written permission of the publisher except for brief passages excerpted for review and critical
purposes.
Printed in the United States of America.
Disclaimer
This book was prepared by members of the Society of Petroleum Engineers and their well-qualified colleagues from material published in the recognized technical literature and from their own individual experience and expertise. While the material presented is
believed to be based on sound technical knowledge, neither the Society of Petroleum Engineers nor any of the authors or editors herein
provide a warranty either expressed or implied in its application. Correspondingly, the discussion of materials, methods, or techniques
that may be covered by letters patents implies no freedom to use such materials, methods, or techniques without permission through
appropriate licensing. Nothing described within this book should be construed to lessen the need to apply sound engineering judgment
nor to carefully apply accepted engineering practices in the design, implementation, or application of the techniques described herein.
ISBN 978-1-61399-719-2
10 9 8 7 6 5 4 3 2 1
Society of Petroleum Engineers
222 Palisades Creek Drive
Richardson, TX 75080-2040 USA
http://store.spe.org
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1.972.952.9393
Preface
In 1989, the Society of Petroleum Engineers (SPE) began working on Recent Advances in Hydraulic Fracturing, Monograph
Series Vol. 12, which was published in 1989. The technical editors were John L. Gidley, Stephen A. Holditch, Dale E. Nierode, and
Ralph W. Veatch Jr. The book was the first in the SPE Monograph Series to be organized with different “expert” authors for each
chapter. The technical editors developed an outline and assigned the best experts for each topic to write the chapter. The result was
a monograph that set the tone for technology transfer for a complex technical operation. Recent Advances in Hydraulic Fracturing
(Monograph 12) captured the current technology (in the 1980s), but it also included the fundamental knowledge that was in the literature dating back to the 1960s. The technology, however, was focused on hydraulic fracturing in reservoirs where vertical fractures
were created in vertical wells, with the most common reservoir involved at that time being a tight gas or tight oil sandstone reservoir.
This new book, Hydraulic Fracturing: Fundamentals and Advancements, is a comprehensive update to Monograph 12. In the
nearly 30 years since it was published, the science, technology, and application of hydraulic fracturing have experienced explosive
growth. Perhaps the largest factor in the increased application of hydraulic fracturing has been the use of the technique to stimulate
horizontal wells in shale reservoirs, sometimes called the “shale revolution.” The industry is achieving economically recoverable
oil and gas from microdarcy and nanodarcy formations that were not considered viable candidates for oil and gas production in 1989.
The use of horizontal drilling in these tight oil and gas reservoirs, combined with multistage hydraulic-fracture treatments, has
revolutionized the oil and gas industry.
The 18 chapters of Hydraulic Fracturing: Fundamentals and Advancements follow the general structure of Monograph 12 in that
each chapter addresses the many and varied important aspects required in hydraulic fracturing. The author team of 26 subject-matter
experts represents a diversity of talent, background, and experience. All have published extensively in their fields of specialty and have
demonstrated an extraordinary ability to clearly explain these technical processes.
We believe this book is unique in the depth and breadth of its coverage in each technical area, and it is long overdue considering
the explosive increase in technology, especially in the last 10 years. Each chapter begins with an overview that describes its scope
and summarizes the area covered. To those already experienced in hydraulic fracturing, each chapter might be viewed as standing
alone, although cross-referencing between chapters permits identification of related areas. The authors frequently present illustrative
problems to demonstrate the application of technology and have endeavored to make the material as instructive as possible.
Finally, even though every book at the time of its publication is already partially out of date, we believe that the authors of this work,
by their unfailing diligence to keep abreast of new technology, have truly captured the significant, most recent technologies required
for success in hydraulic-fracturing applications.
Jennifer L. Miskimins
Stephen A. Holditch
Ralph W. Veatch Jr.
v
Acknowledgements
A book of this magnitude does not “just happen”. Such an undertaking involves numerous parties, contributing at all levels, to reach
a successful conclusion.
First, to Steve Holditch and Ralph Veatch, two giants in the world of hydraulic fracturing, for initiating the idea of an update to
Monograph 12 so many years ago and for their generous support of me in continuing their efforts.
To the authors, contributors, and technical reviewers, many of who contributed in numerous ways to this effort, you are the reasons
for the quality and excellence that I believe is present in every page: Ghaithan Al-Muntasheri, Msalli Al-Otaibi, Bob Barree, Lucas
Bazan, Larry Britt, Ernie Brown, Hernan Buijs, Chris Clarkson, David Craig, David Cramer, Hans de Pater, Robert Duenckel, John
Ely, Joe Frantz, Chris Fredd, Chris Green, Gang Han, Kyle Haustveit, Ray Herndon, George King, John McLennan, David MiltonTayler, Carl Montgomery, Siavas Nadimi, Karen Olson, Vibhas Pandey, Harsh Patel, Mark Pearson, Kumar Ramurthy, Subhash Shah,
Norm Warpinski, Leen Weijers, Bill Wheaton, Jesse Williams-Kovacs, John Wright, Kan Wu, and Ding Zhu.
To the Society of Petroleum Engineers’ staff, who were always available to answer questions and gently steered us all through
this process: Jane Eden, Marie Garsjo, David Grant, Valerie Jackson, Melinda Mahaffey Icden, Shashana Pearson-Hormillosa, Ingrid
Scroggins, Glenda Smith and Rebekah Stacha.
To the family and friends of all those listed above who have put up with long nights and missed weekends, we all appreciate your
support in this endeavor.
Finally, to the pioneers of hydraulic fracturing and all who have continued to advance the science to where we are today, you have
our gratitude.
Jennifer L. Miskimins
Editor-in-Chief
vii
Table of Contents
Preface������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� v
Acknowledgements�������������������������������������������������������������������������������������������������������������������������������������������������������� vii
Chapter 1 – Introduction�������������������������������������������������������������������������������������������������������������������������������������������������� 1
1.1 What Has Changed Since Monograph 12������������������������������������������������������������������������������������������������������������ 4
1.2 Geologic Considerations��������������������������������������������������������������������������������������������������������������������������������������� 5
1.3 Conventional vs. Unconventional Reservoirs�������������������������������������������������������������������������������������������������������� 6
1.4 Horizontal vs. Vertical Wellbores��������������������������������������������������������������������������������������������������������������������������� 7
1.5 Other Types of Fracturing Stimulation������������������������������������������������������������������������������������������������������������������� 8
1.6 References������������������������������������������������������������������������������������������������������������������������������������������������������������ 9
Chapter 2 – Pretreatment Formation Evaluation��������������������������������������������������������������������������������������������������������� 13
2.1 Overview������������������������������������������������������������������������������������������������������������������������������������������������������������� 13
2.2 Geologic Considerations������������������������������������������������������������������������������������������������������������������������������������� 15
2.3 Acquiring Properties Using Wireline Logging����������������������������������������������������������������������������������������������������� 21
2.4 Core Analysis������������������������������������������������������������������������������������������������������������������������������������������������������ 29
2.5 Recap: How To Use These Data?����������������������������������������������������������������������������������������������������������������������� 37
2.6 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������������� 38
2.7 References���������������������������������������������������������������������������������������������������������������������������������������������������������� 39
Chapter 3 – Rock Mechanics and Fracture Geometry������������������������������������������������������������������������������������������������ 47
3.1 Overview������������������������������������������������������������������������������������������������������������������������������������������������������������� 47
3.2 Rock Properties�������������������������������������������������������������������������������������������������������������������������������������������������� 48
3.3 In-Situ Stress������������������������������������������������������������������������������������������������������������������������������������������������������ 61
3.4 Fracture-Height Growth in Geologic Media��������������������������������������������������������������������������������������������������������� 66
3.5 Fracture Complexity�������������������������������������������������������������������������������������������������������������������������������������������� 66
3.6 Summary������������������������������������������������������������������������������������������������������������������������������������������������������������ 69
3.7 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������������� 69
3.8 References���������������������������������������������������������������������������������������������������������������������������������������������������������� 70
Chapter 4 – Hydraulic Fracture Modeling�������������������������������������������������������������������������������������������������������������������� 75
4.1 Introduction������������������������������������������������������������������������������������������������������������������������������������������������������� 76
4.2 Modeling Objectives������������������������������������������������������������������������������������������������������������������������������������������ 78
4.3 Basic Physical Principles in Fracture Propagation Models������������������������������������������������������������������������������� 82
4.4 Basic Fracture Modeling Concepts������������������������������������������������������������������������������������������������������������������� 85
4.5 1D and 2D Fracture Growth Models����������������������������������������������������������������������������������������������������������������� 88
4.6 The First Fracture Model Calibration Effort—Identifying Growth Behavior������������������������������������������������������� 90
4.7 Advanced Fracture Modeling Concepts I���������������������������������������������������������������������������������������������������������� 92
4.8 Advanced 3D Fracture Growth Models������������������������������������������������������������������������������������������������������������� 96
4.9 The Second Fracture Model Calibration Effort—Net-Pressure Matching��������������������������������������������������������� 96
4.10 Advanced Fracture Modeling Concepts II������������������������������������������������������������������������������������������������������� 101
4.11 The Third Fracture Model Calibration Effort—Reconciliation With Fracture Diagnostics�������������������������������� 103
4.12 Complex Fracture Models������������������������������������������������������������������������������������������������������������������������������� 113
4.13 Fully Coupled Geomechanical Fracture Models��������������������������������������������������������������������������������������������� 120
4.14 Further Fracture Model Integration and Novel Developments������������������������������������������������������������������������ 129
4.15 Fracture Modeling Advantages and Challenges��������������������������������������������������������������������������������������������� 131
4.16 Thoughts on Future Use and Developments of Fracture Growth Models������������������������������������������������������� 133
4.17 Conclusions���������������������������������������������������������������������������������������������������������������������������������������������������� 135
4.18 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 135
4.19 References������������������������������������������������������������������������������������������������������������������������������������������������������ 136
Chapter 5 – Proppants and Fracture Conductivity���������������������������������������������������������������������������������������������������� 143
5.1 Overview����������������������������������������������������������������������������������������������������������������������������������������������������������� 144
5.2 Introduction������������������������������������������������������������������������������������������������������������������������������������������������������� 144
5.3 Effect of Fracture Conductivity on Well Performance���������������������������������������������������������������������������������������� 145
5.4 Commercial Proppants������������������������������������������������������������������������������������������������������������������������������������� 146
5.5 Laboratory Measurements of Fracture Conductivity����������������������������������������������������������������������������������������� 152
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5.6 Factors Affecting Fracture Conductivity—Proppant Characteristics and Fluids������������������������������������������������ 154
5.7 Factors Affecting Fracture Conductivity—Interactions with the Reservoir�������������������������������������������������������� 158
5.8 Nomenclature��������������������������������������������������������������������������������������������������������������������������������������������������� 162
5.9 References�������������������������������������������������������������������������������������������������������������������������������������������������������� 162
Chapter 6 – Fracturing Fluids and Additives������������������������������������������������������������������������������������������������������������� 165
6.1 Overview��������������������������������������������������������������������������������������������������������������������������������������������������������� 166
6.2 Properties of a Viscous Fracturing Fluid��������������������������������������������������������������������������������������������������������� 166
6.3 Water-Based Fracturing Fluids����������������������������������������������������������������������������������������������������������������������� 167
6.4 Oil-Based Fracturing Fluids���������������������������������������������������������������������������������������������������������������������������� 174
6.5 Alcohol-Based Fracturing Fluids��������������������������������������������������������������������������������������������������������������������� 174
6.6 Emulsion Fracturing Fluids����������������������������������������������������������������������������������������������������������������������������� 174
6.7 Foam-Based Fracturing Fluids������������������������������������������������������������������������������������������������������������������������ 176
6.8 Energized Fracturing Fluids���������������������������������������������������������������������������������������������������������������������������� 178
6.9 Fracturing Fluid Additives������������������������������������������������������������������������������������������������������������������������������� 178
6.10 Waterfracs������������������������������������������������������������������������������������������������������������������������������������������������������� 184
6.11 References������������������������������������������������������������������������������������������������������������������������������������������������������ 185
6.12 Recommended Reading List�������������������������������������������������������������������������������������������������������������������������� 191
Chapter 7 – Fluid Leakoff��������������������������������������������������������������������������������������������������������������������������������������������� 199
7.1 Overview��������������������������������������������������������������������������������������������������������������������������������������������������������� 199
7.2 Introduction����������������������������������������������������������������������������������������������������������������������������������������������������� 200
7.3 Fluid-Leakoff Equation������������������������������������������������������������������������������������������������������������������������������������ 200
7.4 Modeling of Leakoff Coefficient����������������������������������������������������������������������������������������������������������������������� 210
7.5 Laboratory Measurements of Fluid-Loss Parameters������������������������������������������������������������������������������������� 216
7.6 Effect of Key Parameters on Leakoff���������������������������������������������������������������������������������������������������������������� 219
7.7 Advances in Fluid-Loss Additives�������������������������������������������������������������������������������������������������������������������� 223
7.8 Pressure-Dependent Leakoff�������������������������������������������������������������������������������������������������������������������������� 225
7.9 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 227
7.10 References������������������������������������������������������������������������������������������������������������������������������������������������������ 228
Chapter 8 – Flow Behavior of Fracturing Fluids�������������������������������������������������������������������������������������������������������� 233
8.1 Introduction����������������������������������������������������������������������������������������������������������������������������������������������������� 233
8.2 Rheology and Classification of Fluids������������������������������������������������������������������������������������������������������������� 234
8.3 Rheological Characterization of Fracturing Fluids������������������������������������������������������������������������������������������ 235
8.4 Rheological Instrumentation��������������������������������������������������������������������������������������������������������������������������� 240
8.5 Perforation Friction Pressure Loss������������������������������������������������������������������������������������������������������������������ 241
8.6 Newtonian Fluid Flow in Straight Tubulars������������������������������������������������������������������������������������������������������ 246
8.7 Non-Newtonian Fluid Flow in Straight Tubulars���������������������������������������������������������������������������������������������� 246
8.8 Newtonian Fluid Flow in Coiled Tubulars�������������������������������������������������������������������������������������������������������� 252
8.9 Non-Newtonian Fluid Flow in Coiled Tubulars������������������������������������������������������������������������������������������������ 253
8.10 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 256
8.11 References������������������������������������������������������������������������������������������������������������������������������������������������������ 257
Chapter 9 – Proppant Transport���������������������������������������������������������������������������������������������������������������������������������� 261
9.1 Overview����������������������������������������������������������������������������������������������������������������������������������������������������������� 261
9.2 Introduction������������������������������������������������������������������������������������������������������������������������������������������������������� 261
9.3 Fundamentals of Proppant Transport���������������������������������������������������������������������������������������������������������������� 262
9.4 Proppant Transport Within the Fracture������������������������������������������������������������������������������������������������������������ 265
9.5 Proppant Transport in Complex Fracture Network�������������������������������������������������������������������������������������������� 278
9.6 Proppant Flowback������������������������������������������������������������������������������������������������������������������������������������������� 280
9.7 Nomenclature��������������������������������������������������������������������������������������������������������������������������������������������������� 285
9.8 References�������������������������������������������������������������������������������������������������������������������������������������������������������� 285
Chapter 10 – Hydraulic Fracturing-Treatment Design���������������������������������������������������������������������������������������������� 291
10.1 Introduction��������������������������������������������������������������������������������������������������������������������������������������������������� 292
10.2 Outline���������������������������������������������������������������������������������������������������������������������������������������������������������� 292
10.3 Key Influences���������������������������������������������������������������������������������������������������������������������������������������������� 292
10.4 Fracturing-Treatment Design Process���������������������������������������������������������������������������������������������������������� 294
10.5 Treatment Design Workflow�������������������������������������������������������������������������������������������������������������������������� 294
10.6 Key Input Data���������������������������������������������������������������������������������������������������������������������������������������������� 294
10.7 Generating Log-Based Models for Fracture Simulators�������������������������������������������������������������������������������� 295
10.8 Fracturing-Fluid Leakoff Calculations����������������������������������������������������������������������������������������������������������� 295
10.9 Model Calibration������������������������������������������������������������������������������������������������������������������������������������������ 296
10.10 Stress and Rock-Property Calibration Process�������������������������������������������������������������������������������������������� 296
10.11 Fracture Width Calculations�������������������������������������������������������������������������������������������������������������������������� 299
10.12 Well Productivity/Hydraulic Fracture Relationship����������������������������������������������������������������������������������������� 300
10.13 Material Selection: Fracturing Fluids������������������������������������������������������������������������������������������������������������� 301
10.14 Foamed Fracturing Fluids����������������������������������������������������������������������������������������������������������������������������� 302
10.15 Material Selection: Proppants����������������������������������������������������������������������������������������������������������������������� 304
10.16 NPV Calculations for Fracturing Treatments������������������������������������������������������������������������������������������������� 305
10.17 Pump Schedule�������������������������������������������������������������������������������������������������������������������������������������������� 307
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10.18 Proppant-Concentration Schedule���������������������������������������������������������������������������������������������������������������� 308
10.19 Pump Schedule Generation�������������������������������������������������������������������������������������������������������������������������� 309
10.20 Tip-Screenout Design����������������������������������������������������������������������������������������������������������������������������������� 312
10.21 Low-Viscosity-Fluid Design: Slickwater and Hybrid�������������������������������������������������������������������������������������� 312
10.22 Perforating for Hydraulic Fracturing�������������������������������������������������������������������������������������������������������������� 313
10.23 Limited-Entry Design������������������������������������������������������������������������������������������������������������������������������������ 313
10.24 Fracturing-Treatment Design Cases: Pump Schedule���������������������������������������������������������������������������������� 318
10.25 Design Approaches in Unconventional Shale Reservoirs����������������������������������������������������������������������������� 320
10.26 Comprehensive Fracturing-Treatment Design���������������������������������������������������������������������������������������������� 325
10.27 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 333
10.28 References���������������������������������������������������������������������������������������������������������������������������������������������������� 335
Chapter 11 – Well Completions����������������������������������������������������������������������������������������������������������������������������������� 345
11.1 Overview������������������������������������������������������������������������������������������������������������������������������������������������������� 346
11.2 Introduction to Completions�������������������������������������������������������������������������������������������������������������������������� 346
11.3 Well Construction for Hydraulic Fracturing���������������������������������������������������������������������������������������������������� 347
11.4 Completion Strategies for Hydraulic Fracturing�������������������������������������������������������������������������������������������� 367
11.5 Perforating for Hydraulic Fracturing�������������������������������������������������������������������������������������������������������������� 371
11.6 Multistage Placement Control and Treatment Diversion Techniques������������������������������������������������������������ 383
11.7 Considerations for Selecting a Multistage Placement Control Technique����������������������������������������������������� 394
11.8 Additional Well Completion Considerations�������������������������������������������������������������������������������������������������� 398
11.9 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 403
11.10 References���������������������������������������������������������������������������������������������������������������������������������������������������� 404
Chapter 12 – Field Implementation of Hydraulic Fracturing������������������������������������������������������������������������������������ 415
12.1 Overview������������������������������������������������������������������������������������������������������������������������������������������������������� 416
12.2 Treatment Planning��������������������������������������������������������������������������������������������������������������������������������������� 417
12.3 Fracturing Equipment������������������������������������������������������������������������������������������������������������������������������������ 418
12.4 Treatment Execution������������������������������������������������������������������������������������������������������������������������������������� 434
12.5 Treating Pressure Interpretation�������������������������������������������������������������������������������������������������������������������� 454
12.6 Treatment Redesign�������������������������������������������������������������������������������������������������������������������������������������� 463
12.7 Foam Fracturing�������������������������������������������������������������������������������������������������������������������������������������������� 463
12.8 Acid Fracturing���������������������������������������������������������������������������������������������������������������������������������������������� 477
12.9 Coalbed Methane Fracturing Applications���������������������������������������������������������������������������������������������������� 478
12.10 Environmental Considerations���������������������������������������������������������������������������������������������������������������������� 482
12.11 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 484
12.12 References���������������������������������������������������������������������������������������������������������������������������������������������������� 485
Chapter 13 – Fracturing Pressure Analysis��������������������������������������������������������������������������������������������������������������� 489
13.1 Overview��������������������������������������������������������������������������������������������������������������������������������������������������������� 490
13.2 Components of Pumping Pressure����������������������������������������������������������������������������������������������������������������� 492
13.3 Prefracturing and Calibration Tests����������������������������������������������������������������������������������������������������������������� 495
13.4 Treating-Pressure Analysis����������������������������������������������������������������������������������������������������������������������������� 514
13.5 Application to Treatment Schedule Design and Modification�������������������������������������������������������������������������� 520
13.6 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 520
13.7 References������������������������������������������������������������������������������������������������������������������������������������������������������ 521
Chapter 14 – Flowback and Early-Time Production Data Analysis������������������������������������������������������������������������� 523
14.1 Introduction����������������������������������������������������������������������������������������������������������������������������������������������������� 524
14.2 RTA of Flowback and Early-Time Production Data����������������������������������������������������������������������������������������� 525
14.3 Case Studies�������������������������������������������������������������������������������������������������������������������������������������������������� 568
14.4 Summary, Discussion, and Current and Future Work������������������������������������������������������������������������������������� 569
14.5 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 576
14.6 Acknowledgments������������������������������������������������������������������������������������������������������������������������������������������� 580
14.7 References������������������������������������������������������������������������������������������������������������������������������������������������������ 580
Appendix 14.A����������������������������������������������������������������������������������������������������������������������������������������������������������� 586
Appendix 14.B����������������������������������������������������������������������������������������������������������������������������������������������������������� 588
Appendix 14.C����������������������������������������������������������������������������������������������������������������������������������������������������������� 591
Appendix 14.D����������������������������������������������������������������������������������������������������������������������������������������������������������� 594
Appendix 14.E����������������������������������������������������������������������������������������������������������������������������������������������������������� 598
Appendix 14.F����������������������������������������������������������������������������������������������������������������������������������������������������������� 606
Appendix 14.G����������������������������������������������������������������������������������������������������������������������������������������������������������� 608
Appendix 14.H����������������������������������������������������������������������������������������������������������������������������������������������������������� 611
Appendix 14.I������������������������������������������������������������������������������������������������������������������������������������������������������������ 617
Chapter 15 – Fracture Diagnostics����������������������������������������������������������������������������������������������������������������������������� 625
15.1 Overview��������������������������������������������������������������������������������������������������������������������������������������������������������� 625
15.2 Microseismic Monitoring��������������������������������������������������������������������������������������������������������������������������������� 626
15.3 Surface Tiltmeter Monitoring��������������������������������������������������������������������������������������������������������������������������� 638
15.4 Downhole Tiltmeter Monitoring����������������������������������������������������������������������������������������������������������������������� 641
15.5 Radioactive Proppant Tracers������������������������������������������������������������������������������������������������������������������������� 644
15.6 Chemical Fracture Tracers (CFTs)������������������������������������������������������������������������������������������������������������������ 645
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15.7 Distributed Fiber-Optic Sensing�������������������������������������������������������������������������������������������������������������������� 647
15.8 Wellbore Imaging������������������������������������������������������������������������������������������������������������������������������������������ 651
15.9 Review���������������������������������������������������������������������������������������������������������������������������������������������������������� 652
15.10 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 653
15.11 References���������������������������������������������������������������������������������������������������������������������������������������������������� 654
Chapter 16 – Economics of Fracturing����������������������������������������������������������������������������������������������������������������������� 657
16.1 Introduction��������������������������������������������������������������������������������������������������������������������������������������������������� 658
16.2 General Economic and Business Considerations����������������������������������������������������������������������������������������� 658
16.3 Conventional Reservoir Response to Fracture Penetration and Conductivity���������������������������������������������� 660
16.4 Unconventional Reservoir Production Analysis���������������������������������������������������������������������������������������������666
16.5 General Economic Parameters��������������������������������������������������������������������������������������������������������������������� 669
16.6 Hydraulic Fracturing Treatment Costs����������������������������������������������������������������������������������������������������������� 670
16.7 Conventional-Fracturing-Treatment Economics�������������������������������������������������������������������������������������������� 674
16.8 Unconventional-Fracturing-Treatment Economics�����������������������������������������������������������������������������������������681
16.9 Other Considerations������������������������������������������������������������������������������������������������������������������������������������ 686
16.10 Summary������������������������������������������������������������������������������������������������������������������������������������������������������ 689
16.11 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 689
16.12 References���������������������������������������������������������������������������������������������������������������������������������������������������� 690
Chapter 17 – Acid Fracturing�������������������������������������������������������������������������������������������������������������������������������������� 693
17.1 Introduction��������������������������������������������������������������������������������������������������������������������������������������������������� 694
17.2 Candidates for Acid Fracturing��������������������������������������������������������������������������������������������������������������������� 694
17.3 Deciding Between Propped and Acid Fracturing������������������������������������������������������������������������������������������ 698
17.4 Acid/Mineral Reaction����������������������������������������������������������������������������������������������������������������������������������� 699
17.5 Reaction Stoichiometry of Acids������������������������������������������������������������������������������������������������������������������� 699
17.6 Reaction Kinetics of Acids���������������������������������������������������������������������������������������������������������������������������� 705
17.7 Acid Mass Transfer���������������������������������������������������������������������������������������������������������������������������������������� 707
17.8 Acid Types in Well Stimulation���������������������������������������������������������������������������������������������������������������������� 709
17.9 Modeling of Hydraulic Fractures������������������������������������������������������������������������������������������������������������������� 710
17.10 Acid Penetration�������������������������������������������������������������������������������������������������������������������������������������������� 713
17.11 Acid-Fracture Conductivity���������������������������������������������������������������������������������������������������������������������������� 720
17.12 Acid-Fracturing-Treatment Design���������������������������������������������������������������������������������������������������������������� 724
17.13 Simulator-Based Acid-Fracturing Modeling�������������������������������������������������������������������������������������������������� 728
17.14 Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������� 732
17.15 References���������������������������������������������������������������������������������������������������������������������������������������������������� 737
Appendix 17.A: Acid-Fracturing-Treatment Design Example������������������������������������������������������������������������������������� 742
Chapter 18 – Refracturing�������������������������������������������������������������������������������������������������������������������������������������������� 753
18.1 Introduction ���������������������������������������������������������������������������������������������������������������������������������������������������� 753
18.2 Case Histories of Refracturing Treatments ���������������������������������������������������������������������������������������������������� 755
18.3 Determining the Need for Refracturing ���������������������������������������������������������������������������������������������������������� 761
18.4 Candidate Selection���������������������������������������������������������������������������������������������������������������������������������������� 763
18.5 Design Considerations������������������������������������������������������������������������������������������������������������������������������������ 764
18.6 Conclusions���������������������������������������������������������������������������������������������������������������������������������������������������� 766
18.7 Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������� 766
18.8 References������������������������������������������������������������������������������������������������������������������������������������������������������ 766
Index������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ 771
Chapter 1
Introduction
George E. King and Jennifer L. Miskimins
George E. King is a registered professional engineer with 47 years of oilfield experience, having started his career with Amoco in
1971. He currently consults on well completions, interventions, and well failures, working through Viking Engineering. King holds a
BS degree in chemistry from Oklahoma State University and BS and MS degrees in chemical engineering and petroleum engineering,
respectively, from the University of Tulsa.
Jennifer L. Miskimins is the interim department head and an associate professor in the Petroleum Engineering Department at the
Colorado School of Mines. Her research interests focus on the areas of hydraulic fracturing, stimulation, completions, and unconventional reservoirs. Miskimins holds a BS degree in petroleum engineering from the Montana College of Mineral Science and
­Technology and MS and PhD degrees in petroleum engineering from the Colorado School of Mines. She is an active member of SPE.
Contents
1.1
1.2
1.3
1.4
1.5
1.6
What Has Changed Since Monograph 12����������������������������������������������������������������������������������������������������������������� 4
Geologic Considerations�������������������������������������������������������������������������������������������������������������������������������������������� 5
Conventional vs. Unconventional Reservoirs������������������������������������������������������������������������������������������������������������� 6
Horizontal vs. Vertical Wellbores�������������������������������������������������������������������������������������������������������������������������������� 7
Other Types of Fracturing Stimulation������������������������������������������������������������������������������������������������������������������������ 8
References����������������������������������������������������������������������������������������������������������������������������������������������������������������� 9
Hydraulic fracturing is a continuously evolving well stimulation method. It is capable of being adapted to enable, enhance, a­ ccelerate,
or sometimes restore production by reducing flow-path resistance across a wide range of geologic settings ranging from source
rocks to reservoirs. From the recognition of the possibility of hydraulic fracturing in the mid-1940s, the practice has become commonplace in hydrocarbon development around the world. During the past 7 decades, the design and the components of fracturing
have been tuned to efficiently increase production, often by multiple folds of increase, especially in low-permeability reservoirs and
source rocks.
The first intentional and documented hydraulic fracturing test occurred in July 1947 on the Klepper No. 1 well in the Hugoton Field
in Grant County, Kansas, USA (Clark 1949). The location is shown in Fig. 1.1. At the time, the practice was judged to be inferior
to acidizing as a stimulation mechanism (Montgomery and Smith 2010). Even with this less-than-stellar initial effort, the technology was improved as additional treatments were attempted. The first commercial treatments, shown in Fig. 1.2, were pumped by
­Halliburton on 17 March 1949 in Stephens County, Oklahoma, USA, and Archer County, Texas, USA.
Since those first treatments in the 1940s, hydraulic fracturing has become one of the most common and widely used stimulation techniques in the world. Before 2000, wells were mostly vertical, commonly with one fracture per well where stimulation was
required. Between 1950 and 2000, the total of fracture treatments numbered approximately one million (Wikipedia 2019; King 2010).
Since 2000, the percentage of highly deviated wells has increased sharply, and fracture treatments have increased from one or two per
well to a range of 20 to more than 200 in a single well that might now be 3 miles (4.8 km) in length. Although much of this increase
has been in the US where total well counts are pushing two million petroleum-oriented wells, there is an estimated total fracture treatment count of five to six million worldwide. Countries such as China and Argentina are also using the same model of closely spaced
and highly fracture-stimulated wells to produce hydrocarbons from formations with ultralow permeabilities.
In general, the hydraulic fracturing process consists of four steps: pumping a pad fluid (fluid only, no proppant), injection of a
series of slurries (fluid and proppant) with varying proppant concentrations, displacement of the proppant-laden slurry at least to the
point of entry into the formation, and termination of pumping to allow leakoff and formation closure, after which the well is placed
on production. Although these steps are commonly accepted, the industry has experimented with exception to all four steps, including
variation in pad volumes, treatments with no proppants (Mayerhofer et al. 1997), intentional overdisplacement (common in certain
types of horizontal well completions) (Fonseca et. al. 2015), and forced closure (Barree and Mukherjee 1995).
2
Hydraulic Fracturing: Fundamentals and Advancements
Fig. 1.1—First hydraulic fracturing stimulation of a producing
well, the Klepper No. 1, located in Hugoton Field, Grant County,
Kansas, USA, in 1947 (Montgomery and Smith 2010).
Fig. 1.2—Halliburton conducted the first commercial hydraulic
fracturing treatments in Oklahoma and Texas on 17 March 1949
(Montgomery and Smith 2010).
Sand proppant
Blender
Pumper
Welhead
Tubing
Fluid
Fracture
Proppant
Pay
Fracturing
fluid
Fig. 1.3—The general hydraulic fracturing process.
The industry has been using hydraulic fracturing as a
stimulation tool for more than 70 years, and the know­
ledge of the practice in specific areas and formations
continues to improve. New designs are developed, and
new reservoirs are treated. Many times, a practice that
was thought to be obsolete finds use in a new situation.
However, just as frequently, a new method must be developed to ­custom fit an efficient fracture stimulation to a
given reservoir or producing situation. With the right
type of design, almost any type of reservoir can benefit
from a fracturing treatment, although those with lower
­permeabilities or near-wellbore formation damage tend to
benefit the most. Fracture design incorporates controlled
application of pressure, decisions about the fluid type,
selection of injection rate (a speed of rate increase), selection of proppant type and size, and determination of the
total volumes of fluid and proppant to be pumped. Since
its inception, ­fracturing has evolved, but the concept of
applying pressure to create a fracture in rock formations is
the same as in the original 1947 hydraulic fracturing field
trial. Fig. 1.3 shows the basic concept of surface equipment with the treatment taking place downhole, whereas
Fig. 1.4 shows a modern treatment site with the volume of
equipment that is frequently required.
In simple terms, hydraulic fracturing involves applying
a force at the formation rock face sufficient to push against
the inner circumference of a drilled hole to a point where
the rock breaks in tension, and a crack develops outward
directed by a set of internal rock stresses that shape the
inclination and orientation of the fracture as it develops.
This process of establishing and then widening a crack in
rock and packing that crack with proppants, such as sand,
produces a flow path akin to paving a road from the vastness of the countryside into a city center, crossing and
potentially replacing hundreds of narrow footpaths. Like
the road, the fracture gives fluids within the rock a faster
travel path with less resistance to flow than compared to
the more torturous travel route through the pore structure
of the rock. The amount of production increase is dependent on the background permeability of the matrix, where
the lowest rock permeabilities are affected to the greatest
extent (Fig. 1.5).
Hydraulic fracturing starts by creating a crack in the
rock that might be 1⁄16 to ¼ in. wide, but the initial formation breakdown is just a starting point. For a fracture to be
highly effective as a flow path, it must be placed at a point
in the formation that offers
•Access to producible deposits of hydrocarbons
•Formation characteristics and stability ­suitable
to support a distinct flow path (the open fracture)
•Enough matrix permeability to allow fluid flow
into and along the hydraulic fracture
•Stress levels that allow the creation of fractures that are sufficiently wide to accept proppant transport
The mechanical objective of hydraulic fracturing is to
increase contact between the formation and the fracture.
The walls of the fracture are the intersection of billions of tiny pores within the rock that allow fluids to flow into the fracture, much
like thousands of small footpaths spilling onto a road.
Hydraulic fractures are created by generating hydraulic pressure that overcomes the in-situ formation stresses. Fractures grow at
a rate consistent with continued application of pressure, which is supplied by continuous injection of fracturing fluid, thus the term
“hydraulic.” Leakoff of the fracturing fluid into the pores and natural fractures of a formation is a dominant control of the fracture
growth. When the rate of fracturing fluid leakoff to the ever-increasing area of the exposed fracture face reaches the rate of fracturing
fluid injection, the fracture will stop growing. Raising the injection rate will only offset this fluid loss for a time, and eventually the
fluid loss into the created area will catch up with the injection rate. Other controls on fracture growth include natural barriers. These
barriers can be above, below, or lateral to the pay zone that exist as rock layers with differing properties. Far-field barriers, such as
Introduction
3
Folds of Increase in System Permeability
Fig. 1.4—Modern hydraulic fracturing site. Courtesy of Bayswater and Liberty Oilfield Services.
100,000
Matrix permeability
(md)
0.0001
0.001
0.01
0.1
0.5
1.0
10,000
1,000
100
10
1
1.0E-9
1.0E-8
1.0E-7
1.0E-6
1.0E-5
1.0E-4
Ratio of Fracture Area to Total Area
Fig. 1.5—Folds of increase in system permeability created by an unpropped natural or hydraulically created fracture for
a range of initial matrix permeabilities (Barree et al. 2014).
pinchouts, faults, and karsts, also can control fracture growth. Stresses, both in-situ and those created during the fracturing process,
can shape fracture growth and even prevent or severely limit fracture development.
Human controls on fracture growth are the design factors of rate and total volume injected. In general, fractures will grow in
“the path of least resistance” (typically perpendicular to the horizontal least principal stress where vertical stress is larger than horizontal stresses). The extent of hydraulic fracture growth is typically greater in length than height where vertical growth is bounded
by stresses or fracture barriers. The human ability to control or direct growth is severely limited by near and far-field stresses. Human
controls are usually tiny in comparison to forces present in nature. Higher fluid-injection rates, if possible, can be beneficial because
higher pressure is generated, thus widening the fracture at the wellbore and enabling unobstructed proppant entry into the fracture.
Higher wellbore pressure increases the force on the wellbore wall, effectively widening the fracture as shown in Fig. 1.6.
The main purpose of the fracturing fluid is to transmit the necessary force to the formation face to create the fracture and transport
the proppants through the wellbore and into the fracture. Water-based fluids are the most common fluid types, with gelled (linear gel or
crosslinked) and ungelled (slickwater) as the primary options. The addition of gas as a foam or a separate phase might expand the utility
of a fracturing fluid depending on the formation, reservoir pressure, and the types of fluids. Other types of fluid systems include oil-based,
alcohol-based, and emulsions. Treatment preflushes with acids such as 15% hydrochloric acid are commonly used to remove cementing
residue or carbonate deposits in natural fractures and reduce perforation breakdown pressures. There is some discussion, however, about
whether a light brine can accomplish similar pressure reductions by simply filling the pores near the wellbore with an incompressible
fluid. Fracturing fluids and selection criteria are discussed in detail in the Fracture Fluid Additives Chapter of this monograph.
Proppants are intended to keep the fracture open after the hydraulic pressure is released after the treatment. Factors in proppant
selection include density (for transport in the fluid), size (for entry into the fracture and level of flow capacity once in the fracture),
and strength (must offset confining pressures that might increase as formation fluids are removed by production). Wider fractures are
much easier for proppant to enter, but they can come at the price of higher fluid and treatment costs, along with associated gel damage
if gelled systems are used to generate wider fractures or to transport more proppant. Cost of the proppant can be a major consideration
4
Hydraulic Fracturing: Fundamentals and Advancements
Fig. 1.6—An example of the effects of increased rate on fracture width. Two views of the same openhole fracture at
approximately 4,584 ft of depth. At left is a photo of the fracture at a net pressure of ≈400 psi, and at right is the same
fracture at a higher surface injection and net pressure of ≈470 psi with three times the width.
in the case of multistage-treatment wells where millions of pounds of proppant might be used. Proppants used in fracturing have
ranged from various qualities of sand and man-made materials such as ceramics, which excel at flow capacity and strength, to the
unusual offerings of aluminum oxides, glass beads, plastic pellets, walnut shells, and metal balls. Proppant selection and conductivity
behaviors are discussed in detail in the Propping Agents and Fracture Conductivity Chapter of this monograph.
1.1 What Has Changed Since Monograph 12
It probably goes without saying, but much has changed in the world of hydraulic fracturing since the publication of Recent Advances
in Hydraulic Fracturing, SPE Monograph Series Vol. 12 (Gidley et al. 1989), nearly 30 years ago. Improvements and updates are
provided in the various chapters that follow; however, a short list of some of the more critical and impactful changes in hydraulic
fracturing practices is warranted. A list follows, in no particular order of importance or occurrence.
1. Unconventional-Reservoir Development. The increased development of unconventional reservoirs is directly tied to the
practice of hydraulic fracturing. The low-permeability nature of unconventional systems, especially “shale” reservoirs
(classed as mudstones or siltstones), has led to a significant increase in the application of hydraulic fracturing treatments.
Conversely, the application of hydraulic fracturing has led to more and more unconventional reservoirs being developed.
Although the basic application is the same in conventional and unconventional reservoirs, the design of the treatments can be
radically different. Additionally, more wells and more fracture treatments are typically needed in unconventional reservoirs
because of their inherent low permeabilities.
2. Multistage Fracturing on Horizontal Wells. Along with the increased development in unconventional reservoirs has come
the increased use of multistage-fracturing treatments in horizontal wells. Neither horizontal wells nor multiple fracturing
treatments in a given well are new to the industry since Monograph 12; however, the combined use of these techniques has
grown exponentially. Improvements in diversion were needed and have been developed for such systems. Multistage treatments have also led to larger volumes of fluid and proppant used in a given well.
3. Public Controversy. Although hydraulic fracturing has been used since the 1940s, the increase in its use, mostly because
of unconventional-reservoir development, has coincided with an increase in public concerns about the practice (King 2012).
Freshwater contamination concerns were some of the first issues raised and have heightened the industry’s focus on wellbore
integrity and the development of the website FracFocus.org, a chemical disclosure registry (King and King 2013). Induced
seismicity, although mostly a concern with disposal wells, also has been linked to a select number of hydraulic fracturing
treatments (Hurd and Zoback 2012). These fears have contributed to more regulations and bans of the practice in certain
areas (Jacobs 2016).
4. Expanded Diagnostic Capabilities. At the time of the Monograph 12 publication, microseismic measurements were just
being considered and commercialized as potential hydraulic fracturing diagnostic tools. Since then, not only have existing
tools been improved, but additional tools such as distributed sensing fiber optics and flowback tracers have been added to the
repertoire. Both direct and indirect (pressure-measurement, techniques) are available and greatly enhance the understanding
of hydraulic fracture behavior before and after the treatment. However, even as beneficial as these tools are, none provide a
full picture of the treatment behavior. Improvements to the tools and the understanding of what they measure are constantly
being made.
5. Improved Modeling and Computer Power. Computer power has increased significantly since 1989. With this advancement in computing capability, hydraulic fracture modeling capabilities also have improved. These improvements are closely
coupled with a better understanding of how fractures propagate, how proppants transport, etc. The choice of which model to
use ties closely to the desired outcomes or understandings the modeler is seeking. However, even with improved computer
power and codes, the old adage of “garbage in, garbage out” holds true, and improvements in power can go only so far to
expand the knowledge of actual fracturing behavior.
6. Increased Treatment Volumes. In the 1970s, the term “massive hydraulic fracture” (also commonly known as MHF in the
industry) was developed to describe the larger treatments that were becoming popular in many low-permeability reservoirs
at that time. Although large by the criteria of that period, they would be considered small by today’s standards. Especially in
multistage horizontal wells, the volumes of proppants and fluids are frequently in the millions of pounds and millions of gallons, respectively. The level of treatment size continues to be pushed in many regions, but there is also significant discussion
and concern about the benefits of doing so (Arthur et al. 2009).
7. New Fracturing Fluids. In the area of fracturing fluids, some of what is old is now new again. Fresh water and low-viscosity
slickwater systems, originally used in the 1950s and then displaced by more-complex gelled systems, have made a comeback
(Palisch et al. 2008). These low-viscosity fluid systems work well in many unconventional reservoirs, and their use coincides
Introduction
5
with the increased development of these reservoir types. The minimal amount of chemicals needed for such systems also
helps with certain public concerns. With concerns about minimizing water use and the potential formation damage that water
might create, nonaqueous systems such as gelled propane/butane and cryogenic fluids have been tried, but their use is not
commonplace.
8. New Proppant Types. The changes in fluid systems have led to modifications in proppants. Because of the lack of viscosity
in many fracturing fluids, lightweight or low-density proppants have been developed to improve proppant transport. Treated
proppants have brought about such capabilities as embedded scale inhibitors (Fitzgerald and Cowie 2008) and detection of
proppant placement in the reservoir with neutron measurements (Duenckel et al. 2011). Because of the volumes of sand
being pumped and economic considerations such as transportation, traditional sources of sand are being supplemented with
local sources.
9. Well-to-Well Treatment Interference. At the time of the Monograph 12 publication, well-to-well treatment ­interference,
or the growth of hydraulic fractures into offset wells, was a contemporary and much-studied topic. Some interference is direct,
with fracturing fluids and proppants showing up in offset wells, while other reports indicate that the impacts are nondirect
with pressure-only signatures. Although such interference behaviors are not new to the industry, the volume of such has grown
because of the number of wells being drilled, the associated stages being pumped, and the down-spacing of wells in unconventional reservoirs. Mitigation procedures, such as shutting in offset wells during treatments, preloading/pressurizing these wells
with fluids, and regional user groups tracking when treatments are taking place, are being implemented. However, the industry’s understanding and mitigation of interference behaviors are still improving and likely will continue to do so in the future.
1.2 Geologic Considerations
Hydraulic fractures must be differentiated from natural fractures, which are often areally extensive stress features created by massive
subterranean rock movements such as uplifts, faults, and basement slumps over geologic time. By contrast, hydraulic fracturing is a
limited volume of rock alteration, usually impacting far less than 0.1% of the rock mass in the drainage area of a drilled well. This
small alteration, however, often opens or widens natural fractures and creates primary pathways that allow increased flow through
lower-permeability formations, making possible economic production of hydrocarbon reserves that otherwise could not be produced.
Hydraulic fracturing is required in approximately 75 to 90% of all gas and oil wells drilled in North America and in many other wells
worldwide, especially in low-permeability formations such as chalks, tight gas sands, and the mudstones/siltstones known widely
as “shales.” The amount of production increase is dependent on the background permeability of the matrix, where the lowest rock
­permeabilities are affected to the greatest extent, as demonstrated in Fig. 1.5. Variations of fracturing, such as frac packing of weak
and unconsolidated formations, have enabled high production from marine sands with proven reliability (King et al. 2003).
Rocks in nearly all depositional environments have a high degree of variance in composition and structure. In very-low-­permeability
formations such as the mudstones commonly referred to as “producing shales,” effective formation permeability (a measure of flow
capacity through a substance) can vary over three or more orders of magnitude—for example, from the nanodarcy to the microdarcy
scale. In these rocks, where the permeability is 100 to 1,000 times lower than construction quality concrete, fluids will not flow at
economic rates without either widening and stabilizing natural fractures or creating a distinct and stable planar fracture to raise overall
system permeability 1,000 to 10,000 times that of the rock matrix.
Fracturing might also bypass formation damage, re-establishing or improving production in wells where permeability has been
lowered through in-situ damage. Such damage might occur through precipitation of natural scales such as calcium carbonate.
­Additionally, natural fractures might have closed where fluid production has caused internal stress changes because of the removal of
overburden-supporting or confining-load-supporting elements in the reservoir.
The Earth’s crust is a dynamic environment and has been since the earliest moments of its formation. Formation stresses from
stored natural forces such as tectonic movement and local forces create a stress state within the Earth’s upper crust that pushes against,
and sometimes moves, large sections of rock formations. In comparison, the dynamic forces imposed by hydraulic fracturing are
limited time-point source stresses that are miniscule in comparison to natural forces on a global or even a regional scale. Hydraulicfracturing-imposed stress can be significant in a small area, depending on local conditions, but the fracture produced is controlled by a
number of natural factors and limited to an impact zone of a few thousand feet of deep lateral contact and at maximum a few hundred
feet of vertical extent. All local stresses, man-made and natural, must be considered in hydraulic fracturing design.
Hydraulic fractures in formations deeper than ≈1,500 to 2,000 ft generally develop in a vertical plane roughly perpendicular to the
least principal horizontal stress, although exceptions to this behavior can exist (Nolte and Smith 1981). Historically, hydraulic fractures were thought to be roughly equal in lateral growth on both sides of the wellbore, thus the term “half-length” to describe fracture
length. However, field diagnostics and modeling have shown this description to be too simplified, and “tip-to-tip” fracture growth or
off-balanced fracture growth might be better descriptive terms (Daneshy 2004). The growth plane and whether equal bi-wing lengths
are generated depend greatly on the existing geology and in-situ stresses within the rock. Formations are known to vary greatly in
chemical and mechanical composition, and in-situ stress, along even a moderate horizontal length (Rich and Ammerman 2010).
In certain instances where there are naturally occurring fractures or joint sets that create multiple potential pre-existing failure
planes, it is possible for the hydraulic fracturing fluids to enter and follow the natural fracture systems, creating what are called complex or network fractures (Overbey et al. 1988; Gale 2008). These complex systems might open the closed or sealed natural fractures
and are mostly directed by initial stresses in the near-well region and dynamic stress buildup in the far field. Fig. 1.7 demonstrates the
potential complexity created by hydraulic fractures in the presence of natural fractures. Opening existing fractures might be accomplished with approximately 60% of the pressure needed to fracture rock that does not contain natural fractures (Gale et al. 2007).
Limitations on the formation of complex fracturing are that the formation must have existing natural fractures or weak zones and
that the magnitude of the minimum and maximum horizontal stresses must be similar. Other factors, such as choice of fracturing
fluid and rate of application of the fracture (injection rates increased in small steps vs. instantaneous application of maximum rate),
are often required to achieve complex fracturing if the geologic conditions are met (Overbey et al. 1988). Complex fracturing is seen
plainly in the varied patterns created by microseismic monitoring during fracturing operations, and further evidence is provided by
chemical analysis examining returning and produced fluids for changes in total dissolved solids and leach-time-sensitive concentrations of ion pairs lifted from the surface of the rock by fracturing fluids (Bearinger 2013). However, other diagnostics plainly show the
behavior of noncomplex, linear fracture trends (Rich and Ammerman 2010). The presence of extensive complex fracture development
6
Hydraulic Fracturing: Fundamentals and Advancements
Hydraulic fracture
resumes in SHmax
direction at
natural fracture tip
Secondary
natural
fractures N/S
fra
ct
ur
es
S
H
yd
ra
u
m
ax
lic
D
Frac ominan
tn
ture
clus atural
ter W
NW
H
Trace of part
of horizontal
wellbore with
perforation
N
E/
SW
Reactivation
of natural
fractures
≈ 500 ft
Fig. 1.7—Complex fracture growth through natural fracture activation (Gale 2008).
and its impact on production and reserves recovery have been questioned, and work continues on the subject. Some of these discrepancies might simply be a matter of diagnostic tool choice and the behaviors that such tools measure.
1.3 Conventional vs. Unconventional Reservoirs
Hydraulic fracturing techniques are used in conventional and unconventional reservoirs. According to the SPE Petroleum Resources
Management System (PRMS), unconventional resources:
“Unconventional resources exist in petroleum accumulations that are pervasive throughout a large area and are not significantly affected by hydrodynamic influences (also called “continuous-type deposit”). Usually there is not an obvious
structural or stratigraphic trap. Examples include coalbed methane (CBM), basin-centered gas (low permeability), tight gas
and tight oil (low permeability), gas hydrates, natural bitumen (very high viscosity oil), and oil shale (kerogen) deposits.
Note that shale gas and shale oil are sub-types of tight gas and tight oil where the lithologies are predominantly shales
or siltstones. These accumulations lack the porosity and permeability of conventional reservoirs required to flow without
stimulation at economic rates. Typically, such accumulations require specialized extraction technology (e.g., dewatering
of CBM, hydraulic fracturing stimulation for tight gas and tight oil, steam and/or solvents to mobilize natural bitumen for
in-situ recovery, and in some cases, surface mining of oil sands). Moreover, the extracted petroleum may require significant
processing before sale (e.g., bitumen upgraders).” (PRMS 2018).
Hydraulic fracturing is critical in the development of many unconventional reservoir types, including tight gas, tight oil, basincentered gas, and CBM. Hydraulic fracturing enables the economic production of these low-permeability systems and, coupled with
extended-reach horizontal wells, has led to the “shale boom” in the US and Canada (Arthur et al. 2010).
Hydraulic fracturing operations have evolved over time for specific plays, producing continued efficiency improvements. This is
especially true in unconventional shale plays, where development has been on accelerated levels for the past 2 decades, since the
Barnett evolved from a vertical- to a horizontal-well play. For instance, as shown in Fig. 1.8, the average Eagle Ford Shale liquids
Eagle Ford Well Production vs. Months of Operation, for 2010 to 2015
B/D (First full Month
of Production)
500
2015
2014
400
2013
300
2012
2011
200
2010
100
0
Pre-2010
0
12
24
36
48
60
Months of Operation After Completion
Fig. 1.8—Eagle Ford liquid production for 2010 through 2015.
Source: US Energy Information Administration, Drilling Productivity Reports (2016).
Introduction
7
production per well has increased on a yearly basis in the early part of the field development, with enhancements in fracture design
contributing to a significant part of the increase. Improvements of this nature are accelerated by analysis made possible only by
­collection and study of all aspects of geoscience and engineering.
Whether in a conventional or unconventional reservoir, hydraulic fracturing should be thought of as a product that is custom
fitted to a set of formation conditions. When the product of an engineering discipline is 1 to 5 or more miles away from the
designer and applier, customizing the finished product requires a substantial effort to collect data and learn from the successes
and mistakes. The odds of significantly improving fracturing effectiveness in an area diminishes when a cookie-cutter product
is force fitted to a formation that changes inch by inch with several pay and nonpay intervals stacked in layered strata (Vincent
2013). Evolution, not perfection, should be a key objective of any fracturing treatment design. Perfection indicates no further
changes are needed, and while a perfect fracture design might indicate a manufacturing approach to well development in general
and hydraulic fracturing in particular, it could only apply to a set of known and unchanging conditions. Nature is not known to
present that opportunity.
A problem clearly demonstrated by Fig. 1.8 is that although the initial production is rising, the trend of production decline is still an
issue. Identifying the specific cause of decline does not result in total agreement. Part of the very high initial flow rate is clearly flush
production from contacted natural fractures and microfissures that feed into the hydraulic fractures. The second part of the production
history is undoubtedly linked to closure of at least some of these naturally present fractures as supporting pressures are removed (King
2010). Efforts focused on refracturing some of these “shale” wells has produced a quick return in the initial flow rates, followed by a
decline trend similar to the initial production period. This behavior, along with the single-digit recovery of original oil in place from
liquid-rich shales, signifies that the current form of fracturing, although advancing slowly, is not yet ideal for unconventional formations. Development work never ends, and it should not be expected to.
1.4 Horizontal vs. Vertical Wellbores
Although well design and development initially included only one fracture from a vertical well, movement offshore and to land-based
locations requiring small footprints opened up the science of multifractured wells beginning in 1952 and progressing to a patent on
multiple-fractured, highly deviated wells in 1974 (Strubhar and Glenn 1974; Strubhar et al. 1975; King 2010; King 2014). The widespread application of the multifractured horizontal well started after experiments in the Devonian Shale of West Virginia, USA, and
several successful applications in chalks, shales, and sandstones (Overbey et al. 1988; King 2010).
Hydraulic fracturing is a versatile tool for improving production and total recovery, but other engineering-oriented well operations, including drilling and production operations, influence and are influenced by fracturing design and application. One indisputable advance arising from technology improvements in drilling is the horizontal well as a platform for positioning hydraulic
fractures in the reservoir. Horizontal-well drilling technology is not new, with the first horizontal wells drilled in 1929, but until
the 1970s and 1980s horizontal wells were widely used successfully in only a few naturally fractured formations and for water- or
gas-coning control (King 2014). After the joining of horizontal or highly deviated wells and multiple hydraulic fracturing in 1974, a
new type of well evolved that achieved extended reach and, with a single long lateral and scores of small fractures along its length,
could accomplish formation contact equivalent to that of 10 to 30 vertical wells each with a single fracture. Pad operations were
developed and favored for many of these wells and resulted in decreasing the total footprint of well development by up to 90%
(Demong et al. 2013).
Well spacing is usually adjusted to take advantage of the fracture length with consideration given to fracture intersection
­potential with other wells. Often, finding correct well spacing is an expensive process with many wells and fracturing trials
required before an economic balance of recovery and spacing is reached. Pad operations might offer a solution to this ­problem
if the initial pad is allowed to experiment with different spacing in the first few wells to be drilled and fracture stimulated
(Rylance 2013).
Well orientation presents an opportunity to use transverse hydraulic fractures in lower- permeability formations and longitudinal
fractures in higher-permeability formations, as demonstrated in Fig. 1.9. The actual configuration will depend heavily on the formation permeability, the viscosity of the flowing fluid, and the expected flow rates from the individual zones, among other factors.
Although the transverse fractures might produce more total contact area with the formation, they also can present a higher risk of
turbulence in the more tortuous approach to the wellbore that required inward or convergent radial flow in the fracture to enter the
small fracture-to-wellbore contact area. Higher formation permeabilities and higher-viscosity fluids might be affected by this type
of flow-rate-affecting pressure drop. Longitudinal contact of the fracture with the wellbore presents an easier wellbore approach
and entry but much less contact area with the reservoir. Longitudinal fractures might also be preferred in low vertical- to horizontalpermeability systems.
Orientation of the wellbore, relative to the maximum and minimum horizontal stress orientations, and perhaps inclination of the
wellbore relative to the formation layers, will have an impact on most hydraulic fracture development. Well orientation at angles
roughly perpendicular to the maximum horizontal stress is likely to form transverse fractures, which will propagate away from the
wellbore at roughly 90o if the maximum and minimum horizontal stresses are perpendicular to each other and the maximum horizontal stress is along the fracture plane. However, under these conditions, some near-wellbore longitudinal failure growth along the
­secondary fracture growth direction might occur because of near-wellbore stress release as the hole is drilled, potentially leading to
more near-wellbore tortuosity in such situations (Chen and Economides 1995).
Completion designs vary with the characteristics of the formation, the need for increased contact areas, available experience, and
equipment support. In horizontal wells, completed with multistage fracturing treatments, the spacing between fractures is a critical
design consideration. Fracture spacing might generate challenges for breakdown and fracture growth. Close spacing of fractures is
generally believed to create a stress interference or “stress shadow” between an existing fracture and a fracture that is being added,
as demonstrated in Fig. 1.10. Increasing fracture width and modulus raises the stress exerted within the rock, with higher stresses
­inhibiting development of other nearby fractures. The closer the fractures, the higher the stress change, especially for very close
fracture spacing. However, this stress shadowing behavior, which denotes that all fractures are not created equal, must be balanced
with the required numbers of contributing fractures needed to drain the associated reservoir. This conflicting design parameter is an
ongoing issue with no simple solution.
8
Hydraulic Fracturing: Fundamentals and Advancements
Conventional, higher permeability reservoirs
Total rock contact ≈1 million ft2.
3 to 5+ longitudinal fractures
Unconventional completion, low-permeability reservoirs.
Total rock contact ≈100 million ft2.
20 to more than 100 transverse fractures
Fig. 1.9—Longitudinal fractures and transverse fractures placed from horizontal wells.
Stress Change vs. Hydraulic Fracture Spacing
(assumes fracture width = 0.05 in.)
100,000
Modulus = 1,000,000 psi
Modulus = 2,000,000 psi
Modulus = 3,000,000 psi
Modulus = 5,000,000 psi
Stress Change (psi)
10,000
1,000
100
10
0
10
20
30
40
50
60
70
80
90
100
Hydraulic Fracture Spacing (ft)
Fig. 1.10—Theoretical stress shadow generated by close spacing of 0.05-in.-wide fractures for various Young’s moduli
in a horizontal well (Waters et al. 2009).
1.5 Other Types of Fracturing Stimulation
Hydraulic fracturing is not the only type of fracturing used as a stimulation technique in the petroleum industry, and care should
be taken to separate the techniques and goals of such treatments. Explosive-driven fracturing has a history dating back to the late
1800s when gunpowder, dynamite, and nitroglycerine were used to stimulate wells (Rison 1929). Explosive fracturing, which has
an extremely quick pressure-rise time as shown in Fig. 1.11, mostly produces a shattering effect on the borehole wall. The explosive
behavior creates cracks that penetrate a few feet from the wellbore, rubblizes the surrounding formation, and frequently damages the
well’s casing.
Introduction
9
10
Fracture regimes in rock
9
Effective Wellbore Diameter (in.)
Soft rock
Soft rock
7
6
Hard rock
Hard rock
8
Explosive regime boundary
Hydraulic fracturing boundary
5
4
Multiple fracture
regime
Explosive fracture
regime
3
Hydraulic fracture
regime
2
1
0
0.001
0.01
0.1
1
10
Pressure-Rise-Time (milliseconds)
Fig. 1.11—Energy release levels comparing explosive, propellant, and hydraulic fracturing (Cuderman and Northrop 1986).
Propellants deliver a slower energy release than explosives that is referred to as “deflagration.” The deflagration process is still
significantly faster when compared to hydraulic fracturing processes. But it generates pressure in a way to overcome stress planes
and create cracks that might propagate in multiple directions, and not just perpendicular to minimum stress as with most hydraulic
fractures. Although useful for bypassing near-wellbore damage, the fractures created by these materials are not comparable with those
that can be created through the force generation of high-pressure pumping over several hours.
Penetration of explosive- or propellant-initiated fractures into the formation is characteristically short, often no more than 20 to
30 ft. The processes do appear, from wellbore cleanout experiences and laboratory results, to create a large amount of fragmented
formation debris that might reduce or eliminate the need for proppants (Young et al. 1986; Schmidt et al. 1980; Wieland et al. 2006).
Drawbacks to the high-energy systems are the inability to form long fractures, the risk of casing or cement damage, and perhaps the
inability to carry proppant. Advantages are limited use of water; quick, pressure-assisted cleanup; breakthrough of formation damage that might not otherwise be treatable; and height containment. In general, propellant stimulation techniques serve a very small
selection of treatment candidates (a niche) and do not replace the ability of hydraulic fracturing to stimulate deep into the reservoir.
1.6 References
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Shale Gas Reservoirs. Presented at the SPE Americas E&P Environmental and Safety Conference, San Antonio, Texas, USA,
23–25 March. SPE-121038-MS. https://doi.org/10.2118/121038-MS.
Arthur, J. D., Coughlin, B. J., and Bohm, B. K. 2010. Summary of Environmental Issues, Mitigation Strategies, and Regulatory
Challenges Associated With Shale Gas Development in the United States and Applicability to Development and Operations
in Canada. Presented at the SPE Canadian Unconventional Resources and International Petroleum Conference, Calgary,
19–21 October. SPE-138977-MS. https://doi.org/10.2118/138977-MS.
Barree, R. D. and Mukherjee, H. 1995. Engineering Criteria for Fracture Flowback Procedures. Presented at the SPE Low Permeability
Reservoirs Symposium, Denver, 19–22 March. SPE-29600-MS. https://doi.org/10.2118/29600-MS.
Barree, R. D., Cox, S. A., Miskimins, J. L. et al. 2014. Economic Optimization of Horizontal Well Completions in Unconventional
Reservoirs. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 4–6 February.
SPE-168612-MS. https://doi.org/10.2118/168612-MS.
Bearinger, D. 2013. Message in a Bottle. Presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference,
Denver, 12–14 August. URTEC-1618676-MS.
Chen, Z. and Economides, M. J. 1995. Fracturing Pressures And Near-Well Fracture Geometry Of Arbitrarily Oriented And Horizontal
Wells. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 22–25 October. SPE-30531-MS. https://
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Clark, J. B. 1949. A Hydraulic Process for Increasing the Productivity of Wells. J Pet Technol 1 (1). SPE-949001-G. https://
doi.org/10.2118/949001-G.
Cuderman, J. F. and Northrop, D. A. 1986. A Propellant-Based Technology for Multiple-Fracturing Wellbores To Enhance Gas
Recovery: Application and Results in Devonian Shale. Society of Petroleum Engineers. SPE Prod Eng 1 (2). SPE-12838-PA.
https://doi.org/10.2118/12838-PA.
10 Hydraulic Fracturing: Fundamentals and Advancements
Daneshy, A. 2004. Analysis of Off-Balance Fracture Extension and Fall-Off Pressures. Presented at the SPE International
Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 18–20 February. SPE-86471-MS.
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Demong, K. L., Boulton, K. A., Elgar, T. et al. 2013. The Evolution of High Density Pad Design and Work Flow in Shale Hydrocarbon
Developments. Presented at the SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, USA, 20–22 August. SPE-165673-MS.
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Duenckel, R. J., Smith, H. D., Chapman, M. A. et al. 2011. A New Nuclear Method to Locate Proppant Placement in Induced
Fractures. Presented at the SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia,
15–18 May. SPE-149102-MS. https://doi.org/10.2118/149102-MS.
Fitzgerald, A. M. and Cowie, L. G. 2008. A History of Frac-Pack Scale-Inhibitor Deployment. Presented at the SPE International
Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 13–15 February. SPE-112474-MS.
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Fonseca, E., Liu, Y., Mowad, B. et al. 2015. Emerging Hydraulic Fracturing Execution Technologies in Unconventional Gas and
Tight Oil. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. SPE-174822-MS.
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Gale, J. F., Reed, R. M., and Holder, J. 2007. Natural Fractures in the Barnett Shale and their importance for hydraulic fracture
treatments. AAPG Bulletin 91 (4): 603–622.
Gale, J. F. 2008. Natural Fractures in Shales: Origins, Characteristics and Relevance for Hydraulic Fracture Treatments. Presented at
the AAPG Annual Convention, San Antonio, Texas, USA, 20–23 April.
Gidley, J. L., Holditch, S. A., Nierode, D. E. et al. 1989. Recent Advances In Hydraulic Fracturing, Vol. 12. Richardson, Texas:
Monograph Series, Society of Petroleum Engineers.
Hurd, O., and Zoback, M. D. 2012. Stimulated Shale Volume Characterization: Multiwell Case Study from the Horn River Shale:
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USA, 8–10 October. SPE-159536-MS. https://doi.org/10.2118/159536-MS.
Jacobs, T. 2016. Seismic Shifts in Oklahoma Lead to Stricter Regulations. J Pet Technol 68 (5). SPE-0516-0044-JPT. https://
doi.org/10.2118/0516-0044-JPT.
King, G. E., Wildt, P. J., and O’Connell, E. 2003. Sand Control Completion Reliability and Failure Rate Comparison With a
Multi-Thousand Well Database. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October.
SPE-84262-MS. https://doi.org/10.2118/84262-MS.
King, G. E. 2010. Thirty Years of Gas Shale Fracturing: What Have We Learned? Presented at the SPE Annual Technical Conference
and Exhibition, Florence, Italy, 19–22 September. SPE-133456-MS. https://doi.org/10.2118/133456-MS.
King, G. E. 2012. Hydraulic Fracturing 101: What Every Representative, Environmentalist, Regulator, Reporter, Investor, University
Researcher, Neighbor, and Engineer Should Know About Hydraulic Fracturing Risk. J Pet Technol 64 (4). SPE-0412-0034-JPT.
https://doi.org/10.2118/0412-0034-JPT.
King, G. E. and King, D. E. 2013. Environmental Risk Arising From Well-Construction Failure--Differences Between Barrier and
Well Failure, and Estimates of Failure Frequency Across Common Well Types, Locations, and Well Age. SPE Prod & Oper 28 (4).
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SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170952-MS. https://doi.org/10.2118/
170952-MS.
Mayerhofer, M. J., Richardson, M. F., Walker, R. N. et al. 1997. Proppants? We Don’t Need No Proppants. Presented at the SPE Annual
Technical Conference and Exhibition, San Antonio, Texas, USA, 5–8 October. SPE-38611-MS. https://doi.org/10.2118/38611-MS.
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doi.org/10.2118/8297-PA.
Overbey, W. K., Yost, A. B., and Wilkins, D. A. 1988. Inducing Multiple Hydraulic Fractures From a Horizontal Wellbore. Presented
at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18249-MS. https://doi.org/10.2118/
18249-MS.
Palisch, T. T., Vincent, M. C., and Handren, P. J. 2008. Slickwater Fracturing: Food for Thought. Presented at the SPE Annual
Technical Conference and Exhibition, Denver, 21–24 September. SPE-115766-MS. https://doi.org/10.2118/115766-MS.
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Rich, J. and Ammerman, M. 2010. Unconventional Geophysics for Unconventional Plays. Presented at the SPE Unconventional Gas
Conference, Pittsburgh, Pennsylvania, USA, 23–25 February. SPE-131779-MS. https://doi.org/10.2118/131779-MS.
Rison, C. O. 1929. Manufacture of Nitroglycerin and Use of High Explosives in Oil and Gas Wells. In Transactions of the Society of
Petroleum Engineers, SPE-929240-G. Richardson, Texas: Society of Petroleum Engineers.
Rylance, M. 2013. Optimizing Remote Unconventional Gas Exploration. Presented at the SPE Unconventional Gas Conference and
Exhibition, Muscat, Oman, 28–30 January. SPE-163987-MS. https://doi.org/10.2118/163987-MS.
Schmidt, R. A., Warpinski, N. R., and Cooper, P. W. 1980. In Situ Evaluation Of Several Tailored-Pulse Well-Shooting Concepts.
Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, USA, 18–21 May. SPE-8934-MS.
https://doi.org/10.2118/8934-MS.
Strubhar, M. K. and Glenn, E. E. 1974. Method of Creating a Plurality of Features from a Deviated Well. US Patent No. 3,835,928.
Strubhar, M. K., Fitch, J. L., and Glenn, E. E. 1975. Multiple, Vertical Fractures From an Inclined Wellbore - A Field Experiment.
J Pet Technol 27 (5). SPE-5115-PA. https://doi.org/10.2118/5115-PA.
Vincent, M. C. 2013. Five Things You Didn’t Want to Know about Hydraulic Fractures. Presented at the ISRM International
Conference for Effective and Sustainable Hydraulic Fracturing, Brisbane, Australia, 20–22. ISRM-ICHF-2013-045
Introduction
11
Waters, G. A., Dean, B. K., Downie, R. C. et al. 2009. Simultaneous Hydraulic Fracturing of Adjacent Horizontal Wells in the
Woodford Shale. Society of Petroleum Engineers. SPE-119635-MS. https://doi.org/10.2118/119635-MS.
Wieland, C. W., Miskimins, J. L., Black, A. D. et al. 2006. Results of a Laboratory Propellant Fracturing Test in a Colton Sandstone
Block. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24–27 September.
SPE-102907-MS. https://doi.org/10.2118/102907-MS.
Wikipedia. Hydraulic fracturing. 2019. https://en.wikipedia.org/wiki/Hydraulic_fracturing (accessed 13 March 2019).
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1 (4). SPE-12840-PA. https://doi.org/10.2118/12840-PA.
Chapter 2
Pretreatment Formation Evaluation
John McLennan, University of Utah; Larry K. Britt, NSI Fracturing LLC;
and Siavash Nadimi, California Division of Oil, Gas, and Geothermal Resources
John McLennan is a USTAR associate professor in the Department of Chemical Engineering at the University of Utah. He has more
than 35 years of experience in the petroleum service and technology sectors, working on projects concerned with subsurface energy
recovery (hydrocarbon and geothermal). McLennan holds a PhD degree in civil engineering from the University of Toronto.
Larry K. Britt is a partner with NSI Fracturing and owns and operates Britt Rock Mechanics Laboratory at the University of Tulsa.
He also serves as an adjunct professor at the Missouri University of Science and Technology. Britt holds a BS degree in geological
engineering and a professional degree in petroleum engineering, both from the Missouri University of Science and Technology. He
is an SPE Distinguished Member.
Siavash Nadimi is an associate oil and gas engineer with the California Division of Oil, Gas, and Geothermal Resources. He has more
than 7 years of experience in reservoir engineering and geomechanics with petroleum service and technology companies. Nadimi
holds an MS degree in rock mechanics from Amirkabir University of Technology, as well as an MS degree in mining engineering and
a PhD in chemical engineering from the University of Utah.
Contents
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Overview������������������������������������������������������������������������������������������������������������������������������������������������������������������ 13
Geologic Considerations������������������������������������������������������������������������������������������������������������������������������������������ 15
2.2.1 Tectonic Setting�������������������������������������������������������������������������������������������������������������������������������������������� 16
2.2.2 Stress Contrast�������������������������������������������������������������������������������������������������������������������������������������������� 17
2.2.3 Natural Fracturing���������������������������������������������������������������������������������������������������������������������������������������� 18
2.2.4 Pore Pressure���������������������������������������������������������������������������������������������������������������������������������������������� 20
2.2.5 Energy Release, Brittleness, Fracability������������������������������������������������������������������������������������������������������ 21
Acquiring Properties Using Wireline Logging���������������������������������������������������������������������������������������������������������� 21
2.3.1 Mud Logging������������������������������������������������������������������������������������������������������������������������������������������������ 21
2.3.2 Wireline Logging Overview�������������������������������������������������������������������������������������������������������������������������� 21
2.3.3 Fracture Characterization Overview������������������������������������������������������������������������������������������������������������ 23
2.3.4 Resistivity-Based Image Logging���������������������������������������������������������������������������������������������������������������� 23
2.3.5 Acoustic Logging for Fracture Detection������������������������������������������������������������������������������������������������������ 25
2.3.6 Stress Orientation and Magnitude��������������������������������������������������������������������������������������������������������������� 25
Core Analysis����������������������������������������������������������������������������������������������������������������������������������������������������������� 29
2.4.1 Young’s Modulus and Poisson’s Ratio���������������������������������������������������������������������������������������������������������� 29
2.4.2 Brittleness and Ductility������������������������������������������������������������������������������������������������������������������������������� 31
2.4.3 Fracture Toughness������������������������������������������������������������������������������������������������������������������������������������� 34
2.4.4 Stress Magnitudes��������������������������������������������������������������������������������������������������������������������������������������� 34
2.4.5 Formation Damage�������������������������������������������������������������������������������������������������������������������������������������� 34
Recap: How to Use These Data?����������������������������������������������������������������������������������������������������������������������������� 37
Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������������������� 38
References��������������������������������������������������������������������������������������������������������������������������������������������������������������� 39
2.1 Overview
Successful design of hydraulic stimulation treatments depends on considering the reservoir geometry, the physical and m
­ echanical
properties of the zones being treated, and the properties of adjacent lithologies. Incorporating the impact of reservoir architecture and the properties of the formation starts with characterizing the geologic conditions of the pay and surrounding lithologies.
14 Hydraulic Fracturing: Fundamentals and Advancements
From a geologic perspective, the primary considerations for treatment design are the distribution of permeability and porosity; the
extent, distribution, and mechanical characteristics of natural discontinuities; the in-situ stress conditions; and the relevant mechanical
properties of the intact reservoir rock. Field and laboratory measurements, logging analyses, and treatment back analyses facilitate the
planning and execution of fracturing treatments (Ely et al. 1995).
The challenges for data acquisition have evolved as fracturing simulators have become more sophisticated. Table 2.1 shows the
data requirements for different classes of hydraulic fracturing simulators and emphasizes the evolution of these numerical methods,
as they have become more elaborate and comprehensive.
Table 2.2 indicates typical data requirements for legacy, semianalytical fracturing simulators for modeling constant-height fracture
propagation. For these models, laboratory or field measurements can be used to determine Young’s modulus, Poisson’s ratio, and the
minimum in-situ stress in the targeted pay zone. Limited laboratory testing might be used to determine the wall-building, fluid-loss
coefficient. This resistance can be coupled with leakoff predictions based on porosity, permeability, filtrate viscosity, and compressibility of the reservoir, or derived from in-situ measurements.
With the relaxation of constant-height restrictions in the numerical simulators that were developed in the 1980s and 1990s, a
designer would need to consider the vertical variations of stresses, mechanical properties, and fluid loss. Table 2.3 shows additional
parameters that could be required.
Model sophistication has continued to evolve as low-permeability formations that are layered, naturally fractured, and laterally
variable have been developed. More-sophisticated modeling might be valuable, particularly at the field scale to minimize the inevitable learning curve. Newer simulation techniques are evolving that might ultimately help refine the appreciation of hydraulic fracture
complexity. Ideally, fully coupled, 3D fracturing simulators will require additional information, and likely the input-parameter uncertainty will need to be quantified. Table 2.4 presents a minimal list of additional data requirements.
Consolidating the obligations for acquiring pretreatment formation information, the generic categories for the data required include
some or all of the following.
Stresses and Pore Pressure. Characterizing the vertical variation of the minimum in-situ stress has been a requirement for
decades. Modern fracturing design requires an additional characterization of the complete stress tensor (total and effective stress
tensors). All three principal stresses in the simulation domain are required, not just the minimum stress in the pay zone. Not
only is the vertical profile of the minimum principal stress required, but the maximum and intermediate stress components are
also needed to effectively predict propagation in naturally fractured environments or where lithologic boundaries can regulate
height growth.
Simulator
2D
P3DH
Planar 3D
Fully 3D
Multiple
Fractures
Pay-zone properties
✓
✓
✓
✓
✓
Poro-thermoelastic coupling
✓
✓
✓
✓
✓
Mechanical properties of adjacent zones
✓
✓
✓
✓
Minimum horizontal stress in adjacent
zones
✓
✓
✓
✓
Propagation mechanics in adjacent zones
✓
✓
✓
✓
Fluid-loss properties in adjacent zones
✓
✓
✓
✓
Nonvertical wells
✓
✓
Maximum horizontal stress
✓
✓
Near-wellbore mechanics
✓
✓
Interface properties
✓
✓
Natural fracture distribution and properties
✓
Table 2.1—Data requirements for different classes of hydraulic fracturing simulators. P3DH = pseudo-threedimensional hydraulic fracture.
Parameter
Modern Methods for Determination
Young’s modulus in pay
Direct measurements in laboratory, calibrated logging data, and rock databases
Poisson’s ratio in pay
Direct measurements in laboratory, calibrated logging data, and rock databases
Minimum in-situ stress in pay
Constrained by tectonic regime, daily drilling and completion reports, calibrated logging
information, diagnostic measurements, and local experience
Flow behavior index
From published service company treatment fluid properties data
Consistency index
From published service company treatment fluid properties data
Fluid-loss parameters
Wall-building contribution might come from service company data; permeability, porosity,
saturation, and compressibility can allow fundamental calculations. Offset-well
treatments will provide some guidance. Diagnostic in-situ testing might be useful.
Proppant properties
From published service company treatment fluid properties data
Table 2.2—Basic parameters for calculations using constant-height fracturing models.
Pretreatment Formation Evaluation
Parameter
Modern Methods for Determination
Young’s modulus in other zones
Direct measurements in laboratory, calibrated logging data, databases
15
Poisson’s ratio in other zones
Direct measurements in laboratory, calibrated logging data, databases
Minimum in-situ stress in other zones
Constrained by tectonic regime, daily drilling and completion reports, calibrated
logging information, diagnostic measurements, and local experience
Treatment-string data
For inferring bottomhole treating pressure
Fracture toughness and similar
considerations impacting propagation
While used in some constant-height methods, this can be used as a controlling
parameter for vertical growth
Trajectory data
Near-wellbore losses for completion program, and provides relative orientation of
wellbore with respect to the principal-stress axes
Completion data
Near-wellbore losses and tortuosity
Table 2.3—Additional data requirements for P3DH and planar 3D fracturing models.
Parameter
Modern Methods for Determination
Dip and dip direction of natural fractures
From seismic surveys, conventional wireline logging, image logging, outcrop
mapping, core inspection
Strength characteristics of natural
fractures
Poorly represented in many cases. User can assume criticality, and if the stresses
are known, strength characteristics can be inferred.
Complete stress tensor
Constrained by tectonic regime, daily drilling and completion reports, calibrated
logging information, diagnostic measurements, and local experience. Breakout
analysis and diagnostic fracture injection testing (DFIT) might be useful.
Table 2.4—Additional data requirements for codes considering natural discontinuities.
Mechanical Properties of the Matrix. Young’s moduli and Poisson’s ratios are input in all zones. Some codes might allow specific
properties for layered environments, reflecting transversely isotropic formation characteristics.
Mechanical Properties of Discontinuities. While the properties of the matrix have always been considered, newer simulations and
reservoir environments increasingly seek to include the properties of natural discontinuities, including natural fractures, faults, and
bedding-plane interfaces. Characterizing the strength and stiffness properties of these weaknesses enables upscaling laboratory values, at a minimum, and ideally enables simulations of complex fracture propagation paths and domains. Sophisticated models draw
on stochastic representations of fracture distributions and dimensions, based on seismic data, outcrop mapping, core analysis, and
logging. Where possible, measurements of aperture, roughness, stiffness, cohesion, frictional resistance, and conductivity of natural
discontinuities are made from imaging, outcrops, or core.
Fluid Loss and Flowback. As is the case with legacy programs, forecasting fluid loss is essential. The complications arise from the
necessity to predict multidimensional fluid loss, moving away from standard Carter fluid-loss methodologies (Koning 1985). It is also
important to account for flow in newly created or reactivated in-situ flaws/fractures/interfaces. It might also be desirable to consider
load recovery, fluid-loss optimization, and multiphase fluid flow during recovery.
Propagation Criteria. With model development, as can be seen from the above requirements, none of the required governing equations has really changed. Specifying a propagation criterion also remains a necessity. Linear elastic fracture mechanics was the
fallback strategy for many years and still is a reasonable approach. It becomes more controversial in situations where a large process
zone is inferred or where large nearby discontinuities muddle assumptions of a square-root singularity. Experience, pragmatism, and
calibration will still be essential elements of propagation prescription.
2.2 Geologic Considerations
All stimulation protocols are modeled on specific geologic environments. In the past, the geologic environment has only been casually
considered. One notable exception is the MWX experiment in which geologic conditions were intimately associated with treatment
response (Lorenz 1985, 2012; Finley and Lorenz 1988; Lorenz et al. 1988, 1989, 1991). However, with the use of more-sophisticated
models and more-complicated treatments, it is important to incorporate geologic constraints with data that improve inference of
in-situ stresses, natural fracturing, and fluid loss. Historically, lithologic characteristics have been considered from perspectives of
containment and fluid/rock interaction. For example, laboratory analytical measurements (X-ray diffraction and X-ray fluorescence)
are long-accepted methods for identifying clay content and type to determine if additives are required (Gray and Rex 1966; Zhou et al.
1997; Ahmad et al. 2018; Marsala et al. 2012; Pierce and Parker 2015; Heij et al. 2016). This is particularly important in formations
where conductivity, rather than connectivity, is required; there is an attendant risk of embedment and diminished conductivity if there
is chemomechanical weakening of the propped surface.
The concept of brittleness has encouraged the assessment of lithologic subtleties in treatment design, at least q­ ualitatively.
Some geoscientists use lithologic indices to assess whether a formation will fracture in a brittle manner—meaning that
­propagation is ­accompanied by a significant local release of energy when new fracture surfaces are created. This is opposed to
the significant e­ xpenditure of energy during ductile deformation without the creation of dilated, conductive fractures (as would
occur during brittle behavior). Early examples of brittleness indices based on lithology are those by Hucka and Das (1974),
Altindag (2003), Rickman et al. (2008), and Wang and Gale (2009). Geologic assessment is also central to determining the
distribution, frequency, and character of natural discontinuities and to constrain in-situ stress environments (Cipolla et al. 1988;
Teufel et al. 1993).
16 Hydraulic Fracturing: Fundamentals and Advancements
Large-scale structural geologic considerations have often been downplayed in treatment design. However, recognizing that the
complete stress tensor (magnitude and direction of the principal stresses) is needed to assess surface area development, large-scale
tectonic controls are useful first-order indicators of the in-situ stress regime. Five large-scale geologic controls can be considered for
acquiring prefracturing formation data: tectonic setting, stress contrast, fracture networks, formation pressure, and energy release
potential. Consider each of these in turn.
2.2.1 Tectonic Setting. The tectonic setting is often a first-order control on the complexity of hydraulic fracturing at a given site.
Increasingly complex tectonic and burial histories elevate stresses and create tectonic fractures that promote increasingly complicated
interactions between induced hydraulic fractures and the natural discontinuities in the rock. One of the earliest acknowledgements of
this was Potocki (2012). He argued that geometric and operational complexity increased progressively from a passive margin setting,
through a foreland basin, strike-slip displacement, up to and including thrusting scenarios. Factors controlling the complexity include
ease of initiation and execution, repeatability from stage to stage, interaction with natural features, lateral spread of the stimulation,
connectivity and effective aperture, and relative permeability impairment.
Consider a passive margin scenario (Fig. 2.1). Recognizing the potential differences between the two principal horizontal stresses,
a monoplanar, bi-wing fracture might be anticipated with the correct completion design. If this is the case, one possible consideration
might be that it is unlikely much complexity can be generated, and the optimal plan might be to maximize length and conductivity
with large-diameter proppant at higher concentrations (likely a crosslinked fluid would also be required). Of course, these generalizations should only be used as a basis for stimulation design because of local complexities. For example, the stress conditions associated
with listric faulting characteristics of the continental margin scenario shown in Fig. 2.2 vary with depth; examples include the Gulf of
Mexico (Nelson 1991) and the MacKenzie Delta in the Canadian Northwest Territories (Snowden 1988) where different treatments
are usually appropriate at different depths.
Crustal stretching
Crustal stretching
Crustal thinning
Normal faulting
Sedimentation
Open marine conditions
Ocean
Sedimentation
Oceanic crust
Volcanic passive margin
Dykes and
igneous intrusions
Seaward dipping reflectors
formed by lava flow
Ocean
Oceanic crust
Fig. 2.1—The stress regime in a passive margin setting is characterized by contrast between maximum and minimum
horizontal stresses and a relatively simple burial history. This figure shows, from top to bottom, continental rifting and
thinning of the crust and lithosphere, followed by formation of an oceanic basin. The modern Red Sea is an example.
The continental crust subsides and there is normal faulting. Ultimately, sediments accumulate in the passive margin
(Wikipedia 2019).
Pretreatment Formation Evaluation
17
Listric faulting
Depth subsea
Sea level
Stress
Total vertical stress
Total minimum
horizontal stress
Zone where faults coalesce
(detachment or décollement)
Fig. 2.2—Listric faults on continental margins lead to stress regimes where the minimum principal stress changes
from vertical to horizontal with depth. These simple tectonic interpretations are useful, and local complexities are
relevant.
More-complicated tectonic settings will test intuition further. Consider a foreland basin as shown in Fig. 2.3. In that setting,
r­ eservoirs can be formed in sediment-filled troughs that are relatively unstructured, bounded on the deeper side by a mountain belt. The
buried sediments shed from the mountains locally contain folds and faults, which can be normal, strike slip, or thrust faults. Depending on the degree of relaxation over geologic time, the sediments can still exhibit substantial complexity derived from the orogeny.
This intuitive design process becomes even more complicated when considering a foreland basin environment, shown schematically in Fig. 2.3. An orogenic (mountain building) event and subsequent erosion and sediment accumulation in the basin, with potential cycles of uplift and reburial, can lead to a complicated spatial variation in natural fracturing, faulting, and stress conditions. The
specific stress conditions and the pressure gradient are variable. To oversimplify, one could argue that there will be a moderate number
of healed or partially healed natural fractures that could be effectively accessed by slickwater or hybrid treatments. More-complicated
uplift and burial history can be responsible for either over- or underpressure; either situation is relevant to selecting the appropriate
fluid and surface horsepower requirements. As a starting point, if it is possible that proppant will be placed in a multiplicity of natural
fractures, a slickwater treatment might be optimal.
Unlike the burial history of a passive margin, there can be multiple episodes of uplift and burial. Two burial histories of prominent
reservoirs characterized by low mobility are shown in Fig. 2.4. The modest degree of complexity and interconnectivity might be the
reason slickwater treatments have been successful in some of these domains.
With increasing tectonic complexity, strike-slip regimes can offer challenges that are even more significant. Is it possible to prop
shear-induced fractures formed by the reactivation of faults or healed fractures? What sort of geometry will be created? Are the faults
or fractures present metastable; is there a possibility of sensible injection-induced seismicity? In the even more extreme situations
of reverse and thrust faulting (Fig. 2.5), hybrid treatments and diversion might be necessary to inhibit the preferential formation of
fractures parallel to bedding (subhorizontal for thrusts), which might not be effective for hydrocarbon recovery.
A serious question is how long are stress differences maintained as formations creep and relax (Sone and Zoback 2014). There
are further complications to comprehending the current stress field and understanding how a hydraulic fracture will evolve; consider
situations such as that shown in Fig. 2.6, which demonstrates multiple geologic events. Unravelling the history and the current stress
field is complicated; however, it must be completed to maximize recovery from many reservoirs.
2.2.2 Stress Contrast. Global tectonic control can sometimes be more fully understood by looking at the current in-situ stress
regime, in particular the difference in magnitude between the principal stresses. In an isotropic, homogeneous medium, hydraulic
fractures will seek to be perpendicular to the minimum principal stress. This alignment is less likely when the contrasts between
two or all three of the principal stresses are small, and/or when preferential planes of weakness are superimposed on this simplified
isotropic environment.
Foreland basin system
Orogen
Wedge top
Foredeep
Forebulge
Backbulge
Loading because
of topography
Loading because
of topography
Fig. 2.3—Orogenic activity causes faulting and forms basins that are subsequently filled with sediments eroded from
the uplifting mountains. Stress conditions are more complicated. Uplift and burial sequences promote natural fracturing
(modified after DeCelles and Giles 1996).
18 Hydraulic Fracturing: Fundamentals and Advancements
Age (Ma)
372
D
0
300
M
P
P
Rundle Gp.
200
Tr
J
100
K
0
Pg
0 O S
Ng
D
2,000
4,000
Depth (ft)
Burial Depth (m)
0.6
1.35
2.0
Slave point Fm.
2.5
2,000
3,400
P
T
J
K
Fm
E OM
L.cret
Strawn/Atoka
180(°F)
8,000
14,000
450
Barnett
210(°F)
240(°F)
12,000
Wat gas to dry gas
1.35–2.0% RO
Canyon
150(°F)
6,000
10,000
OI to Wat gas
0.6–1.35% RO
3,000
P
120(°F)
Exshaw Fm.
1,000
M
90(°F)
Early generation
10% to 25%
400
350
Main phase
25% to 65%
300
Late generation
65% to 90%
250 200 150
Time (Ma)
(a)
100
50
0
t=0
(b)
Fig. 2.4—More-complicated burial histories can result in the vicinity of foreland basins. The left-hand panel (a) shows
a Horn River equivalent (Lonnee and Machel 2006) for the Slave Point Formation, immediately south of the Horn River
Basin in northeastern British Columbia. A burial history plot for the Barnett Shale (Jarvie et al. 2005) is shown at right (b).
In either case, the repeated uplift and burial might have created enough natural fractures (filled or otherwise) to influence
treatment-fluid selection.
Songpan-garzê
basin
NW
Longmen shan
Jiaoziding
0
–4
–8
km
uan
ich
Be
thr
W. Sichuan basin
Tangwangzai
Qinglinkou
SE
st
ba thru
Majiao
ust
Transpressional zone
Basement
Cretaceous
Upper triassic
Permian
Devonian
Sinian-ordovician
Jurassic
Lower triassic
Carboniferous
Silurian
Sub-sinian basement
0
10
20 km
Fig. 2.5—Thrust faulting regimes. Unroofing (separation of layers) and subhorizontal fracturing are favored by the vertical
to subvertical orientation of the minimum principal stress. This tectonic regime and cross section are also relevant for
the 2008 Mw = 7.9 earthquake in Chengdu, Sichuan Province, China. The Longmen Shan Thrust Zone consists of multiple
reverse faults dipping northwest. The slip direction of the thrusts is toward the southeast (after Jia et al. 2006).
Imagine a situation in which there is a moderate contrast between the maximum and minimum principal stresses and the intermediate principal stress is vertical, as in the passive-margin or strike-slip situations described earlier. For an extensional situation [passive
margin or horst and graben (basin and range)], relatively simple hydraulic fractures might be desirable, and stages or clusters might
be smaller because the “spread” of the fracture network is reduced.
Consider the situation shown in Fig. 2.7a. This is a situation, possibly in a passive margin, where there is a significant contrast
between the maximum and minimum horizontal stresses. The geometry can be expected to be relatively simple. Complications can
arise in a strike-slip environment where conjugate fractures bracket a fracture aligned with the maximum horizontal stress (Fig. 2.7b).
Here, the utility and/or feasibility of developing conductivity in the conjugate fractures needs to be considered. Using 100-mesh proppant or similar fine-mesh proppant could reduce fluid loss or help prop shear features with small apertures. Hybrid treatments might
enable opening of the shear fractures followed by width development and propping.
At the other extreme, shown in Fig. 2.8a, stress homogeneity could favor a more diffuse fracture network, enabling effective
­opening of primary stress-driven hydraulic fractures and reopened/reactivated natural fractures. This could be an ideal regime for
slickwater treatments. As a precautionary note, azimuth change does not necessarily imply a low-stress contrast bias. The intermediate
case in Fig. 2.8b is more complicated.
The message here is the importance of stress-field determination, including the complete stress tensor. Field methods are well
publicized (see for example, Abou-Sayed et al. 1978; Fjær et al. 2008; Zoback 2010; Barree et al. 2007; McLennan et al. 1986; and
many other publications).
2.2.3 Natural Fracturing. In Fig. 2.9, Feltham (2005) reveals how complicated stress variation and natural fracturing can be, with
local variations in lithology and in different parts of a geologic structure. The role of the natural fractures was strongly demonstrated
in the MWX project (Lorenz 2012). Williams-Stroud et al. (2012) articulated that the next challenge is defining and considering the
natural fractures. The industry is beginning to accept that fracture propagation can be influenced by natural fractures. The challenge
when designing a treatment is to infer the distribution and mechanical characteristics of these fractures and whether they are regional
or local (Fig. 2.10).
Pretreatment Formation Evaluation
19
(b)
(a)
Fig. 2.6—This is an example of complexity from superimposed and changing stress conditions in the Putumayo Basin,
Colombia (left). The schematics (right) show evolution and inversion of the Pre-Eocene extensional faulting (top) and
subsequent, ­
Post-Eocene transpressional faulting (bottom). Note the change in the maximum stress (modified from
Rossello et al. 2006).
sHmin
sHmax
sHmax
sHmax
(a)
(b)
Fig. 2.7—In a situation where there is a significant contrast between the maximum and minimum principal stresses, one
possibility could be a relatively simple, near-planar fracture (at left). If pre-existing conjugate fractures are present, the
decision is whether to try to prop those or not. This can be encouraged by hybrid treatments and/or strategic diversion.
sHmin
sHmin
sHmax
(a)
sHmax
(b)
Fig. 2.8—“Diffuse” fracture networks can be foreseen in situations where the maximum and minimum stresses are
relatively isotropic (a). At the right, (b), there is more stress contrast, and more-complicated treatments (hybrids
possibly) might be considered to effectively prop all fractures and encourage conductive connections to the wellbore.
20 Hydraulic Fracturing: Fundamentals and Advancements
Type 2 fractures
Type 1 fractures
(a)
σ1
σ1
σ2
Conjugate shear fractures
(b)
σ1
Type 3 fractures
120°
σ1
σ1
σ2
60°
σ1
Fig. 2.9—This figure, from Feltham (2005), shows the complexity of the fracture system and the associated stress fields that
need to be considered, even in a relatively straightforward tectonic setting. There are spatial variations along the thrust.
Regional Fracturing
Tectonic Fracturing
Orthogonal regional fractures in
antrim shale (after nelson)
Fold-related tectonic fractures in a
danish chalk anticline (after nelson)
Fig. 2.10—Is a natural fracture system regional or local? Does a treatment need to be customized, or is a standard
procedure acceptable? At left is a depiction of a regional fracture system. The treatment in the field can account
for fluid loss and interaction with these fractures and might not need to be substantially changed from location to
location, all other parameters being equal. Local geologic hazards are another story (for example, local structure-related
stress variations, fracturing, and faulting). Another example relates to complications in fracture treatments in karstic
carbonates or chimneys (Nelson 2001).
The role of natural fractures in fluid loss has been appreciated since the late 1970s (Nolte 1979). In the 1990s, Barree and Winterfield (1998) directed attention to bedding plane shear. Dozens of recent publications have evaluated the propagation of fractures near
pre-existing natural fractures (Daneshy 1974; Renshaw and Pollard 1995; Olson and Taleghani 2009; Sessety and Ghassemi 2012;
Rahman and Rahman 2013; Chuprakov et al. 2013; Wu and Olson 2014; Yew and Weng 2014; Zhou et al. 2015; Zhang et al. 2014).
On the basis of current understanding, forecasting the interaction between hydraulic and natural fractures depends on knowledge of
the far-field stress field (and its expression near a fracture), the native conductivity of the fracture (healed, open, or partially healed),
and the resistance to shearing, dilation, and propagation of the natural fracture itself (Weng 2014). The greatest challenge to using the
latest generation of fracturing models might be in establishing the distribution, morphology, and mechanical/transport properties of
natural fractures and bedding plane interfaces. Close interaction with geoscientists is required.
2.2.4 Pore Pressure. Pore pressure historically has been considered a driller’s problem. In hydraulic fracturing, there has always been
a concern that low pore pressure would reduce the load recovery, and there are also concerns about proppant flowback. Knowledge
of the in-situ pore pressure becomes essential when the potential for shear fracturing is considered. The sliding and dilation of any
natural fracture that is not aligned with a principal stress depends on the effective stress and how it affects frictional resistance. The
initial pore pressure can be determined from offset wells, mud weights used to subdue the pressure during drilling, DFITs, wireline
surveys, or local experience.
The ramifications of the magnitude of the formation pressure for stimulation are significant. Since the work of Salz in the 1970s
(Salz 1977), the coupling between reservoir pressure and total in-situ stress has been appreciated. Overpresssured zones often will
experience elevated in-situ stresses. Because many premium low-permeability plays are overpressured, this poroelastic stress dependency can lead to undesirable out-of-zone growth. Some implications of overpressure are discussed in Padin et al. (2014). A relevant
case history is provided by Gui et al. (2016).
Pretreatment Formation Evaluation
21
At the other end of the spectrum, the industry has long been aware of the consequences of treating in underpressured formations,
whether it is elevated leakoff into underpressured, moderately permeable formations, fluid loss into natural fractures, or the increasing
relative importance of phase blocking (Law 2013).
2.2.5 Energy Release, Brittleness, Fracability. While brittleness and fracability values can be inferred and used to select landing
zones and qualitatively assess barriers, incorporating them into numerical simulations is still challenging. In fact, one might still ask,
“What is fracability?” The answer might be that fracability is a colloquialism slang that suggests tensile fracturing might dominate,
and that the energy expended during failure creates open, extensive, conductive fractures (although maintenance of conductivity is not
guaranteed). There is confusion as to whether this implies a single dominant discontinuity or a complex network of fractures. There
is also confusion as to whether this implies a contained or vertically extensive fracture. Presume that complexity and containment
are separate criteria that need to be dealt with separately for a stimulation treatment to be effective. Presume further that brittleness
can help in the determination of fracability. The role of complexity in effective stimulation and production is unsettled, as a number
of articles suggest. Some of the recent publications considering “complexity” include Sherman et al. (2015), Wilson (2015), Sierra
(2016), Waters and Weng (2016), Jackson and Orekha (2017), and Yu et al. (2018).
In the past, the main indicator of a “fracability” parameter has been some form of brittleness index (BI). Continuing with that
assumption, it can be presumed that brittle behavior can be correlated to fracability. BIs were derived in anticipation of finding a
reliable parameter that would lead to better control of fracture geometry and containment. The expectation was that this could then
translate into better production and lower well-construction costs. Currently, one main problem with using a brittleness index is that
there is no consensus within the fracturing community about its definition. As a result, three categories of brittleness indices have been
developed with dozens of definitions. These three categories of brittleness indices are based on mineralogy, combinations of moduli,
and combinations of strength parameters. Laboratory measurements of brittleness are described later in this chapter.
2.3 Acquiring Properties Using Wireline Logging
Well logging is central to all aspects of reservoir evaluation, reservoir management, and well construction—hydraulic fracturing in
particular. Conventional well logging technologies are described in numerous references (Schlumberger 1991; Doveton 1999; Asquith
and Krygowski 2004). Advances in drilling and logging technology facilitate real- or near-real-time data acquisition from tools placed
in the actual drillstring assembly (Darling 2005). Logging-while-drilling (LWD) technologies have expanded the ability to profile
directionally drilled wells (Jackson and Fredericks 1996; and many since then). Evolving technologies to process drilling information
at the bit (Haecker et al. 2017) offer future promise.
Openhole wireline logging is used to obtain depth-continuous data that indirectly denote physical, chemical, and structural properties of the relevant formations. Casedhole wireline logging evaluates the cement bond and its potential influence on fracture initiation
or indicates how flow has been partitioned during production. Tracer surveys and fiber-optic monitoring are described in the Fracture
Diagnostics chapter in this monograph. While fracturing engineers immediately recognize the value of wireline logs, in practice, mud
logs might be equally valuable. Mud logging records drilling parameters including weight, torque, drag, and the rate of penetration
(ROP). These logs also incorporate visual identification of cuttings (lithology and possible indications of natural fractures) in addition
to invaluable information related to gas and oil shows, losses, or overpressure.
2.3.1 Mud Logging. Mud logging records essential drilling activities and parameters, including geologic records, drilling parameters
(e.g., ROP and well pressure), mud characteristics, and oil and gas shows. Drill cuttings can provide detailed information about the
penetrated formations. Any indication of oil or gas in a well during drilling is called a “show.” It is remarkable how many completion
decisions are based on shows, regardless of subsequent sophisticated wireline logging programs. A mud-logging unit has two main
responsibilities during drilling (Crain 2018; Darling 2005; Ellis and Singer 2007). These are
1. Monitoring drilling parameters and gas/liquids/solids returns from the well. The aim is to provide real-time feedback during
drilling. These data are valuable for stage selection, inference of mechanical properties in the absence of other data, and
possibly natural fracture detection.
2. Providing technical information for formation evaluation and stage selection, providing qualitative assessment of fluid loss,
and suggesting the presence of natural fractures. Bit response and lithology are qualitative proxies for stresses and mechanical properties, and oil or gas shows indicate desirable target zones.
2.3.2 Wireline Logging Overview. Exploration geologists rely on wireline logs to determine formation architecture, transport and
storage properties, and hydrocarbon saturation. From the perspective of stimulation, these logs are relevant for ensuring that treatments are performed in regions of acceptable or desirable reservoir quality. The completions engineer is interested in transcribing
these data to fluid-loss parameters, indications of natural fracturing, stress profiles, and mechanical properties such as Young’s modulus and Poisson’s ratio. Regardless, it is prudent to take the measures necessary to obtain acceptable logging data where possible.
Generally, the properties of the wellbore wall are affected by hydraulic pressure from the drilling mud, and local disaggregation and
partial wellbore failure during drilling. In addition, certain tools are affected differently by pore fluids and matrix. Washouts, enlarged
sections, and fluid invasion of the wellbore can jeopardize or complicate porosity and resistivity measurements. Invasion of mud
filtrate can also affect resistivity measurements (Inteq 1992).
Several conventional logging methods or combinations can be used to characterize natural fractures. These include the dual laterolog and other resistivity tools, acoustic logging, gamma ray logging, caliper logging, photoelectric logging, and temperature logging
(Crain 2018; Ellis and Singer 2007; Laongsakul and Dürrast 2011; Serra 1984). These standard logs are useful even though “newer”
logging methods for accurate fracture characterization—such as the Formation MicroScanner (FMS) (Bourke et al. 1989), the Formation Microimager (FMI), borehole televiewers, and Dipole Shear Imaging (Patterson et al. 2013)—are more quantitative and provide
higher resolution.
What can be learned from well logs? Start with porosity, fluid saturation, and clay content. Porosity determination is covered extensively in numerous references (for example, Asquith and Krygowski 2004; Darling 2005). Resistivity, image logging, and acoustic
22 Hydraulic Fracturing: Fundamentals and Advancements
logging are described briefly because of their importance to stimulation design. Resistivity is particularly useful for high grading
reservoir prospectivity in clay-rich, shaley (or at least low-permeability) formations. Image logging identifies natural fractures and can
be used in stochastic forecasting of fracture frequency (Ivanova 1995; LaPointe et al. 2017). Acoustic measurements provide loggingbased (colloquially referred to as “dynamic”) values of Young’s modulus and Poisson’s ratio. Acoustic or sonic logging might also
provide approximations of in-situ stresses.
2.3.2.1 Standard Logging Methods. The gamma ray is a standard log used in locating completions and making qualitative assessments of hydraulic fracturing height growth and fluid loss. Many elements that are present in rock are naturally radioactive. A gamma
ray log measures the cumulative number of gamma rays reaching a scintillation counter as the tool moves upward past a section.
Classically, elevated gamma ray counts might be attributed to shaley formations. It can be an effective indicator of total organic
carbon (TOC) and kerogen (Fertl and Chilingar 1988). There are exceptions, including sandstones with high radioactivity because
of basement provenance of their constituents. Real insight in terms of distinguishing specific mineralogy and clay content can be
derived if the elemental contributions to the total gamma ray count can be separated. The spectral gamma ray does this. Natural
gamma ray spectroscopy records potassium, thorium, and uranium abundance. Because of the solubility of uranium components in
hydrocarbons and water, it can transfer through pre-existing fractures. Therefore, even the humble gamma ray log reading elevated
uranium saturation in fractures can be useful. During drilling, mud penetrates into open fractures and then deeper into the formation.
Generally, there is a substantial resistivity contrast between the formation and the mud filtrate. Therefore, deeper-reading electrical
logs can indicate fractures that have been filled with mud filtrate. Higher resistivity values are expected opposite healed or mineralized fractures. Penetration of barite-loaded mud into open fractures causes sharp peaks of the photoelectric index, Pe, in front of a
fracture. Consequently, conventional logging has value, not only for assessing saturation, clay content, and mineralogy, but also as a
qualitative indicator of natural fracturing.
2.3.2.2 Saturation and Clay Content. Electrical resistivity, conductivity, or induction measurements date from the early part of the
twentieth century. They have particular value for elevated saturation levels in clean formations with minimal clays. Low electric resistance, in the presence of clay, decreases the apparent hydrocarbon saturation in electrical measurements. With the current emphasis on
production from low-permeability formations, much attention has been paid to evaluating TOC and hydrocarbon saturations in shaley
formations (LeCompte and Hursan 2010; Passey et al. 1990; Pemper et al. 2009). The degree to which clays lower resistivity depends
on the volume and distribution of the clay minerals (de Witte 1950). Again, understanding the geologic environment is paramount
to understanding the reservoir environment that intrinsically governs the growth of a hydraulic fracture network. Consider several
reservoir scenarios: laminated sandstone and clay-rich layers, dispersed clays, and shales or mudstones where clay content is elevated
or the clay specifically participates in formation integrity (structural clay).
First, consider formations composed of clay-rich zones interbedded with hydrocarbon-bearing clastic rocks (similar arguments can
be made for carbonates). Data from electrical logs in this type of formation can be used to estimate fluid loss or to assess potential
propagation barriers, whether they are local or global. In a relatively simplified presentation, the total resistivity can be expressed as
formations “in series”:
1 1 − Vsh Vsh
=
+
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(2.1)
Rt
Rsand
Rsh
where Rsand and Rsh are resistivity of the clean reservoir sand and the interlaminations of clay-rich shale, respectively, and Vsh is
the shale fraction. Rt is the measured total resistivity. The shale volume can be estimated from the gamma ray or the SP readings
(Stieber 1973).
According to the familiar Wyllie relationship, this can be rewritten as (ignoring explicit consideration of bound water or gas)
1 (1 − Vsh ) Sw
V
=
+ sh , ��������������������������������������������������������������������������������������������������������������������������������������������������������������(2.2)
Rt
Fsand Rw
Rshale
n
where Fsand is the formation resistivity factor of the clean sand and n is the saturation exponent. The water saturation can be estimated
as
1n
 1
V  F R 
Sw =  − sh  sand w  . ����������������������������������������������������������������������������������������������������������������������������������������������������(2.3)
R
R

shale  (1 − Vsh ) 
 t
As a second example that is particularly useful in shalier formations, there are situations where the clay is dispersed throughout
the formation, within both the matrix and the lining and infilling pores. This can be a scenario in which, in comparison to laminated
formations, the overall water saturation increases in the formation, while the fluid mobility decreases. When resistivity or similar
measurements are made, the current is conducted through a network composed of pore water and dispersed clays. Development of
methods for determining properties in this environment has been ongoing for decades. Techniques have been proposed by de Witte
(1950), Archie (1942), Simandoux (1963), Waxman and Smits (1968); and Clavier et al. (1984). Archie’s fallback equation for calculating water saturation in low-clay, clastic, or carbonate reservoirs is
Swn =
aRw
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(2.4)
φ m Rt
where a is the cementation factor, φ is the porosity, and m is the formation factor. The drawback to this model is that it assumes that
100% of the current from the logging tool is transmitted through the fluid in the pore space. Recognizing this, the Waxman-SmitsThomas method considers conductivity of minerals in the clay matrix.
Pretreatment Formation Evaluation
Swn =
23
a
FRw
, F = , ��������������������������������������������������������������������������������������������������������������������������������������������������(2.5)

m
Rw BQv 
Rt  1 +
S 

v
where F is formation resistivity factor for clay-free matrix, n is saturation exponent for clay-free matrix, B is specific counterion
activity, Qv is quantity of cation-exchangeable clay present (mEq/mL of pore space), CEC is cation-exchange capacity (mEq/100 mL),
a is cementation factor, and m is cementation exponent.
While resistivity is central to resource identification, its role might be even more important for imaging logs and assessing the
presence of natural fractures. Readers can refer to standard logging analysis textbooks to understand the calculation methodologies
and complexities.
2.3.3 Fracture Characterization Overview. A number of logs can suggest that fractures are present; indicate fracture-prone lithologies; recognize fracture infill or precipitates, including calcite or uranium salts; or respond to the disruption of acoustic velocity
caused by the fractures. Beyond these qualitative indicators, attributes of natural fractures or discontinuities can be quantified with
image logs (using resistivity or acoustic imaging).
In the absence of image logs, conventional logs are still widely used to infer the presence of natural fractures. Some of the possibilities for inferring the presence of fractures use basic resistivity logging principles (Crain 2018). Typical tools include the highresolution laterolog and an azimuthal resistivity image (ARI) log, which makes 12 directional measurements around the borehole
circumference. Its vertical resolution and penetration are superior to conventional laterolog tools. Images from the ARI imager complement image logs from the Ultrasonic Borehole Imager (UBI) and the FMI full-bore formation microimager because of the tool’s
sensitivity to features beyond the borehole wall and its lower sensitivity to shallow features. By flagging the azimuthal heterogeneities, the resistivity images from the ARI imager avoid misinterpretation that could occur with an azimuthally averaged resistivity log
(Schlumberger). There are various similar sensors, for example, the Azimuthal Focused Resistivity (AFR™) sensor, which provides
directional resistivity measurements while drilling. Greater resolution can be provided by the FMS image log, a Schlumberger trademark. Other service companies provide similar tools, however, no specific tool is endorsed here. Imaging tools allow determination of
fracture porosity, estimation of fracture permeability, and measurements of orientation and frequency.
2.3.3.1 Using Standard Wireline or LWD for Fracture Evaluation. Sibbit and Faivre (1985) introduced a method for estimating
fracture aperture using dual laterolog data and mud filtrate resistivity, Rmf. With limited resolution and no azimuthal discrimination,
randomized fracture distributions were assumed. With these necessary approximations, vertical and horizontal apertures can be estimated as shown in Maeso et al. (2014). These aperture estimates are shown in Eq. 2.6, with Rs and Rd indicating shallow and deep
resistivity values, respectively.
For vertical fractures,
4
 1
1   10 Rmf 
,
wf =  −  
 Rs Rd   4 
and for horizontal fractures,
4
 1
1   10 Rmf 
wf =  −  
 R R   12 
s
. ������������������������������������������������������������������������������������������������������(2.6)
d
FMI_STAT_DiP_APP
0
Similarly, Luthi and Souhaite (1990) proposed a relationship between
fracture width and excess current as a tool crosses a fracture:
b
w f = cIRmf
R1x −0 b, ������������������������������������������������������������������������������� (2.7)
where wf is fracture aperture (in.), I is excess current (μA∙mm/V), Rmf is
mud resistivity (Ω∙m), Rx0 is background formation resistivity (Ω∙m), c is
0.004801 (μm−1), and b is 0.863.
2.3.4 Resistivity-Based Image Logging. Developing wellbore images
is possible using optical, acoustic, and resistivity measurements. Tools
such as the FMS and FMI perform radial microresistivity measurements,
generically known as resistivity image logs. Tool pads contacting the wellbore record this microresistivity. On the basis of relative resistivity values
from pad to pad, the resistivity traces are translated into images of the
wellbore surface. In the image shown in Fig. 2.11, low resistivity can be
­attributed to fluid-filled fractures or shalier formations, shown in black.
High-­resistivity regions, such as low-permeability zones and healed fractures, appear in white. Mineralized or hydrocarbon-filled fractures with
high resistivity are shown in lighter-colored, sinuous curves; whereas
water-filled fractures with lower resistivity appear as black sinusoidal
traces. Porous or shaley sands will be gray or a mix of yellow-brown, with
darker colors suggesting higher resistivity and possibly lower porosity.
Resistivity is not the only imaging technology. A rotating acoustic
transducer is used in borehole televiewers. Emitted ultrasonic waves propagate radially/spherically toward the borehole wall and are reflected back.
The transducer measures the travel time and the amplitude of the returning waves. Open fractures do not reflect acoustic waves, and are generally
represented as black/dark features in a colored acoustic image.
MD
(ft)
1:100
FMI_STAT_DiP_APP
dega 360 0
dega 360
Heated
Heated
16.57
240.69 –0.35
168.23
FMI_DYN
FMI_STAT
0
2.6E+02 –4.9E+03 3.2E+03
Classification
Bed_Bd
Condu
Condu
Fault
MicroF
Resisti
Image orientation° Image orientation°
Tensile
E
S
W NN E
S
W N Dip_TRU
TENS N
0 90 180 270 360 0 90 180 270 360 0 dega 90
5,390
5,400
5,410
5,420
Fig. 2.11—Example of an FMI result with dipping
fractures relative to the borehole axis as sinusoidal
curves. The processed data with dip direction and
dip angle are shown above (after Laongsakul and
Dürrast 2011).
24 Hydraulic Fracturing: Fundamentals and Advancements
There are other acoustic imaging technologies such as cross-dipole shear-wave tools (Halliburton), dipole shear imaging (Schlumberger), or deep shear wave imaging (Bolshakov et al. 2011; Patterson et al. 2013). Monopole and dipole transmitters and receivers
in modern sonic logging tools enable recording of compressional- and shear-wave arrivals in slow and fast formations. Sets of dipole
transmitters and receivers are arranged orthogonally in cross-dipole tools. Accordingly, shear data can be recorded in two directions.
The minimum and maximum travel times are obtained from the two acoustic velocities. The ratio of these shear-wave travel times
times can be used as a representation of formation anisotropy. Anisotropic data can be used for fracture detection, tectonic studies,
stress analysis, and hydraulic fracture design (Crain 2018). Compared to standard imaging,
“Cross-dipole technology has extended the depth of evaluation some 2 to 4 ft around the borehole by measuring the
azimuthal shear-wave anisotropy induced by fracturing. A shear wave reflection imaging technique developed recently
provides a method for fracture characterization in a much larger volume around the borehole with a radial extent of approximately 60 ft. This technique uses a dipole acoustic tool to generate shear waves that radiate away from the borehole and
strike a fracture surface. The tool also records the shear reflection from the fracture. The shear wave reflection, particularly
the SH [sic horizontally polarized shear] waves polarizing parallel to the fracture surface, is especially sensitive to open
fractures, enabling the fractures to be imaged using this dipole-shear reflection data. We use case examples to demonstrate
the effectiveness of this shear wave imaging technology that maps fractures up to 60 ft away and even detects fractures that
do not intercept the borehole” (Bolshakov et al. 2011).
Imaging techniques enable the fracturing specialist to infer properties of natural fractures that could be useful for hydraulic fracturing planning. These include the porosity and permeability of the fractures intersecting the wellbore, and the frequency, distribution,
and strike and dip trends.
2.3.4.1 Fracture Porosity. Fracture porosity is generally small (Crain 2018; Ellis and Singer 2007) but might be relevant in fractured basement reservoirs or when dual porosity analyses are undertaken. The procedure for estimating fracture porosity is to integrate
apertures and frequencies (intensities) determined from image logs into stimulation and production models. Industry trends are moving toward integrating stimulation and production models. Some methods of conventional porosity determination, including sonic
porosity and dual laterolog (Boyeldieu and Winchester 1982), can help with the inference of fracture porosity.
2.3.4.2 Fracture Aperture. The analyst is interested in fracture aperture and associated fracture fill to infer leakoff, and possibly determine the geometric complexity of a pumped treatment and favorable/unfavorable initiation locations (stage sizes, cluster
locations, etc.). The methods for aperture determination range from basic pixel-counting image analysis to inverting resistivity data
numerically. For the latter, a resistivity-inversion model and the mud-filtrate resistivity are used to calculate aperture. These algorithms exploit the concept of higher electrical conductivity in larger open fractures. Because of the resolution and minimum size of the
pixels in image logs, electrode spacing on the tool, and erosion of the wellbore adjacent to the fractures, the minimum size by which
a fracture can be presented on a log is approximately 1 mm.
2.3.4.3 Fracture Orientation. Dipmeter and image logs are used for assessing the dip and dip direction of the structure and stratigraphy of formations and morphology of fractures. Although there are different methods for characterizing fracture sets in situ, image
logs can directly measure fracture frequency as well as their orientation (Cornet 2013). A planar fracture cutting a cylindrical wellbore
will appear as a sinusoid in the logging presentation. As shown in Fig. 2.12, the amplitude of the sinusoid, A, and the radius of the
drilled hole, rw, can be used to calculate the dip of a fracture (or fault), θ:
θ = tan −1
A . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(2.8)
2rw
N
E
S
W
N
N
Fracture
Horizontal
bedding plane
Fig. 2.12—Sketch showing that a fracture intersecting a well appears as a sinusoid on an unwrapped image (Kim and
Narantsetseg 2015).
Pretreatment Formation Evaluation
25
Dip direction can be inferred from similar geometric relationships. The procedures stem from having at least three directionally
discrete points on the circumference of the wellbore to define a plane. The azimuth is determined from the sinusoidal apex, wellbore
inclination, and wellbore azimuth. Real-world complexity can interfere with classical sinusoidal intersections. In any case, postprocessing routines can deconvolute most situations.
2.3.4.4 Fracture Permeability. As with fracture porosity, permeability attributed to fractures is calculated from their measured
frequency and calculated apertures (Nelson 1985; Crain 2018). Consider the following relationships that can be used to estimate
permeability attributable to natural fractures.
kfrac =
ξφ 2f
≡ ξφ f w 2f ≡ ξλ f β f w 3f , ��������������������������������������������������������������������������������������������������������������������������������������������������(2.9)
λ 2f β 2f
where ξ is 8.44 × 1013, ϕf is fracture porosity (fractional), λf is fracture frequency (fractures per meter), βf is number of primary fracture directions (1 for single subhorizontal or subvertical, 2 for orthogonal subvertical, and 3 for chaotic or brecciated), wf is fracture
aperture (m), and kfrac is fracture permeability (md).
2.3.5 Acoustic Logging for Fracture Detection. Since shear
waves attenuate in the presence of fractures, their amplitude is a useful fracture indicator of these fractures. More qualitatively, a characteristic chevron pattern in a full-waveform display is an indicator
of fractures intersecting the borehole wall (Ellis and Singer 2007).
Stoneley waves—boundary, or interface, waves that ­typically
propagate along a solid/solid interface—can be useful in a similar fashion. There is significant amplitude reduction in waves
propagating through a fractured zone. This can be identified by
a ­variable-density log or microseismogram presentation (Paillet
1980; Sandor et al. 1996). Fig. 2.13 demonstrates schematically
that these low-frequency tube waves push fluid back into ortho­
gonal fractures, leading to a reduction in amplitude.
In addition to transmission techniques, reflection methods can
provide useful information. Service companies have a v­ariety
of tools that rely on azimuthal reflection of ultrasonic waves
(approximately 500 kHz). These tools are useful for cement-bond
­evaluations and for fracture detection (Ellis and Singer 2007).
Condition
Receiver
Effect
Attenuated
e
r
ctu
Fra
Permeable
formation
Reflected
Attenuated
and slowed
down
2.3.5.1 Borehole Televiewer. The borehole televiewer is an
acoustic wellbore imaging tool that covers the full circumference
Stoneley
of the borehole wall. It can operate in all downhole environments
wave
except gas-filled holes. Pulsed acoustic energy is emitted by a
rotating transducer, and signals are received by the same transducer
after partial reflection at the wellbore wall. The acoustic image of
Transmitter
the wellbore is constructed from the amplitudes of the reflected
pulses. The amplitudes are affected by the shape and rugosity (surface roughness) of the wellbore, contrast between the wall mateFig. 2.13—Schematic of the Stoneley wave traveling
rial and the drilling mud, and absorption of the acoustic energy by
along the interface in a wellbore intersected by an open
the drilling mud. Modern ultrasonic imaging tools compensate for
fracture. The wave is both attenuated and reflected at the
these effects with software, focused transducers for improving resboundary of the fracture. The velocity of Stoneley waves
olution, and centralization. Trade names such as the Circumferenis reduced as formation permeability increases. These
tial Acoustic Scanning Tool, the Circumferential Borehole Imaging
waves are also attenuated and slowed down in higherLog, and the UBI are examples of modern imaging tools (Faraguna
permeability formations. Because there are a number
et al. 1989; Hayman et al. 1998; Seller et al. 1990). These tools are
of mechanisms for attenuation of these waves, other
useful for fracture detection, wellbore-stability assessments, breaklogging and core measurements are usually required to
out evaluations, and stress estimations.
more uniquely distinguish between the possible causes
Fig. 2.14 is an example of fracture detection from an ultrasonic
of the observed amplitude reduction (modified from
borehole televiewer. In this log, breakouts are shown by darker
Ellis and Singer 2007).
colors, indicating lower acoustic amplitudes. Breakouts are quasiaxial spallation zones caused by stress concentrations around the
wellbore. In a situation in which the wellbore is aligned with a principal-stress direction, the enlarged wellbore axis will be normal
to the largest stress in a plane that is orthogonal to the axis of the wellbore. As a precaution, note that en-echelon fracturing or
breakouts can indicate misalignment between the local wellbore trajectory and the principal stresses. En echelon describes parallel
or subparallel, closely spaced, overlapping or step-like minor structural features in rock, such as faults and tension fractures, that
are oblique to the overall structural trend (Schlumberger Oilfield Glossary).
2.3.6 Stress Orientation and Magnitude.
2.3.6.1 Wellbore Failure. Drilling a well results in stress concentrations around it. Drillers realize that increasing the mud weight
too much will cause lost circulation by forming a hydraulic fracture. The wellbore trace of this fracture is usually aligned with
26 Hydraulic Fracturing: Fundamentals and Advancements
Acoustic Amplitude
51
91
131
171
11
211
Azimuth (degrees)
90
180
270
0
360
3,322.5
3,323.0
3,323.5
Depth (m)
3,324.0
3,324.5
3,325.0
3,325.5
3,326.0
3,326.5
Fig. 2.14—Example of breakout detection using an
ultrasonic borehole televiewer. The breakouts are
rotated because of a drilling-induced slippage of
localized faults (Barton et al. 1997). Courtesy of the
Society of Professional Well Log Analysts.
2
νD =
v 
0.5  p  − 1
 vS 
2
 vp 
 v  − 1
S
and E D = ζρ b
the ­maximum horizontal stress for a vertical wellbore. Drillers
also know that reducing the mud weight can result in two possible
phenomena: Formation pressure is not subdued and a “kick” is
taken and/or the increasing effective stress concentration results in
compressive failure (spalling or shearing) that forms diametrically
opposed breakouts. In a vertical wellbore, the breakout axis is parallel to the minimum horizontal stress (Fig. 2.15) whereas tensile
failure because of elevated hydraulic pressure occurs perpendicular
to the minimum horizontal stress. Therefore, by imaging wellbores,
with geometric manipulations for holes that are not aligned with
a principal stress, the orientation of the principal stresses can be
predicted from the failure type on the wellbore. Breakouts induced
by compression can be detected using four-arm- or six-arm-oriented caliper logs or with electrical or acoustic imaging, whether
obtained by wireline or LWD. It might be possible to estimate the
magnitude of the horizontal stresses by using the angular extent of
the breakout (Laongsakul and Dürrast 2011).
2.3.6.2 Cross-Dipole Sonic Logs. Evolution in sonic logs has
increased their use in determining the orientation of natural fractures. In addition, compressional-wave slowness and fast and slow
shear-wave travel time are useful for identifying anisotropy, bright
spots, and mechanical properties.
Cross-dipole tools can be used to infer principal-stress directions.
Dipole transmitters propagate low-frequency waves efficiently at
approximately the bulk shear-wave velocity. The transmitters and
receivers are aligned and arranged azimuthally on the tool. Because
the shear-wave velocity is stress sensitive, it is a function of the
orientation of the source and the receivers that are affected by
the near-wellbore stress concentrations, which vary azimuthally
around the wellbore, and consequently by the differences in the
far-field stresses. The tool generates both slow and fast waves that
propagate parallel to the least and greatest stresses, respectively,
perpendicular to the wellbore.
By assuming formation isotropy, the velocity of wave propagation can be simply related to certain elastic properties and
the ­formation’s bulk density. Values for Young’s modulus and
­Poisson’s ratio can be calculated continuously along the ­wellbore.
These are frequently referred to as dynamic elastic properties, as
opposed to static properties that are determined by mechanical
loading of samples in the laboratory (this is discussed further
below). Compressional- and shear-wave velocities and formation
bulk density are required for calculation of these dynamic elastic
parameters. These velocities are the reciprocals of ­compressionaland shear-wave travel times. Compressional-and shear-wave
travel times are also referred to as slownesses, and are indicated by
nomenclature such as DTC and DTS, respectively. Dynamic Poisson’s ratio νD and dynamic Young’s modulus ED can be ­calculated
as follows (Archer and Rasouli 2012; Ellis and Singer 2007).
2
, 0 ≤ ν D ≤ 0.5 , ν D =
3v 2p − 4 vS2
v 2p − vS2
v 
0.5  p  − 1
 vS 
2
 vp 
 v  − 1
S
, 0 ≤ ν D ≤ 0.5 , ������������������������������������������������������������������������������������(2.10)
, ������������������������������������������������������������������������������������������������������������������������������������������������������������(2.11)
where νD is dynamic Poisson’s ratio (dimensionless), vP is ­compressional-wave velocity (m/s or ft/sec), vS is shear-wave ­velocity (m/s
or ft/sec), ED is dynamic Young’s modulus (GPa or psi), ζ is units conversion factor (as required), and ρ b is bulk d­ ensity (kg/m3 or
lbm/ft3).
The vertical stress can be estimated from the bulk-density profile and the formation’s true vertical depth. The acoustoelastic parameters are used to approximate the maximum and minimum horizontal stresses as shown in Eq. 2.12.
Pretreatment Formation Evaluation
27
sH
sq
sr
B
q
qb
sn
B′
Failed zone
(breakout)
Stable zone
Fig. 2.15—Schematic of a breakout. Modifications of the Kirsch equations can be used to constrain stress magnitudes
on the basis of the widths of wellbore breakouts and the presence or absence of tensile wall fractures induced by
drilling. These equations apply to a well that is aligned in a principal-stress direction. This case is for a vertical well
(Haimson et al. 2010).
TVD
σ V = ∫ ρ ( z) g dz
0
c55 − c44
. ������������������������������������������������������������������������������������������������������������������������������������������������������������(2.12)
AE
c −c
σ Hmin = σ V − 55 66
AE
σ Hmax = σ Hmin +
ith significant simplifications, analysts have estimated horizontal in-situ stresses by taking advantage of the concept of uniaxial
W
strain. Fundamental approximations using this principle have been bolstered and modified with vague parameters to account for
“external” strain in different directions. Some of the earliest work in this area, performed to overcome basic uniaxial assumptions that
were flawed, has incorporated supplementary components to represent tectonic stresses, thermal stresses, and inelastic effects (see, for
example, Eaton 1969; Breckels and Van Eekelen 1982; Abou-Sayed 1982; McLennan et al. 1982; Blanton and Olsen 1997; Zhang and
Zhang 2017). Carefully recognizing these concepts and calibrating with actual in-situ stress measurements is strongly recommended.
The magnitude of the horizontal stresses can be grossly approximated using equations such as the following (Archer and Rasouli
2012; Hayavi and Abdideh 2016):
σ Hmin =
C
ν
E
σ v − α Pp + α Pp +
(ε Hmin + νε Hmax ), where α = 1 − g �������������������������������������������������������������������������� (2.13)
1−ν
1−ν2
Cb
σ H max =
C
ν
E
σ v − α Pp + α Pp +
(ε Hmax + νε Hmin ), where α = 1 − g , ��������������������������������������������������������������������������(2.14)
1−ν
1−ν2
Cb
(
(
)
)
where σHmin is total minimum horizontal principal stress (MPa or psi or bar, or other), σHmax is total maximum component to account
for tectonic strain in the maximum direction, Cg is compressibility of the solid constituents (grains) (GPa−1 or psi−1), and Cb is bulk
compressibility of the formation (GPa−1 or psi−1).
Relationships such as Eqs. 2.13 and 2.14 assume that the material is isotropic. Biot’s poroelastic parameter indicates how much of
the total in-situ stress is “carried” by the formation pressure; the remainder is carried by the interactions among the solids (or grains)
by frictional resistance, cementation, and compressibility. The bulk compressibility is the reciprocal of the bulk modulus for a homogeneous, isotropic medium.
While the stresses can be different in different directions, the mechanical properties are directionally invariant in an isotropic
­material. Only two elastic parameters (two of E, ν, and K) are required to develop elastic relationships between stresses and strains.
28 Hydraulic Fracturing: Fundamentals and Advancements
There are also elastic relationships for calculating Young’s modulus, Poisson’s ratio, and the shear modulus in more-complicated
media, such as transversely isotropic and orthotropic media. Transverse isotropy requires five elastic constants to interrelate stress
(whereas an isotropic material requires only two properties, Young’s modulus and Poisson’s ratio). A transversely isotropic material
can be envisioned as a layered medium in which properties in the plane of a layer are directionally invariant but properties in the direction perpendicular to the layering are different. An orthotropic medium is even more complicated, requiring nine elastic properties for
characterization.
For example, for a linearly elastic medium the stresses and strains can be related as
 σ xx   C
C12

  11
 σ yy   C21 C22
 σ   C
zz
 =  31 C32
σ ij = Cij ε ij or 
 τ yz   0
0

 
0
 τ zx   0
 τ   0
0
 xy  
C13
0
0
C23
0
0
C33
0
0
0
C44
0
0
0
C55
0
0
0
0   ε xx 


0   ε yy 

 , ����������������������������������������������������������������������������������(2.15)
0   ε zz 

0   γ yz 


0   γ zx 
C66   γ xy 


where σij is stress tensor in three dimensions (MPa or psi or bar), εij is strain tensor in three dimensions (dimensionless), and Cij is
elastic stiffness tensor.
The elastic stiffness tensor shown enfranchises the mechanical properties in three dimensions for a transversely isotropic medium,
such as a horizontally bedded formation. It is sometimes easier to write this in terms of the compliance matrix, which is the inverse
of the stiffness matrix. The compliance matrices for an isotropic and a transversely isotropic medium are shown in Eqs. 2.16 and 2.17
(after Jaeger et al. 2007).
For isotropic,
 1

 E
 ε xx   − ν


  E
 ε yy   ν
 ε   −
 zz  =  E
 γ yz  

  0
 γ xz  
 γ  
 xy   0

 0

1
E
ν
−
E
ν
E
ν
−
E
1
E
0
0
1
2G
0
0
0
0
1
2G
0
0
0
0
−
ν
E
−
0
0
0
0
0
0




0   σ xx 
  σ yy 


0   σ  , ��������������������������������������������������������������������������������������������������(2.16)
zz


  τ yz 
0 

τ
  xz 


0   τ xy 

1 + ν 
E 
0
and for transversely isotropic,
 1

 E
 ε xx   − ν
E

 
 ε yy   ν ′

−
 ε 
 zz  =  E ′

 γ yz 

  0
 γ xz  
 γ  
 xy   0


 0

ν
E
1
E
ν′
−
E′
−
v′
E′
ν′
−
E′
1
E′
−
0
0
0
0
0
0
0
0
1
2G ′
0
0
0
0
1
2G ′
0
0
0
0




0   σ xx 

  σ yy 

0

  σ zz 
  τ  , �������������������������������������������������������������������������������������������� (2.17)
0   yz 
  τ xz 


0   τ xy 

1+ν 

E 
0
where, for an isotropic medium E is Young’s modulus and ν is Poisson’s ratio, and, for a transversely isotropic medium E is Young’s
modulus in the plane of the layering (usually bedding, possibly dominant fracture planes, etc.), E′ is Young’s modulus normal to
the plane of the layering, ν is Poisson’s ratio for loading in the plane of the layering, ν′ is Poisson’s ratio for loading perpendicular
to the plane of the layering, G is shear modulus in the plane of the layering, and G′ is shear-modulus normal to the plane of the
layering.
Specialists have used dynamic properties and transversely isotropic compliance or stiffness relationships, as shown in Eq. 2.15, to
infer in-situ stresses. For example, three orthogonal shear moduli can be obtained from cross-dipole sonic logs. In fact, with this type
of log, C44, C55, and C66 might be different depending on the differences between the fast and slow shear velocities and the anisotropy
Pretreatment Formation Evaluation
29
of the material. The relationship between the shear moduli changes with radial depth, and changes of the corresponding effective
stress can be presented for a vertical well as shown by Sinha et al. (2006):
C44 − C66 = AE (σ ′V − σ ′Hmax )
C55 − C66 = AE (σ ′V − σ ′Hmin)
C55 − C44 = AE (σ ′Hmax − σ H′ min ) , ��������������������������������������������������������������������������������������������������������������������������������������������������(2.18)
AE = 2 + C456 G
C456 = C155 − C144 2
where σV is total vertical stress; σ′V is effective vertical stress; σHmax is total maximum horizontal stress; σ′Hmax is effective maximum
horizontal stress; σHmin is total minimum horizontal stress; σ′Hmin is effective minimum horizontal stress; C44 is slow-shear modulus; C55
is fast-shear modulus; C456, C144, C155 are nonlinear constants found by processing; and G is shear modulus in a selected reference state.
By using the compliances directly calculated in Eq. 2.18, as well as nonlinear constants from data processing, cross-dipole sonic
data can be used to infer stresses in transversely isotropic media. As always with stress estimation from analytical relationships, calibration with actual stress measurements (such as the minimum principal stress from a DFIT as discussed in Chapter 13 Fracturing
Pressure Analysis) is required.
2.4 Core Analysis
The objective of hydraulic fracturing is to design and execute a fracture stimulation treatment that achieves the desired fracture dimensions to maximize a well’s production rate and ultimate reserves recovery. There are several critical parameters for achieving this
objective, which generally fall into two distinct categories:
1. Parameters over which we have little control but need to understand
2. Parameters that we control but which have a lesser impact on the process
The first category includes fracture height, fluid-loss coefficient, fracture length, conductivity, tip effects, Young’s modulus, Poisson’s
ratio, ductility, and brittleness. The second category includes pump rate and fracturing-fluid viscosity. The importance and interdependence of these categories is best understood by reviewing the relationships between the governing equations in numerical models
and the fracture geometry, and pressure. The fracturing-fluid viscosity, pumping rate, and fracture length have a limited effect on the
net pressure. In some basic semianalytical relationships, the net pressure is directly related to the fracture height and nearly directly
related to the Young’s modulus of the formations that are penetrated by the fracture. Young’s modulus determines the fracture width
and affects the pressure decline after shut-in. This section addresses the determination of these parameters through core analysis.
2.4.1 Young’s Modulus and Poisson’s Ratio. Elastic deformation (which is recoverable if the applied loading is removed) of a material is prescribed by Young’s modulus and Poisson’s ratio. These properties are described in numerous standard textbooks. The modulus used in many hydraulic fracturing simulations of net pressure, fracture width, and pressure decline is the plane-strain modulus, E′.
Eq. 2.19 shows the relationship between the plane-strain modulus, E′; Young’s modulus, E; and Poisson’s ratio, ν.
E′ =
E . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(2.19)
1− ν2
Effective Stress (ksi)
Young’s modulus and Poisson’s ratio represented in Eq. 2.19 are static measurements from triaxial compression tests on core. In these
tests, the loading conditions are substantially different than those experienced by a formation during sonic/acoustic logging in which
a small pressure pulse is applied for a short period of time. In the static testing scenario, a sample is monotonically loaded to a higher
stress level in a relatively slow fashion (Fjær 1999). With the exception of sporadic and repeated steps of fracture propagation, width
changes are pseudostatic and best approximated with a pseudostatically determined modulus.
In a conventional test, a cylindrical core sample with a 2:1 ratio of length to diameter is loaded axially at a constant confining
pressure, which represents the in-situ stress conditions. The rationale for this length-to-diameter criterion is twofold. First, it leaves
a central portion of the core unaffected by frictional effects
3
because of the modulus mismatch between sample endcaps and
the rock (Jaeger et al 2007). Second, the ultimate failure for
2.5
most rocks subjected to triaxial compressive loading is localLinear elastic region
ization of failure and formation of a catastrophic shear fracture.
2
For most rock types, this shear fracture will form at an angle of
approximately 30° from the axis of the maximum compressive
1.5
Unloading cycle
load. Thus, a 2:1 ratio of length to diameter allows a throughgoing shear fracture to form at a failure angle of 30°, without
1
interacting with the end caps. Britt et al. (2004) argue that this
criterion, although generally followed by the industry, is unnec0.5
essary if the sample is not taken to failure, as in the case of the
Loading cycle
measurement shown in Fig. 2.16.
0
In addition to the axial stress, axial and lateral strains are
0
0.00005 0.0001 0.00015 0.0002 0.00025 0.0003
monitored during the test and used to determine Young’s modAxial Strain (in./in.)
ulus and Poisson’s ratio. A number of authors have reviewed
the effect of Young’s modulus on the fracturing process. Rahim
and Holditch (1992), for example, investigated the effect of Fig. 2.16—Hard rock triaxial compression test (Britt et al. 2004).
30 Hydraulic Fracturing: Fundamentals and Advancements
Effective Stress (ksi)
Effective Stress (ksi)
Young’s modulus on fracture geometry and the resulting fracture dimensions. Smith et al. (1982) investigated the effect of Young’s
modulus on fracture width and net treating pressure. In that study, the effect of Young’s modulus on fracture width was measured
with a downhole, closed-circuit camera while bottomhole treating pressure was measured. These measurements were used to validate fracture-geometry modeling assumptions.
Fig. 2.16 (Britt et al. 2004) plots axial strain during a triaxial compression test on a carbonate core sample. Note that the axial strain
is linear throughout nearly all of the loading and unloading cycles. This sample was not taken to failure and showed no evidence of
destruction of the internal rock fabric. The slope of the linear portion of the axial strain curve represents the linear elastic constant,
Young’s modulus. In this example, Young’s modulus was determined to be 11.0 × 106 psi. From this compression test, Poisson’s ratio
could also be determined as the ratio of the average lateral strain to the average axial strain. For situations where the stress/strain
relationships are not as linear, Young’s modulus is determined as the tangent to the curve at a stress level that reflects in-situ conditions. Similarly, Poisson’s ratio is calculated as the negative ratio of a small differential of radial to axial strain. Poisson’s ratio was
determined to be 0.32 in this example.
Fig. 2.17 shows a plot of the axial strain as a function
0.7
Linear elastic region
Ductile region
of the axial stress for a triaxial compression test performed
0.6
on a weakly consolidated core sample. As shown, the rock
sample exhibits linear elastic behavior during the early por0.5
tion of the compression loading cycle. However, at some
point, the poorly cemented fabric of the sample begins to
0.4
rearrange or deform. This strain hardening region, although
not symptomatic of catastrophic failure of the sample,
0.3
does represent permanent deformation of the core plug.
0.2
As a result, when the sample is unloaded, the unloading
Hysteresis
path does not track the stress/strain behavior of the load0.1
ing cycle. This phenomenon is called hysteresis. Ductile
behavior is demonstrated. Recognize that generally all core
0
0
0.0002 0.0004 0.0006 0.0008 0.001 0.0012
samples during destructive compression testing have ductile
Axial Strain (in./in.)
behavior. In high-modulus, high-strength rock, however, the
ductile region occurs at or near the confined compressive
Fig. 2.17—Unconsolidated-rock triaxial compression test
strength of the sample (failure point) and, therefore, is not
(Britt et al. 2004).
always evident.
Fig. 2.18 shows a plot of the axial strain as a function of
axial deviatoric stress during a triaxial compression test on
60
a sandstone core sample. As shown, the sample was loaded
Linear elastic
axially to failure at a constant confining pressure. Notice the
50
small deviation from linearity before failure. This represents
the ductile region that was described previously.
40
In addition to determining the basic elastic constants,
Young’s modulus and Poisson’s ratio, triaxial compression
30
testing can also be used to determine the confined compressive strength of the sample. If triaxial compression testing
20
is performed at several confining pressures, and coupled
Confined compressive
10
with unconfined compression and tensile test data, a repstrength
resentative failure envelope can be constructed and used to
0
estimate formation failure. It is preferable to have the test0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
ing performed on similar samples from the same depth, or at
Axial Strain (in./in.)
least the same facies or hydraulic unit. It is also possible to
carry out multistage triaxial testing on a single sample that
Fig. 2.18—High-strength, high-modulus rock subjected to
is ­progressively exposed to higher confining pressures. The
triaxial compression testing (Britt et al. 2004).
drawback or limitation to such sample testing occurs when
the sample exhibits either ductile failure or catastrophic
­failure. Ductile failure is seen in Fig. 2.17 with the deviation from the linear elastic line and confirmed by the unloading cycle not
returning to the origin. Catastrophic failure of the sample is shown in Fig. 2.18.
As discussed, triaxial compression tests are static measurements. However, dynamic measurements are often used to build mechanical earth models for fracture modeling and analysis. These dynamic measurements are generally obtained with dipole sonic or moresophisticated tools to acquire compressional- and shear-wave data in situ along the wellbore, as previously discussed. These logging
measurements, although extremely valuable, must be calibrated to the static measurements. Ultrasonic measurements taken on core
samples in the laboratory can be useful for this calibration. The dynamic Young’s modulus has been found to be as much as twice as
large as the static Young’s modulus. This difference can become even more extreme for poorly consolidated formations.
Many studies have compared static and dynamic elastic properties (Elissa and Kazi 1988; Hilbert et al. 1994; Martin and Haupt
1994; Fjær 1999; Sone and Zoback 2013). One study (Britt and Schoeffler 2009) showed a strong correlation between the static and
dynamic Young’s moduli. Fig. 2.19 is a plot of dynamic vs. static Young’s modulus from that work. Fig. 2.19 shows that both clastic
reservoirs and prospective shale reservoirs can exhibit similar correlation characteristics.
Dynamically determined elastic properties are frequency dependent. However, the difference between the Young’s modulus determined from a dipole sonic log with a frequency of 5 to 15 kHz and ultrasonic measurements at a frequency of 300 to 500 kHz is
approximately 10% for higher-modulus materials. Although small, even these differences can be eliminated by making low-frequency
sonic measurements on the core.
If calibrating static data are not available, dynamic elastic parameters can be used to approximate static rock properties
using correlations or correction factors. Numerous correlation equations are available (Wang 2000; Nes et al. 1998; Brotons
et al. 2016).
Pretreatment Formation Evaluation
16.000
Dynamic E (106 psi)
14.000
12.000
31
Clastics
Prospective shales
Non-prospective shales
10.000
8.000
6.000
4.000
2.000
0.000
0.000
2.000
4.000
6.000
8.000
Static E (106 psi)
10.000
12.000
Fig. 2.19—Dynamic to static Young’s modulus correlation. Linear regression gave a static-to-dynamic relationship with
R 2 = 0.85 (modified after Britt and Schoeffler 2009).
Stress
2.4.2 Brittleness and Ductility. The terms brittleness and ductility
Elastic strain Plastic strain
εel
εpl
are often used to describe formations: how they fail and how fracτmax Rock strength
tures propagate in them. These terms are diametrically opposed to
each other, since a brittle rock is not ductile and a ductile rock is not
Yield point
brittle. Generally, the use of these terms falls into three distinct categories or indices. These indices are based on mineralogy, on elastic
properties, or on the values of the physical stress/strain response
τres
from a triaxial compression test. This latter category has a specific
meaning to rock mechanics. This meaning has been described by
Residual strength
Holt et al. (2011) and Yang et al. (2013) with some specificity as
Total strain: εtot
shown in Fig. 2.20. This figure shows a generic stress/strain curve
from a triaxial compression test taken to failure. A blue line overlies
the early stress/strain data, representing the linear elastic region.
The slope of the blue line represents Young’s modulus. Sample failStrain
ure occurs at τmax, which indicates the rock strength. The yield point
of the sample is identified as the intersection of the blue line and Fig. 2.20—Generic stress/strain curve demonstrating
the failure stress transposed onto the actual stress/strain data. The rock brittleness and ductility.
elastic strain is represented by the data to the left of the yield point,
and the plastic strain is represented by the data to the right of the
yield point, which is limited by the sample failure. Finally, the residual strength of the rock, τres, is represented after the peak stress
has been reached.
Brittleness was defined by Coates and Parsons (1966) by an index, denoted as BI in Eq. 2.20, as the ratio of the elastic strain, εel,
to the total strain at failure, εtot.
BI =
ε el
,
ε tot
BI =
τ max − τ res , ��������������������������������������������������������������������������������������������������������������������������������������������������������(2.20)
τ max
Brittleness was also defined by Bishop (1967) using the post-failure behavior of the rock. Eq. 2.21 shows Bishop’s BI, defined as the
ratio of the difference between the rock strength, τmax, and residual strength, τres, to the rock strength.
BI =
τ max − τ res . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������(2.21)
τ max
A rock shows distinct brittle behavior as each of these indices (Eqs. 2.20 and 2.21) approaches a value of unity. The formation is
considered to be ductile or behaving plastically as the two indices approach a value of zero.
Some years later, representing brittleness as a function of elastic properties became popular. There are two generic methods for
using elastic properties to indicate brittle tendencies. These include the Rickman et al. (2008) brittleness method and the Goodway et
al. (2006) fracability method. Rickman et al. developed a BI that includes both Poisson’s ratio and Young’s modulus. They considered
that these elastic properties represent a rock’s tendency to fail and the ability to maintain a fracture, respectively.
Although ductile shales make good hydrocarbon traps and seals, they make poor oil and gas reservoirs because the formation will
want to heal any natural fissures or induced hydraulic fractures. It is further postulated that brittle shales are more likely to be naturally
fractured and are likely to respond well to a fracture treatment. This argument considers that more-brittle rock will have a higher Young’s
modulus E and a lower Poisson’s ratio, making it easier to initiate and propagate fractures, either natural or induced. If stress correlates
with Poisson’s ratio in these formations, this might be an added consideration—lower in-situ stresses might favor hydraulic fracture
development. The Rickman BI as shown in Eq. 2.22 is suitable for use with data from triaxial compression tests on core, or ultrasonic
data from core, or in-situ data from sonic logs. In Rickman’s relationship, Young’s modulus E is expressed in units of 106 psi.
32 Hydraulic Fracturing: Fundamentals and Advancements
(
)
(
)
 E +1
  ν − 0.4

× 100  + 
Brittleness = 
× 100 . ��������������������������������������������������������������������������������������������������������������(2.22)
 E − 1
  0.15 − 0.40

(
)
The caveat, of course, is that Young’s modulus and Poisson’s ratio are elastic parameters that have no formal correlation with the
behavior of a material after yield has occurred. The rate at which energy is dissipated or load-bearing capacity is reduced, after yield,
is the true indication of brittleness or ductility.
Goodway’s fracability relationship is similarly based on Young’s modulus and Poisson’s ratio, using Lamé’s constants λ and μ.
In homogeneous and isotropic materials, λ is the incompressibility constant and characterizes a rock’s resistance to fracture dilation.
The rigidity constant, μ, describes a rock’s resistance to shear deformation. These parameters are defined in Eq. 2.23. These are suited
for ultrasonic analysis of core samples for assessment of sonic log data and for laboratory triaxial compression test data (although
Rickman’s analysis can be simpler).
Static or Dynamic
Dynamic
Eν
λ=
2
2
1 + ν 1 − 2ν or λ = ξρ v p − 2vs , ���������������������������������������������������������������������������������������������������������������������������������� (2.23)
(
µ=
)(
E
2 1+ ν
(
)
)
(
µ = ξρ v
)
2
s
where E is Young’s modulus (psi or GPa, or other), ν is Poisson’s ratio (dimensionless), ρ is bulk density (gm/cm3 or kg/m3) lbf/ft3
or other, vp is compressional-wave velocity (m/sec or ft/sec, or other), vs is shear-wave velocity (m/sec or ft/sec, or other), ξ is units
conversion factor, and λ,and μ are Lamé’s parameters.
When the fracability concept was used to evaluate the Barnett Shale, it was determined that the more-brittle parts of this formation
had fracability ratios, λ /μ, of less than 1.00 and approaching 0.75. The same precautions apply as for Rickman-type analyses. Considering ratios of Lamé’s parameters only indicates elastic response and does not specifically denote brittle/ductile behavior after yield.
A second generic method of evaluating brittleness includes mineralogically based methods that were first proposed by Jarvie
et al. (2007). These methods are best applied by conducting X-ray diffraction evaluations or by using Fourier-transform infrared
spectroscopy on the core. These mineralogical methods can be applied to log-derived data but only after extensive petrophysical
calibration with core data. Jarvie and his colleagues investigated the Barnett Shale and developed a BI in which quartz was recognized
as the brittle constituent and clay and calcitic minerals were considered as the ductile constituents. The Jarvie BI (with mineralogic
components expressed as volume fractions) is defined as
BI =
Quartz
. ����������������������������������������������������������������������������������������������������������������������������������������������������(2.24)
Quartz + Calcite + Clay
Another brittleness index was proposed by Wang and Gale (2009) in which the volume fraction of dolomite was included in the
brittle mineralogy (quartz and dolomite) and the TOC was included as one of the more-ductile components. That index is shown in
Eq. 2.25.
BI =
Quartz + Dolomite
. ����������������������������������������������������������������������������������������������������������������������(2.25)
Quartz + Dolomite + Calcite + TOC + Clay
Britt (2008b) proposed a BI based on the hardness of the rock. The BI included silicates (quartz and feldspars) and carbonates (calcite, dolomite, and siderite) as the more-brittle components, and the various clay mineralogies as the more-ductile components. Britt
and Schoeffler (2009) extended this work to show the relationship between the clay content, Young’s modulus, and the conductivity
of an unpropped fracture at confining pressure. That work showed that higher clay content and lower values of Young’s modulus lead
to more-ductile behavior. Conversely, and more important to this discussion of brittleness, the lower the clay content, the higher the
Young’s modulus, and the more brittle the rock becomes. Britt (2008b) suggested that the prospective shales in North America were
actually not shales (<45% clay) but were fine-grained clastic formations. Britt provided a dynamic-to-static Young’s modulus correlation for clastics and prospective shales to support this assertion (Fig. 2.19). Jin et al. (2014) proposed a similar BI with silicate
and carbonate mineral constituents as the brittle components and clays as the more-ductile minerals. This index is shown in Eq. 2.26.
BI =
Quartz + Feldspar + Calcite + Dolomite + Siderite
. ������������������������������������������������������������������������������������������������(2.26)
Quartz + Feldspar + Calcite + Dolomite + Siderite + Clay
As with brittleness methods based on elastic parameters, these are indices only and do not necessarily correlate quantitatively with
brittle or ductile tendencies after yield stress has been exceeded.
Additional core tests, which are related to a formation’s brittleness or ductility, include embedment and unpropped-fracture conductivity tests. An embedment test is used to determine the conductivity that is lost because of proppant embedding into the fracture
face. Conductivity is the product of the fracture width (propped or otherwise) and the effective permeability of the fluid under consideration; that fluid could be water during flowback or hydrocarbons during production. The more brittle the rock, the less conductivity that is lost through embedment and vice versa. Fig. 2.21 shows the results of an embedment test conducted on a low-modulus,
high-clay content plug of the Haynesville core. Fig. 2.21 is a plot of closure pressure vs. displacement. As the stress was increased
from 1,000 to 8,000 psi, the incremental displacement was nearly linear. At a closure stress of 4,000 psi, nearly 43% of a grain diameter had been lost to embedment (0.118 lbm/ft2). At a closure stress of 8,000 psi, nearly 70% of a grain diameter had been lost. This
equates to nearly 0.2 lbm/ft2 of lost conductivity through embedment. However, at a closure stress of 10,000 psi, the embedment or
lost conductivity more than doubled from that experienced at a closure stress of 8,000 psi to 166% of a grain diameter or 0.412 lbm/ft2
Pretreatment Formation Evaluation
33
12,000
At 8,000-psi closure stress
69.60% of a grain diameter
was lost to embedment!
Closure Stress (psi)
10,000
At 10,000-psi closure stress
166.10% of a grain diameter
was lost to embedment!
Proppant embedment of
0.192 lbm/ft2 at 8,000-psi
closure stress
8,000
Proppant embedment of
0.412 lbm/ft2 at 10,000-psi
closure stress
6,000
4,000
2,000
0
0.000
0.010
0.020
0.030
0.040
Incremental Displacement (in.)
0.050
0.06
Fig. 2.21—A Haynesville Shale embedment test (Britt and Schoeffler 2009).
of conductivity lost. Embedment tests can prove to be quite valuable to fracture design, especially in more-ductile formations where
significant conductivity is lost. A fracture design in a formation such as that represented by the Haynesville core requires significantly
more conductivity than one in more-brittle, tight gas, or unconventional shale reservoirs.
Similarly, the unpropped conductivity is relatively greater for more-brittle rocks. In more-ductile formations, the unpropped conductivity becomes negligible even with modest drawdown/depletion. As a result, this type of core test is important in naturally fissured
reservoirs or if water is being considered as a fracturing fluid for induced fractures. Water can result in poor proppant transport and a
significant portion of the induced fracture being unpropped. Fig. 2.22 is another example of how conductivity can vary from formation to formation.
While these methods and concepts are useful and widely adopted, there is room for improvement. Brittleness and ductility are
actually characteristics of how energy is dissipated in a material and cannot be determined completely from static elastic properties.
Many materials that fracturing engineers are familiar with also behave in a more-ductile or brittle-fashion depending on the rate at
which they are loaded.
Natural Fissure Permeability (md)
1,000,000
100,000
Utica (3 Tests)
Woodford
Eagle ford (4 Tests)
10,000
Hard
Barnett (7 Tests)
Fayetteville
Medium
Montney
1,000
Soft
Horn river
100
0
1,000
Marcellus (5 Tests)
2,000
3,000
4,000
Effective Stress (psi)
5,000
6,000
Fig. 2.22—Unpropped conductivity tests show significant formation dependency (Britt et al. 2016).
34 Hydraulic Fracturing: Fundamentals and Advancements
2.4.3 Fracture Toughness. The role of fracture toughness in hydraulic fracture propagation and containment has been the subject
of much discussion over the years (for example, Abou-Sayed et al. 1978). Laboratory tests on core give values for the apparent
toughness of approximately 1,000 psi in. This is often used as a default value in simulations. However, these laboratory results
are a function of fracture geometry and experimental parameters, and are subject to scale or boundary effects as the fracture in
a laboratory sample grows near the edge of the core (Lim et al. 1994). Fracture toughness tests on laboratory samples require a
sample that contains a crack of known length. The test then measures the critical stress intensity factor, KIC, at which the pre-existing
crack is reinitiated. While fracture toughness (critical stress intensity factor) is a material property, it can be preferable to measure
apparent values under representative in-situ conditions, particularly when linear elastic fracture mechanics concepts can no longer
be assumed because of elevated in-situ stresses, development of a substantial process zone, elevated temperatures, or nonlinear
responses (Labuz et al. 1985; Roegiers and Zhao 1991; Stoeckhert et al. 2016). With the ongoing interest in the interaction with
discontinuities and the possibility of instantaneous propagation in a direction that is not aligned with a far-field principal stress,
there is increasing interest in measuring Mode II (sliding) critical stress intensity factors, subcritical crack growth, and upscaling
(Yew and Weng 2014; Olsen 2003).
Fracture-tip effects can play a significant role in the fracturing process, and are defined by the net-pressure equation. Apparent
fracture toughness is the dominant parameter in these tip effects. However, these effects only play an important role in the net pressure
in low-modulus formations with fracture height growth where fracturing fluids with low viscosity are used. Conventional simulations
suggest that tip effects have little importance to the net pressure for most formations with higher Young’s moduli, and/or as the fracture
length becomes larger (Jeffrey 1989; Bunger et al. 2005).
The definition of tip effects and what is meant by fracture toughness can be described loosely by the following analogy. Consider
two examples in which one is a windshield of a car, and the second is a pile of sand in the backyard. Both are made up of 100% silica
and have a chip or crack in them, and both are hit with an axe. In the window example, the crack or fracture propagates rapidly across
the window when it is hit. In the sand pile example, when hit with an axe, no fracture propagates and the axe head is buried in the
sand. This is an example of a high-toughness material as it relates to fracture propagation, while the harder windshield with a higher
modulus is an example of a low-toughness material in which the fracture propagates easily. Even prospective shales in North America
appear to have a modulus that is sufficiently high to minimize the tip effects. On the other hand, unconsolidated formations in the Gulf
of Mexico can have low moduli. This is an example in which fracture and tip effects would dominate.
Tip effects are particularly important in interpretation of DFIT measurements. Fracture toughness, process zone extent and contribution, and the extent of any nonpressurized zone near the tip all come into play in discerning key formation properties during
diagnostic testing (Barree et al. 2014). Concepts put forward by Potocki (2012) are also relevant in correlating fracture toughness,
process zone, geologic setting, complexity, treating pressure, and post-shut-in evaluations of impairment of propagation because of
the nature of the process zone preceding the fracture tip and the tectonic setting.
2.4.4 Stress Magnitudes. Principal-stress magnitudes and directions are of great importance to hydraulic fracturing. It is difficult
to infer principal stresses from core analysis, although some approximations have been made by using assumptions of transverse
isotropy and the coefficient of earth pressures at rest (Eaton 1969; Sarker and Batzle 2008; and many others). Similar predictions are
common in logging analysis. For example, the vertical stress can be determined by integrating a density log from the surface through
the formation of interest. The minimum horizontal stress is likely best determined from diagnostic fracture injection/decline testing, but can at least be estimated by interpretation of dipole sonic logs. When the values of the two principal stresses are known, the
maximum horizontal stress can then be inferred from breakdown pressure data. There are several methods for estimating the principal
stresses from core analysis. Economides and Nolte (1989) outline some of these methods.
One legacy technique is the anelastic (time-dependent elastic behavior) strain relaxation (ASR) method (Nagano et al. 2015).
To conduct an ASR evaluation of the principal-stress magnitudes, it is necessary to measure multidimensional changes in a core’s
dimensions as soon as it is recovered to the surface (the equipment needs to be at the wellsite on the rig floor when the core barrel is
laid down). Ideally, the core is oriented (either scribed, image log over the same depth, or paleomagnetic orientation of the core). To
conduct an ASR evaluation, the core is immediately instrumented once it is laid on the rig floor and the strains are measured as they
relax. During the time it takes to cut, retrieve, and lay down the core, most of the elastic recovery and some of the inelastic strain
recovery are lost. The absolute magnitudes, however, can be inferred by assuming direct proportionality of the relative magnitude of
strain recovery with the different stress magnitudes.
2.4.5 Formation Damage. Understanding formation damage is essential to the successful design and implementation of a hydraulic
fracture treatment and for maximizing post-fracture well performance. Formation damage, as it relates to hydraulic fracturing, is
generally characterized as being either natural or induced. Typical examples of damage mechanisms in natural formations are the
migration of fines, scale formation, and swelling clays. Examples of induced formation damage include gel damage to the proppant
pack, viscous fingering through the proppant pack, the effects of unbroken fluid on proppant pack permeability, capillary pressure and
water-block effects, and the effects of time and temperature on fracture conductivity. The presence of unbroken fracturing fluids with
a significant yield stress is another cause of formation damage (Balhoff and Miller 2002; Barati et al. 2009; Friedel 2006; Ayoub et al.
2006a, 2006b). Excessive drawdown might be required to produce back this polymer. With each of these mechanisms, the completion
and fracture stimulation can damage the formation, or they can be used as a means of remediation. Each of these topics is discussed
in more detail in this section.
The migration of fines is a damage mechanism that can affect any reservoir, although unconsolidated formations are the most susceptible. Formation particles or fines tend to migrate toward the wellbore in the produced fluids. Near the wellbore, or in the proppant
pack, these particulates can bridge in pore throats and restrict well productivity. Historically, gravel packing was the principal means
of controlling bridging within these reservoirs; however, fines migration can occur in the gravel pack itself. Over the years, frac packs
(a combination of a tip-screenout fracture design and gravel-pack completion) have been implemented to limit and/or mitigate the
productivity lost because of fines migration. The concept is to have any particle movement controlled at the fracture/reservoir interface
with little productivity loss, rather than in the proppant pack or gravel pack where lost productivity can be excessive. The application
of frac-pack completion technology in the Gulf of Mexico and around the world has dramatically improved reserves recovery and
well life in unconsolidated formations.
Pretreatment Formation Evaluation
35
Over the years, operators conducting frac-pack completions in unconsolidated formations have reported twofold to fourfold
increases in well performance. Fig. 2.23 shows a scanning electron microscope (SEM) photograph taken after a fines-migration test.
That test was conducted in the laboratory by combining a core sample with a proppant pack while flowing through the material. This
figure shows the core/proppant interface and highlights the potential damage fines migration can cause should the migrating fines
plug the proppant pack or reach the near-wellbore region. In this figure, the proppant is the larger, nominally spherical particles. The
finer-grained formation penetrates into the proppant pack and can significantly reduce proppant-pack conductivity. Migrating fines
can seriously affect low-permeability reservoirs. In these reservoirs, because of the small pore throats, even clay-sized particles can
plug the pore throat and affect productivity.
Another mechanism of formation damage is swelling clays, which can reduce the permeability or degrade the formation. This can
occur from clay movement through ion exchange or dispersion. Interaction of completion or fracturing fluids with cores containing
sensitive clays should be tested in the laboratory so that additives can be included in the treating fluid as necessary. The first step in
such testing is to identify the mineralogical constituents of the formation of interest. These tests can determine the compatibility of
the completion and fracturing fluids with the formation as well as determine if the formation is sensitive to a particular salt concentration or pH.
The most common clay with the greatest swelling potential is sodium montmorillonite (smectite). In contact with fresh water,
smectite can swell to many times its initial volume, greatly reducing permeability if it plugs pore throats. Fortunately, in many of the
shale reservoirs throughout the world, geologic history has precluded the occurrence of smectite in large quantities. It is much more
common to see smectite bound in a mixed-layer smectite/illite structure that has much less swelling potential and is far less destructive to formation permeability.
Although smectitic constituents might not be a large component of deeper, hotter reservoirs (or reservoirs that have been buried
and uplifted), it is still highly recommended that appropriate testing be conducted to be sure that any formation damage is limited or
mitigated. A generic clay-swelling test is conducted by placing a 1-in.-diameter × 2-in.-long core plug into a Hassler-type sleeve core
holder. Confining pressures and temperatures consistent with field conditions should be applied and permeability measured by flowing
through the core once at a low flow rate with a nondamaging brine. This establishes a baseline condition. Permeability measurements
are then made using various KCl (or similar) concentrations, and fluids with a range of pH are injected into the core.
Fig. 2.24 is a plot of such a fluid sensitivity test conducted on a sample from a reservoir located offshore Trinidad. As shown, a
5% potassium chloride (KCl) fluid was injected into the core sample and a base permeability of 555 md was measured. When a 2%
KCl fluid was subsequently injected, the retained permeability dropped by only 6% to 521 md. Next, a 2% KCl fluid with a neutral
pH was injected, followed by a 2% KCl fluid with high pH. As shown, the total loss of retained permeability was less than 8% for
the 2% KCl fluid with a low pH, and 10% for the 2% KCl fluid with a high pH. Finally, the original 5% KCl fluid was injected and
the retained permeability was measured to be 531 md, a loss of only 4% retained permeability throughout this test. As a precautionary note, much more severe sensitivity can be experienced, particularly in samples with lower porosity. While Fig. 2.24 is relevant
for high-permeability formations, the issue might be equally critical for low-permeability formations. Damage of fracture faces and
consequent reduction in strength can lead to embedment. In scenarios with high proppant concentrations, this might be tolerable.
In situations in which proppant loading is low and/or proppant diameter is small, this embedment can lead to a relevant reduction
in conductivity (Okrad et al. 2011).
As previously noted, many forms of formation damage can be induced during hydraulic fracturing. These mechanisms include gel
damage; viscous fingering; unbroken-gel flow; capillary pressure (water-block) effects; proppant degradation because of time, temperature, and pressure; and yield stress effects (discussed below). They require fracturing fluid cleanup to limit or mitigate damage
(Penny and Jin 1996; Samuelson and Constien 1996).
Fig. 2.23—SEM photographs of core/proppant interface showing fines migration (Britt et al. 2000).
36 Hydraulic Fracturing: Fundamentals and Advancements
580
Retained Permeability (md)
Fluid sensitivity tests
5% KCl
560
540
5% KCl
2% KCl
520
2% KCl, pH = 8.5
2% KCl, pH = 10
500
0
200
400
Injection (mL)
600
Fig. 2.24—Fluid sensitivity testing of pH and KCl concentrations (Britt et al. 2000).
Fractional Reduction in Permeability, 1–k /ki
Damage from gel residue left in a fracture has long been recognized as a problem in the industry. Cooke (1975) stated, “The residue from guar polymer is the most important material presently used in fracturing fluids that can cause fracture conductivity reduction!” For a long time after that statement, little was done to address the damaging effects of gel residue. This situation has improved
with recent advancements in breaker technology. A breaker is usually an oxidizing agent or a consortium of bacteria (depending on
the temperature) that reduces the viscosity of a fluid by breaking long-chain molecules into shorter segments. The problem is also
less common with the increased use of slickwater as fracturing fluid in low-permeability applications. Slickwater is water typically
pumped with small concentrations of friction reducer, bactericide, and corrosion inhibitor. Gel loading is small although the frictionreduction package can be polymers.
There are many situations in which viscosified fluids are still used, either in modest- to high-permeability formations or in hybrid
treatments. Pope et al. (1996a) studied guar removal after hydraulic fracturing in the Codell Formation of Colorado, while Willberg et
al. (1997) studied gel cleanup in the Cotton Valley Formation in east Texas. These studies showed that load recovery is not a driver of
fracturing-fluid cleanup. A better gauge of cleanup would be to measure the amount of polymer recovered because polymer recovery
and load recovery are not always proportional. The east Texas work showed that in formations that produce significant formation
water, connate water production begins almost immediately on flowback and occurs even before gas breakthrough. In addition, both
publications noted that flowback polymer concentrations are generally less than or equal to the average pump-in polymer concentrations, and that only approximately 35% of the total guar pumped is recovered. In addition, the flowback rate did not affect the amount
of polymer recovery when formation water was also produced.
Damage because of viscous fingering of fluids through the proppant pack can be correlated with the reduction in the effective porosity of the pack. Pope et al. (1996b) found that only a slight reduction in the effective porosity of the pack could yield a large reduction
in the permeability of the retained proppant pack.
Thus, viscous fingering, fines migration, proppant crushing, cement contamination, and entrainment of formation particulates
transported by fluids into the proppant pack can impair productivity. Fig. 2.25 is a plot of the fractional retained permeability as a
1.0
0.9
A 20% reduction in porosity results
in a nearly 60% reduction in
permeability (k is permeability, φ is
porosity, subscript i indicates initial)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Fractional Reduction in Porosity, 1–f/f i
Fig. 2.25—Fractional retained permeability vs. porosity reduction (Britt 2008a).
Pretreatment Formation Evaluation
37
function of the fractional reduction in porosity. This figure shows that the permeability is dramatically impacted with a reduction in the
porosity in the proppant pack. As shown, a 20% reduction in the proppant-pack porosity resulted in a 60% loss in the proppant-pack
permeability. This makes any retention of gel residue, formation fines, proppant fines, or cement a serious issue.
Productivity impairment can occur even when polymer loading is minimal, particularly in lower-permeability plays. Capillary
effects or water block can cause formation damage (Holditch 1979). Comprehending capillary pressure and relative permeability and
assessing the change of the capillary pressure in damaged zones are important to assessing this form of damage. If the absolute or
relative reservoir permeability is reduced by fracturing-fluid invasion and the capillary pressure in the damaged zone increases, water
from the treating fluid is drawn to the damaged zone. Unless pressure drawdown during production or flowback is large enough to
overcome the capillary effects in the damaged zone, the imbibed water is trapped and hydrocarbon flow will be impaired. However, if
the formation permeability is not damaged by fracturing-fluid invasion, no serious damage will occur when the pressure drawdown is
greater than the capillary pressure. In such a situation, for a gas reservoir, the cumulative production is independent of this capillary
pressure. In fact, it is sometimes argued that countercurrent imbibition can increase gas production.
Another damage mechanism relates to unbroken gel. Voneiff et al. (1993) found that highly viscous unbroken gel left in a fracture
after cleanup can result in nearly a 30% recovery loss for a tight gas well. Unbroken fracturing fluids can reduce the initial gas rate
by as much as 80% and flatten the production decline. Voneiff et al. also found that the effects of unbroken gel and poor cleanup
played out over years of production. This was more acute as the fracture length increased and more unbroken fluid was recovered with
continued production. Although their field examples were from the Frontier Formation in the western United States, well testing has
identified similar problems in other tight gas reservoirs. Fig. 2.26 highlights the effect of unbroken-fluid viscosity on gas-production
rate and cumulative gas recovery. As shown, unbroken gel has a dramatic and deleterious effect on well performance.
Certain polymeric fluids used in drilling and stimulation have a yield stress such that a finite stress must be applied to the fluid
for shearing to occur. In a drilling fluid, this yield stress impedes settling of cuttings when there is no circulation. In hydraulic
fracturing, proppant settlement is resisted. For these generalized non-Newtonian fluids, conceptually, it has been determined
that polymer left in a fracture after filtrate (mostly water) has leaked off exhibits a significantly different rheology than the
fluid that was originally pumped. In particular, there is a threshold pressure gradient before flow commences. This yield-stress
concept has been validated in the laboratory by a number of investigators. Simulations also demonstrate that it can be either a
key component or a hindrance to fracturing-fluid cleanup and post-fracturing well productivity. Fig. 2.27 shows a plot of the
flow-initiation gradient vs. the average polymer concentration. This plot shows laboratory test readings with and without breaker.
These tests show that the use of breaker greatly reduced the negative effects of yield-stress behavior. The criterion for damage is
represented by an artificial flow-initiation gradient. No-flow initiation gradient is evident when the average polymer concentration is less than 400 to 500 lbm/Mgal and breaker is used. Conversely, the flow initiation gradient is 0.0143 times the average
polymer concentration when breaker is not used. This work further shows that if typical yield values for fracturing fluid are used
(i.e., 0.05 to 17 Pa), then fracture initiation gradients of approximately 0.03 to 14 psi/ft are required to effectively clean up the
entire fracture length.
2.5 Recap: How to Use These Data?
As lower-permeability reservoirs are developed, integrating geologic information becomes progressively more relevant as the data
increasingly point to a requirement to understand the geology. Faulting and fault properties can assist in constraining the in-situ
stress field. The industry has progressed to considering the complete stress tensor, rather than simply the magnitude of the minimum
horizontal stress. Integrating all disciplines—such as drilling information, in-situ and laboratory testing, and sophisticated logging
information—is gaining importance. This geologic context is also relevant for higher-permeability applications.
In assessing hydraulic fracture treatment design and optimization, there has been a new awareness in determining the properties
of discontinuities, which can be as important as the properties of the matrix. The concepts of brittleness and fracability have become
part of the vocabulary, as has intuition related to complexity. All are governed by mechanical stratigraphy and in-situ stresses, and
potentially mitigated by intelligent “engineered” stimulation design.
Finally, there is an increasing relevance for regulatory and environmental oversight as operations are increasingly required to
show good governance and earn the social license. Controlling out-of-zone growth, recognizing issues related to tectonic settings in
which above-normal seismicity is possible, developing new monitoring methods, and mitigating deleterious aspects of operations are
0.026 md, 650 ft Fracture length
Note: cp denotes viscosity of
fracturing fluid in proppant pack
800
1 cp
600
50 cp
400
1,000 cp
200
10,000 cp
No fracture treatment
0
0
50
100
150
200
250
Cumulative Time (days)
300
350
1,400
Cumulative Production (MMscf)
Production Rate (Mscf/D)
1,000
1,000
0.026 md, 650 ft Propped fracture length
Note: cp denotes viscosity of
1 cp
fracturing fluid in proppant pack
50 cp
1,000 cp
800
10,000 cp
1,200
600
400
No fracture
200
0
0
2,000
4,000
6,000
8,000
Cumulative Time (days)
10,000
Fig. 2.26—Gas rate and cumulative recovery vs. time (after Voneiff et al. 1993). At left are production rates for presumed
residual fluid in the proppant pack. The residual fluids are differentiated on the basis of viscosity. At right are equivalent
cumulative production curves.
38 Hydraulic Fracturing: Fundamentals and Advancements
20
No breaker
Flow-Initiation Gradient (psi/ft)
18
Breaker
16
Breaker delays filter-care buildup
but difficult for breaker to infiltrate
Linear (no breaker)
14
y = 0.0143x
R 2 = 0.7873
12
10
8
(p / L)FIG = 21.8t
6
 f  1/2
k
4
2
0
0
200
400
600
800
1,000
Average Polymer Concentration (lbm/1,000 gal)
1,200
Fig. 2.27—Yield power-law laboratory test results (after May et al. 1997). This relationship has a correlation coefficient,
R 2, of 0.7873. Porosity is indicated by φ , permeability by k, and the pressure gradient along the length of the sample to
initiate flow by ∂P/∂∂L.
important. Integrating new concepts, such as brittleness, to better engineer completion design will help the fracturing engineer achieve
the ultimate goal of maximizing reserves recovery in a safe and efficient manner.
2.6 Nomenclature
a
=
cementation factor, dimensionless
I
=
excess current, μA∙mm/V
A
=
amplitude of the sinusoid for an image log,
m [ft]
k
=
absolute permeability, m2, darcies
=
fracture permeability, m2 [md]
0.863 in Eq. 2.7
kfrac
=
b
=
m
=
formation factor, dimensionless
B
specific counterion activity, dimensionless
=
n
=
saturation exponent, dimensionless
BI
brittleness index, dimensionless
c
=
0.00481, μm−1 in Eq. 2.7
Cb
=
bulk compressibility of a formation, GPa−1
[psi−1]
Cij
=
elastic stiffness tensor
C44
=
slow-shear modulus, GPa [psi]
C55
=
fast-shear modulus, GPa [psi]
=
formation nonlinear constants
Rt
=
measured total resistivity, Ω∙m
=
background formation
resistivity, Ω∙m
C456, C144,
C155
rw
=
radius of drilled hole, in.
Rd
=
deep resistivity value, Ω∙m
Rmf
=
mud-filtrate resistivity value, Ω∙m
Rs
=
shallow resistivity value, Ω∙m
Rsand
=
resistivity of the clean reservoir
sand, Ω∙m
Rsh
=
resistivity of the interlaminations of
clay-rich shale, Ω∙m
Cg
=
compressibility of the solid constituents
(grains), GPa−1 [psi−1]
Rx0
CEC
=
cation-exchange capacity, mEq/100 mL
Sw
=
water saturation, fractional
=
shale fraction, fractional
E
=
Young’s modulus, GPa [psi]
Vsh
E′
=
Young’s modulus normal to the plane of
the layering, GPa [psi]
Qv
=
quantity of cation-exchangeable clay
present, mEq/mL of pore space
ED
=
dynamic Young’s modulus, GPa [psi]
wf
=
fracture aperture, m [in.]
F
=
formation resistivity factor for clay-free
matrix, dimensionless
βf
=
Fsand
=
formation resistivity factor of clean sand,
dimensionless
n umber of primary fracture directions
(1 for single subhorizontal or subvertical,
2 for orthogonal subvertical, and 3 for chaotic or brecciated)
G
=
shear modulus in the plane of the layering,
GPa [psi]
λ and μ
=
Lamé’s parameters
εij
=
G′
=
shear modulus normal to the plane of the
layering, GPa [psi]
strain tensor in three dimensions,
dimensionless
εel
=
elastic strain, dimensionless
Pretreatment Formation Evaluation
39
εtot
=
total strain at failure, dimensionless
τmax
=
rock strength, Pa [psi]
θ
=
dip of a fracture or fault or bedding,
degrees
τres
=
residual strength, Pa [psi]
λf
=
σij
=
fracture frequency, fractures/m
stress tensor in three dimensions, MPa
[psi]
v
=
Poisson’s ratio, dimensionless
σV
=
total vertical stress, MPa [psi]
v′
=
Poisson’s ratio for loading perpendicular to
the plane of the layering, dimensionless
σ′V
=
effective vertical stress, MPa [psi]
σHmax
=
total maximum horizontal stress, MPa [psi]
σ′Hmax
=
effective maximum horizontal stress, MPa
[psi]
vD
=
dynamic Poisson’s ratio, dimensionless
vP
=
compressional-wave velocity, m/s [ft/sec]
vS
=
shear-wave velocity, m/s [ft/sec]
σHmin
=
total minimum horizontal stress, MPa [psi]
ξ
=
8.44 × 10
σ′Hmin
=
ζ
=
units conversion factor (as required)
effective minimum horizontal stress, MPa
[psi]
ρ
=
density, kg/m3or gm/cm3 [lbm/ft3]
ϕ
=
porosity, fractional
ρb
=
bulk density, kg/m3or gm/cm3 [lbm/ft3]
ϕf
=
fracture porosity, fractional
13
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Chapter 3
Rock Mechanics and Fracture
Geometry
Norm R. Warpinski, Halliburton
Norm R. Warpinski served as a Technology Fellow at Halliburton in Houston, Texas, where he oversaw the development of new tools
and analyses for hydraulic fracture mapping, reservoir monitoring, hydraulic fracture design and analysis, and integrated monitoring solutions for reservoir development. He retired from the company in July 2016. Warpinski holds a BS degree in mechanical engineering from
Illinois Institute of Technology and MS and PhD degrees in mechanical engineering from the University of Illinois, Champaign/Urbana.
Contents
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Overview������������������������������������������������������������������������������������������������������������������������������������������������������������������ 47
Rock Properties������������������������������������������������������������������������������������������������������������������������������������������������������� 48
3.2.1 Overview���������������������������������������������������������������������������������������������������������������������������������������������������� 48
3.2.2 Behavior of Linear Elastic Materials����������������������������������������������������������������������������������������������������������� 48
3.2.3 Isotropic Elastic Rock Properties��������������������������������������������������������������������������������������������������������������� 51
3.2.4 Shale Rock Properties������������������������������������������������������������������������������������������������������������������������������� 54
3.2.5 Coalbed Methane Rock Properties������������������������������������������������������������������������������������������������������������ 56
3.2.6 Importance of Elastic Rock Properties������������������������������������������������������������������������������������������������������� 58
3.2.7 Fracture Toughness and Fracture-Tip Behavior����������������������������������������������������������������������������������������� 58
3.2.8 Poroelastic Properties�������������������������������������������������������������������������������������������������������������������������������� 59
3.2.9 Strength of Rocks�������������������������������������������������������������������������������������������������������������������������������������� 59
3.2.10 Log-Derived Elastic Properties������������������������������������������������������������������������������������������������������������������ 60
In-Situ Stress����������������������������������������������������������������������������������������������������������������������������������������������������������� 61
3.3.1 Overview���������������������������������������������������������������������������������������������������������������������������������������������������� 61
3.3.2 Direct Stress Measurements���������������������������������������������������������������������������������������������������������������������� 62
3.3.3 Log-Derived Stress Calculations���������������������������������������������������������������������������������������������������������������� 64
3.3.4 Other Stress Evaluation Techniques���������������������������������������������������������������������������������������������������������� 65
3.3.5 Advanced Sonic Measurements and Stress Anisotropy���������������������������������������������������������������������������� 65
3.3.6 Drilling-Induced Fractures and Breakouts�������������������������������������������������������������������������������������������������� 65
3.3.7 Stress Information�������������������������������������������������������������������������������������������������������������������������������������� 65
Fracture-Height Growth in Geologic Media�������������������������������������������������������������������������������������������������������������� 66
Fracture Complexity������������������������������������������������������������������������������������������������������������������������������������������������� 66
Summary����������������������������������������������������������������������������������������������������������������������������������������������������������������� 69
Nomenclature����������������������������������������������������������������������������������������������������������������������������������������������������������� 69
References��������������������������������������������������������������������������������������������������������������������������������������������������������������� 70
3.1 Overview
Our understanding of hydraulic fracture growth and behavior has changed considerably since Recent Advances in Hydraulic
Fracturing (Gidley et al. 1989) was published. Since that time, fracture diagnostic technology has advanced enormously, core recoveries of hydraulic fractures have been obtained, additional tests in mines have been documented, and sophisticated laboratory and
modeling studies have helped improve our understanding of fracturing in a complex geologic environment. In addition, fracturing
of horizontal wells has skyrocketed and different approaches to both fluid systems and proppants have been developed. As a result,
we now see hydraulic fracturing as spanning a spectrum of behaviors ranging from singular planar fractures to complex networks of
induced or activated features, any of which can be influenced by specific completion and fracturing approaches. This new reality is
particularly true in coalbed methane and shale reservoirs, two resources that were barely on the radar screen at the last writing.
Nevertheless, the basic rock mechanics principles that are used to model a fracture remain unchanged, although the application
to any specific type of fracture process may vary widely. For example, Young’s modulus, Poisson’s ratio, permeability, fracture
48 Hydraulic Fracturing: Fundamentals and Advancements
toughness, Biot’s coefficient, and the various other properties measured in the laboratory affect fracture opening and growth according to well-accepted fundamental laws, and the methods for determining these properties in the laboratory are essentially the same
as described in Recent Advances in Hydraulic Fracturing. What has primarily changed is our recognition that a complex geologic
environment with natural fractures, bedding planes, lithologic discontinuities, and other heterogeneities is likely to create additional
mechanisms that must be accounted for to adequately model or evaluate fracture behavior. Features such as anisotropy, complex
layering, slippage along planes of weakness, fissure openings, scale-dependent mechanisms, stress bias, and many other mechanisms
are likely to induce gross changes in fracture behavior, at least in those reservoirs where the geology is favorable for such features to
be present.
There have been considerable changes in our methods for obtaining the necessary data to perform any modeling or evaluation studies. At the time Recent Advances in Hydraulic Fracturing was written, most rock and reservoir properties were determined directly
from core analysis, stress tests or other small-volume injections, and well testing. Since then, the focus has moved to using logs to
estimate most of the important properties, and the methods used to extract these properties from the log measurements are discussed
in this chapter. Nevertheless, engineers need to be aware that most log measurements are often only estimates of the properties that
are based on some idealized assumptions, and it will always be a good idea to perform occasional checks using direct measurements
to ensure that the assumptions are valid. In addition to the log measurements, there is also a need to quantify other properties that help
us design and evaluate fracturing treatments in coal seams and gas shales.
Probably the largest changes associated with rock-mechanics analyses for hydraulic fracturing are a result of taking a much closer
look at fracturing from minebacks, cored fractures, laboratory tests, and fracture diagnostics such as microseismicity. These investigations have shown that a “fracture” often consists of multiple subparallel fractures, that they might offset and veer at heterogeneities,
that fracture height often does not conform to expectations from stress measurements, that slippage along bedding planes or natural
fractures might “decouple” the fracture behavior, and that fractures might induce widespread shear within a reservoir and/or widespread fracture dilation, depending upon rock/reservoir/treatment conditions. As a result, we need to effectively characterize the geological and geomechanical conditions of the reservoir that is being treated, an aspect that was never emphasized in Recent Advances
in Hydraulic Fracturing.
Although fracture behavior is now understood to be more complicated than considered previously, the analyses given in Recent
Advances in Hydraulic Fracturing to assess fracture height and opening as a function of stress are correct, but somewhat incomplete.
However, no attempt is made to improve on those analyses in this chapter because such analyses belong in the domain of the fracture
model, where it is possible to account for many of the complexities described above. Nevertheless, some discussion of the various
mechanisms is given to provide a basis for selecting possible options when using a fracture model or evaluating fracture diagnostic
results.
Left out of this chapter are any fracture diagnostics for measuring fracture growth, because the pertinent chapter in Recent
Advances in Hydraulic Fracturing delved into temperature measurements in great detail, and also introduced radioactive tracers,
video cameras, and microseismic monitoring. Those have been consigned to the Fracture Diagnostics Chapter. However, the results
obtained from those diagnostics are important to our understanding of the theory and methods used to model and evaluate fracture
treatments.
3.2 Rock Properties
3.2.1 Overview. It is necessary to characterize rock properties to calculate rock deformation, fracture, failure, and stress induced
by the hydraulic fracturing process. The deformation of most interest here is the opening width of a hydraulic fracture in response
to the internal pressure, but deformation is also important for proppant embedment and crushing calculations, fracture diagnostic
analyses, stress calculations, and various other aspects of fracturing and completion technology. Fracturing, or more specifically the
propagation of fractures, has historically been concerned with the use of linear elastic fracture mechanics (LEFM) to determine the
growth of a fracture in length and height, but now might also have significance relative to the complexity observed in reservoirs such
as gas shales. Failure has not previously been an important element of conventional hydraulic fracturing modeling or analysis, but
the application of “frac-pack” technology in unconsolidated sands, the calculation of stresses in basins, the stability of horizontal
wellbores, and many other facets of completion and stimulation technology make it important to understand the failure characteristics
of the reservoir rock. Stress calculations associated with overburden loading, stress induced by the fracture, fissure opening, induced
microseismicity, and many more phenomena are now important pieces of the design and evaluation that require an analysis of rock
properties.
3.2.2 Behavior of Linear Elastic Materials. Most of the calculations that will be performed in association with hydraulic fracturing
will be primarily concerned with the elastic behavior of rocks. Historically, most of the rocks that were hydraulically fractured were
relatively isotropic and straightforward isotropic analyses could be performed. Many of the unconventional reservoirs now being
exploited have layered features that result in some degree of anisotropic behavior that could have important implications for hydraulic
fracturing and associated completion design.
3.2.2.1 Linear Elastic Isotropic Behavior. The elastic properties of rocks are those that govern the deformation behavior. In most
instances it will be assumed that the rocks are “linear elastic”; that is, they follow Hooke’s law for small strains, which for isotropic
materials is given by
ε1 =
σ
σ
σ1
− ν 2 − ν 3 , ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.1)
E
E
E
ε2 =
σ
σ
σ2
− ν 1 − ν 3 , ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.2)
E
E
E
Rock Mechanics and Fracture Geometry
ε3 =
49
σ
σ
σ3
− ν 1 − ν 2 , ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.3)
E
E
E
τ
γ 12 = 12 2G , ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.4)
γ 23 =
τ 23
2G
, ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.5)
τ
γ 13 = 13 2G , ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.6)
where E is Young’s modulus, G is the shear modulus or modulus of rigidity, ν is Poisson’s ratio, ε is the strain, σ is the stress, γ is the
shear strain, τ is the shear stress, and the 1, 2, and 3 subscripts refer to Cartesian directions; in the following discussion, the 1 and 2
directions will be horizontal and the 3 direction will be vertical. In many applications, the stresses are ordered from 1 to 3 according to
their magnitude, which is often convenient for Mohr circle calculations, for example, but the definition of stiffness coefficients discussed
in the next subsection requires a set nomenclature regarding directionality. This is the reason for defining the 3 direction as vertical.
Linear elasticity presumes that the strains are linear functions of the stresses and vice versa, with the proportionality constants
associated with the elastic properties. The units for σ, E, and G are those of stress (e.g., psi or MPa) while ε and γ are unitless because
strain is defined as a change in length divided by the original length.
Eqs. 3.1 through 3.6 can also be written in the convenient matrix form given below. Note that the lower left segment of the material
property matrix is not shown because all of the elements are zeros and the matrix is symmetric.












ε11
ε 22
ε 33
2ε13
2ε 23
2ε12
 1

 E
  −ν
 
  E
  −ν
 
= E
 
 
 
 
 
 



−ν
E
1
E
−ν
E
−ν
E
−ν
E
1
E
0
0
0
0
0
0
1
G
0
1
G

0 


0   σ 11
 σ
22

0   σ 33


0   σ 13
  σ 23

0   σ 12

1 
G 





 . ����������������������������������������������������������������������������������������������������(3.7)






It is often useful to write the stresses as a function of the strains. Eqs. 3.1 through 3.6 would now be written as
σ 11 =
E
(1 − v ) ε11 + vε 22 + vε 33  , ������������������������������������������������������������������������������������������������������������������������������(3.8)
+
1
v
( )(1 − 2v ) 
E
 vε11 + (1 − v ) ε 22 + vε 33  , ������������������������������������������������������������������������������������������������������������������������������(3.9)
E
 vε11 + vε 22 + (1 − v ) ε 33  , ����������������������������������������������������������������������������������������������������������������������������(3.10)
σ 22 =
(1 + v )(1 − 2v ) 
σ 33 =
(1 + v )(1 − 2v ) 
τ 12 = 2Gε12 , ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.11)
τ 13 = 2Gε13 , ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.12)
τ 23 = 2Gε 23. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.13)
It is also convenient to write these same equations in a matrix form in terms of stiffness coefficients; this approach tends to be used
in geophysical applications where sonic velocities are measured. In this form, they are given as











σ 11
σ 22
σ 33
σ 12
σ 13
σ 23

 
 
 
 
=
 
 
 
 

C33 C12 C12
0
0
0
C12 C33 C12
0
0
0
C12 C12 C33
0
0
C44 0
0
0
C44 0
C44












ε11
ε 22
ε 33
2ε12
2ε13
2ε 23





 , ����������������������������������������������������������������������������������������������(3.14)





50 Hydraulic Fracturing: Fundamentals and Advancements
where
C33 =
C12 =
E (1 − v )
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.15)
(1 + v )(1 − 2v )
vE
(1 + v )(1 − 2v )
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.16)
C44 = G . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.17)
3.2.2.2 Linear Elastic Anisotropic Behavior. Many unconventional reservoirs have layered features that have physical properties
vertically across the layers that differ from those horizontally along the layers. Such behavior is called vertical transverse isotropy
because the vertical axis is a symmetry axis.
When dealing with vertical transverse isotropy, it should be clear that the vertical and horizontal moduli are different and that
more material constants are needed. This behavior is given below, where the subscripts indicate the directionality of the property
(horizontal, h; vertical, v; or cross, vh or hv).












ε11
ε 22
ε 33
2ε13
2ε 23
2ε12




 
 
 
 
 
=
 
 
 
 
 





1
Eh
− vh
Eh
−vvh
Ev
0
− vh
Eh
1
Eh
−vvh
Ev
0
−vhv
Eh
−vhv
Eh
1
Ev
0
1
Gvh





0
0
  σ 11
  σ 22

0
0
  σ 33

 σ
0
0
13

  σ 23

1
0
  σ 12
Gvh

2 (1 + vh ) 

Eh

0
0





 . ������������������������������������������������������������������������������(3.18)






Two aspects of the rock property matrix require a note. First, the matrix is required to have symmetry and this requires that
ν vh ν hv
=
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.19)
Ev Eh
Second, the horizontal shear modulus, G, is given by
G=
2 (1 + ν h )
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.20)
Eh
For anisotropy, it is also convenient to use the stiffness coefficients in the compact matrix form. Such a form is typically what is
used when sonic velocities are measured to determine dynamic elastic coefficients.











σ 11
σ 22
σ 33
σ 13
σ 23
σ 12

 
 
 
 
=
 
 
 
 

C11 C12
C13
0
C12 C11
C13
0
C13 C13
C33
0
C44



0 0 

0 0 

0 0 

C44 0  

C66  


0
0
ε11
ε 22
ε 33
2ε13
2ε 23
2ε12





 . ����������������������������������������������������������������������������������������������(3.21)





There appear to be six constants, but C66 can be written in terms of C11 and C12 as C66 = (C11 – C12)/2, or quite often as C12 as a function
of C11 and C66. This should be evident from the definition of the horizontal shear modulus. The various Cij coefficients can be written
in terms of the directional Young’s moduli and Poisson’s ratios as


E
Eh  1 − h ν v2 
Ev 

C11 =
, ����������������������������������������������������������������������������������������������������������������������������������������������������(3.22)


Eh 2
1
1
ν
ν
ν
+
−
−
( h )
v
h
Ev


E

Eh  h ν v2 + ν h 
 Ev

C12 =
, ����������������������������������������������������������������������������������������������������������������������������������������������������(3.23)


Eh 2
(1 + ν h )  1 − ν v − ν h 
Ev


Rock Mechanics and Fracture Geometry
C33 =
C13 =
(
Ev 1 − ν h2
)


(1 + ν h )  1 − Eh ν v2 − ν h 
Ev


Ehν v (1 + ν h )




(1 + ν h )  1 − Eh ν v2 − ν h 
Ev
51
, ��������������������������������������������������������������������������������������������������������������������������������������������������(3.24)
, ����������������������������������������������������������������������������������������������������������������������������������������������������(3.25)
C44 = G , ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.26)
C66 =
Eh
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.27)
2 (1 + ν h )
Alternatively, given the stiffness coefficients, the Young’s moduli and Poisson’s ratios are given as
Ev = C33 −
Eh = C11 +
C132
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.28)
C11 + C12
C132 ( −C11 + C12 ) + C12 ( −C33C12 + C132 )
C11C33 − C132
, ������������������������������������������������������������������������������������������������������������������������(3.29)
νv =
C13
, ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.30)
C11 + C12
νh =
C12C33 − C132
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.31)
C11C33 − C132
G = C44 . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.32)
Static measurements of these stiffness coefficients are difficult because they require sampling in multiple orientations, and it might
be difficult to obtain samples with identical properties given the small-scale layering that is often found. Dynamic measurements can
be made on a single sample (a rock cube modified by additional 45° angled sides), although there is subsequently an issue associated
with relating dynamic and static measurements if the static value is desired.
3.2.3 Isotropic Elastic Rock Properties. The examples given in Recent Advances in Hydraulic Fracturing are still consistent with
the methods in which the static elastic properties are measured in the laboratory. The stress vs. strain curves are measured during the
compression of the rock sample, and appropriate sections of the curves are analyzed to determine the values of the elastic constants
(normally E and ν). From these constants, G and K can be calculated. However, K can also be measured relatively easily by sealing an
instrumented sample in a pressure vessel and recording the volumetric change as a function of pressure. For isotropic materials, the
relationship between the elastic constants from which G and K can be calculated from E and ν are
G=
E
, ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.33)
2 (1 + ν )
K=
E
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.34)
3(1 − 2ν )
Similarly, the dynamic elastic moduli, which are determined by measuring compressional and shear velocities through the sample,
are calculated using the equations given in Recent Advances in Hydraulic Fracturing, but there is much more emphasis on dynamic
properties now because of the interest in log-derived measurements. A later subsection in this chapter will discuss log-derived properties and correlations between static and dynamic moduli, but the equations relating the elastic constants and the velocities are given
here because of their importance. They can be written as
E = ρVS2
( 3V − 4V )
(V − V )
2
P
2
S
2
P
2
S
( )
( )
2
 VP

 3 VS − 4 
 , ����������������������������������������������������������������������������������������������������������������������������(3.35)
= ρVS2 
2

 VP
 VS − 1


G = ρVS2 , ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.36)
ν=
V − 2V
2 VP2 − V
2
P
(
2
S
2
S
( )
( )
VP
)
=
2
VS
−2
2

V
2  P V − 1
S


, ����������������������������������������������������������������������������������������������������������������������������������������������(3.37)
52 Hydraulic Fracturing: Fundamentals and Advancements
where VP and VS are the compressional and shear velocities, respectively. The equation for ν is only a function of the velocity ratio
and is often given as shown on the right side of Eq. 3.37. While the dynamic velocities can be measured in the laboratory using ultrasonic equipment, it is now more likely that they will be obtained from dipole sonic logs or other advanced logging tools, as will be
discussed later.
An example of the variability expected in rock properties is given in Fig. 3.1. The plots on the left show the static Young’s modulus and Poisson’s ratio obtained in triaxial tests on core plugs sampled in a horizontal orientation. The results reported here are for
confining stresses approximately equivalent to the net confining stress in the reservoir. The right-hand plots show the gamma ray
log and sonic log measurements through the sections where these material properties were obtained, and the column on the far right
describes the rock type of each sample. The highest-moduli materials are the clean siltstones that generally have very low porosity.
The lowest moduli are found in the mudstones, but no measurements were made of the rock properties of coals found in the section
below 7,000 ft. [The coals can be identified by the low gamma response and low compressional-wave (P-wave) velocities; shear-wave
(S-wave) velocities were not obtained in the coals.]
Depth (ft)
4,860
4.1 x 106
3.4 x 106
4.5 x 106
0.24
0.21
0.21
4.3 x 106
3.2 x 106
0.17
0.25
Sandstone
Silty mudstone
0.23
0.18
0.24
Carbonaceous mudstone
Sandstone
Silty mudstone
0.16
0.28
0.22
0.15
Siltstone
Muddy siltstone
Sandstone
Siltstone
5.0 x 106
3.7 x 106
5.3 x 106
0.19
0.16
0.18
Sandstone
Sandstone
Sandstone
2.5 x 106
3.7 x 106
0.17
0.18
Mudstone
Sandstone
2.2 x 106
0.23
Mudstone
5.9 x 106
5.2 x 106
0.20
0.26
Siltstone
Muddy siltstone
6.4 x 106
0.16
Siltstone
4.2 x 106
3.7 x 106
5.3 x 106
4.1 x 106
4.3 x 106
4.4 x 106
3.6 x 106
0.22
0.21
0.23
0.20
0.23
0.19
0.16
Siltstone
Sandstone
Sandstone
Muddy siltstone
Sandstone
Sandstone
Sandstone
7,820
2.8 x 106
0.19
Mudstone
7,840
5.1 x 106
0.16
Sandstone
5.8 x 10
5.1 x 106
0.22
0.09
Sandstone
Siltstone
8,120
2.9 x 106
4.0 x 106
0.24
0.17
Mudstone
Sandstone
8,140
3.8 x 106
4,880
4,900
4,920
4,940
4,960
5,700
5,720
Depth (ft)
5,740
5,760
2.0 x 106
3.8 x 106
3.3 x 106
Vs
Vp
Muddy siltstone
Muddy siltstone
Sandstone
5,780
5,800
5,820
3.0 x 106
5,840
5,860
8.0 x 106
4.4 x 106
5.6 x 106
5,880
6,400
6,420
Depth (ft)
6,440
6,460
6,480
6,500
6,520
6,540
6,560
6,580
Depth (ft)
7,080
7,100
7,120
7,140
7,160
7,180
7,240
Depth (ft)
7,260
7,280
7,300
7,320
7,340
7,360
7,380
Depth (ft)
7,800
7,860
6
7,880
7,900
7,920
Depth (ft)
8,080
8,100
8,160
2,000,000
4,000,000
6,000,000
8,000,000
Young’s Modulus (psi)
0.18
0.0
0.1
0.2
0.3
Poisson’s Ratio
0.4 0
Siltstone
50
100 150 0
GR
5,000 10,000 15,000 20,000
Velocity (ft/sec)
Fig. 3.1—Young’s modulus and Poisson’s ratio values of Mesaverde Formation rocks, correlated with gamma ray (GR)
and velocity log measurements. Data are from a multiwell experiment (Northrop and Frohne 1990). Vs = S-wave velocity;
Vp = P-wave velocity.
Rocks usually exhibit only a small amount of stress sensitivity relative to the in-situ values. Fig. 3.2 shows measurements of
Young’s modulus at various confining stresses from selected samples from the data set in Fig. 3.1. While unconfined moduli (zero
stress) might not be representative of the reservoir conditions, once there is some reasonable stress on the samples there are usually
Rock Mechanics and Fracture Geometry
53
only small variations in properties. This behavior breaks down somewhat at higher stress levels, although the highest levels shown in
Fig. 3.2 are not realistic reservoir conditions for this rock.
9,000,000
8,000,000
Young’s Modulus (psi)
7,000,000
4,913 ft
5,806 ft
6,000,000
6,417 ft
5,000,000
6,438 ft
6,519 ft
4,000,000
6,561 ft
3,000,000
7,817 ft
7,837 ft
2,000,000
1,000,000
0
0
2,000
4,000
6,000
Confining Stress (psi)
8,000
Fig. 3.2—Stress sensitivity of Young’s modulus for Mesaverde rocks from a multiwell experiment (Northrop and
Frohne 1990).
The stress sensitivity of Poisson’s ratio for these same samples is shown in Fig. 3.3. The unconfined Poisson’s ratio might be higher
than the true in-situ value, but other than this anomaly the value of Poisson’s ratio tends to increase with increasing confining stress.
0.40
0.35
4,913 ft
0.30
Poisson’s Ratio
5,806 ft
0.25
6,417 ft
6,438 ft
0.20
6,519 ft
0.15
6,561 ft
7,817 ft
0.10
7,837 ft
0.05
0.00
0
2,000
4,000
6,000
Confining Stress (psi)
8,000
Fig. 3.3—Stress sensitivity of Poisson’s ratio for the Mesaverde Formation from a multiwell experiment (Northrop and
Frohne 1990).
Table 3.1 gives some additional rock property measurements as a function of depth, lithology, and confining stress for rocks
a­ ssociated with the Travis Peak Formation in east Texas, taken from the Staged Field Experiment #1 (Gas Research Institute 1988).
These measurements are from triaxial tests on core plugs of both sandstones and the surrounding mudstones. There is a large amount
of variability in the modulus values as a function of lithology.
A third set of data of static rock properties (Gas Research Institute 1999) is from the Mounds Drill Cuttings Injection Project
­(Moschovidis et al. 2000) that took place in central Oklahoma targeting the Wilcox Sandstone and Atoka Shale. Data from four
samples of different lithologies are shown in Table 3.2 as a function of confining stress and orientation.
54 Hydraulic Fracturing: Fundamentals and Advancements
Depth
(ft)
Confining Stress
(psi)
Young’s Modulus
(106 psi)
Poisson’s Ratio
Description
6,159
0
2.7
0.2
Mudstone
6,159
1,500
2.5
0.2
Mudstone
6,159
3,000
2.4
0.18
Mudstone
6,159
3,000
2.4
0.24
Mudstone
6,164
3,000
2.9
0.24
Mudstone
6,166
0
4.3
0.2
Mudstone
6,166
1,500
3.6
0.22
Mudstone
6,190
0
3.7
0.35
Sandstone
6,190
1,500
4.3
0.33
Sandstone
6,190
3,000
4.2
0.31
Sandstone
6,193
0
4.0
0.37
Sandstone
6,193
1,500
4.7
0.39
Sandstone
6,193
3,000
4.5
0.42
Sandstone
6,224
0
4.0
0.27
Mudstone
6,224
1,500
3.7
0.35
Mudstone
6,224
1,500
3.5
0.21
Mudstone
6,224
3,000
4.7
0.34
Mudstone
6,226
0
8.7
0.2
Mudstone
6,226
1,500
8.3
0.32
Mudstone
6,226
1,500
6.2
0.18
Mudstone
6,226
3,000
9.2
0.32
Mudstone
7,421
0
4.0
0.31
Sandstone
7,421
1,500
6.1
0.32
Sandstone
7,421
3,000
5.2
0.32
Sandstone
7,444
0
2.6
0.19
Sandstone
7,444
1,500
4.9
0.25
Sandstone
7,444
3,000
4.6
0.28
Sandstone
7,461
0
7.5
0.25
Sandstone
7,461
1,500
7.1
0.27
Sandstone
7,461
3,000
6.9
0.27
Sandstone
7,483
0
3.8
0.24
Mudstone
7,483
1,500
3.6
0.24
Mudstone
7,483
3,000
3.7
0.29
Mudstone
7,489
0
4.4
0.17
Mudstone
7,489
1,500
4.4
0.23
Mudstone
7,489
3,000
3.9
0.24
Mudstone
7,489
3,000
4.3
0.20
Mudstone
Table 3.1—Static moduli of sandstones and surrounding lithologies within the Travis Peak Formation (after Gas
Research Institute 1988).
3.2.4 Shale Rock Properties. The development of unconventional reservoirs, such as shale gas and shale oil in particular, has
brought into focus different rock properties than are typically required for a sandstone or carbonate. These shale reservoirs have
permeabilities that are often significantly less than 1 µd, they have a substantial amount of relatively mature organic matter and a
mixed wettability system, they often exhibit highly anisotropic behavior, they are usually undersaturated to water, and they might
have both microfractures and macrofractures, some or most of which might be rehealed. The rocks are difficult to test because
they deteriorate rapidly with drying and stress relief, and they are anisotropic so that material properties vary significantly with
direction.
All of these factors contribute to a wide range of special considerations that likely apply to these reservoirs and affect fracture
growth, leakoff, cleanup, and other parts of the process. There is a limited amount of information published on rock properties of
these shales; Goodway et al. (2010) show some shale data for geophysics applications. They indicate that Young’s modulus for the
Rock Mechanics and Fracture Geometry
Depth
(ft)
Orientation
Confining Stress
(psi)
Young’s Modulus
(106 psi)
Poisson’s Ratio
Description
2,678
V
1,350
5.9
0.34
Atoka Sandstone
2,678
V
1,500
6.5
0.29
Atoka Sandstone
2,678
V
1,750
6.0
0.24
Atoka Sandstone
2,678
V
2,250
7.3
0.23
Atoka Sandstone
2,678
H
1,995
7.1
0.22
Atoka Sandstone
2,702
V
1,330
8.2
0.38
Viola Dolomite
2,702
V
1,480
10.4
0.38
Viola Dolomite
2,702
V
1,730
8.4
0.39
Viola Dolomite
2,702
V
2,230
9.7
0.43
Viola Dolomite
2,702
H
2,106
11.7
0.34
Viola Dolomite
1,948
V
1,350
1.8
0.28
Atoka Shale
1,948
V
1,500
1.8
0.23
Atoka Shale
1,948
V
1,750
2.0
0.30
Atoka Shale
1,948
V
2,250
2.1
0.26
Atoka Shale
1,948
H
1,995
3.1
0.19
Atoka Shale
2,678
V
1,330
3.3
0.32
Woodford Shale
2,678
V
1,480
2.8
0.31
Woodford Shale
2,678
V
1,730
2.9
0.39
Woodford Shale
2,678
V
2,230
4.2
0.32
Woodford Shale
2,678
H
2,106
5.4
0.29
Woodford Shale
55
Table 3.2—Static moduli from rocks associated with the Mounds Drill Cuttings Injection Project, Oklahoma (after Gas
Research Institute 1999). V = vertical; H = horizontal.
Barnett Shale ranges from approximately 3.8 to 5.0 million psi, and Poisson’s ratio varies from 0.18 to 0.29. The rocks with higher
Young’s modulus and lower Poisson’s ratio values are considered more “brittle.”
Anisotropy is a feature of many of the shales that are commonly found in unconventional North American resources. Information
can be found in a number of papers (Sone and Zoback 2013; Lin and Lai 2013; Sondergeld et al. 2010; Abousleiman et al. 2007;
Jansen et al. 2015; Li et al. 2013; Sone and Zoback 2010) that shows significant anisotropy between vertical and horizontal directions.
Figs. 3.4 and 3.5 show examples of measurements from various reservoirs based on the studies noted above.
12
Young’s Modulus (million psi)
Vertical
Horizontal
10
8
6
4
2
s
iou
Va
r
le
vil
es
Ha
yn
rd
dfo
W
oo
gle
Ea
Ba
rn
Fo
r
d
ett
0
Fig. 3.4—Anisotropic measurements of static Young’s moduli for various shale reservoirs.
56 Hydraulic Fracturing: Fundamentals and Advancements
Young’s Modulus (million psi)
10
9
Woodford
8
Woodford
7
Barnett
6
Barnett
5
Haynesville
4
Haynesville
3
Eagle Ford
2
Eagle Ford
1
Longmaxi
0
0
0.1
0.2
0.3
Poisson’s Ratio
0.4
0.5
Fig. 3.5—Anisotropic measurements of static Young’s modulus vs. Poisson’s ratio for various shale reservoirs. In the
legend, a circle next to a reservoir name indicates a horizontal measurement; a triangle indicates a vertical measurement.
Fig. 3.4 shows measured static Young’s moduli for various shale reservoir rocks in the vertical and the horizontal direction. It
should first be noticed that there is a large amount of variability in the values, probably because of the highly layered nature of these
reservoirs, with some relatively competent layers sandwiched between clay-rich or organic-rich layers. In general, the anisotropy ratio
(horizontal/vertical) ranges from approximately unity to as much as three or even higher.
Fig. 3.5 shows a plot of Young’s modulus vs. Poisson’s ratio for the vertical and the horizontal direction in several shales. Many
authors use a plot like this to show brittleness, although while brittleness often correlates with these properties, actual brittleness is not
in any way dependent on either. In such an application, a “brittle” material would have a large Young’s modulus and small Poisson’s
ratio, thus plotting in the upper left quadrant of the graph.
Data from various reservoirs are scattered across this plot, and it is difficult to draw many conclusions about the behavior of the
various reservoirs. One reason for the scatter is the layering, as discussed for Fig. 3.4, but another reason is the difficulty of accurately
measuring Poisson’s ratio in shale, both with regard to test procedures and to analysis of the data.
An interesting study of the failure of anisotropic materials was performed by Ambrose (2014) and provides data on the anisotropic
elastic properties of the Bossier Shale and Vaca Muerta Shale. Table 3.3 provides information on the horizontal and the vertical static
Young’s modulus and the horizontal and the vertical Poisson’s ratio as a function of confining stress. Both of these shales exhibit
strongly anisotropic behavior. Some of the properties of the Bossier Shale are highly stress dependent, while the Vaca Muerta Shale
shows less stress dependency.
Formation
Bossier
Vaca Muerta
Confining Stress
(psi)
E Vertical
(106 psi)
E Horizontal
(106 psi)
Poisson’s Ratio
Vertical
Poisson’s Ratio
Horizontal
0
2.34
4.32
0.097
0.396
1,000
2.25
7.16
0.138
0.324
3,000
2.25
6.71
0.129
0.248
6,000
2.28
7.54
0.137
0.26
10,000
2.61
8.19
0.174
0.359
1,000
2.65
3.8
0.186
0.420
2,500
1.68
3.76
0.176
0.249
5,000
2.12
3.52
0.195
0.225
20,000
2.35
4.44
0.154
0.25
Table 3.3—Static anisotropic moduli for Bossier Shale and Vaca Muerta Shale (Ambrose 2014).
In addition to anisotropic behavior, many shale reservoirs can exhibit nonlinear behavior because of stress or strain associated with
fracturing or production. This “creep” can have severe effects on both proppant embedment and production through stress-sensitive
natural fractures. Sone and Zoback (2010) suggest that it is primarily the lower-modulus shales that exhibit creep.
3.2.5 Coalbed Methane Rock Properties. Like shales, coals have many unique properties that need to be considered in stimulating
and producing this resource. Coals are soft, weak rocks with cleats that often need to be dewatered, and have most of the gas reserves
adsorbed on the surface of the coal. The mechanical properties of the coal have an important impact on fracture width, proppant
embedment, and the stress sensitivity of the cleat system, while the cleat system and stress conditions might increase fracture complexity compared with other reservoirs.
Young’s modulus of coal typically ranges from 100,000 to 1,000,000 psi (Holditch et al. 1988). Abass et al. (1990) conducted
laboratory experiments that showed that coal moduli are very stress sensitive, with values ranging from 250,000 psi unconfined to
approximately 750,000 psi at 5,000-psi confining stress, as shown in Fig. 3.6. Lu and Koehler (1989) performed in-situ modulus
Rock Mechanics and Fracture Geometry
57
1,000,000
900,000
Young’s Modulus (psi)
800,000
700,000
600,000
500,000
Sample 1
400,000
Sample 2
300,000
Sample 3
200,000
Sample 4
100,000
0
0
1,000
2,000 3,000 4,000 5,000
Confining Pressure (psi)
6,000
Fig. 3.6—Young’s modulus of coal as a function of confining stress, after Abass et al. (1990).
tests using borehole pressure cells and found even greater stress sensitivity, with in-situ Young’s modulus values that were less than
100,000 psi at roughly 1,500 psi, and 725,000 to more than 1,000,000 psi as stress conditions approached failure during mining. The
in-situ ­Poisson’s ratio ranged from 0.2 to 0.3, with values increasing slightly with increasing stress.
Some additional data on coal elastic properties have been given by Khodaverdian (1994) and are shown in Figs. 3.7 and 3.8.
Fig. 3.7 shows Young’s modulus as a function of net confining stress, with measurements both at zero pore pressure and with some
pore pressure. The sample is a medium volatile bituminous coal from Pennsylvania.
700,000
Young’s Modulus (psi)
600,000
500,000
400,000
300,000
200,000
No pore pressure
With pore pressure
100,000
0
0
500
1,000 1,500 2,000 2,500 3,000 3,500
Net Confining Stress (psi)
Fig. 3.7—Measurement of Young’s modulus vs. confining stress of coal, after Khodaverdian (1994).
The interpretation of the dependence of Young’s modulus on stress is based on the behavior of the cleats under loading. The cleats
start to close and the material becomes stiffer as stress increases.
Poisson’s ratio for coal, as shown in Fig. 3.8, is generally higher than for most sedimentary rocks, although there is a significant
amount of scatter. Coal also shows a stress sensitivity, as seen from the relatively higher (and more scattered) values at the lowest
confining stresses.
Fracturing in coal seams often results in high treating pressures that Holditch et al. (1988) attribute to a number of factors including complexity, shear slippage along cleats, poroelastic effects resulting from high leakoff into the cleats, and coal fines. Complexity
might include multiple fractures, T-shaped fractures, or even the development of a network. The shear slippage along cleats, when it
occurs ahead of the fracture tip, can result in poor transmittal of stress and difficulty in propagating the fracture. Coal fines might plug
the fracture tip or might increase the fluid viscosity.
58 Hydraulic Fracturing: Fundamentals and Advancements
0.50
0.45
Poisson’s Ratio
0.40
0.35
0.30
0.25
0.20
0.15
0.10
No pore pressure
With pore pressure
0.05
0.00
0
500
1,000 1,500 2,000 2,500 3,000 3,500
Net Confining Stress (psi)
Fig. 3.8—Measurement of Poisson’s ratio vs. confining stress of coal, after Khodaverdian (1994).
3.2.6 Importance of Elastic Rock Properties. It is easy to see the effect of these parameters on fracture openings. For a 2D (infinitely long) fracture of constant height, the width of the fracture (Sneddon and Elliott 1946) is a function of the pressure and the
fracture compliance, given by
w = C∆P =
(
) ∆ P, ������������������������������������������������������������������������������������������������������������������������������������������������������(3.38)
2 1−ν2 h
E
where C is the compliance, ΔP is the net pressure (total pressure minus the closure stress), and h is the fracture height. The fracture compliance, C, is inversely proportional to Young’s modulus, and only minimally a function of Poisson’s ratio because the term
(1 – ν 2) will usually be close to unity for typical values of Poisson’s ratio for sandstones. However, the fracture compliance and width
are directly proportional to the fracture height.
For anisotropic materials, the value of Young’s modulus to be used in fracture width calculations is that of the horizontal modulus,
which is often much larger than the vertical modulus. Currently, logging companies provide both vertical and horizontal stiffnesses,
but it is important to understand that there are significant assumptions made to do so. Three of the five stiffness values can be obtained
from measurements of the velocities of the compressional, shear, and Stonely waves. There are still two unknown stiffnesses, and
these are obtained by making two assumptions collectively called the ANNIE model (Schoenberg et al. 1996), for which the Thomsen
parameter known as δ is assumed to be zero and the two shear stiffnesses are assumed equal. This gives two equations to solve for
the other unknowns, yielding C13 = C33 − 2C44 and C12 = C13. There is no universal justification for either of these assumptions, and log
measurements of anisotropic stiffness coefficients should be scrutinized carefully.
Rock properties are also often used for calculations of the in-situ stress resulting from both gravity loading and tectonics. Poisson’s
ratio is the parameter controlling gravity loading for an isotropic material under uniaxial strain (vertical load), but Young’s modulus
is necessary if tectonic loading is included. For anisotropic materials, the horizontal and the vertical Young’s modulus and Poisson’s
ratio are needed for even the simplest calculation of gravity loading.
3.2.7 Fracture Toughness and Fracture-Tip Behavior. As with the elastic constants, the discussion about LEFM and fracture toughness in Recent Advances in Hydraulic Fracturing is still valid, but the whole concept of fracture mechanics associated with hydraulic
fracturing has undergone intense scrutiny and study to help us understand and interpret field results. There is a general perception that net
pressures in field treatments are often considerably greater than would be expected from purely elastic processes. Numerous mechanisms
have been hypothesized to influence fracture growth, including plasticity, dilatancy, complex layering, scale-dependent properties, and
others. Although many of these concepts have merit and are incorporated into models in some manner, there have been no comprehensive
experiments that have validated them at the field scale, so there is considerable subjective analysis required to use these concepts. A major
problem for rock mechanics practitioners is that there are few or no specific parameters that either are being measured or can be measured in the laboratory or in the field to evaluate the propensity for most of these mechanisms to have a significant effect on the fracture.
3.2.7.1 Fracture-Tip Processes. Clearly, if there are properties of a given rock mass or rock layer that impede fracture growth beyond
that expected from LEFM, these properties might alter the growth characteristics and final dimensions of a fracturing treatment. Using
the fundamental equation of LEFM, the stress (or alternatively internal pressure) necessary to propagate a fracture is calculated from
the propagation condition
K I = σβ π a ≥ K Ic . ����������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.39)
to give
σ≥
K Ic
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.40)
β πa
where KIc is the critical stress intensity factor, a is the crack length, and β is a factor that depends on the fracture shape (Martin 2000).
One way of looking at these additional fracture-tip processes is that they increase the critical stress intensity factor and thus result in
an increase in the net pressure needed to propagate the fracture.
Rock Mechanics and Fracture Geometry
59
Dilatancy (Cleary et al. 1991; Gardner 1992; van den Hoek et al. 1993) was probably the first concept proffered to explain high
treatment pressures. Dilatancy associated with a crack tip is a potentially nonlinear behavior that causes the rock adjacent to a new
fracture surface to expand into the open fracture because of the stress conditions around the tip, thus reducing the fracture width and
the capability for fluid to enter into the near-tip region. In this way, it acts like a mechanism to increase the size of the unwetted tip
region, which more importantly is unpressurized if no fluid can enter into it. No laboratory experiments have ever demonstrated that
dilatancy exists [some suggest that it does not (van Dam et al. 2002)], but this might be because it is something that would only be
significant at a much larger scale, such as that found in actual field fractures.
In attempting to assess the possibility of some new tip mechanics, other researchers investigated whether plasticity might cause
such dilatant behavior or some similar effect (Holder et al. 1993; Yew and Liu 1993). None of these efforts could show more than a
minor effect on fractures in conventional reservoirs, but studies of soft rock formations have shown that plasticity should have a large
effect (Martin 2000).
In addition to dilatancy, another suggested concept was that of a large scale dependence of fracture toughness in rocks
­(Shlyapobersky et al. 1988). It was postulated that the size of the fracture had an influence on the fracture toughness because of the
formation of a scale-dependent process zone, and that field-sized fractures might have apparent fracture toughness values that were
more than an order of magnitude greater than laboratory values. It can be shown that such effects would have a significant impact on
both length and height growth (Thiercelin et al. 1989) if they exist. Unfortunately, it is difficult, if not impossible, to measure such
effects at the scale necessary.
In general, these types of mechanisms have suggested that either the rock behavior changes (stiffens/strengthens) or the fluid lag
region (the unwetted zone at the fracture tip) increases. Both of these effects can be shown by modeling to increase pressure and
fracture width, shorten fracture length, and potentially increase height growth. If these mechanisms are real, have a significant effect,
and can be validated, the challenge is to formulate methods for (1) objectively implementing and (2) determining properties that can
be usefully employed. The implementation belongs to the modeling domain, the properties to the rock measurement domain.
The level of tip effects necessary to affect fracturing can be estimated by considering the following simplistic example. For a 2D
plane-strain fracture, β in Eqs. 3.39 and 3.40 is equal to 2 . For this case, a fracture with a length of 200 ft (it might be more appropriate to think of the dimension as being the fracture height) and a typical fracture toughness of 1,500 psi- in. would require 12 psi
to keep it open, illustrating how minimal the effects of the toughness are for relatively large fractures. If the toughness were increased
by an order of magnitude, the pressure required would be 120 psi. This amount is becoming significant, but it is still relatively low
compared with typical treatment pressures. It would require a fracture toughness that was 20 to 30 times greater than that measured in
the laboratory to significantly affect a treatment, taking 240 to 360 psi just to continue fracturing the rock. This analysis ignores any
frictional effects, leakoff, and other important factors, but it does give some insight into the relative importance of fracture toughness
and the level of tip effects necessary to be considered important.
3.2.8 Poroelastic Properties. An understanding of the poroelastic properties of rocks is important for correctly assessing the behavior of the rock mass under the combined effects of both stress and pore pressure, as discussed in Recent Advances in Hydraulic
Fracturing. This is normally accomplished by using the effective-stress concept, whereby the external stress is offset to some degree
by the pore pressure, with a relation in the form of
σ eff = σ − α P, ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.41)
where σ is the external stress, α is the poroelastic parameter, and P is the pore pressure. The poroelastic parameter, often called Biot’s
coefficient, is a function of a specific type of rock behavior, such as deformation, failure, transmissivity, or other processes. In the case
of rock failure, this parameter has been found to be close to unity and is then called the Terzaghi effective stress. More generally, α is
a function of rock parameters and might vary with stress and pressure. For deformation, which is usually the property of most interest
for hydraulic fracturing, Biot’s coefficient is often given as
α = 1−
K
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.42)
Ks
where K is the bulk modulus of the rock and Ks is the bulk modulus of the skeletal material (without the pores). While this formulation
is applicable for conventional reservoirs, many of the assumptions that are required to derive it might not be appropriate for unconventional reservoirs such as tight sands and shales, and care should be taken when using the effective-stress concept in such reservoirs.
Robin (1973) provides an excellent discussion of effective-stress laws, their derivation, and issues associated with their use. The case
of anisotropic materials is also much more complicated because it involves directionally dependent stiffness.
3.2.9 Strength of Rocks. The strength of rock is not usually considered important for hydraulic fracturing, except as applied through
the fracture toughness concept. However, in many unconventional reservoirs where natural fractures might be activated as a result of
the stimulation (e.g., in coals and shales), the strength of the reservoir rocks and bounding materials might enter into some advanced
analyses. In addition, the tensile strength of the rocks is occasionally used in estimating the maximum horizontal stress from openhole
hydraulic fracture stress measurements.
In dealing with rock behavior, it is always necessary to account for the pore pressure, which tends to neutralize the effect of stress.
As noted in the preceding subsection, the general approach for rock failure is that it follows the Terzaghi effective-stress law, which
is stress minus the pore pressure.
For tensile failure, the stress condition is given as
σ − P > T , ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(3.43)
where σ is the smallest (most-tensile) stress acting on the rock, P is the pore pressure, and T is the tensile strength.
60 Hydraulic Fracturing: Fundamentals and Advancements
For compressive failure, the simplest and most tractable model is the Coulomb model. It stipulates that failure occurs when the
maximum stress on a plane exceeds a stress that is a function of the minimum stress on the plane and of appropriate rock properties.
This is usually given as
σ max − P > Co + (σ min − P ) tan 2 β n , ����������������������������������������������������������������������������������������������������������������������������������������������(3.44)
where Co is the uniaxial compressive strength and βn is the angle between the failure plane normal and the maximum stress on the
plane. In practice, this criterion is found to be unrealistic for many rocks and more-complicated approaches are used (e.g., Jaeger
et al. 2007), particularly where finite-element codes are used. More-sophisticated approaches might include 3D loading or anisotropic
failure.
3.2.10 Log-Derived Elastic Properties. Elastic properties can be estimated from sonic velocities determined by various logging
tools. To calculate all of the elastic properties of interest for fracturing, it is necessary to measure the compressional (P-wave) and shear
(S-wave) velocities, as well as the rock density at every point where a value is desired. In many cases, it will also be necessary to measure other properties to make appropriate corrections for porosity, organic content, or other intrusive factors. The subject of log measurements is outside the scope of this chapter, and an evaluation of the accuracy of these types of measurements has been performed
by Barree et al. (2009), so this subsection is concerned only with the use of dynamic property measurements for fracture applications.
It is well-known that dynamic moduli vary considerably from static moduli measured in a laboratory load frame (Lama and
Vutukuri 1978), but it is also true that static moduli might be of questionable accuracy because of irreversible core damage that
occurs upon unloading, handling, drying, or other processes that alter the core from its original in-situ state. This is further complicated by the additional issue of anisotropy, which is often significant in many of the rocks bounding the reservoir and in many of the
unconventional reservoirs themselves. Nevertheless, it is a static modulus that is required for fracture models and analyses, and the
necessary steps in static testing must be performed to minimize damage or to make the necessary corrections from dynamic moduli.
Unfortunately, there is no rigorous methodology for meeting either of these requirements, and a number of different approaches can
be found in the literature.
Barree et al. (2009) provide some comparisons of dynamic-to-static properties of a variety of rock types. Fig. 3.9 shows a comparison for Poisson’s ratio, while Fig. 3.10 shows a comparison for Young’s modulus. In general, there is seldom any obvious trend
for Poisson’s ratio, with dynamic measurements being quite variable and equally likely to be higher or lower than the static value.
For this reason, any corrections to Poisson’s ratio are difficult and dynamic Poisson’s-ratio values should always be used with caution for important calculations. Young’s modulus shows a much more defined trend of higher values when measured dynamically
compared to statically. An often-used rule of thumb is that the static modulus is one-half of the dynamic modulus, but as can be seen
in Fig. 3.10, the deviation is much more variable than that rule of thumb would suggest. Barree et al. (2009) review some methods
for making corrections.
0.4
Static Poisson’s Ratio
0.35
Low axial stress PR
High axial stress PR
Linear (low axial stress PR)
Linear (high axial stress PR)
y = 0.9575x
y = 0.9258x
0.3
0.25
0.2
0.15
0.1
0.1
0.15
0.2
0.25
0.3
Dynamic Poisson’s Ratio
0.35
0.4
Fig. 3.9—Comparison of dynamic and static Poisson’s ratio (PR), after Barree et al. (2009).
Britt and Schoeffler (2009) present a correlation between the static and dynamic Young’s moduli of numerous unidentified shales.
As shown in Fig. 3.11, they find that static Young’s moduli vary from approximately 3 to 8 million psi for most of the shales of interest
(prospective shales) and that the correlation for gas shales is similar to the correlation for clastic rocks in general. The “nonprospective shales” are classified as clay-rich, highly laminated shales, typical of those that cause drilling problems and other issues, but the
relatively ductile Haynesville Shale moduli are also at the low end of the modulus range for prospective shales and not much different
from some of the nonprospective shales.
Rock Mechanics and Fracture Geometry
61
Static Young’s Modulus (million psi)
14.000
Low axial stress dyn E
High axial stress dyn E
12.000
10.000
8.000
6.000
4.000
2.000
0.000
0.000
2.000
4.000
6.000
8.000
10.000
Dynamic Young’s Modulus (million psi)
12.000
14.000
Fig. 3.10—Comparison of dynamic and static Young’s moduli, after Barree et al. (2009).
16.000
Dynamic E (106 psi)
14.000
Clastics
Prospective shales
Nonprospective shales
12.000
10.000
8.000
6.000
4.000
2.000
0.000
0.000
2.000
4.000
6.000
8.000
10.000
12.000
Static E (106 psi)
Fig. 3.11—Example comparison of static and dynamic moduli (E ) for shales, after Britt and Schoeffler (2009).
3.3 In-Situ Stress
3.3.1 Overview. As discussed in some detail in Recent Advances in Hydraulic Fracturing, in-situ stress is one of the primary controlling factors in hydraulic fracturing. The hydraulic fracture propagates perpendicular to the smallest principal stress, essentially taking
the path of least resistance through a reservoir, but it also has its height and length growth controlled to some extent by the variations
in the minimum principal stress that exist throughout the reservoir. It is unfortunate that accurately measuring the total in-situ stress
state is difficult because the stresses affect many facets of well construction, stimulation, and production operations.
The in-situ stresses that exist in a reservoir are primarily a result of the weight of the overburden rocks. This weight pushes on the
deeper layers and attempts to squeeze them laterally to accommodate the stress. If these deeper layers are constrained laterally, then
the result of the overburden weight is a partial lateral loading that depends largely on Poisson’s ratio. This behavior is the rationale
for stress calculations based upon dipole sonic log measurements of compressional (P-wave) and shear (S-wave) velocities, and the
calculation of a dynamic Poisson’s ratio that can be derived from those velocities.
However, the Earth is more complex than the simple “uniaxial strain” behavior that is described above. The lateral constraint might
not be zero, but could range throughout both positive and negative values creating a strain boundary condition. Faults and structure
also create perturbations in the stress field that might be modeled as either stress or strain boundary conditions, depending on the
exact conditions. The rock might not behave elastically, either through creep or natural fracturing, resulting in a variable and uncertain Poisson’s ratio. The poroelastic behavior of many rock types (particularly for very-low-permeability rocks) is ill-defined, and
incorporation of the correct “net” stress might be uncertain. So, even though stress logs are routinely used in the industry, it should
always be noted that these are simply the best calculations available and not necessarily as accurate as is required for quality analyses.
62 Hydraulic Fracturing: Fundamentals and Advancements
The “gold standard” for stress measurements is the hydraulic fracture method, and this method has changed somewhat since Recent
Advances in Hydraulic Fracturing. Although microfracture stress measurements are still performed where possible, the primary
approach for directly measuring stress in a reservoir is through the use of a diagnostic fracture injection test (DFIT) using a G-function
approach. This approach will be discussed in a following subsection and in the Fracturing Pressure Analysis Chapter.
3.3.2 Direct Stress Measurements. For all practical purposes, direct stress measurements in oil and gas applications consist only of
variations of the techniques used to measure hydraulic fracturing stress. Other measurement techniques, such as overcoring, which is
used in mining, are impractical in a deep wellbore. Hydraulic fracture stress measurements can be subdivided into openhole measurements, which are seldom performed because of wellbore stability concerns, and casedhole measurements that can be safely made
after the well is constructed.
3.3.2.1 Openhole Measurements. Although very few openhole stress measurements are performed because of well stability concerns, the possibility of using such measurements to determine the maximum stress acting on the wellbore in addition to the minimum
principal stress makes their application important to cover briefly. The first injection into a competent interval in a wellbore usually
requires “breaking down” the formation and often results in very high pressures to overcome the stress concentrations around the
wellbore and the tensile strength (or other appropriate fracture resistance) of the rock. When shut in, the pressure then drops quickly
to an instantaneous shut-in pressure and then slowly decays down to the reservoir pressure. Once equilibration is reached, a second
injection will result in a different “reopening” pressure that now reacts only to the stress concentrations around the wellbore. Because
these stress concentrations depend in a known way on the in-situ stresses, the reopening pressure of the second injection provides a
means to estimate the maximum principal in-situ stress (Bredehoeft et al. 1976).
In the simplest case of a vertical well with the minimum stress equal to the horizontal stress (the usual situation), the reopening
pressure, Pr, is a function of the stress concentrations around the wellbore at its minimum point. It is given by
Pr = 3σ min − σ max − Po , ����������������������������������������������������������������������������������������������������������������������������������������������������������������(3.45)
where σmin is the minimum horizontal stress, σmax is the maximum horizontal stress, and Po is the reservoir pressure. If the minimum
stress can be determined from the shut-in behavior (discussed in Recent Advances in Hydraulic Fracturing and in the next subsection)
and the reservoir pressure is known, then the maximum stress can be calculated. A check of this value can be obtained by using a
modification of the equation for the original breakdown, where
Pb = 3σ min − σ max − Po + T . ����������������������������������������������������������������������������������������������������������������������������������������������������������(3.46)
Pb is the breakdown pressure, and T is the tensile strength of the rock or is suitably modified to account for more-comprehensive
fracture mechanics behavior. Fig. 3.12 gives a schematic of ideal breakdown and reopening behavior.
Breakdown pressure
Reopening pressure
Pressure
Shut-in
Closure
Time
Fig. 3.12—Example of pressure behavior during breakdown and reopening cycles.
There is an inherent problem with using the breakdown pressure in that the tensile strength might be degraded because of flaws in
the wellbore, or the existence of natural fractures in the zone being tested. It is advisable to run an openhole imaging log both before
and after this test to assess the wellbore condition and to determine the fracture azimuth at the wellbore. Because it is nearly impossible to estimate the excess pressure needed to initiate a fracture during breakdown, the reopening pressure is usually deemed more
reliable for stress analyses.
3.3.2.2 Casedhole Measurements. Most stress measurements are performed in cased-and-cemented wells through perforations. When
conducted with small injections to evaluate reservoir bounding layers, these are usually termed “microfracs.” They are described in
some detail in Recent Advances in Hydraulic Fracturing. When larger injections are performed in the pay interval, these are usually
called calibration tests or a variety of other names (e.g., DFITs). These are important tests that (1) yield reasonably accurate measurements of the closure stress (some average minimum stress in the pay interval) and (2) provide information on nonideal fracture
mechanisms and formation permeability (Nolte 1979; Mukherjee et al. 1991; Mayerhofer et al. 1995; Barree and Mukherjee 1996).
The basic analysis used in analyzing a DFIT is a result of the pressure-decline analysis pioneered by Nolte (1979). The use of the
G-function and its derivative has provided a powerful tool by which to analyze fracture behavior by examining the pressure falloff
after shut-in. This function will be discussed in detail in the Fracturing Pressure Analysis Chapter. As part of this analysis, the use of
a superposition derivative function can be diagnostic for fracture closure.
Rock Mechanics and Fracture Geometry
63
Nolte defined a dimensionless time function as
g ( ∆t D ) =
1.5
t − tp
4
1 + ∆t D ) − ∆t D1.5 , with ∆t D =
, ������������������������������������������������������������������������������������������������������������������(3.47)
(


3
tp
where tp is the total pump time and t is the time since the beginning of pumping. Eq. 3.47 is valid for high fluid leakoff but generally
holds over a large range of conditions. The G-function can now be defined as
G ( ∆t D ) =
4
4
 g ( ∆t D ) − g ( ∆t Do )  =  g ( ∆t D ) − go  , ������������������������������������������������������������������������������������������������������������������(3.48)
π
π
where ΔtDo is the dimensionless time at shut-in and go is the dimensionless time function at shut-in.
When this transformation is performed, the pressure decline after shut-in can be expressed as
P ( ∆t D ) =
π rpC L E t p
2h
G ( ∆t D ) , ��������������������������������������������������������������������������������������������������������������������������������������������������(3.49)
with the derivative given by
dP π rpC L E t p
=
= P * . ��������������������������������������������������������������������������������������������������������������������������������������������������������������(3.50)
dG
2h
When this derivative is plotted against the G-function, the result should be a flat line through closure, which then deviates after
the fracture begins to close on itself. In practice, this is often difficult to tell and a simpler diagnostic is to plot G dP/dG against the
G-function. This function also has the advantage of being diagnostic of many types of nonideal behavior. Fig. 3.13 shows an example
of a case presented by Craig et al. (2000) with normal leakoff. The point where the G dP/dG function begins to flatten is interpreted
as closure, and that pressure is the closure stress.
Normal Leakoff
1,000
Pressure
2,650
Fracture closure
500
G dP/dG
dP/dG or G dP/dG
Pressure (psi)
3,500
dP/dG
1,800
0
3
G-Function
6
0
Fig. 3.13—Example of closure behavior for normal leakoff, after Craig et al. (2000).
Pressure-Dependent Leakoff (Fissure Opening)
500
Pressure
3,100
Fissure opening
250
Fracture closure
G dP/dG
dP/dG or G dP/dG
Pressure (psi)
3,500
dP/dG
2,700
0
2.5
G-Function
5
0
Fig. 3.14—Example of closure behavior for abnormal leakoff, after Craig et al. (2000).
64 Hydraulic Fracturing: Fundamentals and Advancements
As shown in Fig. 3.14, also from Craig et al. (2000), nonideal behavior such as pressure-dependent leakoff can also be ascertained.
This nonideal behavior does not seem to interfere with the ability to pick a closure point.
3.3.3 Log-Derived Stress Calculations. The methodology used to calculate stress from log-derived dynamic properties is briefly
described in Recent Advances in Hydraulic Fracturing. If some restrictive assumptions are made about the in-situ behavior of rocks
through their geologic history, it is possible to calculate the horizontal stress that would be expected from the weight of the overburden. The approximation of the conditions under which this occurs is termed uniaxial strain, which means that the lateral boundaries of
the layers are constrained so that they do not move. If it is also assumed that the rocks are isotropic and behave elastically (no creep
or fracturing), then an equation for the horizontal in-situ stress can be written as
σh =
ν
(σ OV − α P ) + α P , ������������������������������������������������������������������������������������������������������������������������������������������������������(3.51)
1−ν
where ν is Poisson’s ratio, σOV is the overburden stress, P is the pore pressure, and α is the poroelastic parameter, Biot’s coefficient.
The overburden stress is usually derived by integrating the density log to determine the weight of the overburden at any depth.
More generally, Eq. 3.51 can be written for a real rock/reservoir/basin system as
σ ih =
νi
i
i
σ OV − α 1i P i + α 2i P i + σ tect
+ σ anel
, ����������������������������������������������������������������������������������������������������������������������������(3.52)
1−νi
(
)
where the superscript i now refers to the ith layer, the two Biot’s coefficients (α) might be different because of anisotropy in the
i
i
rocks, σ tect
is the tectonic stress in any individual layer, and σ anel
is any anelastic behavior that the rocks might undergo as a result of
the overburden weight or tectonic stresses. It is important to note that the tectonic stress might be different in each layer depending
on how the tectonics are applied (e.g., stress or strain boundary conditions). Because many of these parameters are unknown, the
simple form of the equation is typically used and all of the complexities of the rock mass are ignored. For this reason, stress logs
should always be considered estimates of the actual stress state, even if they are supposedly calibrated with a few direct in-situ
stress measurements.
Fig. 3.15 shows an example of a stress log taken from the Baxter Shale (Higgins et al. 2008) after it has been corrected using
hydraulic fracture measurements to estimate the values. The difference in stress vertically between layers can be used in fracture
models to estimate height growth.
MD 5,000
10,000
psi
15,000
10,100
10,200
10,300
10,400
10,500
10,600
10,700
10,800
10,900
11,000
11,100
11,200
11,300
11,400
11,500
11,600
11,700
11,800
11,900
12,000
12,100
12,200
ISIP ∆
Overburden
Max horz stress
12,300
12,400
Min horz stress
12,500
12,600
Pore pressure
Fig. 3.15—Example stress log from the Baxter Shale (Higgins et al. 2008). ISIP is the instantaneous shut-in pressure
after fracturing.
Rock Mechanics and Fracture Geometry
65
3.3.4 Other Stress Evaluation Techniques. There are a number of other methods that are used to estimate or calculate the in-situ
stress from other properties. Semidirect measurements include measurements of the damage induced on core samples resulting from
release of the in-situ stresses, such as anelastic strain recovery, circumferential anisotropic velocity measurements, differential strain
curve analysis, and others. Another method that has a good theoretical foundation is calculating the stress state on the basis of the
failure characteristics of the various rock layers on the assumption that all rocks are in a state of incipient failure. Techniques such as
overcoring and others that directly measure the strain resulting from relief or application of stress are common in mines, but they are
difficult to perform in deep wells and thus are not used. While these techniques see occasional use in research wells or other specialized applications, they are not routine measurements performed by the industry.
3.3.5 Advanced Sonic Measurements and Stress Anisotropy. Methods of borehole measurements of sonic velocities are advancing
rapidly, and it is now possible to measure anisotropic moduli of the formations under some restrictive assumptions (Sinha et al. 2008).
If this can be done, then it is possible that more-accurate calculations of the stress induced by both the overburden weight and the
tectonic forces can be formulated. Higgins et al. (2008) give an example from the Baxter Shale in Wyoming where computed stress
contrasts are several hundred psi greater than if isotropy is assumed.
3.3.6 Drilling-Induced Fractures and Breakouts. Drilling- or coring-induced fractures are useful for determining the orientation of
the in-situ stress field, and thus the azimuth of a hydraulic fracture. These features are typically fractures that are initiated at the drill
bit and then propagated as tensile features through high mud weights, induced tension, or a combination of both.
Similarly, breakouts are also routinely used to determine stress orientations and occasionally to estimate stress magnitudes (e.g.,
Zoback 2007). Breakouts are shear failures that occur as a result of the stress concentrations around the wellbore relative to the mud
weight used during drilling. Breakouts are aligned in the minimum stress direction (opposite the fracture orientation).
3.3.7 Stress Information. Abundant data have been published on in-situ stress throughout the world, and one of the most useful of
these publications is the World Stress Map. It was originally compiled by Zoback (1992) and now resides at the Geophysical Institute
of the University of Karlsruhe in Germany. Additionally, there is considerable information now becoming available about regional
stresses. Fig. 3.16 is an example of the stress orientation data for Texas and Oklahoma, taken from Lund Snee and Zoback (2016).
It provides ­information on expected hydraulic fracture azimuths in various regions where data are available.
Fig. 3.16—Example of the stress map for Texas and Oklahoma, after Lund Snee and Zoback (2016).
66 Hydraulic Fracturing: Fundamentals and Advancements
3.4 Fracture-Height Growth in Geologic Media
Fracture growth in layered sedimentary formations is a topic that has been widely examined theoretically, in the laboratory, and in the
field. While it is clear that the in-situ stresses are the main factor controlling fracture height, there are many other aspects of a layered
rock sequence that can influence fracture growth vertically across the layers. This is particularly true if the fracture crosses into layers
with different stress, moduli, and toughness, but also if the layer interface has properties that might affect fracture behavior.
Recent Advances in Hydraulic Fracturing delves into the 2D height growth problem in some detail with respect to stress and
toughness by using standard LEFM approaches. In particular, a symmetric three-layer case with higher bounding stresses could be
evaluated using Simonson et al. (1978).
 h /2  π
+ ( P − σ 2 ) ��������������������������������������������������������������������������������������������������������������������������� (3.53)
= (σ 2 − σ 1 ) sin −1 
 h /2 + hs  2
2 ( h /2 + hs )
π K Ic
and can be rearranged as
σ 2 − P 2 −1  h /2 
K Ic
−
, ������������������������������������������������������������������������������������������������������������(3.54)
= sin 
σ 2 − σ1 π
 h /2 + hs 
π ( h /2 + hs )(σ 2 − σ 1 )
where P is the net pressure, σ1 is the stress in the pay zone, σ2 is the stress in the bounding layers, h is the total fracture height, hs is
the amount the fracture has penetrated into the bounding layers, and KIc is the fracture toughness of the bounding layers. Eqs. 3.53 and
3.54 are corrected here for typographical errors in Recent Advances in Hydraulic Fracturing, and they show that in-situ stress variations are likely to be the main factor controlling fracture height in any reservoir if KIc takes on typical laboratory values. Excessively
high KIc values would be effective in restricting fracture growth (Thiercelin et al. 1989).
As discussed earlier, this analysis ignores many elements that might have an important impact on fracture growth, including those
items discussed in the preceding section. Additionally, modulus effects are ignored because they are impossible to include in an
analytical solution as given in Eqs. 3.53 and 3.54, but the effects of modulus on fracture height growth have been included through
approximate formulations (e.g., Cleary 1980; Van Eekelen 1980) as noted in Recent Advances in Hydraulic Fracturing, or through
more-sophisticated finite-element models.
As discussed by Van Eekelen (1980) and Smith et al. (2001), these effects are generally small and cannot be expected to provide
significant containment of fractures. Gu and Siebrits (2008) also show that low-modulus layers surrounding a higher-modulus pay
zone can be restrictive because of a lowered stress intensity factor. This also depends on the relative fracture toughness of the different
materials.
An interesting problem develops when one attempts to assess the potential for a fracture to cross an interface with dissimilar
material properties. If LEFM is applied, at first glance it appears that any interface will terminate a fracture. The square root of the
stress-intensity factor at the tip of the crack decreases when approaching an interface with a higher modulus and eventually goes to
zero, suggesting that a crack will stop growing before reaching the interface. In reality, this problem is much more complicated than a
simple stress-intensity calculation, as discussed in some detail by Cleary (1978), although there generally will be some retardation or
enhancement of fracture growth near an interface that depends primarily on the distance from the interface and the material properties.
This type of behavior might also increase the likelihood of fracture blunting, interfacial cracks, and offsets at interfaces if fractures
reinitiate at some other location.
It is well-known that weak interfaces can blunt fracture growth, and such a mechanism is often cited for the use of KhristianovichGeertsma-de Klerk models (Nierode 1985). Examples of blunting have been noted in mineback experiments (Warpinski et al. 1982;
Warpinski and Teufel 1987; Jeffrey et al. 1992; Zhang et al. 2007) and laboratory experiments (Anderson 1981; Teufel and Clark
1984). While it is generally expected that weak interfaces will be most important at shallow depths where friction resulting from the
overburden stress is at a minimum, other factors such as overpressuring or embedded particulates (equivalent to fault gouge) can
clearly minimize frictional effects even at great depths. Weak interfaces have the potential for totally stopping vertical fracture growth,
initiating interface fractures, or causing offsets in the fracture. In addition to restricted growth effects, weak interfaces above and
below the reservoir can decouple the fracture walls (Barree and Winterfeld 1998; Gu and Siebrits 2008), resulting in poor coupling
of the fracture pressure in the reservoir to the fracture outside of the weak interfaces. This reduced coupling would create narrower
fractures in the layers across the interface and much wider fractures within the reservoir rock.
Many mechanisms, including those described above and others, can be bundled to describe fracturing across a succession of interfaces. The combination of the bimaterial interface effects described above, interfaces with little or no strength, and a wide variety of
interfaces stacked up in a typical sedimentary sequence leads to a high likelihood that fracture growth will be affected. The possibility
that such layered media could contain hydraulic fractures has been derived from fracture diagnostic information (Warpinski et al.
1998; Wright et al. 1999; Griffin et al. 1999). It is easy to conceive of multiple mechanisms serving to blunt, kink, offset, bifurcate, or
restrict growth in various layers, much as a composite material hinders fracture growth across it. Various methods are now being used
to model such behavior (Wright et al. 1999; Miskimins and Barree 2003; Weijers et al. 2005).
This is a complicated problem that has no simple solution at this time, because it is impossible to measure interface properties at
depth (they would also be affected by temperature, pore pressure, and stress), and even the characterization of properties and stresses
of individual layers is beyond current capabilities. Regardless, fracture models are using “complex layering,” “decoupling,” and other
mechanisms to attempt to empirically include such effects. In general, these are implemented in a way that typically requires some
empirical information to “calibrate” the behavior correctly.
3.5 Fracture Complexity
One of the primary areas where the understanding of hydraulic fracturing has improved in recent years is in the recognition of a
wide variety of fracture complexity that can occur as a result of geologic and stress conditions. Although a considerable amount of
complexity was observed in mineback experiments (Warpinski et al. 1981; Diamond and Oyler 1987; Jeffrey et al. 1992; Jeffrey et al.
2009), some of the cored hydraulic fractures (Warpinski et al. 1993; Branagan et al. 1996) in tight sand formations documented that
such complexity could also occur under typical reservoir conditions.
Rock Mechanics and Fracture Geometry
67
These studies generally showed that multiple fracture planes could be common, that T-shaped fractures could occur in coals or other
rocks with similar interfacial conditions, and that some interaction with the natural fractures in the reservoir would be likely. In general, the complexity in a reservoir is associated with discontinuities, both from layering and from natural fractures and faults. Fig. 3.17
shows a photograph of a mined-back fracture (Warpinski and Teufel 1987) that has intersected a natural feature and has been offset.
This fracture was created with a crosslinked-gel fluid system carrying 20/40-mesh colored sand, on the order of 1 lbm/­gal black,
2 lbm/gal red, and 3 lbm/gal blue proppants. The photograph shows that the natural feature, either a fault with minimal displacement
or a natural fracture, has been widely filled with red proppant and has probably screened out. The hydraulic fracture extends only a
few feet past the fault, and only black sand is present in this short section. The main fracture has both red and blue sand, and there is
also a secondary strand. It is clear that this discontinuity has severely altered the propagation of the fracture, resulting in much more
downward growth and no further length extension on this wing.
Tip of hydraulic
fracture
Sand in
fault/fracture
Fault or natural fracture
Secondary branch of
hydraulic fracture
Main hydraulic fracture
Fig. 3.17—Example of a hydraulic fracture being offset and probably screened out at a discontinuity in the reservoir,
after Warpinski and Teufel (1987).
Another example that demonstrates the effect of layering is shown in Fig. 3.18, where a fracture in a coal seam has been blunted
and reoriented at an interface between the coal and the surrounding rocks (Zhang et al. 2007). T-shaped fractures are common in coal
seams because mining after fracturing for methane relief has often revealed them. What is unknown is how other types of formations
and a variety of conditions might produce similar complicated pathologies.
Although a T-shaped fracture is an extreme case of interfacial influence, interfaces have a wide variety of effects on fractures and
can cause many types of complex behavior.
Fig. 3.19 shows an example of a cored hydraulic fracture from the Mesaverde Formation in the Piceance Basin, where approximately 30 fracture strands were observed over a 4-ft interval (Warpinski et al. 1993). This fracture was created with a typical
crosslinked-gel stimulation at a depth of more than 7,000 ft in a tight sandstone. The source of this complexity has not been clearly
established, although it is likely to be a result of tip process effects that have been enhanced by layering and natural fractures in this
reservoir. This example shows that the complexity observed in mineback tests is not a result of unusual rock conditions, but might be
found in any reservoir that has varying lithology and natural fractures.
Even more impressive is the complexity that has been documented in some shale reservoirs through microseismicity and other
geophysical techniques; it is on a much larger scale than has ever been anticipated on the basis of both theoretical understanding and
laboratory experiments. The Barnett Shale is the clearest example of a complex reservoir being activated, primarily by injection of
low-viscosity fluid at high rates (Fisher et al. 2002). The complexity has been attributed to low horizontal stress bias (the two horizontal stresses are almost the same) in the reservoir and the presence of a natural, weakly rehealed fracture system orthogonal to the
maximum stress azimuth. When coupled with the injection of large volumes of low-viscosity fluid at high rates, a combination of
hydraulic fracture(s) and reopened natural fractures dilates in more than one plane, creating a network of wide areal extent. It is probably an extreme case of fissure opening, but when created with high-rate waterfracturing and low concentrations of proppant it serves
to generate a relatively large stimulated volume that otherwise would be inaccessible to the wellbore.
Fisher et al. (2002) provide the type case for a network fracture system with the Barnett Shale example shown in Fig. 3.20. This is a
vertical well (before the use of horizontal wells in the Barnett) that was monitored microseismically from an offset well, and was also
monitored using both surface and downhole tiltmeters. The microseismic data are interpreted as representing a “network” with fracture
planes in both the northeast (maximum stress azimuth) and the northwest (a natural fracture azimuth). The width of the “fairway” of
microseisms is approximately 700 ft, presumably indicating that the difference in horizontal stresses is low enough to allow natural
fractures to be activated and opened in both planes. The actual movement of fluid is supported by the “killed” wells, which are offset
68 Hydraulic Fracturing: Fundamentals and Advancements
Roof rock
500 mm
60–70 mm
200 mm
1600 mm
200 mm
Coal
60–80 mm
Obstructed
Fig. 3.18—Schematic of a T-shaped fracture in a coal seam (Zhang et al. 2007).
75
st
Fir ture
c
fra
11
75
al
tur
Na cture
fra
10
le
ho
Up
12
75
al
tur
Na cture
fra
13
75
Vertical
4
751
st
La ure
ct
fra
Fig. 3.19—Photograph of a cored hydraulic fracture from the Mesaverde Formation; there are approximately 30 separate
fracture strands over a 4-ft interval. Core was taken in a deviated well at approximately 55° (as shown in the picture) with
the top at the right (Warpinski et al. 1993).
Rock Mechanics and Fracture Geometry
69
500
300
Northing (m)
100
Observation well
–100
“Killed” wells
–300
–500
–700
Tiltmeter length (45% volume NW orientation)
–900
–300
–100
100
300
Easting (m)
500
700
900
Fig. 3.20—Example of microseismic data, “killed” wells, surface tiltmeter fluid distribution, and downhole tiltmeter
fracture length, after Fisher et al. (2002).
vertical producing wells that became loaded with fracturing fluid and would not produce gas until the fracturing fluid was unloaded.
Note that two of the killed wells are outside of the microseismic zone, but this is because of the extent of microseismicity exceeding
the monitoring distance. Had there been a monitoring well in the northeast corner, it is quite likely that microseisms would have been
detected far past what was actually observed from the observation well on the west side. The surface tiltmeter data also support the
network concept because the surface tiltmeter inversion has 45% of the volume in the northwest orientation. Finally, downhole tiltmeters in two offset wells near the tip of the fracture network support the observed length.
Other shale reservoirs might or might not exhibit the same degree of complexity, although the use of horizontal wells with multiple
stages and multiple perforation clusters per stage likely fosters the generation of more complexity than would be obtained by fracturing a vertical well. Clearly, the in-situ stresses, the natural fractures already existing in the reservoir, the brittleness of the shale rocks,
the shale reservoir hydrocarbon (gas or oil), and other formation factors all need to be considered when attempting to stimulate these
reservoirs.
3.6 Summary
The basic physics associated with the opening of a single pressurized fracture in a homogeneous rock mass has not changed much
since 1989 when Recent Advances in Hydraulic Fracturing was published. Much additional work has been performed on determining properties and stresses from logs, accounting for the layered structure of a sedimentary sequence, and developing techniques
for evaluating a reservoir through calibration injections. The primary change in the technology has come through the increased
recognition of the role of reservoir complexities (e.g., natural fractures, stress conditions, and layering) in altering the behavior of
the hydraulic fracture. The widespread occurrence of multiple fracture planes (observed in most minebacks and cores), fracture
networks in shales, T-shaped fractures in coals, and a wide assortment of fracture pathologies from surface tiltmeter measurements
has focused attention on the importance of the geology of the reservoir in treatment behavior. Fracturing is a complex interaction
between the injected material and the reservoir characteristics; neither can be neglected in any simulation or assessment of treatment
results and conditions.
3.7 Nomenclature
a
=
fracture length for stress intensity
­calculations, ft
C33
=
stiffness coefficient in 33 plane, psi
C44
=
stiffness coefficient in 44 plane, psi
=
stiffness coefficient in 66 plane, psi
C
=
fracture compliance, ft/psi
C66
CL
=
leakoff coefficient, ft/ min
E
=
Young’s modulus of isotropic rock, psi
Eh
=
Young’s modulus of rock in horizontal
direction, psi
Ev
=
Young’s modulus of rock in vertical
­direction, psi
Co
=
uniaxial compressive strength, psi
C11
=
stiffness coefficient in 11 plane, psi
C12
=
stiffness coefficient in 12 plane, psi
C13
=
stiffness coefficient in 13 plane, psi
70 Hydraulic Fracturing: Fundamentals and Advancements
go
=
pressure falloff time at shut-in,
dimensionless
γij
=
shear strain in i, j plane, dimensionless
δ
=
Thomsen parameter controlling near-­
vertical anisotropy, unitless
ΔP
=
net fracturing pressure (pressure minus
closure stress), psi
g(ΔtD)
=
pressure falloff time, dimensionless
G
=
shear modulus of isotropic rock, psi
Gvh
=
shear modulus of anisotropic rock, psi
G(ΔtD)
=
Nolte G-function for pressure falloff
­analysis, dimensionless
ΔtD
=
falloff time after injection, dimensionless
ΔtDo
=
time at shut-in, dimensionless
h
=
fracture height, ft
εi
=
normal strain in i-direction, dimensionless
εij
=
strain in i-direction on plane with normal
in j-direction, dimensionless
ν
=
Poisson’s ratio of isotropic rock,
dimensionless
νh
=
Poisson’s ratio for horizontal response to
horizontally applied stress, dimensionless
νhv
=
Poisson’s ratio for horizontal response to
vertically applied stress, dimensionless
νi
=
Poisson’s ratio in ith layer for stress
calculations, dimensionless
νv
=
Poisson’s ratio for vertical response to
vertically applied stress, dimensionless
νvh
=
Poisson’s ratio for vertical response
to ­horizontally applied stress,
dimensionless
ρ
=
rock density, g/cm3
hs
=
thickness of initial fracture zone, ft
K
=
bulk modulus of isotropic rock, psi
KI
=
stress intensity factor at tip of fracture,
psi- in.
KIc
=
critical stress intensity factor
(fracture toughness) of rock, psi- in.
Ks
=
bulk modulus of skeletal rock material, psi
P
=
pore pressure in rock, psi
*
P
=
negative slope of G-function plot, psi
Pb
=
breakdown pressure during fracturing, psi
i
P
=
reservoir pressure in ith layer, psi
Po
=
reservoir pressure, psi
Pr
=
reopening pressure on subsequent injections
after breakdown, psi
P(ΔtD)
=
falloff pressure as function of dimensionless
time, psi
σ
=
external stress, psi
i
anel
=
horizontal anelastic stress applied in ith
layer, psi
σeff
=
effective stress (stress minus pore pressure
multiplied by Biot’s parameter), psi
σh
=
horizontal in-situ stress at depth, psi
σ
i
h
=
horizontal in-situ stress for ith layer, psi
σi
=
normal stress in i-direction, psi
σij
=
stress in i-direction on plane with normal
in j-direction, psi
σ
rp
=
ratio of leakoff height to total height of
fracture, dimensionless
t
=
time, seconds
tp
=
total pump time of injection, seconds
T
=
tensile strength of rock, psi
VP
=
P-wave velocity, ft/sec
VS
=
S-wave velocity, ft/sec
w
=
fracture width, ft
α
=
Biot’s poroelastic coefficient, dimensionless
σmax
=
maximum stress on rock element, psi
α1i
=
Biot’s poroelastic coefficient for ith layer
response to vertical loading, dimensionless
σmin
=
minimum stress on rock element, psi
σOV
=
in-situ overburden stress at depth, psi
i
σ tect
=
horizontal tectonic stress applied to ith
layer, psi
σ1
=
stress in pay zone, psi
σ2
=
stress in bounding layers, psi
τij
=
shear stress in i-direction on plane with
normal in j-direction, psi
α2i
=
Biot’s poroelastic coefficient for anisotropic
ith layer response to vertical loading,
dimensionless
β
=
geometric stress intensity parameter,
dimensionless
βn
=
angle between failure plane normal and
maximum stress on plane, degrees
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Cleary, M. P., Wright, C. A., and Wright, T. B. 1991. Experimental and Modeling Evidence for Major Changes in Hydraulic F
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Chapter 4
Hydraulic Fracture Modeling
Leen Weijers, Liberty Oilfield Services; Hans de Pater, Fenix Consulting Delft B.V.
Leen Weijers is the vice-president of engineering at Liberty Oilfield Services LLC. He has played a key role in the calibration of
fracture-growth models using various fracture diagnostics such as tiltmeter and microseismic-fracture-mapping technologies. Weijers
holds a doctorate from the Faculty of Mining and Petroleum Engineering at Delft University of Technology in the Netherlands.
Hans de Pater is a partner, consultant, and general manager of Fenix Consulting Delft, working primarily on rock-mechanics-related
projects and fully coupled rock-mechanical reservoir simulation. He holds a PhD degree in applied physics from Delft University of
Technology.
When the facts change, I change my mind. What do you do, sir?—John Maynard Keynes
It is better to be roughly right than precisely wrong.—John Maynard Keynes
Contents
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Introduction�������������������������������������������������������������������������������������������������������������������������������������������������������������� 76
Modeling Objectives������������������������������������������������������������������������������������������������������������������������������������������������� 78
4.2.1 Improve Proppant Placement���������������������������������������������������������������������������������������������������������������������� 78
4.2.2 Well-to-Fracture Connectivity����������������������������������������������������������������������������������������������������������������������� 78
4.2.3 Vertical Height Coverage����������������������������������������������������������������������������������������������������������������������������� 79
4.2.4 Fracture Conductivity vs. Fracture Length Trade-Off������������������������������������������������������������������������������������ 79
4.2.5 Fracture Conductivity vs. Multiple-Fracture-Complexity Trade-Off��������������������������������������������������������������� 81
Basic Physical Principles in Fracture Propagation Models�������������������������������������������������������������������������������������� 82
Basic Fracture Modeling Concepts�������������������������������������������������������������������������������������������������������������������������� 85
4.4.1 Net Pressure������������������������������������������������������������������������������������������������������������������������������������������������ 85
4.4.2 Friction Pressure������������������������������������������������������������������������������������������������������������������������������������������ 86
4.4.3 Fracture Closure Stress������������������������������������������������������������������������������������������������������������������������������� 86
4.4.4 Fluid Leakoff and Efficiency������������������������������������������������������������������������������������������������������������������������� 87
4.4.5 Fracture Compliance������������������������������������������������������������������������������������������������������������������������������������ 88
1D and 2D Fracture Growth Models������������������������������������������������������������������������������������������������������������������������ 88
4.5.1 Derivation of a Static 1D Fracture Model����������������������������������������������������������������������������������������������������� 88
4.5.2 2D Fracture Models������������������������������������������������������������������������������������������������������������������������������������� 89
4.5.3 Early 3D-Fracture Models���������������������������������������������������������������������������������������������������������������������������� 90
The First Fracture Model Calibration Effort—Identifying Growth Behavior�������������������������������������������������������������� 90
Advanced Fracture Modeling Concepts I����������������������������������������������������������������������������������������������������������������� 92
4.7.1 Observations������������������������������������������������������������������������������������������������������������������������������������������������ 92
4.7.2 Tip Effects���������������������������������������������������������������������������������������������������������������������������������������������������� 92
4.7.3 Incorporating Tip Effects into Fracture Models�������������������������������������������������������������������������������������������� 92
4.7.4 Simultaneous Growth of Multiple Fractures������������������������������������������������������������������������������������������������� 93
4.7.5 Minimizing vs. Encouraging Multiple Fracture Growth��������������������������������������������������������������������������������� 95
4.7.6 Approximating Fracture Complexity With “Equivalent” Multiple Fractures���������������������������������������������������� 95
Advanced 3D Fracture Growth Models�������������������������������������������������������������������������������������������������������������������� 96
The Second Fracture Model Calibration Effort—Net-Pressure Matching����������������������������������������������������������������� 96
4.9.1 Net-Pressure History Matching�������������������������������������������������������������������������������������������������������������������� 97
4.9.2 Derivation of a Radial Net-Pressure Feedback Model��������������������������������������������������������������������������������� 97
4.9.3 Net-Pressure History-Matching Variables���������������������������������������������������������������������������������������������������� 98
4.9.4 Net-Pressure History-Matching Example����������������������������������������������������������������������������������������������������� 99
76 Hydraulic Fracturing: Fundamentals and Advancements
4.10 Advanced Fracture Modeling Concepts II�������������������������������������������������������������������������������������������������������������� 101
4.10.1 Diagnostic Observations�������������������������������������������������������������������������������������������������������������������������� 101
4.10.2 Case History�������������������������������������������������������������������������������������������������������������������������������������������� 102
4.10.3 Composite Layering Effect����������������������������������������������������������������������������������������������������������������������� 102
4.11 The Third Fracture Model Calibration Effort—Reconciliation With Fracture Diagnostics��������������������������������������� 103
4.11.1 Derivation of a 3D Net Pressure and Geometry Feedback Model����������������������������������������������������������� 104
4.11.2 Calibrated Power-Law Fracture Models��������������������������������������������������������������������������������������������������� 104
4.11.3 Net-Pressure-History and Fracture Geometry Matching Example���������������������������������������������������������� 105
4.11.4 Fracture Geometry Database������������������������������������������������������������������������������������������������������������������ 107
4.11.5 Case Histories����������������������������������������������������������������������������������������������������������������������������������������� 109
4.12 Complex Fracture Models�������������������������������������������������������������������������������������������������������������������������������������� 113
4.12.1 Discrete Fracture and Distinct Element Models��������������������������������������������������������������������������������������� 113
4.12.2 Nonplanar Fracture Models��������������������������������������������������������������������������������������������������������������������� 119
4.13 Fully Coupled Geomechanical Fracture Models���������������������������������������������������������������������������������������������������� 120
4.13.1 Introduction���������������������������������������������������������������������������������������������������������������������������������������������� 120
4.13.2 Relating Fracture Simulation to Reservoir Simulation����������������������������������������������������������������������������� 123
4.13.3 Applications��������������������������������������������������������������������������������������������������������������������������������������������� 126
4.14 Further Fracture Model Integration and Novel Developments������������������������������������������������������������������������������� 129
4.14.1 Fracture Models Coupled With Reservoir/Production Models����������������������������������������������������������������� 129
4.14.2 Field Statistics and Fracture Models/Production Models������������������������������������������������������������������������� 130
4.15 Fracture Modeling Advantages and Challenges���������������������������������������������������������������������������������������������������� 131
4.15.1 Fracture Modeling Advantages���������������������������������������������������������������������������������������������������������������� 131
4.15.2 Limitations of Fracture Models����������������������������������������������������������������������������������������������������������������� 131
4.15.3 The Challenge of Poor and Incomplete Model Inputs������������������������������������������������������������������������������ 132
4.15.4 Summary������������������������������������������������������������������������������������������������������������������������������������������������� 133
4.16 Thoughts on Future Use and Developments of Fracture Growth Models�������������������������������������������������������������� 133
4.16.1 Future of Hydraulic Fracture Modeling: The Big Picture�������������������������������������������������������������������������� 133
4.16.2 Input Side of Fracture Modeling From Geology and Completion������������������������������������������������������������� 134
4.16.3 Effectiveness of Calibration��������������������������������������������������������������������������������������������������������������������� 134
4.16.4 Output Side to Reservoir Simulation�������������������������������������������������������������������������������������������������������� 134
4.17 Conclusions����������������������������������������������������������������������������������������������������������������������������������������������������������� 135
4.18 Nomenclature�������������������������������������������������������������������������������������������������������������������������������������������������������� 135
4.19 References������������������������������������������������������������������������������������������������������������������������������������������������������������ 136
4.1 Introduction
Fracture propagation modeling has undergone significant improvements since the last SPE Monograph (Gidley 1989) was released.
The completions industry, which had focused on conventional darcy and millidarcy rock up to that time, found a way to successfully expand into unconventional rocks with micro- to nanodarcy permeabilities. The significant improvements in fracture modeling
have occurred partly because simulations were able to be based on in-situ diagnostics, the commercialization of which has helped to
advance the understanding of fracture growth behavior, particularly how this behavior can be influenced in unconventional rock such
as shale.
The application of hydraulic fracturing has greatly increased over the last 2 decades. Fig. 4.1 shows a historical overview of
one of the metrics in hydraulic fracturing that has changed considerably through the Shale Revolution: stage count (Gallegos and
Varega 2015). As the industry gradually changed and the application of fracturing technology widened, the theories about fracture
600,000
Yearly Stage Count
500,000
400,000
300,000
200,000
100,000
0
1940
1950
1960
Stages, US land (coras)
1970
1980
Stages, US land (USGS)
1990
2000
2010
2020
Stages, US land (IHS, Liberty)
Fig. 4.1—US stage count over the last 7 decades of hydraulic fracturing (Gallegos and Varela 2015; Coras Research
2018; Weijers et al. 2019). Fracturing activity in stage count has increased nearly 20-fold since 2000. Differences in stagecount estimates between 2001 and 2013 for the three sources mostly originate from incomplete stage-count information
and varying assumptions of stage intensity per unit of lateral length in horizontal wells.
Hydraulic Fracture Modeling
77
growth behavior have gradually changed, reinforced by more frequent and better observations of what is actually happening
in situ.
For much of the 1980s and 1990s, fracture modelers were polarized along the lines of certain theories that formed the basis of commercially available fracture models, of which there were several. Fracture modelers’ divisions by “faiths” were predominantly driven
by their beliefs in the underlying assumptions of each model. The source of these divisions was the complicated coupling of physical
processes in models and the lack of knowledge and data about what actually happens in situ.
Early work in the multiwell experiment (MWX) sites increasingly became relevant in the early 2000s when it became possible to
directly measure and simulate fracture geometries in real time, through downhole tiltmeter and microseismic fracture mapping. Once
asked by a reporter about a flaw in his theory, John Maynard Keynes responded “When the facts change, I change my mind. What do
you do, sir?” The proliferation of direct fracture diagnostics has caused the “facts” of how fractures grow to change, and the industry
has responded, gradually incorporating this new reality into its fracture propagation models. Today, commercially available fracture
propagation models honor the basic physics of fracture growth (as far as they are known) and can be calibrated with direct observations (which sometimes are in conflict with the physics in some models).
The industry has various motivations for conducting fracture modeling. First and foremost is a goal to increase well production and
reduce treatment costs by optimizing fracture treatments. While this can comprise a wide range of topics, optimization often centers
around achieving appropriate zonal coverage, fracture conductivity, fracture length, and issues of increasing/decreasing fracture
complexity. Fracture optimization might also focus on reducing premature screenout problems or helping control where most fracture
growth should occur, for example, to achieve deep penetration in a specific layer or minimize production of unfavorable components
from adjacent layers.
Typically, fracture engineers run fracture growth models to determine how changes in fracture treatment design impact production
response. For such considerations they generally care about the “big picture,” and therefore require only an engineering approximation for optimized fracture geometry—not a detailed scientific evaluation. Keynes captures such differing sentiment between science
and engineering perfectly in his quote, “It is better to be roughly right than precisely wrong.” In another opinion, a modeling approach
with this philosophy will effectively optimize production. It is better to get the main physical mechanisms and calibration right and
obtain an approximate answer, than to worry about the details of growth in a small subsection of the fracture system.
Through the US Shale Revolution, fracturing operations have increasingly focused on pumping efficiencies, gradually moving
operations to “factory mode,” where measurements for model calibration might be collected only at the onset of a development
campaign, and once under normal development operations it is difficult to obtain additional data for model calibration. In more
“conventional” international fracturing projects, meanwhile, diagnostic measurements and model calibration are more commonplace because of the different economic situation, with fewer wells, which are much more expensive. Finding the right balance
between “science” and “engineering” is always a struggle in the modern completions industry, and the balance is different for every
company. As shown in Fig. 4.2, the level of sophistication of the fracture model solution should fit the details and intensity of the
calibration data.
It is up to the experienced user to make reasonable and realistic assumptions in developing accurate models that reflect the actual
fracture growth in a specific area and formation. In this chapter, the focus is to maximize the inclusion of measured data in models and
improve the practical use of models by helping the user make reasonable assumptions. Specific models and their physical assumptions
have been explained in detail in previous monographs, and it is not the intension here to repeat those descriptions. Rather, this chapter
will describe two exciting new aspects of 21st century fracture modeling: cross-checking model output with measured data and, where
it occurs, adapting these models to approximate complex fracture growth in shale.
In summary, the industry and its modeling efforts have gone through significant improvements in both simulation and diagnostic
technology in the last 2 decades. Keynes’ first quote captures the dramatic changes that have been seen in industry models—from
the initial simplistic assumptions used in 2D models with perfectly confined fracture height, to almost radial growth tied to observation of high net pressures; then to somewhat confined growth vs. more-excessive lengths observed in direct fracture diagnostics.
Fracture model “sophistication”
“Precisely wrong”
Coupled
fracture models
Gridded-3D
fracture models
Complex
fracture models
Parameterized-3D
fracture models
Pseudo-3D
fracture models
2D fracture models
Power-law
fracture model
“Back-of-the-envelope”
model
“Roughly right”
Fluid test Logs
Leakoff
Mechanical core tests Flowing core tests
Net pressure
Out-of-zone stress tests
Interface measurements
Far-field fracture diagnostics
Wellbore diagnostics
Calibration data “quality / intensity”
Fig. 4.2—Balancing the complexity or sophistication of a fracture model with the details of measurements available for
model calibration.
78 Hydraulic Fracturing: Fundamentals and Advancements
Model calibration has become an integral step of the hydraulic fracture simulation process, and models have become more reliable
tools to help the completion engineer design more effectively, but it would be a mistake to use historical understanding as a guide
for future performance.
4.2 Modeling Objectives
The main motivation for hydraulic fracture modeling is to better understand the process and its sensitivities to more effectively stimulate the reservoir in a safe and sustainable manner, while maximizing revenues over the life of a well.
The first tier of success in a fracture treatment might simply be to “get the job away,” as close to design as possible and avoid
premature screenouts. However, hydraulic fracturing is not done just for “proppant disposal,” but for well stimulation. In some rare
cases, a screenout might even turn out to be a success, when near-wellbore conductivity is vital.
The second tier of fracture treatment success is to optimize production economics (see the Economics of Fracturing Chapter)—for
example, minimizing the cost per produced quantity of hydrocarbon (USD/BO, USD/BOE, or USD/Mscf) using either the production
of a specified time period (e.g., the first year) or, when evaluating the production response over the lifetime of a well, section or field,
maximizing net present value (NPV) or return on investment (ROI).
Fracture treatment optimization might focus on creating appropriate fracture conductivity, possibly by achieving a tip screenout
(TSO) in high-permeability sand-control applications. It might also focus on avoiding or minimizing fracture growth into waterbearing or lower stress layers. This analysis can only be conducted properly if fracture engineers understand how fractures could grow
during and after a fracture treatment, and what conductive flow path becomes available for oil and gas production.
4.2.1 Improve Proppant Placement. A fracture model that conducts real-time injection diagnostics and treatment evaluations can
be a powerful tool to successfully place a job design. Fig. 4.3 provides an example of such a job where real-time evaluation helped
identify treatment problems and assess the effectiveness of a solution, and ultimately helped to successfully complete the design.
In this example (Weijers et al. 2000a), a sequence of diagnostic injections (Gas Research Institute 1995) was conducted on a New Mexico vertical well to help identify fracture closure, net pressure, fracture slurry efficiency, perforation friction, and near-wellbore friction
(tortuosity). During the first stepdown test, tortuosity was determined to be extremely high, at 1,700 psi at the expected pump rate. This
observation led to the conclusion that proppant placement on this job, like previous jobs in this area, was likely going to be problematic.
On the basis of this observation, it was decided to pump two low-concentration proppant slugs to locally screen out a subset of the
multiple near-wellbore fractures—the expected source for high tortuosity. Significant pressure relief was observed as these proppant
slugs arrived at the perforations, where they most likely enabled a simpler fracture geometry. Lower tortuosity was confirmed during
a second stepdown test, indicating that the slugs indeed created a more favorable near-wellbore fracture geometry. The confirmation
of reduced complexity helped redesign the final proppant ramp with higher proppant concentrations, which then helped to achieve an
overall higher dimensionless conductivity that was needed for a fracture system in this moderate-permeability reservoir.
This example shows how a fracture model with all additional on-board real-time evaluation tools can help identify potential treatment problems so that design changes can be made to help overcome them. This is the simplest use of fracture models.
4.2.2 Well-to-Fracture Connectivity. While effective proppant placement is crucial, there is also a requirement to have a good connection
between the wellbore and the far-field fracture. A highly conductive connection is especially important in higher-permeability completions.
1,400 psi Friction
Reduction (1st Slug)
Proppant conc (lbm/gal)
Btm prop conc (lbm/gal)
Surf press [casing] (psi)
Slurry flow rate (bpm)
20.00
6,000
Max surface pressure 6,000
psi
No tortuosity at
end of
pumping
S/D#2: 300
psi
tortuosity
16.00
4,800
S/D#1: 1,700
psi tortuosity;
Small perforation
friction
12.00
3,600
16.00
80.0
12.00
60.0
8.00
2,400
Increased max
prop concentration
8.00
40.0
4.00
20.0
4.00
1,200
0.00
0
20.00
100.0
0.0
28.0
56.0
84.0
112.0
0.00
0.0
140.0
Time (minutes)
Fig. 4.3—Application example for fracture modeling where proppant (prop) placement is a challenge. S/D = stepdown
test. Btm = bottomhole pressure. Prop conc = proppant concentration.
Hydraulic Fracture Modeling
79
While large overdisplacements in shale wells have shown that a conductive connection is of less importance, landing zone rock properties
more often impact fracture job injectivity and proppant placement success. Models can help assess near-wellbore proppant placement and
perforation-cluster efficiencies, and much of this topic is covered in the Fracture Pressure Analysis Chapter.
4.2.3 Vertical Height Coverage. Fracture height growth is a critical consideration in fracture designs. On one hand, there might be
zones that should be avoided, for example, because of the presence of high water content. On the other hand, fracture height coverage
might need to be maximized if a relatively thick zone or multiple pay zones are required to be produced.
Fig. 4.4 shows an example of a calibrated model for the Lance Formation in Wyoming. As discussed in Malone et al. (2009), knowledge about fracture growth and an understanding about effective growth barriers help determine vertical spacing between fractures to
achieve appropriate vertical coverage for production.
One of the most important challenges in the Jonah Field in Sublette County, Wyoming, is to obtain effective fracture height
coverage over the entire Lance Formation (2,800 ft). The Lance Formation in Jonah Field is composed of a stacked sequence of 20 to
50 fluvial channel sands, interbedded with associated over-bank siltstone and floodplain shale deposits. Within this interval the net-togross ratio varies from 25 to 40%. Sandstone bodies occur as individual 10- to 25-ft-thick channels, and stacked channel sequences
are greater than 200 ft in some cases.
Tiltmeter and microseismic fracture mapping have been conducted on hundreds of propped-fracture treatments in the Jonah Field.
These direct height growth measurements helped to obtain an understanding about the effectiveness of shale barriers in controlling
vertical height growth. A calibrated fracture model was developed that ties the log analysis to the mapped fracture growth behavior.
These improvements in predictive modeling have led to better insight into fracture growth behavior in the Lance Formation, and
subsequently led to the development of a new perforation strategy and fracture treatment design to obtain effective coverage of the
Lance Formation.
Fig. 4.5 shows an example of the influence of sequencing fracture treatments in multiple horizontal wells, using a model that can
incorporate stress shadowing from fractures from previous stages in the same well or from fractures created in other horizontal wells.
In this example for the Midland Basin, a “straddling” sequence with the top and bottom fractured before the middle main-target zone
resulted in 13% more created surface area than a “top down” fracture sequence.
Another example of fracture height growth control is preventing fracture growth into specific zones, such as into a water-bearing
zone. An example of this is provided in Shaoul et al. (2013), where an aggressive TSO design was used and fracture geometries are
estimated from net-pressure history matching, thus limiting fracture height growth through implementation of an approximate maximum fluid volume and proppant mass for each stage. This strategy kept downward fracture growth at least 80 ft away from a waterbearing zone at 8,535-ft true vertical depth (TVD).
The estimated propped-fracture dimensions are shown, relative to the planned standoff from the free-water level (FWL), in
Fig. 4.6. Only the first fracture is believed to have grown below the planned standoff because of the extra fluid pumped from an
unplanned shut-down during the pad.
4.2.4 Fracture Conductivity vs. Fracture Length Trade-Off. Another use of models in fracture treatment adjustment or redesign
is to generate appropriate conductivity. As shown in Fig. 4.7, this type of model implementation is critical for successful fracture
Fig. 4.4—Results from a fracture staging routine that uses a calibrated model for the geometry of fractures pumped in
the Jonah Field Lance Formation.
80 Hydraulic Fracturing: Fundamentals and Advancements
20,400
20,600
–8,000
21,000
Toe fault
–8,100
20,800
Central fault - 1
20,200
Open faults
Fig. 4.5—Conductivity profile for a fracture sequencing analysis with a fracture model that incorporates stress shadowing
associated with fractures from previous stages and from other wells.
21,200
21,800
22,000
9,500
8
15,500
13,750
14,25014,000
14,500
14,750
15,250 15,000
o
Top r
5
11,750
12,250 12,000
12,500
9,750
–8,100
7
13,000 12,750
13,50013,250
–8,000
ndes
tliege
To
2
1
22,200
rite
10,000
6
–8,200
15,750
21,600
yd
a anh
p werr
4
3
–8,300
21,400
11,000 10,750
11,500 11,250
10,250
10,500
–8,200
48/19a-3
–8,300
48/19a-C1 definitive
–8,400
–8,400
Planned stand Off 8455 ftTVDSS
–8,500
FWL 8535 ftTVDSS
–8,500
–8,600
–8,600
20,200
20,400
20,600
20,800
21,000
0
21,200
21,400
21,600
21,800
22,000
22,200
100 200 300 400 500m
Fig. 4.6—Application example for fracture modeling to achieve high-permeability TSO design.
Hydraulic Fracture Modeling
Btm prop conc (lbm/gal)
Slurry rate (bbl/min)
Observed net (psi)
50.00
100.0
750.0
Prop conc (lbm/gal)
Net pressure (psi)
50.00
750.0
TSO
40.00
80.0
600.0
81
40.00
600.0
Pad fluid volume adjusted based
on leakoff behavior following
crosslink gel minifracture
Breakdown injection
30.00
60.0
450.0
30.00
450.0
Minifracture
20.00
40.0
300.0
20.00
300.0
10.00
20.0
150.0
10.00
150.0
0.00
0.0
0.0 0.0
60.0
120.0
Time (minutes)
180.0
240.0
0.00
300.0 0.0
Fig. 4.7—Application example for fracture modeling to achieve high-permeability TSO design. Prop conc = proppant
concentration. Btm = bottomhole pressure.
treatment and production in high-permeability rock, where initiation and follow-through of a TSO is critical. In this example of a
Kuparuk fracture treatment in a high-permeability reservoir (Pospisil et al. 1995), prefracture diagnostic injections of water and
a crosslinked-gel minifracture are implemented to determine fracture closure stress in the target zone, net pressure beyond the
areas of the perforations and near-wellbore tortuosity in the main body of the fracture, and fracturing-fluid efficiency and leakoff
for crosslinked gel. All these measurements are conducted and implemented in the fracture remodel before the propped fracture
treatment.
The minifracture pressure-falloff behavior is used to determine slurry efficiency, which in turn determines the pad fluid volume
needed to initiate a TSO during the subsequent stages using proppant-laden fluid assuming idealized TSO behavior. TSO initiation
is then followed by a significant increase in the net pressure, indicating growth of just the fracture width, while fracture length
and height growth are arrested because of insufficient proppant-carrying capacity of fluid near the fracture tip. This is a highly
engineered process that delivers levels of fracture conductivity (through width inflation) that cannot be achieved without reaching
TSO behavior.
This approach generally focuses on obtaining desirable dimensionless conductivity. For example, in an approach described by
Soliman et al. (2004) and shown in Fig. 4.8, a “best design area” is defined that is limited by two dimensionless-conductivity (FcD)
curves—for example, 1.6 and 30. On the right side, the best design area is limited by the maximum realistic treatment volume. Toward
the right and the top of the productivity index (PI), fracture volumes increase (as length and conductivity increase) and a limit is provided through a cutoff volume that is associated with obtaining a fracture length that reaches a user-defined fraction of the drainage
area. The fracture volume calculation can be based on calibrated model settings that tie fracture length and height growth to fracture
volume. The goal of this design and optimization exercise might be to maximize PI, and in many cases an evaluation of the economics
of design changes is also conducted in conjunction with this analysis.
4.2.5 Fracture Conductivity vs. Multiple-Fracture-Complexity Trade-Off. Whereas the previous example shows a trade-off
encountered in modest- to high-permeability rock, the trade-off of conductivity vs. in-stage complexity is generally one for unconventional shale plays. This trade-off, driven by formation permeability, is further discussed in the chapter on Hydraulic ­Fracturing
Treatment Design. In these cases, complexity, or multiple fracture growth, is often achieved through limited-entry fracture
­treatments in spaced perforation clusters along a portion of the lateral within a stage of the horizontal well. Generally, a specified
fluid volume or proppant mass is intended to be placed per unit of lateral feet. That volume or mass is then distributed over a set of
fractures initiating from perforation clusters.
In an example from Agarwal et al. (2019), a fracture and production simulator is run consecutively for several scenarios to evaluate
cumulative-oil-production response at different fracture spacings (Fig. 4.9). On the basis of the 1-year cumulative oil production, this
simulation shows that there is no benefit to decreasing the fracture spacing below 120 ft. The production acceleration at lower fracture
spacing scenarios (i.e., less than 120 ft) is more than offset by the decrease in fracture length and conductivity based on constant
proppant loading per lateral length unit. The long-term production (e.g., a 5-year cumulative oil production) increases with fracture
82 Hydraulic Fracturing: Fundamentals and Advancements
Permeability 0.1 md Well Spacing 320-Acre Hole Diameter 7.875 in.
10,000 9
Pl
8
7
6
5
4
3
Fracture Conductivity (md-ft)
2
6
5
4
3
2
1,000 9
8
7
6
5
4
3
2
100 9
8
7
6
5
4
3
CfD
2
10
0
100
200
300
1
400
500
600
Fracture Half Length (ft)
700
800
900
10
30
1,000
Cumulative Oil SC (bbl)
600,000
500,000
400,000
300,000
Fracture spacing = 40 ft (Xf = 419 ft, Fc = 81 md-ft)
Fracture spacing = 80 ft (Xf = 521 ft, Fc = 114 md-ft)
Fracture spacing = 120 ft (Xf = 570 ft, Fc = 137 md-ft)
Fracture spacing = 160 ft (Xf = 602 ft, Fc = 154 md-ft)
Fracture spacing = 200 ft (Xf = 628 ft, Fc = 166 md-ft)
Fracture spacing = 240 ft (Xf = 650 ft, Fc = 176 md-ft)
200,000
100,000
0
0
1
2
3
4
5
6
7
Time (year)
8
9
1-year and 5-Year Cumulative Oil (bbl)
Fig. 4.8—Fractured well production increase example.
10 11
1-Year Cumulative Oil
5-Year Cumulative Oil
550,000
500,000
450,000
400,000
350,000
300,000
250,000
0
40
80
120
160
200
240
280
Fracture Spacing (ft)
Fig. 4.9—Cumulative-oil-production sensitivity to fracture spacing at constant proppant loading of 970 lbm/ft. Left:
Cumulative oil vs. time at various fracture spacings. Right: 1- and 5-year cumulative oil vs. fracture spacing, showing
optimal spacing at approximately 120 and 200 ft, respectively.
spacing up to 200 ft. The optimal fracture spacing will depend on the balance between maximum short-term and long-term production. For this area, a 120 ft fracture or cluster spacing appears optimal when maximizing the 1-year (short-term) production, while still
resulting in “acceptable” long-term production.
4.3 Basic Physical Principles in Fracture Propagation Models
As shown in Fig. 4.10, a variety of physical processes play a role during hydraulic fracture growth. This paragraph considers a
­schematic of a cross section of a fracture of half-length Lf along the x-axis, with the fracture’s central entrance at the right side at the
borehole. Assuming most fractures are vertical, this simplistic picture would therefore represent a horizontal slice through the center
Hydraulic Fracture Modeling
of this fracture. The schematic greatly exaggerates fracture width
over fracture length to help show how these physical processes
impact the fracture at point x along the fracture half-length.
Assume that five main processes play a role during initiation
and propagation of this fracture:
1. Viscous fluid flow defines the relationship between
pressure drop in the fracture and the viscosity of the
fluid and honoring conservation of momentum.
2. Fluid leakoff honors conservation of mass so that the
fluid injected equals fluid in the fracture plus fluid lost
because of leakoff into the formation.
3. Elastic deformation couples pressure within the fracture to the dilation of the crack.
4. Fracture propagation implements a formulation of tip
behavior to control when growth occurs.
5. Proppant transport modeling determines the distribution of proppant in the fracture.
An explanation follows of the processes from top to bottom
for simplified hydraulic fracture simulators.
Viscous Fluid Flow in the Fracture. When flowing a viscous
fluid through pores, pipes, or parallel plates, an associated frictional pressure drop causes the pressure at a downstream point
to be lower than the pressure at a point before it. This frictional
pressure drop is described in detail by the Navier-Stokes equation, also known as the equation of motion for fluid flow. For
laminar flow between two parallel plates (a reasonable assumption because fracture half-length is much greater than fracture
width), the momentum-conservation equation simplifies to Darcy’s law, which can be applied to local points along the fracture
(Fig. 4.11).
 w3   ∂ p 
q =V •w =  
 µ   ∂x 
 ∂ p  qµ
or   = 3
 ∂x  w
83
pf
pw
Viscous fluid flow
Vx
V1
Fluid leakoff
pf – σc
Elastic deformation
Ww
W
pf – σc
K
Fracture propagation
Vs Vc
Proppant transport
w
Ww
rw
X
rw + Lf
Fig. 4.10—Basic hydraulic fracture growth mechanisms
that are incorporated in most fracture models.
w = width
Q
h
dx
pf = px
pf = px − dp
Fig. 4.11—Laminar fluid flow between parallel plates.
 ∂p Vµ
;   = 2 . ��������������������������������������������������������������������������������������������������������(4.1)
 ∂x  w
In general terms, the fracture pressure gradient toward the tip of the fracture is inversely proportional to the cube of the local
fracture width wx and proportional to local fluid velocity vx. In Eq. 4.1, V denotes the average fluid velocity in the fracture, w denotes
the fracture width, ∂p denotes the pressure drop over the length δX, Q denotes the total flow rate with q denoting the flow rate per
unit height Q/h. For a Newtonian fluid, μ– = 12μ where μ represents the apparent viscosity. Therefore, if a fracture doubles its width
while friction remains the same, the flow velocity increases by a factor of four while the flow capacity increases by a factor of eight.
Achievable flow rate in a fracture is therefore very sensitive to fracture width changes.
This sensitive relationship is an important phenomenon in hydraulic fracturing (for example, when dealing with simultaneously
propagating multiple fractures). Propagation of multiple fractures tends to increase the net pressure because of reduced widths and
flow capacity. For example, in comparison to a single fracture with a specific width, for three identical fractures with one-third of that
width the flow rate reduces to 3 × (1/3)3 = 1/9 of the flow rate for the original fracture, assuming the net pressure at the entry point
remains the same.
Fluid Leakoff From the Fracture Into the Permeable Formation. As the fracture propagates through permeable rock, highpressure fluid inside the fracture leaks off into the reservoir, where the pore pressure is lower. Flow into the reservoir is driven by the
magnitude of the pressure differential between the fluid in the fracture and the fluid in the pore space. The exposure time during which
fluid is touching the fracture surfaces drives leakoff behavior also because longer exposure leads to greater volumetric fluid loss. The
process is governed by the law of mass conservation, which states that the total volume of incompressible fluid pumped into the
fracture should be equal to the sum of the current fracture volume and the leakoff fluid volume at any given time:
ti
∫ Qdt = V
fracture
0
ti
+ Vleakoff = γ 1wi Li H i + ∫
0
Kl
2 Ai dt , �����������������������������������������������������������������������������������������������������������������(4.2)
t − ti ( x )
where ti represents the injection period; γ1 is the fracture width shape function; wi, Li, and Hi are the respective fracture width at the
wellbore, total length, and total height at time i; Kl is the Carter leakoff coefficient for a simplified model; and Ai is the time-dependent
fracture surface area at time i.
Deformation of the Rock. This creates a fracture width profile that is dependent on an opening force distribution of fluid pressures
inside the fracture and a closing force associated with the confining stress applied to the fracture surface by the formation. A fracture
is compliant: to open the fracture, the pressure in the inside of the fracture needs to be higher than the externally applied compressive
stress. The difference between these stress distributions results in a positive net pressure pnet.
84 Hydraulic Fracturing: Fundamentals and Advancements
Sneddon’s generalized fracture width equation at any position along the length of the fracture depends on that net pressure distribution, where its value at any point along the fracture profile contributes to the fracture width profile shape at any point along the
fracture:
w(ρ ) =
2Rf 1
du
u
π E ∫ρ u 2 − ρ 2 ∫0
spnet ( s ) ds
u2 − s2
. ��������������������������������������������������������������������������������������������������������������������������������������������(4.3)
This represents the elastic deformation of rock because of fluid pressure (as provided by equilibrium and Hooke’s law).
Fracture Propagation into the Formation. This is generally implemented in fracture models through the simplified concept of the
stress intensity factor for Mode I fracture growth behavior (fracture opening) KI. The fracture propagates once the stress intensity
factor is equal to or exceeds the fracture toughness or critical stress intensity factor of the rock KIc.
K I = pnet γ k R f
with K I ≥ K Ic . ������������������������������������������������������������������������������������������������������������������������������������������������(4.4)
This simple equation is often implemented in fracture models and is referred to as linear elastic fracture mechanics (LEFM). The
functional coefficient γk depends on the near-tip fracture geometry and equals 4/π for a radial fracture. With typical fracture toughness for sandstone at approximately 1,000 psi in0.5, at least 1,000 psi net pressure is required to advance a starter crack with a radius
of approximately ¾ in. Once the fracture grows to a radius of say 100 ft, only approximately 2 psi net pressure is required to further
advance this fracture. In other words, fracture toughness is important during the very early stages of a fracture treatment, but not so
much during the later parts.
In some cases, the fracture propagation criterion is molded into a fracture energy intensity criterion, where the “leverage” of the
fracture fluid pressure must overcome the molecular bonds that hold the material together.
Proppant Transport. Proppant transport modeling is often based on tracking the proppant in each stage (or substage). The proppant
transport model is coupled to the leakoff model to handle slurry dehydration. The proppant transport model is coupled to the fracture
growth model to handle proppant drag effects. Proppant transport is a complex process, but most models incorporate proppant settling
and proppant convection.
Proppant settling represents the movement of proppant grains within the fluid system they are embedded in. Settling velocities
for crosslinked fluids are practically zero but can be substantial for low-viscosity fluid systems such as slickwater or fresh water. In
the latter types of jobs, proppant can settle into a proppant bank at the bottom of the fracture and initiate a local TSO where further
downward growth is arrested through the presence of this bank. The balance between viscous and gravitational forces is embodied in
Stokes’ law for the settling velocity vs of an unobstructed particle with radius Rp:
vs =
(
)
2 ρp − ρ f
gRp2 , ��������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.5)
9
µ
where ρp and ρf represent the specific density of the particle and the fluid it is embedded in, g represents the gravitational acceleration,
and μ represents the dynamic viscosity of the fluid system, assuming a Newtonian-fluid system.
Proppant convection represents the mechanism of differential movement of different treatment stages because of density differences and fluid viscosity (Cleary and Fonseca 1992). Higher proppant loadings in the later part of a treatment results in higher slurry
densities, which may displace lighter slurries already present in the fracture system.
 ( ρ − ρ min ) gw 
vc = γ cn w  max
, ��������������������������������������������������������������������������������������������������������������������������������������������������������(4.6)
µ


where ρmin and ρmax represent the minimum and maximum specific densities of the various slurries pumped during a fracturing job,
w represents the average fracture width, and γcn represents a shape factor, while assuming a Newtonian fluid system.
For both proppant transport mechanisms, as slurry dehydrates, proppant drag effects will slow fracture growth. Complete dehydration of proppant in one stage will stop fracture extension. Stopping fracture extension in all directions leads to “fracture ballooning”
in an apparent TSO.
Other Physical Mechanisms. In addition to these five main physical phenomena captured in the fracture growth models, commercial
fracture modeling software also often includes the capability to model many other general processes, including but not limited to
• Wellbore model. The fracture growth modeled occurs deep in the subsurface, while measured parameters mostly originate at
surface. The wellbore model provides a numerical model for calculating friction drop in the wellbore and keeps track of how
hydrostatic pressure changes for slurry-laden fluids. The wellbore model tracks pumped fluid volumes vs. wellbore volume and
can therefore track when proppant arrives at the perforations. It can also handle volumetric and frictional pressure changes for
CO2-and-N2 foam treatments and can generally handle flow split between multiple perforated intervals.
• Perforation and near-wellbore model. The steps from measured conditions at surface are projected at downhole conditions
through the wellbore model, and then to within the main fracture through the perforation and near-wellbore model. Most
models have the capability to conduct a rate stepdown test to determine perforation and near-wellbore friction at a specific
time during a treatment, and can then calculate, generally through power-law relationships, how perforation and near-wellbore
friction behavior changes as a function of rate and time. Some models incorporate rules for how perforation friction can be
affected by erosion as a function of the total amount of proppant pumped within each perforation (Cramer 1987).
Hydraulic Fracture Modeling
85
• Fracture leakoff model. In a more simplistic parameterized 3D model, leakoff can be simplified into a single “reference layer,”
where overall leakoff into other layers is calculated with respect to this “reference layer.” Other models can calculate true multilayer leakoff using a 2D gridded leakoff model that can handle variation in space as well as time. More exotic leakoff models
can evaluate dynamic filter-cake effects (building and eroding) and filtration with linear invasion and crossflow (McGowan
1999)
• Fracture temperature model. Modeling heat transfer in the wellbore and the fracture is required to calculate how cold surface
fluid affects bottomhole wellbore temperature for fluid crosslinking or viscosifying effects and proppant transport in the fracture. Many models have attempted to include a simplified grid-based heat-transfer model for calculating heat transfer between
fracture fluid and reservoir. (Ramey 1962; Willhite 1967).
• Acid fracturing model. In addition to handling proppant-laden fluids and creating propped fracture width and conductivity,
many models can also incorporate mass transfer and reaction kinetics for acids that help create etched fracture width. Use of
a heat-transfer model is key for accurate reaction kinetics. Models use a Nierode-Kruk (1973) correlation for calculating the
acid fracture conductivity on the basis of etched width.
• Backstress (poro-elastic) model. Most industry models have no interactive coupling between the fracture and reservoir effects.
A backstress model is a very simplified model to incorporate the poro-elastic effect on changes in fracture closure stress
resulting from leakoff of fracturing fluid, which can in turn affect the fracture growth of the modeled fracture, especially with
respect to height growth. This poro-elastic adjustment is significant only for incompressible fluid (i.e., oil reservoirs or highly
overpressured gas/condensate reservoirs), where models can increase the fracture closure stress in permeable layers because
of an increase in pore pressure.
In addition, various models are attempting to incorporate corrections for stress-shadowing effects of nearby fractures, as generated from previous stages in the same well or from past stages in nearby wells. In multiwell completions in stacked target zones, this
feature might help to determine a proper sequencing of fracturing stages to ensure that most of proppant is placed in zones where
conductivity is required.
4.4 Basic Fracture Modeling Concepts
4.4.1 Net Pressure. Fig. 4.12 provides a graphical representation for net pressure. For the sake of completeness, net pressure is
defined as the difference between the pressure in the fracture itself
and the total minimum horizontal in-situ stress, which equates to
the fracture closure stress:
Closure pressure
(2,000 psi)
pnet = pfrac − σ closure . ���������������������������������������������������������������(4.7)
A critical step in fracture model calibration is to properly
define the measurements that are needed to determine the resultant observed net pressure and to ensure that proper assumptions
Pressure inside fracture
can be made for the many parameters that drive that net-pressure
(2,500 psi)
behavior. In the subsequent text, net pressure has been adopted for
simulation and matching descriptions, but this could be more corFig. 4.12—Definition of net pressure.
rectly described as net treating pressure inside the main body of the
fracture near the wellbore, but beyond the perforations and a possible near-wellbore restriction. As detailed in the Eq. 4.8 this is herein
referred to as observed net pressure (pnet,obs).
Fracture models require many assumptions, and when conducting net-pressure history matching of treatments there is a need to
ensure that the observed net pressure is properly anchored in a direct measurement of surface or bottomhole pressure (Gas Research
Institute 1998).
The anchoring requirement relates the following equation for the observed net pressure pnet,obs to several independent components:
pnet,obs = psurface + ∆phydrostatic − ∆pfriction − σ closure . ��������������������������������������������������������������������������������������������������������������������������������(4.8)
The first component in this equation is the measured surface pressure psurface. While direct bottomhole pressures might sometimes be
available, mostly in vertical wells through an open deadstring or bottomhole pressure gauge, the operational efficiencies necessary for
the Shale Revolution have meant that unconventional fracture measurements are almost exclusively performed at the surface, where
surface pressure measurements at the wellhead are recorded in the data van.
Service-company field engineers will generally collect data for the second component, the hydrostatic head Δphydrostatic, which
translates the surface pressure measurement to a downhole pressure estimate during pump shutdown. Hydrostatic head changes are
determined from the integrated specific fluid density over the vertical fluid column in a wellbore:
∆phydrostatic = ∫
bottomhole
surface
ρ z g d z. ����������������������������������������������������������������������������������������������������������������������������������������������������������(4.9)
In addition to measuring the surface pressure at the wellhead, slurry rate and proppant concentration are also needed to properly
determine the makeup of fluid in the wellbore and the specific densities of various slurry concentrations in the wellbore for each treatment schedule. This requires correct real-time “staging” to align the actual fracture treatment specifics with the original treatment
design, so that the model relates to the correct fluid and proppant properties during that specific portion of the fracture treatment. In
addition, it is critical that wellbore trajectory and location of perforations be defined. It is also important to track proppant and fluid
types, and their individual specific densities.
86 Hydraulic Fracturing: Fundamentals and Advancements
4.4.2 Friction Pressure. The third component in Eq. 4.8 represents total friction Δpfriction, which brings the sequence in the calculation
to a bottomhole pressure within the main body of the fracture, and which is made up of three individual components:
∆pfriction = ∆pwellbore + ∆pperf + ∆pnwb . ����������������������������������������������������������������������������������������������������������������������������������������������(4.10)
Frictional pressures exist while pumping, but they reduce to zero when pumping stops. Friction components can be estimated
(Weijers et al. 2000a) during a rate stepdown test, which enables most commercial fracture modeling software to unravel total bottomhole friction into two individual components through a least-squares fit that uses the different flow-rate dependencies of each of
these components:
∆pBH friction = ∆pperf + ∆pnwb = β perfQ 2 + β nwbQ 0.5 . ����������������������������������������������������������������������������������������������������������������������������(4.11)
The details of this analysis step are provided in the Fracturing Pressure Analysis Chapter. The main challenge to properly solving Eq. 4.11 for any time during a fracture treatment is that the typical value of the observed net pressure pnet,obs is relatively small in
comparison to the value of other components in the equation. As a result, if significant uncertainties exist to determine parameters in
Eq. 4.8, large errors might pass down into pnet,obs.
In most horizontal shale wells, wellbore friction can be significant because fluid is pumped at a high rate through thousands of feet of
pipe. Wellbore friction in such a well can amount to several thousands of psi, while the net fracture pressure is often in the range of 500
to 2,000 psi. In addition, operators often decide to use a “limited-entry” perforation strategy, which typically elevates perforation friction to at least 500 psi, and usually much more. Finally, near-wellbore friction is often the wildcard, but can be significant, sometimes
more than 1,000 psi at desired pump rates in horizontal wells because of misalignment of the lateral trajectory and the far-field stresses.
Another challenge with all these friction components is that they can vary significantly over the duration of a fracturing job. Models often interpolate between β-factors in Eq. 4.11 if multiple rate stepdowns are conducted. Some models use a perforation friction
erosion model to forecast how perforation friction changes with the mass of proppant pumped through a perforation (Cramer 1987)
during the job.
Because the number of stepdown tests is limited for practical purposes, this further impacts the ability to determine observed net
pressure throughout the fracture treatment. Given these large friction components during pumping, fracture modelers often resort to
collecting some treatment data when they know the exact magnitude of all friction components: zero friction when there is no pumping. Unfortunately, this strategy of focusing on shutdown data is at odds with the shale industry’s ever-increasing pumping efficiencies.
4.4.3 Fracture Closure Stress. As a final component in Eq. 4.8, the bottomhole fracturing pressure obtained through the first three
components in the equation now needs to be combined with Eq. 4.7 to arrive at an observed net pressure in the fracture.
In the unconventional plays, measuring fracture closure is generally conducted before the main fracture treatment during a series
of diagnostic injections. Because of the low leakoff in shale fractures and the focus on pumping efficiencies, a closure stress measurement in shale fractures is now conducted through a diagnostic fracture injection test (DFIT), which typically occurs a few days or
weeks before the first fracture treatment in a horizontal shale well. The details of this analysis are provided in the Fracturing Pressure
Analysis Chapter. Closure stress is a key anchor point to determine the observed net pressure in the field.
Generally, fracture closure stress is measured using pressure-decline analysis following a slickwater injection, and it is generally
assumed that this measurement represents the closure stress in the pay zone. A generic version of this test is shown in Fig. 4.13. In
addition, before the propped-fracture treatment, a minifracture, often called a “fluid efficiency test” or “data frac” is performed to
enable the stimulation engineer to measure a leakoff coefficient that is then used to help determine fracturing-fluid efficiency, which
indirectly reveals something about rock permeability. The “anchor points” obtained from these diagnostic injections are used to
“calibrate” the fracture model in a simple sense. Closure stress and permeability (under fracturing conditions) for the pay zone are
thus determined and updated in a fracture propagation model.
A quick way to determine net pressure at the end of an injection period is to use a slightly modified version of Eq. 4.7:
pnet, EOJ = ISIP − σ closure , ����������������������������������������������������������������������������������������������������������������������������������������������������������������(4.12)
Bottomhole pressure
where fracture closure is determined from the point where the pressure decline stops showing linear behavior as a variety of diagnostic graphs (see the Fracturing Pressure Analysis Chapter). The difference between the correctly determined instantaneous
εEOJ ≅
tclosure
tclosure + tinjection
ISIP
pnet, EOJ = ISIP − σclosure
σclosure
Q
tpumping
pnet,EOJ
Permeability
Pore pressure
tclosure
Fig. 4.13—Generic diagnostic injection with rough estimates of net pressure and fluid efficiency at the end of the
injection through a fracture closure pick.
Hydraulic Fracture Modeling
87
shut-in pressure (ISIP) and closure, both determined for bottomhole condition, then represents the net pressure in the main body
of the fracture at the end-of-the-job (EOJ) pumping period.
If fracture modeling is anticipated during or after a treatment, a sequence of diagnostic injections such as these recommended in
Table. 4.1 should be considered to help plan for a proper measurement of net pressure. In higher-permeability formations, quick,
simple, and inexpensive injection diagnostics provide calibration anchor points for confident real-data net-pressure analysis. Necessary
anchor points include closure pressure, ISIP (net pressure) match points, pressure-decline behavior and wellbore, perforation, and nearwellbore friction. Effective real-time or post-fracturing, real-data analysis requires some level of injection diagnostics on every fracturing treatment. Correctly performing simple diagnostic injection procedures can add as little as 20 minutes to treatment execution time.
During hydraulic fracturing in shales, these diagnostics to determine closure are not practical during the job, as it can take hours
or days for a fracture to close following a small diagnostic injection. Therefore, operators often pump a DFIT when the well is first
drilled and cemented, allowing pressure decline data to be recorded for several weeks before pumping equipment arrives on location,
thus minimizing idle time for fracturing equipment during fracturing operations. This injection/decline sequence then provides a
fracture-closure stress, pore-pressure and permeability estimate for the reservoir near the toe-stage of the horizontal well.
Diagnostic Step
When
Fluid and Volume
Purpose / Results
XLOTs/breakdown injection/ Always
rate stepdown/pressure
decline
≈50–100 bbl KCI
Establish injectivity; obtain small-volume ISIP;
estimate closure pressure and formation
permeability
Crosslinked-Gel Minifracture New areas
with proppant slug/
Real-time pad
rate stepdown/pressure
resizing TSO
decline
treatments
≈100–500 bbl fracture Leakoff calibration
fluid including
Net-pressure sensitivity to volume and crosslinked gel
25–50 bbl proppant Characterize fracture entry friction
slug (possible range
Evalute near-wellbore reaction to proppant
0.5–5 lbm/gal)
Screen out or erode near-wellbore multiple
fractures
End Fracturing Rate
Stepdown/PressureDecline Monitoring
Always
Minimum of 10 minute
decline data
Characterize fracture entry friction
Post-fracturing leakoff calibration
DFIT
Low-permeability
reservoirs
25–50 bbl and
5–10 bbl/min
Measure closure, permeability, and pore pressure
before fracturing equipment arriving to location
Table 4.1—Overview of diagnostic injections and their purpose.
With these measurements and requirements, fracturing engineers have a reliable source for the observed net-pressure response, or
at least of the predicted net-pressure trends during the job.
4.4.4 Fluid Leakoff and Efficiency. As stated in Eq. 4.2 earlier in this chapter, the leakoff volume from the fracture at any given time is
ti
Vleakoff = ∫
0
Kl
2 Ai dt , ����������������������������������������������������������������������������������������������������������������������������������������������������������(4.13)
t − ti ( x )
where ti represents the injection period, Kl the Carter leakoff coefficient and Ai the time-dependent fracture surface area at time i.
Fracture slurry efficiency is a critical parameter associated with the volume of the fracture at any given time. One of the main goals
for modeling is to determine fracture dimensions at any given time during the fracturing job, and specifically at the end of the fracturing job or at closure. If the engineers have an independent method to determine the volume of the fracture at the end of the job, then
they are closer to determining fracture length, height, and width because the product of these would be equal to the fracture volume.
By definition, slurry efficiency is equal to the ratio of fracture volume and pumped volume:
ε=
Vfracture
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.14)
Vpumped
As shown in Fig. 4.13, fracture slurry efficiency can be “guesstimated” from the ratio of closure time to the sum of closure time
and injection time:
ε EOJ ≅
t closure
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.15)
t closure + t injection
Eq. 4.15 is a significant simplification of the actual slurry efficiency, as it assumes no pressure dependence of leakoff behavior, and
assumes that leakoff volume is a linear function of time. For a more accurate estimate, use Nolte’s dimensionless closure-time equation (Nolte 1986) to determine slurry efficiency at the end of an injection period:
ε EOJ =


 

1
1
1
1 − π 
  . ���������������������������������������������������������������������� (4.16)
4
−
+

−1/2
3/2
 2
−1 
1/2

5  (1 + t cD )3/2 − t cD

1
t
t
sin
1
t
+
+
+
cD ) cD
cD )

(
(
   

{
}
In general, the simplified efficiency Eq. 4.15 delivers slurry efficiencies within approximately 10% of the actual efficiency value
determined with equation Eq. 4.16.
The next few sections detail how practitioners use the independent determination of fracturing fluid efficiency at the end of an
injection period, through an estimate of fracture closure, to “lock” in the fracture volume at that time. Because a main goal of fracture
88 Hydraulic Fracturing: Fundamentals and Advancements
modeling is to determine the individual dimensions of effective fracture length, height, and average width combined over potential
multiple fractures, the volume provides the product of these three dimensions. As such, efficiency, and through it, fracture volume, are
very important steps toward the calibration of a fracture model.
4.4.5 Fracture Compliance. If Sneddon’s generalized equation for fracture width Eq. 4.3 is used and it is assumed that there is a
constant net pressure along the fracture (ignoring fracture pressure changes resulting from frictional effects from moving fluid) and
a homogeneous linear elastic rock, and the width is calculated in the middle of a radial fracture, Sneddon’s equation simplifies to the
product of the net pressure and fracture compliance C:
wwell = Cpnet =
γ Rf
pnet , ��������������������������������������������������������������������������������������������������������������������������������������������������������������(4.17)
E
where the fracture opening modulus is represented by
E=
E
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.18)
4 1−ν2
(
)
Fracture compliance is thus the deformation per unit load, the inverse of fracture stiffness. A high compliance makes it easier to
deform the rock, or in this case, to open the fracture. The fracture opening (width) is larger when the fracture radius Rf is larger because
more leverage is provided.
For a nonradial fracture shape, the fracture compliance is dictated by the shortest of these dimensions. In most observed cases,
fracture height is significantly smaller than the overall fracture length, and fracture compliance is determined by fracture height.
The width w will be smaller when the Young’s modulus E of the rock is high. The functional coefficient γ depends on the loading
distribution along the fracture (i.e. the pressure profile) and boundary conditions. The lower bound for γ, for a radial fracture with
constant net pressure, is 2/π and the upper bound, for a fracture with a constant height, is unity.
This simple Eq. 4.17 can help the practitioner to understand some of the fundamental analysis tools in the industry. For example,
take the Nolte plot for identification of fracture growth modes (Nolte 1979). Nolte’s growth Mode III represents TSO behavior and can
be recognized with a unit slope in a net-pressure vs. pump-time log-log plot. If it is assumed that the radius Rf of the fracture system
remains constant during a TSO, Eq. 4.17 now represents a proportional relationship between fracture width and net pressure. As the
fracture width is assumed to be the only remaining growing fracture dimension during a TSO, the fracture width would be directly
proportional to the volume pumped, and if the job is pumped at a constant rate, it would therefore be directly proportional to the pump
time. This therefore represents a proportional relationship between net pressure and pump time, hence the unit slope in a log-log plot
of net pressure vs. pump time.
4.5 1D and 2D Fracture Growth Models
4.5.1 Derivation of a Static 1D Fracture Model. Now that several basic fracture modeling concepts have been provided, it is possible to apply these in a derivation of the simplest fracture model. This will provide insights into sensitivities of input parameters into
general fracture models. In this section, the concepts of elastic deformation of a fracture have been combined with fluid mechanics toward
w = width
a simplified fracture model. The aim of this is to show how net pressure depends on a variety of parameters in a static ID fracture system.
The term “1D” refers to a changing fracture width with time, while the
Q
h
dimension of fracture length remains static.
First, it is necessary to detail a few assumptions: fluid flow is in steady
L
state; the fluid is incompressible; the fracture has a constant fracture
width w over its entire fracture length L; the fracture length L is constant
p=0
p = pnet
(no growth); and there is zero pressure at the open end of the parallel
plates. The assumptions are shown in Fig. 4.14.
Fig. 4.14—Assumptions for a static 1D fracture
As shown earlier, fracture compliance depends on the shortest fracmodel.
ture dimension, so in the case of L>>h the compliance function in Eq.
–
4.17 simplifies to C = h / E .
Because these plates are parallel over their length L, the pressure drops linearly as a function of distance along the length, and the
average net pressure p– is equal to half the net pressure at the entrance injection point:
∂ p pnet
=
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.19)
∂x
L
p=
pnet
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.20)
2
Substituting Eqs. 4.19 and 4.20 into the momentum-conservation Eq. 4.2 and the fracture opening Eq. 4.3 yields
q=
Q  w 3   ∂ p   w 3   pnet 
=
=

 . ������������������������������������������������������������������������������������������������������������������������������������������(4.21)
h  µ   ∂ x   µ   L 
w = pC =
pnet h
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.22)
2 E
Hydraulic Fracture Modeling
89
Now the flow-rate equation is arranged in terms of pnet while substituting the width w in equation Eq, 4.22 and rewriting it in
terms of flow rate Q. It can be then be calculated with the required pressure pnet at the injection entry point to drive flow through
the plates:
pnet =
(QL µ )1/4 ( 2E )
h
3/4
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������(4.23)
This is a static solution for net pressure where the fracture dimensions do not grow. However, this net-pressure solution is very
similar to that of a Perkins-Kern-Nordgren (PKN) model for fracture growth, which was further explored by Ken Nolte, and which is
discussed in Section 4.6 of this chapter.
4.5.2 2D Fracture Models. Howard and Fast (1957) derived the first fracture approximately 10 years after the first fracture treatment was conducted. In this paper, the authors introduce the concept of a single-only-fracture fluid-leakoff coefficient to determine
how much fracture surface area is created as a function of pumped fluid volume, while assuming a constant fracture width. As
such, this is the first 2D fracture model, where fracture surface area is tied to fracture design parameters through various leakoff
mechanisms.
Two commonly used 2D fracture propagation models originated in the 1960s, coupling elastic deformation and the rupture of brittle
materials with fluid dynamics: the PKN model (Perkins and Kern 1961; Nordgren 1972) and the Khristianovic-Geertsma-de Klerk
(KGD) model (Khristianovic and Zheltov 1955; Geertsma and De Klerk 1969; Daneshy 1973). As shown in Fig. 4.15, these models
generally combine the physics of Darcy flow through parallel plates with the Sneddon (1946) equation for fracture deformation as a
function of a pressure distribution, in conjunction with a mass-balance equation, to keep track of fracture fluid vs. leakoff fluid using
a Carter-type leakoff mechanism.
The main difference in the implementation of these 2D models was how they handled fracture compliance: in the PKN model,
elastic opening or fracture width was tied to the height of the fracture, whereas in the KGD model the fracture width was proportional
to the length of the fracture. With the assumption of a constant pressure in the fracture, the PKN model results in an elliptical cross
section vs. height and a sliding opening at the layer interface for the KGD model. Because the shortest fracture dimension generally
drives fracture compliance, the PKN model is more appropriate for use in fractures with a high length/height aspect ratio, whereas the
KGD model is more appropriate when the length/height aspect ratio is small.
The “2D” annotation in these models refers to a change in the fracture half-length and width dimensions as a function of time and
volume pumped, as the fracture height remains constant. The KGD model assumes formation slippage at the layer interface between
the layer in which the fracture is located and the layer above or below the fracture, thus making out-of-zone growth physically impossible. In the PKN model, expected net pressures are relatively low and are expected to remain lower than the closure stress contrast
between the main propagation layer and neighboring layers.
For these initial concepts, fractures were expected to be confined only to the target pay zones they were intended to stimulate, as
upward and downward out-of-zone growth was expected to be absent or minimal because of a higher closure stress in surrounding
layers. During these early days of fracturing, the main target was often sandstone, with zones above and below the target consisting
of shales. The horizontal stress or fracture closure stress in these shales is generally higher because of a higher Poisson’s ratio, thus
resulting in a higher horizontal stress because of the transfer of the weight of the overburden in the formations surrounding the pay
interval.
Therefore, at the time it was believed that the “constant height” assumption in early fracture models was a reasonable representation of actual fracture growth, given the expectation of low net pressures in relation to realistic sand/shale closure stress contrasts.
Pseudo 3D
2D PKN
2D KGD
Full 3D
Nonplanar
Parameterized 3D
Complex
Hydraulic
fracture
σH
Fig. 4.15—Fracture propagation models.
Natural σh
fracture
90 Hydraulic Fracturing: Fundamentals and Advancements
Fracture height
4.5.3 Early 3D-Fracture Models. While the constant-height assumption made it possible to establish relatively simple equations for
growth in fracture length and width as a function of pumped volume, it also provides a major constraint for the applicability of these
models. In some situations, for example in thick rock strata with little closure stress contrast, the fixed height assumption is unrealistic.
Planar 3D models were developed mostly in the 1980s, with the appearance of significantly increased computing power, and these
simulations were increasingly used to determine how fractures grew in length, width, and height over time for a created fracture that
propagates in a vertical plane. 3D models can be broadly divided into three categories: pseudo-3D models (P3D), parameterized or
lumped 3D models, and fully meshed 3D models (Fig. 4.15).
Pseudo-3D models incorporate assumptions similar to
those of the previously discussed 2D models and formulate
Equilibrium Fracture Height
the physics rigorously, assuming planar fractures of arbitrary shape in a linearly elastic formation, 2D fluid flow in
the fracture, power-law fluid behavior, and LEFM to define
fracture propagation. Pseudo-3D models adjust fracture
height along the fracture on the basis of local fracture prespfrac
1
sure (along the length of the fracture), with the local height
σmin H
based on an equilibrium height equation for each “disconnected cell” along the fracture length (Fig. 4.16). Therefore,
2
these models are considered more representative if height
3
∆σ
confinement is present. These models often run a separate
H
proppant-transportat model in sequence with the geometry
calculation.
σmin
σmin + ∆σ
As previously stated, pseudo-3D models use LEFM and
Pressure in fracture p frac
generally predict very low net fracturing pressures associated with calculations of fracture propagation under most
realistic circumstances (Fig. 4.17). These estimated low
net pressures have two main consequences. First, estimated
Fracture Profile
net pressures could remain well below the expected closure stress contrast with neighboring formations, causing
the fracture dimensions forecasted by this model to remain
1
confined to the main initiation layer. The low net pressures
2
do not generally encourage out-of-zone growth and often
result in fractures with limited to no height growth. As
shown by Eq. 4.17, low net pressures also result in nar3
rower fracture widths. When conforming to mass balance,
σmin H
the volume “lost” to lower width and lack of out-of-zone
height growth is compensated with greater calculated
fracture lengths.
∆σ
4.6 The First Fracture Model Calibration
Effort—Identifying Growth Behavior
Cross section
Until the 1970s, companies had been pumping small treatments (skin fractures) using simple models and nomographs
with some success, but when large treatments of so-called
massive hydraulic fractures (MHF) were attempted, there
were many failures. For this reason, Amoco started a program in 1978, led by Ken Nolte, to aid in the understanding of hydraulic
fracture growth, with a goal of developing technology for data acquisition and improved fracturing design.
In a series of papers, Nolte and Smith (1979) and Nolte (1979, 1982, 1986a, 1986b, 1988a, 1988b) derived a version of equation
Eq. 4.23, the 1D-solution for net pressure where the fracture dimensions remain static. Interpretation of the pressure during fracturing,
and implicitly net pressure, was used to determine how the fracture geometry grew with time. The main interpretive tool developed
from this work on growth behavior is a log-log plot of net pressure vs. pump time, shown in Fig. 4.18.
Fig. 4.16—Equilibrium fracture height calculation in pseudo3D models.
Wellbore
Use predicted
net pressure
Net
pressure
Pay
Pump rate
Predicted net pressure
Pump time
Fig. 4.17—Early pseudo-3D fracture models did not use real-data feedback and generally showed very low net pressure
in confined fractures.
Hydraulic Fracture Modeling
91
Field Data
Net Pressure (pn psi)
Variable injection rate
2,000
II
I
III-a
II (?)
1,000
(5 MPa)
500
II
I
40
60
IV
III-a
Prop began
100
200
400
600
IIIb
1,000
Time (minutes)
Log (pn)
Idealized Data
pfc
I
III-b
II
III-a
IV
Inefficient
extension for pn ≥ pfc,
“Formation capacity”
Log Time or Volume
Fig. 4.18—Identification of fracture growth Modes I–IV in Nolte’s original paper (1979).
This net-pressure solution Nolte derived is very similar to that of a PKN model for fracture growth. This is no coincidence because
assumptions for the 1D model in Eq. 4.23 and a PKN model are similar. In the PKN model, a fracture with a constant height grows
away from a wellbore with its length increasing as a function of pump time to a power 4/5. This means that most of the injected
volume helps to create fracture length. When length-to-time is substituted into the power-law Eq. 4.23, it can be deduced that net
pressure is a function of pump time to a power of 1/5. This relationship ties to Nolte’s fracture growth Mode I (Nolte 1979), where a
1/5 slope in a log-log plot of log pnet vs. log tpump denotes confined height growth—similar to the main assumption of confined height
in the PKN model.
Nolte used observed (net) pressure to maintain this desirable state of growth, where most growth is expected to be confined to
the zone of interest. Once the observed net pressure reaches a “controlling pressure,” fractures could start growing out of zone. This
behavior of fracture height growth, referenced as Mode II fracture growth, is associated with leveling of the net-pressure slope with
pump time, to a near-zero slope. Nolte did note that this pressure behavior could also be explained by fissure opening.
A downside to this Mode II growth behavior, also exhibited in growth Mode IV, is that fracture length growth becomes much less efficient than in growth Mode I. Nolte’s main remedy to maintain Mode I growth for longer is to lower net pressures. Referring to Eq. 4.23,
Nolte suggests this can primarily be achieved with viscosity because the range in viscosity change from crosslinked gels to slickwater
spans several orders of magnitude. As a secondary parameter, with a much smaller application range, Nolte lists pump rate. A reduction
in these parameters does provide more risk for successful proppant placement, and trade-offs need to be carefully considered.
The Nolte (1979) Mode III fracture growth has been detailed previously, where an arrest in fracture tip extension in a radial fracture results in direct proportionality between net pressure and fracture width, fracture volume, and pump time. Identification of a
unit slope in a Nolte log-log plot with log pnet vs. log tpump is taken to denote a TSO, often a desired outcome for a fracturing job in
high-permeability formations. In cases where a log-log slope steeper than a unit slope is observed, the cause is generally a premature
screenout closer to the wellbore, often the connection between the wellbore and the fracture.
Finally, Nolte’s Mode IV fracture growth is associated with a negative log-log slope of net pressure vs. pump time. This behavior
is associated with unrestricted fracture height growth.
Nolte was the first to admit that this implicit net-pressure evaluation relies on idealized data. There are two main challenges associated with Nolte’s assignment of fracture growth modes: challenges to identify the correct net pressure during pumping because it can
be heavily masked by friction components and impacts of other growth mechanisms, such as the simultaneous growth of multiple
fractures and other phenomena described in Section 4.7.
Eq. 4.23 is also of vital importance for other aspects of the completion industry. Consider its importance in step-rate tests,
which are often conducted to determine if hydraulic fracturing is being efficiently achieved in high-permeability water injection
wells. Eq. 4.23 represents the observation of a log pressure increase weakly proportional to the log rate (to a power 1/4) for an
open fracture while also observing more of a unit slope in a closed fracture. This is a key observation point to determine injecting
fluid in the permeable matrix or creating a fracture in water injection wells. In water injection wells, conducting a step-rate test,
as proposed by Nolte (1979), allows the identification of fracture opening (that can be used as an upper bound of fracture closure).
Finally, Eq. 4.23 provides bounds for the relationship between near-wellbore pressure and pump rate, something the industry uses
when conducting stepdown tests (SDTs). In one extreme case, an initial fracture causing near-wellbore tortuosity might be completely
immobile, resulting in a relationship between pressure and rate similar to that in Eq. 4.1 where pnwb ~ Q. As noted, in the case of
equation Eq. 4.23 where parallel plates can move because of changes in pressure (while remaining parallel), the relationship changes
to pnwb ∝ Q1/4. For practical purposes in the field, the matrix inversion required to determine near wellbore friction (and perforation
friction) generally uses the following proportionality between near-wellbore friction and rate: pnwb ∝ Q1/2.
92 Hydraulic Fracturing: Fundamentals and Advancements
4.7 Advanced Fracture Modeling Concepts I
4.7.1 Observations. After development of pseudo-3D models in the early 1980s, the industry was excited about its new-found
knowledge regarding the physics of fracture growth and how that behavior could be captured in fracture models. Medlin and Fitch
(1983) and Shlyapobersky (1985) and Shlyapobersky et al. (1988) changed that notion and showed that an important calibration step
was missing when using these models.
Medlin and Fitch (1983) and Shlyapobersky et al. (1985, 1988) were the first to measure net pressures in the field. They found
that observed net pressures were consistently far higher than net pressures predicted by pseudo-3D models and parameter sensitivity
was inconsistent with observations in the field. Specifically, models were much more sensitive to injection-rate and fluid-viscosity
changes than what was seen in the field. For example, on orders of magnitude, changes in viscosity (changing fracturing fluid from
slickwater or KCl water to linear gel or crosslinked gel), theoretical net-pressure changes were expected to increase at least 10-fold,
while the field-related observed change was significantly smaller, perhaps an increase in the level of net pressure by only a factor
of 2 or 3.
The premise of the Shlyapobersky et al. work was that if net-pressure calculations in models are not very consistent with netpressure observations in the field, there is likely also a significant discrepancy between actual fracture dimensions and those predicted
with models. Therefore, it was postulated that accurate model fracture dimensions are not obtained accurate model fracture dimensions unless the net pressure behavior associated with fracture growth is matched. While it is still possible to use erroneous modeling
assumptions, through net-pressure matching there is at least a chance that the fracture geometry will be correct (Fig. 4.19).
As additional confirmation of these higher observed net pressures, their research found circumstantial evidence in the form of
fracture half-lengths being shorter than expected in models based on production data and pressure-buildup tests. Shlyapobersky
et al. (1988) and Shlyapobersky (1985) speculated that possible causes for this discrepancy are a layer of small cracks (“process
zone”) around the tip of a larger hydraulic fracture that increases apparent fracture energy as opposed to the LEFM incorporated
in fracture models at that time and simultaneous growth of multiple fractures as opposed to the simple planar fracture assumed
in models.
4.7.2 Tip Effects. When discussing the critical stress intensity factor in Section 4.3, this phenomenon ignored theory that has been
known since Barenblatt (1959) introduced the concept of the cohesive tip zone. Incorporation of LEFM acts as a significant simplification in fracture growth models, which is not applicable unless the importance of this cohesive zone is irrelevant. Where LEFM
incorporates the energy required to rupture atomic bonds, the actual hydraulic fracture process in rock with fabric heterogeneity
(microcracks and flaws) incorporates a mechanism of scale dependency, where the apparent fracture energy needed to break the rock
increases with the size of the hydraulic fracture.
Fracture modelers have sometimes used a workaround to incorporate this effect, either by increasing the rock’s fracture toughness
or by increasing its Young’s modulus. These workarounds still fail to address the scaling with fracture growth and result in unrealistic
physics, which in turn hides certain aspects of true fracture growth behavior. For example, for a given net-pressure observation, a high
and physically unrealistic Young’s modulus results in relatively narrow widths and long fracture lengths, whereas increased resistance
to fracture growth at the fracture tip results in wider and shorter fractures.
Shlyapobersky et al. (1992, 1998) and Wen et al. (1996) conducted experiments to better understand fracture tip processes and to
reveal the fracture process zone. They observed a process zone with complex bifurcations into multiple fractures at the tip as well as
a zone near the fracture tip that remained dry.
Chudnovsky et al. (1996) provided detailed insight into the cause and consequences associated with “tip effects.” The causes of
mechanisms that are grouped together in the term “tip effects” are a fluid lag region near the fracture tip (confirmed by lab experiments), a cohesive zone (“bridging”) near the fracture tip where rock rupture is incomplete, and a “process zone” ahead of the fracture
tip where plastic deformation and opening of microfractures occurs. The authors proposed a new fracture tip model (the “crack layer
concept”) to describe this interaction between the crack and the process zone, resulting in greater energy dissipation at the fracture tip
in comparison to the idealized fracture tip geometry used in LEFM.
4.7.3 Incorporating Tip Effects into Fracture Models. Chudnovsky (1996) defines the crack layer as a microscopic entity encompassing the fracture tip and the surrounding array of microdefects. Both an active and an inert zone of fracture growth is identified,
with leading and trailing edges defined in the active zone. The active zone, where damage nucleates into a local instability, is generally
significantly smaller than the total length of the fracture.
Instead of a single toughness parameter used in LEFM models, Chudnovsky introduces three independent parameters to characterize material toughness—two for the material and one history-dependent parameter.
Wellbore
Use measured
net pressure
Net
pressure
Pay
Matching measured net pressure
with model net pressure
Pump time
Fig. 4.19—Net-pressure matching “feedback” required model’s incorporation of multiple fractures and “tip effects,”
resulting in shorter fractures with more out-of-zone height growth.
Hydraulic Fracture Modeling
93
PZ evolution in lueder limestone
A
Interconnected PZ in 3D tests
C
PZ in torry buff sandstone
B
Fig. 4.20—Shlyapobersky’s observation of a fracture process zone and the dry fracture tip in a few of a created fracture
surface in few different rock types (1998). The photo on the right also shows a cross-sectional view with bifurcation of
the fracture tip.
Instead of explicitly modeling the crack layer dynamics, Cleary (1980a) follows a strategy, used in some lumped-3D fracture
models, to model the consequences of tip effects on the pressure distribution in a fracture. As shown in Fig. 4.21, a parameter γ2 is
introduced, which controls the near-tip pressure drop and thus the overall level of net pressure in the fracture. This parameter mimics increased fracture growth resistance at the tip. This parameter can range from 0.4 for the LEFM case down to 0.0001 to model
observed levels of fracture growth resistance in rock.
4.7.4 Simultaneous Growth of Multiple Fractures. The simultaneous growth of multiple hydraulic fractures is both man-made and
caused by natural phenomena. The man-made cause is tied to multiple-fracture initiation points along a long, perforated interval with
numerous perforations, while natural causes are tied to bifurcation of hydraulic fractures as they intersect natural fractures (Weijers
et al. 2000b) and layer interfaces (Warpinski and Teufel 1984; Barree and Winterfeld 1998; Chudnovsky et al. 2001; de Pater et al.
2015), and also originate from the complexities created at the fracture tip (Shlyapobersky et al. 1992, 1998).
Multiple hydraulic fractures are fractures that grow simultaneously from a wellbore and penetrate far into the formation during a
fracture treatment. It has long been known that multiple fractures are almost always present near the wellbore, because of individual
fracture initiation from many perforations in a cased-hole perforated completion or from existing (natural or drilling induced) fractures along an open-hole interval. However, it was often assumed in the past that only a single fracture propagated on either side of
the (vertical) wellbore beyond this near-wellbore region. Other fractures were assumed either to coalesce in the near-wellbore region
or cease growth because of the stress influence from the other nearby fractures, as the fracture system found the lowest amount of
energy to propagate. Evidence from core-through, mine-backs and laboratory experiments (Fig. 4.22), however, has indicated that
multiple hydraulic fractures often continue throughout fracture growth. Fracture designs in low-permeability shales use this growth
mechanism to maximize fracture complexity to create massive fracture surface area, while fracture treatments in higher-permeability
Pressure
Fluid-filled
fracture body
Near-tip
fracture zone
Net-pressure decline with distance along
length at the wellbore represents Y2
Perimeter
of fracture
pnet
σc
Positive net pressure
Pf > σc ⇒ Kl+
Negative net pressure
Pf > σc ⇒ Kl–
pp
0
Propagation criterion:
Kl+ – Kl– ≥ Klc
Nonlinear elastic model
(Y2 = 0.0001)
Linear elastic
model (Y2 = 0.4)
Kl+ ≈ (γk) σ √R
Where σ = Pf – σc
and Kl+≈Kl–>> Klc
Direction of
fracture growth
X
Wfrac
Dry tip region
Nonlinear elastic model
Linear elastic model
X
Fig. 4.21—The pressure profile in a propagating fracture (left), and the expected impact of these “tip effects” on the
overall net pressure and fracture width profile along the half-length of the fracture (right).
94 Hydraulic Fracturing: Fundamentals and Advancements
MWX cored hydraulic fracture
31 Fracture strands over 4 ft
Interval
– Vertical fractures
– Proppant washed out
During drilling
55° Well deviation
7,150 ft TVD
M
σh,min T
σh,max
M
M
M
W
σh,min
σh,max
σu
R
M
A
R
W
σu
(a)
(b)
Fig. 4.22—Observations of fracture complexity in the field and in the laboratory (Warpinski et al. 1991 and Teufel 1994;
Weijers et al. 1995).
rock aim to create simple fractures that focus on high-fracture conductivity, which can only be achieved with a fracture aperture that
can accept high proppant loading.
Multiple fracture growth can be triggered by fracture initiation in deviated and horizontal wells where the fracture makes a large
angle with the preferred plane, so that complex fracture growth is sustained beyond the region of the wellbore. In addition to this
human-induced way to create multiple fractures, fracture complexity is dependent on perforations and can be also induced by use of
multiple perforation clusters in wells that are oriented to generate transverse fractures, which are commonly used in horizontal-well
completions.
One recent development in horizontal shale well design evolution is that operators sometimes use up to 10 or more perforation
clusters in conjunction with extreme-limited-entry (XLE) perforating. Perforation-clustering schemes in horizontal shale wells have
gradually migrated to XLE perforation designs with an increasing number of perforation clusters with fewer perforations per cluster,
or more clusters with smaller perforations. This active push for more fracture complexity (Weddle and Pearson 2017) shows that
these extreme limited-entry designs achieve close to 100% perforation connectivity, throughout the fracture job despite perforation
erosion, in keeping all clusters taking fluid and proppant. In addition, perforation manufacturers have improved perforation-hole-size
consistency, even in off-centered horizontal perforation guns, which is also helping the push to seek simultaneous multiple fracture
growth directly from the wellbore. The man-made complexity is all in the near-wellbore region, and then the rock in the reservoir
adds further to this.
The evidence for multiple fracture growth is widespread. As shown in Fig. 4.22, multiple far-field hydraulic fractures have been
directly observed in the field during several core-through and mine-back experiments (Warpinski et al. 1991; Branagan et al. 1996)
and in the laboratory (Weijers and de Pater 1992; Weijers 1995; van de Ketterij and de Pater 1997). These fractures contained offsets
at geological discontinuities such as joints, confirming that multiple fractures can be caused by bifurcation at natural-fracture intersections. Fractures observed in the laboratory turned as they grew and developed with en echelon multiple branches.
Complex fractures were first identified in mine-backs, but initially dismissed by the industry as a byproduct of the shallow depth
at which these tests had been conducted. They were then observed by early Los Alamos fracture mapping of geothermal injections
(Murphy et al. 1986), which set off efforts to create massive fracture networks in enhanced geothermal systems (EGS).
The first commercial shale development in the US, in the Barnett Shale, was driven by several practical engineers, who embraced
fracture mapping because it provided the first observation of complex fracture growth, thus providing an understanding of how shale
could become economically productive through the creation of fracture complexity by slickwater fracture treatments. This first simulated map of hydraulic fracture growth in shale during a slickwater treatment (Fisher et al. 2002, 2004) showed what appeared to be
a complex fracture system with multidirectional fractures, creating along a 1-mile long and 1,200-ft-wide area that Fisher coined the
fracture “fairway.” This complex network was caused by a preferred fracture plane that was roughly orthogonal to pre-existing natural
fractures. The low-viscosity slickwater fluid enabled opening of both orthogonal planes effectively; potentially this might allow production contribution from a largely increased surface area of this orthogonal fracture system.
This observation of increased complexity was corroborated with surface tiltmeter mapping, which also showed complexity in
two orthogonal orientations, and additionally in a vertical direction associated with layer debonding. Direct proof of the existence
of a complex network came from five offset wells in a fracture-mapping project dubbed “The fracture that changed everything,”
also shown in the Fracture Diagnostics Chapter, for which production was temporarily “killed” by the complex propped-fracture
system. Once cleaned out, these five wells also received a production boost from the complex “plumbing” network created in the
treated well.
Multiple fractures also featured prominently in a few joint-industry projects, such as the Mounds Drill Cutting Injection project
(Moschovidis et al. 1999; Griffin et al. 2000). A main observation from this project: Reinjection of cuttings into an existing fracture
does not necessarily happen because new fractures at other azimuths could develop instead because of stress-shadow changes associated with the “propped” width of the original fracture(s). As such, a disposal domain can develop with changing fracture azimuths
for subsequent injections because of constant alterations of the orientation of the preferred fracture plane. The fracture azimuth span
is dictated by the horizontal stress bias. A secondary observation in this project, corroborated by tiltmeter fracture mapping, is that
fracture growth exhibits significant layer debonding (discussed in more detail in Section 4.10).
Fracture diagnostic observations have shown that many hydraulic fractures might not be single and planar, aligned with the
wellbore, and confined to the target zone. The recent wealth of direct fracture diagnostic data has shown that there are significant
Hydraulic Fracture Modeling
95
discrepancies between how fractures are expected (or designed) to grow and how they actually grow (Wright et al. 1999). Observations have included T-shaped fractures, horizontal fractures, fractures that grow along multiple planes, fractures that bifurcate at layer
interfaces because of differences in mechanical properties (Wright et al. 1999), fracture reorientation because of injection-rate and
viscosity changes (Weijers et al. 1999), and fracture reorientation because of production/injection-induced stress changes (Wright
et al. 1994a, 1994b, 1995) and interference from other fractures that remain open after they are created and thus leave a residual
stress (Griffin et al. 2000). In this section, however, the discussion is limited to fracture complexities that arise from the simultaneous
propagation of multiple subparallel hydraulic fractures.
Why does growth of multiple fractures occur at all? From a minimum-energy standpoint, the propagation of a single fracture
would be favorable. This might be true in a perfect material without any local weaknesses and when fracture initiation occurs at a
single point.
Growth of multiple hydraulic fractures is not only determined by controllable completion and stimulation practices. Bifurcation
of a hydraulic fracture could occur wherever it intersects a natural fracture. In naturally fractured reservoirs (virtually every rock is
naturally fractured to some degree), multiple hydraulic fractures are potentially initiated and propagated, often in increasing numbers
as more natural fractures are intersected by the growing hydraulic fractures. This process is self-reinforcing, as the propagation of
multiple hydraulic fractures tends to elevate the net fracturing pressure, which in turn makes it easier to initiate hydraulic fracture
propagation at newly intersected natural fractures.
4.7.5 Minimizing vs. Encouraging Multiple Fracture Growth. In line with the general fracture treatment design changes made in
the Barnett Shale, the technology focus for fracture treatments in current US shale plays has been on stimulating longer stages with
ever more clusters in the hope of creating an ever-larger stimulated reservoir volume (SRV) that contributes to production using the
following completion changes:
• Larger created fracture network.
{{ Longer laterals to access more rock and hydrocarbons at a lower incremental cost.
{{ An increase in proppant mass and fluid volume.
{{ Fewer chemical additives, reduced additive volumes, and a move to friction reducer slickwater (and recently high-viscosity
fiction reducers), as well as a general change to less costly, more-local, and lower-quality sand (a change from White Sand
to Brown Sand, led by operators in Texas) and recently an increasing use of 100-mesh sand. Overall, the industry uses fewer
chemical additives, and smaller additive volumes to place 1 lbm of sand in formation.
• Denser created fracture distribution.
{{ Higher stage count and an increase in stage intensity (smaller distance between stages).
{{ Higher rate, increasing rate per lateral foot.
{{ Changes in perforation strategy toward XLE with fewer perforations and more clusters/fracture initiation locations for better
overall fracture distribution.
{{ Diverter technology. The industry has developed a range of dissolvable and nondissolvable particulates to temporarily
block flow into subsets of stage clusters, aiming to achieve a more equivalent distribution of fractures and surface area
complexity.
While multiple fracture growth in each stage is a necessity in shale plays, it is often a source of potential problems in conventional
plays and vertical/deviated wells. The simultaneous propagation of multiple hydraulic fractures can have significant consequences for
both propped-fracture-treatment execution and the obtained propped-fracture geometry, if more than one fracture receives a significant volume of treatment fluids.
• A significantly increased screenout potential because individual multiple fracture widths are smaller than the width of a single
fracture.
• Shorter, narrower fractures because the fluid and proppant must be shared by several multiple hydraulic fractures. The total
width of all fractures added together, however, is larger than for a single fracture, resulting in higher near-wellbore proppant
concentration. Despite the high proppant concentration, near-wellbore conductivity will generally be lower than for a single
fracture because narrower fractures are more prone to the effects of proppant embedment and polymer-residue damage.
• Complex fracture growth during the hydraulic fracture treatment can sometimes be problematic from a proppant-placement
perspective. From a perspective of wellbore-to-fracture connectivity, it can also have major consequences. The redistribution
of proppant from a single (wide) fracture to several (narrower) multiple fractures can result in increased damage from polymer
residue, reduced effective fracture width because of proppant embedment and filter-cake residue, and increased sensitivity to
pressure losses from non-Darcy and multiphase flow.
• Higher net pressures. This can be partly because fractures open against each other and compete for fracture width, and partly
because of tip effects caused by the process zone around a fracture tip (see Section 4.3.4). In coalbed-methane (CBM)
fractures, these higher net pressures could potentially damage the rock permeability surrounding the fracture.
• There is one potential benefit from fracture complexity in conventional reservoirs, and that is that it might reduce the risk of
proppant production at higher rates because the risk of proppant production is higher at higher proppant concentrations.
By spreading the proppant among several fractures, the proppant concentration per fracture is lower, which helps keep the
proppant in place.
4.7.6 Approximating Fracture Complexity With “Equivalent” Multiple Fractures. Simple fracture models have been used to
model the impact of multiple fracture interaction through an elevated modulus to account for the interacting stress shadows between
fractures. In this scenario, the simultaneous growth of multiple “competing” fractures changes the fracture dimensions of a radial
fracture. The achievable fracture half-length decreases as the number of fractures increases because fluid and proppant must be shared
by more fractures. The fracture width for each individual fracture becomes smaller than the width of a single fracture, but the total
96 Hydraulic Fracturing: Fundamentals and Advancements
width of all fractures combined increases with an increasing number of multiple fractures. The smaller individual-fracture widths
would then (and often do) lead to problems regarding the placement of proppant in the fracture, resulting in a bridging screenout
(Weijers et al. 2000b).
The effect of an increase in the number of fractures, nfrac, on the predicted net fracturing pressure, pnet, fracture radius, R, and
fracture width w is calculated as follows:
2
pnet, n = pnet nfrac3 ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.24)
−2
Rn = Rnfrac9 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.25)
−5
wn = wnfrac9, ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.26)
where pnet,n, Rn, and wn represent the actual net pressure, fracture radius, and fracture width (respectively) experienced with nfrac
multiple fractures instead of a single fracture. This methodology is not coupled because the stress impact of one fracture geometry on
another is only explicitly modeled. Instability problems in models can be caused by flow split between fractures, as zonal injectionrate splitting is a function of net pressure to the fourth power, so small pressure changes result in dramatic zonal rate changes. Some
models offer a solution for this problem by locking flow split—for example, for limited-entry completions.
Explicit modeling of individual-fracture wings in multiple hydraulic fracture growth scenarios is discussed in Section 4.12.
4.8 Advanced 3D Fracture Growth Models
Parameterized-3D models and full-3D models were developed in the 1980s and 1990s to incorporate multiple fracture growth and tip
effects and provide more flexibility to honor observations (pressure/time history) while benefiting from improvements in computing
power. Computer codes were developed by a variety of industry groups: TerraTek (Clifton and Abou-Sayed 1981; Clifton and Wang
1988), MIT (Cleary 1980; Cleary et al. 1983; Crockett et al. 1986; Settari and Cleary 1986), and various other research and commercial
entities (Palmer and Luiskutty 1984; Thiercelin et al. 1985; Smith et al. 2001; Barree 1983; Meyer 1986, 1989; Abou-Sayed et al. 1984).
Full-3D models incorporate full coupling between the pressure distribution and the fracture width distribution in the entire
fracture in many nodes along the fracture. Because the pressure profile and the width profile are highly coupled with each other
and the relationship is relatively sensitive, these 3D fracture propagation models often require significant time before a stable solution is obtained. The gridded formulation for deformation and flow allows for more-extensive modeling of the physics associated
with all processes—for example, associated with shear decoupling and slippage at layer interfaces. Full-3D models incorporate
the ability to match net pressures later, with some of the later models (Hsu et al. 2012) incorporating the actual physics of fracture
“tip effects.”
Parameterized 3D models run much faster because they make assumptions about the expected vertical and horizontal pressure profile along the fracture given various influence functions for a variety of conditions the model is subjected to. The trade-off is that these
models calculate fracture propagation only in a few distinct points along the face of the fracture, which are then connected through
concentric ellipses, and that these models cannot account for any fracture propagation other than along an elliptical shape. In addition,
the vertical and horizontal pressure influence functions show the expected impact of specific physical conditions, without rigorously
modeling all the physical processes associated with it. The actual physics of fracture “tip effects” and simultaneous multiple fracture
growth is not implicitly incorporated into the model. Instead, these models provide an estimate of the potential net-pressure effect of
fracture overlap/interaction as well the impact on the net pressure profile in the fracture associated with higher tip resistance.
Use of parameterized 3D and full-3D models can bring significant philosophical differences between respective users. It is often
stated that full-3D models require more input parameters to run than are generally available, and that significant assumptions must be
made to run them. If that is the case, then why go in so much detail regarding the shape of the fracture? On the other hand, if much of
this data is available, why calculate fracture growth only in the shape of ellipsoids?
Mathematical models make sense only if there is a proper balance between the number of variables solved and inputs. With increased
accuracy there is the potential to highlight factors that are hidden when “lumped together” in simple simulators. Further, accuracy is
never improved by allowing the inexperienced user the ability to change parameters arbitrarily or by adding degrees of freedom in
problems that are data-limited in principle. One of the main benefits of both models is that they allow incorporation of more-complex
fracturing mechanisms (e.g., fracture tip effects, multiple fractures, permeability barriers). In most present-day fracture modeling
software, the philosophical gap for use of various models is bridged because most software platforms provide a multitude of different
models, including parameterized 3D versions and full-3D versions, and the user can select whichever model is the most appropriate
for the reservoir data provided. Recent work (de Pater et al. 2018) illustrated the important issue of how difficult it is to predict fracture
height growth, even in full 3D models, which also require calibration for different reservoirs. In this case, given the need to calibrate
both full-3D models and parameterized 3D models and the lack of suitable data for input into full-3D models, the use of parameterized
3D models is still technically justified in most cases.
4.9 The Second Fracture Model Calibration Effort—Net-Pressure Matching
The discrepancy between the net pressure in models and field observations led modelers to incorporate net-pressure history matching
as an integral part of the workflow to better understand fracture growth behavior. Some fracture models (Crockett et al. 1986) focused
on capturing the large-scale physics of fracture growth, such as honoring large-scale elasticity and mass balance, while calibrating a
simplified approximation with-full-3D growth model, laboratory tests, and field observations. This was the start of the development
of parameterized 3D models.
Practical consequences of net-pressure matching were that fractures in updated models became generally wider, taller, and shorter.
Where previously fractures were expected to screen out faster because of smaller widths, the new models calibrated through netpressure matching allowed completion engineers to be more comfortable with lower gel loadings, smaller pad volumes, and higher
proppant concentrations.
Hydraulic Fracture Modeling
97
4.9.1 Net-Pressure History Matching. Hydraulic fracturing is a complex process affected by many unknown and variable factors.
Analysis of typical hydraulic fracturing data is further complicated by the indirect coupling of measured surface parameters (e.g.,
pressure, rate) to downhole fracture growth. In the past, a lack of engineering analysis tools and techniques to deal with this complexity resulted in an industry focus on theoretical fracture results based on pre-job estimates. The complication of using measured field
data (i.e., real data) was avoided, or was dealt with only in a simplified manner.
By avoiding or oversimplifying the message in the real data, knowledge about fracture growth behavior and obtained fracture
dimensions was relatively limited and causes for fracture-treatment problems were sometimes poorly understood. Honoring the message in real data can improve understanding about fracturing in any given area and result in economic fracture-treatment optimization
by improving fracture design, decreasing fracture-treatment cost, and/or improving post-fracture production response.
Advancements in engineering methodology along with new software tools and improved field procedures have resulted in routine
feedback of fracture treatment data to the engineer. This methodology, called “real-data fracture pressure analysis,” uses a quick,
simple set of diagnostic injection procedures to calibrate the use of a flexible fracture model incorporating realistic fracture growth
mechanisms. Real-data fracture pressure analysis is the engineering process of using the feedback from actual fracture behavior for
treatment design, execution, and evaluation. Far from being a science activity, real-data fracture analysis is an engineering process in
which feedback from field fracture-treatment behavior is used to provide engineering guidance for treatment design and execution,
and increasingly this analysis is being carried out on the fly.
Net pressure is the single most important variable in fracture pressure analysis because it is directly related to fracture length,
width, and height, and it can be directly measured from the surface. The technique of net pressure-history matching after the job is
used to match a theoretical-model net pressure to the actual or observed net-pressure behavior, with potential solutions constrained
by a combination of diagnostic injection behavior and engineering judgments. The result is a fracture geometry estimate that is firmly
linked to the actual treatment behavior.
This real-data methodology is not a cure-all. The complexity of hydraulic fracturing sometimes still defies explanation, and in some
cases, nature might can be extremely uncooperative with all efforts to successfully place proppant. Also, real-data analysis does not
lessen the role of engineering judgment and experience. However, real-data analysis always provides a significant step forward in
engineering capabilities beyond traditional fracture engineering techniques not using real-data feedback.
Several commercial fracture growth simulators are currently available that allow a stimulation engineer to history match bottomhole treatment data or observed net fracturing pressure with output from the model, to match and determine what occurred during a
treatment.
The advantage of using net pressure as opposed to bottomhole pressure for pressure matching purposes is that the “signal” (net
pressure) is much smaller than the “noise” (bottomhole pressure). So, history matching net pressure is basing the analysis only on the
“signal” and not on “signal + noise.” Some commercial software is set up to history match surface treating pressures instead of net
pressure or bottomhole pressure. This approach is even less ideal because it introduces more noise into the history matching process,
making it harder to concentrate modeling efforts on what really matters—net pressure as it directly relates to fracture dimensions.
The use of log-log plots for history matching of either bottomhole pressure or surface pressure also reduces the accuracy of the entire
history-matching process because the net pressure is so much smaller than the bottomhole pressure or surface pressure that any mismatch in net pressure (which is most important) is practically invisible on the log-log scale.
4.9.2 Derivation of a Radial Net-Pressure Feedback Model. This section considers the simplest fracture model that uses feedback
from real-data injection diagnostics before a fracture treatment. This back-of-the-envelope model is the simplest model for model calibration through the direct measurement of a net pressure and a fluid efficiency, both determined at the end of an initial injection period.
Now to consider two equations that describe radial fracture growth. First, consider the mass-conservation Eq. 4.2, which is updated
for a radial fracture model and which basically states that the total volume of fluid remaining in the fracture is equal to the product of
the fracture dimensions:
2
ε V = π R 2 w . ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� (4.27)
3
On the left side of Eq. 4.27, slurry efficiency multiplied with volume pumped represents the total fluid volume of the fracture system. The right side list the fracture volume as the product of its dimensions, where it is assumed that the average fracture width over
the fracture surface area is equal to 2/3 of the fracture width at the injection point at the well.
The second equation to consider is Sneddon’s fracture-width equation (from Eq. 4.3) rewritten for a radial fracture:
w≈
2 pnet R
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.28)
π E
It is possible to determine net pressure and slurry efficiency independently for the end of the treatment, which can now be solved
for this system of two equations with two unknowns for the main fracture dimensions:
1
 3 εVE  3
R=
 . ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.29)
 4 pnet 
1
2
3
 6 εVpnet
w= 3
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.30)

2
π E 
This system of equations can now be used to determine approximate fracture dimensions from two independent real-time measurements, e,and pnet; a critical rock mechanical parameter, E and the total fluid volume pumped V.
98 Hydraulic Fracturing: Fundamentals and Advancements
4.9.3 Net-Pressure History-Matching Variables. At this point in the analysis, the goal is to match the theoretical-model net pressure to the actual or observed net pressure. Fracture model inputs of fluid type, injection rate, and proppant loading are fixed by the
actual treatment data. Other model parameters such as elastic rock properties, closure stress profile, rock permeability, fracturing fluid
leakoff, and multiple fracture assumptions, must then be adjusted so that observed net pressure is matched across the entire sequence
of injections.
A net-pressure matching approach uses the observed net pressure in Eq. 4.8 as the “ground truth” and uses changing modeling
assumptions to approximately match it with a model net pressure
pnet,model ≈ pnet,obs . ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.31)
Basically, this process compares a “top-down” approach where a measurement of surface pressure results in an observed net
pressure in the fracture with a “bottoms-up” approach where bottomhole properties and assumptions result in a model net-pressure
response.
Some practitioners favor an approach of bottomhole pressure matching where a model bottomhole pressure is matched to a calculated bottomhole pressure rooted in a surface pressure measurement.
While both approaches are similar, the scale of the matches favors a net-pressure matching approach for a change of improved
accuracy of the final match. Net-pressure matching generally occurs up to net pressures of approximately 2,000 psi, whereas bottomhole pressures often exceed 10,000 psi. The impact of the fracture on that large bottomhole-pressure range is small, and it is more
likely that this approach focuses on matching observed frictional components with model frictional components, risking that the effect
of the hydraulic fracture on pressure response is ignored.
The approach for adjusting fracture model parameters will vary with formation properties, completion strategy, and fracturetreatment design. All the parameters are interlinked to some extent: adjusting one will affect the others. Because there is no
standard-issue formation layout, completion design, and fracture design, there is no standard cookbook procedure for net-pressure
history matching. A systematic and careful approach is therefore required to ensure that the resulting solutions are both feasible
and consistent.
There is not always complete agreement among industry experts as to the mechanisms that control net-pressure behavior. However, in some manner, observed net pressure must be matched for the results to have any usefulness. It is always far better to match
observed net pressure, providing bounds on possible mechanisms, than to simply ignore the observed net pressure in the analysis
process.
When using a simple, systematic approach, the number of variables that a fracture model user must evaluate to obtain a net
pressure history match is limited to a handful of parameters. Note that these matching parameters are general and apply to all commercial fracture models. The reason that these parameters can be used as matching parameters is that typically their exact value is
not known. A net-pressure match in simple simulators can generally be obtained by matching both level and decline of net pressure
using the following “level” and “slope” parameters (Fig. 4.23). These parameters are often referenced as “knobs” tied to physical
parameters.
Variables that mostly affect the total level of net pressure during an injection are:
• Elastic rock properties. Static Young’s modulus is the only rock mechanical property of concern during a fracture treatment.
There is no significant fracture growth sensitivity to Poisson’s ratio, other than from the impact of Poisson’s ratio (over
geologic time) on formation stress. Young’s modulus is generally estimated on the basis of data obtained from the rock of
interest or from other similar rocks. Potentially useful data might include lithology and porosity, static core measurements,
and dynamic (log- or laboratory-based) measurements. Because the dynamic modulus is much less sensitive to rock discontinuities, it can be a factor of two or more greater than the static modulus, and thus dynamic modulus (obtained from sonic
logs) should be used with caution. In general, fracture modeling requires a reasonable estimate of static Young’s modulus,
not a precise value. An increase in modulus results in a higher model net pressure, a larger fracture geometry, and lower
fluid efficiency. With a fixed observed net pressure and an unconfined (radial) fracture, modeled half-length is proportional
to modulus to approximately the 1/3 power, resulting in a 15% change in fracture half-length for a 50% change in modulus.
Purist net pressure matchers might argue that the Young’s modulus can be determined from several sources and should not
be considered a matching parameter.
• “Decline slope” parameters
• Permeability
• Wall-building coefficient
• Pressure-dependent leakoff
• “Level” parameters
• (Sand-shale) closure stress contrast
• Fracture complexity
• Tip effects coefficient
• Proppant drag exponent
• Tip screenout backfill coefficient
• (Young’s modulus)
• “Geometry” parameters
• Composite layering effect
• Crack opening/width coupling coefficient
Fig. 4.23—General net-pressure matching parameters divided into parameters that affect the slope of the pressure
decline, the overall level of net presure, and the overall fracture geometry.
Hydraulic Fracture Modeling
99
• Fracture complexity (or simultaneous propagation of multiple fractures). Numerous core-throughs and minebacks have
shown that multiple fracture growth can be the rule rather than the exception (Weijers et al. 2000b). Competition between
simultaneously propagating multiple fractures would increase net pressure and need to be accounted for in any fracture
growth simulator.
• Fracture tip effects, which reflect the resistance for fracture growth at the tip. Apart from matching higher net pressures, this
parameter can also be used to change the sensitivity of net pressure to the apparent viscosity of the fluid that is being pumped.
Increased fracture growth resistance at the fracture tip can be caused by plastic deformation and creation of microfractures in
the “process zone” that result in residual tensile cohesion.
• Closure stress contrast between pay and neighboring layers. Closure stress contrast is considered a fracture confinement mechanism. It is possible to estimate the closure stress in layers outside the pay by interpreting dipole sonic data and by evaluating
parameters such as Poisson’s ratio and pore-pressure depletion. Although there remains uncertainty regarding the value of the
closure stress in other layers, many modelers now consider the closure stress contrast fixed and off-limits as a net-pressure
matching parameter. They generally honor their closure stress measurement in the initiation interval and the stress contrast
observed in the sonic-log inferred stress data. Therefore, the use of this parameter is in a gray area between a measurement
and matching parameter.
• Proppant drag in the fracture. Fluid friction along the fracture (between wellbore and fracture tip) increases with the average
proppant concentration in the fracture, just like wellbore friction increases when a proppant laden slurry is pumped following
clean fluid. The exact increase in friction along the fracture face, however, is dependent on a multitude of parameters such as
fracture-wall roughness. Because it is not possible to know the exact impact, modelers often use a multiplier of the theoretical
effect to obtain a net-pressure history match.
Variables that mostly affect the slope of the pressure decline following an injection are
• Formation permeability. Leakoff from any injection can be matched by changing formation permeability. However, this
parameter is also often “locked in” on the basis of a permeability measurement, for example, from a prefracturing DFIT.
Note that the estimated permeability from a DFIT is under elevated (injection) pressures, which might be higher than the
permeability observed when producing the well. Some models incorporate pressure-dependent permeability to account for
this phenomenon.
• Wall-building coefficient. Once permeability is measured or “locked in” following an early injection where it has been used
as a matching parameter, leakoff behavior from a crosslinked gel minifracture can be used to determine a wall-building coefficient. However, this parameter is also often treated as a parameter that is measured in the laboratory and is off-limits for
matching. In addition, this parameter is not applicable for use as a matching parameter in slickwater jobs used in most shales
because this fluid does not exhibit wall-building capabilities.
• Pressure-dependent leakoff. DFIT or extended leakoff test (XLOT) pressure declines often exhibit pressure-dependent leakoff
(i.e., higher leakoff at elevated net pressures). Once again, this can be treated as a measurement if it is available or a “knob”
to match net pressures.
Once the model net pressure matches the observed net pressure, and the right assumptions are made in the model, it is hoped that
the model reflects the nature of the fracture growth and that fracture half-length and height have been estimated.
Unfortunately, as Section 4.11 will show, that hope is often not justified because there are various shortcomings in the net-pressure
matching process. Net-pressure matching is an indirect diagnostic technique (i.e., the fracture geometry is inferred from net pressure
and leakoff behavior); also, net-pressure matching solutions are nonunique. The net-pressure matching technique is most useful when
results are integrated or calibrated with results from other diagnostics, such as production and well-test-analysis data, and/or with
direct fracture diagnostics such as tiltmeter and microseismic mapping data.
4.9.4 Net-Pressure History-Matching Example. This example comprises a Pakenham Field (Permian Basin) fracture-treatmentoptimization example (Wright et al. 1998), which shows a technical progression from an initial (uncalibrated) extreme fracture confinement to the use of real-data feedback in a net-pressure match.
As shown in Fig. 4.24, diagnostic injections are conducted before the main fracture treatment, mainly to determine closure stress
and net pressure and to provide ample pressure decline data to match net pressures without too much obstruction from friction during
shutdowns.
The initial uncalibrated model net-pressure response for a strongly confined fracture (assumption approaching a 2D fully confined fracture model) is displayed in light green, showing net pressures increasing during pumping because of the confined nature of
the fracture system. Initial net pressures, especially during diagnostic injections, are very low because of an assumption of LEFM.
As shown in Fig. 4.25, the initial fracture half-length for this design run was expected to be near 600 ft, with fracture confinement
mostly to the expected pay zones.
Actual observation of net pressure through a measurement of surface pressures is provided by the black curve, which shows
much higher observed net pressures during the initial injections, and a much gentler increase in net pressure while pumping the main
fracturing job.
To obtain a match of the black curve, the fracture model was rerun to provide a model net pressure in the form of the grey curve in
Fig. 4.24. The following changes had to be made to obtain this match:
• The closure stress contrast between the target zone and the layers above and below the sandstone target zone was lowered
substantially because confinement in fracture height was expected to be responsible for the fast net-pressure rise during the
main fracturing job.
• Matching the higher observed net pressures during the prefracturing diagnostics was achieved through the assumption of more
simultaneous growth of multiple fractures and incorporation of standard “tip effects.”
100 Hydraulic Fracturing: Fundamentals and Advancements
50.00
100.0
2,000
Btm prop conc (lbm/gal)
Slurry rate (bbl/min)
Observed net (psi)
Net pressure (A) (psi)
Prop conc (lbm/gal)
Net pressure (psi)
2,000
50.00
2,000
40.00
80.0
1,600
1,600
40.00
1,600
30.00
60.0
1,200
1,200
30.00
1,200
20.00
40.0
800
800
20.00
800
10.00
20.0
400
400
10.00
400
0.00
0.0
0 0.0
20.0
40.0
60.0
Time (minutes)
0
0.00
100.0 0
80.0
Fig. 4.24—Application example for fracture modeling through net-pressure history matching and use of external
observations. Btm = bottomhole pressure. Prop conc = proppant concentration.
Layer Properties
Rocktype
Shale
Width Pr...
Concentration of Proppant in Fracture (lbm/ft2)
Stress (psi)
5000 10000
50
100
150
200
250
300
350
400
450
500
550
600
1
1.2
1.4
1.6
1.8
2
650
700
0
7650
7700
7750 Sandstone
7800 Sandstone
shale
7850
7900
7950 Siltstone
Proppant concentratiuon (lb/ft2)
8000
0
0.2
0.4
0.6
Layer Properties
Rocktype
Shale
0.8
2.2
2.4
2.6
Width Pr...
Concentration of Proppant in Fracture (lbm/ft2)
Stress (psi)
5000 10000
50
100
150
200
250
300
350
400
450
500
550
1
1.2
1.4
1.6
1.8
2
600
650
700
0
7650
7700
7750 Sandstone
Siltstone
7800 Sandstone
Shale
7850
7900
7950 Siltstone
Proppant concentratiuon (lb/ft2)
8000
0
0.2
0.4
0.6
0.8
2.2
2.4
2.6
Fig. 4.25—Change from originally expected fracture dimensions (top) to dimensions obtained through calibrated
modeling (bottom).
Hydraulic Fracture Modeling
101
Implementing these changes in the model assumptions, together with matching the much higher observed net-pressure level and
more-gradual observed net-pressure rise, resulted in significantly different fracture dimensions show in Fig. 4.25.
One unusual step in this project was that the operator decided to conduct direct measurement of the closure stress in the zones above
and below the target zone through pre-job injections in a few subsequent wells. Whereas the initial justification for extreme confinement was rooted in the expectation of a very high sand-shale closure stress contrast (≈0.3 psi/ft), direct measurement of the sand/shale
closure stress contrast indicated it was much smaller than previously expected (near 0.1 psi/ft).
This example shows the benefits of a strategy where feedback from critical measurements can help to better understand what is
achieved with a fracture treatment in a reservoir. A better understanding of these parameters helps reduce the degrees of freedom
when using fracture propagation models. This might not provide enough information to address the overall non-uniqueness in
model’s results, but it is a step in the right direction and can help the practitioner identify priority areas that might require further
investigation.
4.10 Advanced Fracture Modeling Concepts II
4.10.1 Diagnostic Observations. In the early 2000s, the industry saw a proliferation of direct fracture diagnostics and found that
net-pressure history matching alone is not enough to create models that forecast reliable fracture dimensions. The biggest limitation
of net-pressure history matching is that it is an indirect technique—dimensions are inferred from fracture pressure behavior. The
results of a history match are dependent on the assumptions that are made, and it is possible to create a history match in various
ways.
To address this limitation, it is necessary to calibrate the fracture model not just with an observed net-pressure match, but also with
directly observed fracture dimensions (Fig. 4.26).
Joint-industry projects have been vital for cross checking fracture diagnostic techniques and providing a ground truth to fracture
models. In the late 1990s, the Cotton Valley Consortium and the Mounds Drill Cuttings Injection Project were vital for creation of an
understanding of fracture layer interface discontinuities. In two formations where stress-driven confinement was expected to be most
absent (high net pressure vs. lower stress contrast), fracture diagnostics showed clear confinement because of layer interface effects,
just like those initially postulated by Warpinski and Teufel (1987).
The discrepancies between model-inferred fracture dimensions and those measured with direct fracture diagnostics raised questions about most fracture models. Although many models had moved beyond LEFM to match observed net pressures, most of the
model shortcomings were the result of two limitations common to net-pressure calibrated fracture modeling: the inability to predict
the enhanced fracture containment effects that might be provided by layer/lamination interfaces beyond the containment
effects because of stress and mechanical property contrasts (Chudnovsky 2001) and the inability to capture the dramatic influence
on fracture growth that might result from large-scale reservoir heterogeneities such as natural fractures, small faults and bedding
plane pinchouts. This shortcoming might be more a result of the lack of characterization of reservoir heterogeneities than because of
fundamental model shortcomings.
In addition to the proliferation of commercial fracture diagnostics, these diagnostics were also verified in detail through corethrough experiments (Walker 1997; Warpinski et al. 1998b; Moschovidis et al. 1999; Griffin et al. 2000; Mayerhofer et al. 2000).
Fracture diagnostic observations have shown that many hydraulic fractures might not be single and planar, aligned with the wellbore,
and confined to the target zone. The wealth of direct fracture diagnostic data has shown that there can be significant discrepancies
between how fractures are expected (or designed) to grow and how they grow in reality (Warpinski et al 1998b; Cipolla and Wright
2000). Observations have included T-shaped fractures, horizontal fractures (Wright et al. 1997), fractures that grow along multiple
planes, fractures that bifurcate at layer interfaces because of differences in mechanical properties, fracture reorientation because of
injection-rate and viscosity changes (Weijers 1999), and fracture reorientation because of production/injection-induced stress changes
(Wright et al. 1994a, 1994b, 1995a, 1995b, 1999) and interference from other fractures that remain open after they are created and
thus leave a residual stress (Griffin et al. 2000).
In this chapter, however, the discussion will concentrate on how the industry has adapted and evolved to incorporate
these findings into what are now standard workflows. After net-pressure history matching in the second calibration cycle caused
many people to believe fractures were mostly unconfined because of higher net pressure, direct fracture diagnostics showed that
fractures were actually more confined, and that created hydraulic fracture lengths were typically two to fivefold greater than
fracture heights. The main cause of the lack of fracture height growth was laminations and interface growth effects, rather than
slow height growth.
Wellbore
Use measured
net pressure
Pay
Net
pressure
Matching measured net pressure
with model net pressure
Pump time
Fig. 4.26—Net-pressure matching “feedback” required “composite layering effects,” resulting in less out-of-zone height
growth.
102 Hydraulic Fracturing: Fundamentals and Advancements
4.10.2 Case History. A comprehensive mapping project was conducted in 1998 to study fracture growth during drill-cutting injections (Moschovidis et al. 1999; Griffin et al. 2000). A wealth of fracture diagnostic data was collected—microseismic mapping,
downhole tilt offset-well mapping, surface tiltmeter mapping, tracer logging, and pump-in/decline tests to measure fracture closure.
To top it off, four wells were cored through the created fractures to confirm these diagnostic results.
One of the target zones was in the Atoka Shale at a depth of approximately 2,000 ft. As shown in Fig. 4.27, the gamma ray log
is quite uneventful over a depth of approximately 500 ft. What is particularly interesting in this case history is that the shale target
interval is very thick and continuous, while injection volumes are relatively low. This represents a simple case of fracture growth
in a vertical and horizontal direction of rock that is just about as homogeneous as can be found naturally for a diagnostic project.
Stress tests were conducted (pump-ins of several barrels of water followed by shut-ins for pressure-decline analysis) to see if the
closure stress contrasts between the “target” zones and the surrounding formations changed. These stress tests revealed a nearly
constant stress gradient with depth within the thick and continuous Atoka Shale, with a closure stress gradient of approximately
0.65 psi/ft.
For many fracture growth modelers at the time, these measurements of stress at various depths would have been enough to conclude
that overall fracture growth would probably be close to radial. With net fracturing pressures of approximately 400 psi observed
in the Atoka during drill-cutting injection tests, initial net-pressure matching results inferred a roughly radial fracture geometry
because there were no apparent stress “barriers” to confine fracture height growth. This initial conclusion is represented by the dotted
blue ellipse of the uncalibrated model.
Several drill-cutting injections were conducted in this interval, including five 100-bbl injections that are shown as green ellipses,
measured with offset downhole tiltmeter mapping. Downhole-tiltmeter mapping revealed a greater than 2:1 length-to-height aspect
ratio for 20 of the 23 injections mapped. All these ellipses are similar and show a fracture length/height aspect ratio of approximately
2 or 3, thus showing significant confinement.
In addition to the observation of confinement, surface tiltmeters for these cases often display a significant multiple component
deformation from tilt mapping, indicating a substantial “horizontal component” in the deformation pattern. This is consistent with the
possible debonding of horizontal layers.
Clearly, there is some other cause for this confinement beyond the standard stress/mechanical properties/permeability contrasts
accounted for in “typical” fracture growth models. Because of a lack of freedom to some degree in modeling to increase the closure
stress in the layers above the interval where the fracture initiated (the closure stress is roughly constant throughout the Atoka), it
became clear that another mechanism is responsible for the observed level of confinement. The solid blue ellipses in Fig. 4.27 show
the calibrated model in which a “composite layering” effect was introduced to confine fracture height.
This simple and well-documented example illustrates that fractures can grow confined in the absence of the “classical” confinement
mechanism of closure-stress contrast.
4.10.3 Composite Layering Effect. This “new” mechanism for height confinement was postulated by several people in the 1980s,
but was never incorporated in models, apart from the KGD model, where layer debonding was assumed as perfect layer slippage.
Several researchers (Cleary 1980; Nolte and Smith 1981; Warpinski and Teufel 1984) have speculated about the existence of
other fracture height confinement mechanisms in addition to the standard elastic mechanisms of stress, mechanical properties, and
permeability contrasts between the target zone and adjacent layers.
What mechanism inhibits fracture height growth and results in a fracture (total) length that is more than twice fracture height?
At only 2,000-ft depth in the Atoka Shale, there is little possibility of a sufficiently high in-situ stress contrast (on the order approximately 1,000 psi) to contain fracture height growth. Therefore, other effects must be responsible for the observed fracture height
GR log
1,600
Fracture modeling
(no confinement
mechanism)
1,700
Depth (ft)
1,800
1,900
Fracture modeling
(composite layering
effect)
2,000
2,100
Inferred geometry
from downhole tiltmeter
mapping
2,200
–400
–200
0
200
400
Along Fracture Length (ft)
Fig. 4.27—Uncaliberated model (dotted blue ellipse) and calibrated model (blue ellipse) response in the Atoka
Shale. The calibrated response matches the direct observations (in green) of offset-well downhole tiltmeter mapping.
GR = gamma ray.
Hydraulic Fracture Modeling
Fracture closure stress/
permeability barrier
Interface slippage
103
Composite layering /
width decoupling
Fig. 4.28—Composite layering and width decoupling in concept (left) and in a photo from a mineback from the Nevada
Test Site (Warpinski and Teufel 1987, right). In the concept drawing, the left part shows the “classical” mechanism of
fracture growth confinement because of increased closure stresses in the layers above and below the target zone.
Interface slippage (middle picture) was a mechanism postulated in the 2D KGD model and would result in perfect
confinement at a layer interface. The right side of the drawing shows the composite layering effect of partial rebonding of
layer interfaces. The overall loss of leverage to propagate the fracture tip through layer interfaces results in a reduction
in the growth rate along the height, while the growth rate along layer interfaces (typically along fracture length) is not
affected by the mechanism.
confinement. Practitioners suggest that this could be a result of shear slippage at interfaces and that the fine laminations in the shale
sequences blunt the fracture height growth in the same fashion as composite materials arrest fracture growth. By crudely approximating a “composite layering” effect that slows fracture growth across layers relative to fracture growth along layers, it becomes possible
to match the observed net pressure and match the observed fracture geometry using a 3D fracture model.
The problem is how to know when these effects must be “turned on” in the fracture model and to what degree height growth is
inhibited by layering. Chudnovsky et al. (2001) explains the magnitude of this mechanism in terms of contrast in Young’s modulus
and Poisson’s ratio in subsequent rock layers.
A composite layering effect (Warpinski and Teufel 1984; Barree and Winterfeld 1998; Chudnovsky et al. 2001; Gu et al. 2008;
de Pater 2015) reflects the resistance for fracture growth through layer interfaces (Fig. 4.28). As a fracture tip grows through layer
interfaces, some of these interfaces might become partially debonded and the fracture might start growing again at a local weakness
offset from the original path. The consequence of composite layering is higher frictional pressure drop and loss of leverage along the
fracture height, resulting in a significant decrease in the vertical growth rate. The overall impact of this phenomenon is that the fracture
height slows down in comparison to the growth of fracture half-length.
Layer interface effects cause lower tip pressure and a reduction in leverage from the main body of the fracture that inhibits
fracture height growth. Current fracture modeling efforts are increasingly looking to try to effectively incorporate layer interface
effects into models, with varying degrees of success. One of the main problems has been the inability to characterize and predict
heterogeneity effects when there is a lack of sufficiently detailed reservoir characterization that would allow us to more fully
understand and simulate the necessary processes. A critical step in the understanding of these observations is to perform accurate
measurements of fracture closure stress to eliminate the more conventional large-stress-contrasts mechanism as the potential cause
for confined fracture growth. More importantly, additional research is needed concerning fracture growth and diagnostics through
interfaces/laminations.
The implications for fracture design relate to fracture staging and perforation designs in thick intervals of seemingly homogeneous
reservoirs. If fracture height coverage of the interval in a vertical well is not achieved, additional fracture stages to cover the entire
zone need to be considered. Also, if it was possible to reliably assess containment mechanisms, it would allow designs to more
effectively treat zones of high risk such as those near water-bearing layers or near, gas/water or oil/water contacts. As more operators
complete horizontal wells with hydraulic fractures in thick pay zones, it is critical to assess if fracture height growth covers the entire
pay zone and to evaluate fracturing design changes to better target height growth, rather than length growth.
4.11 The Third Fracture Model Calibration Effort—Reconciliation With Fracture Diagnostics
Following the incorporation of net-pressure matching in the late 1980s, the fracture modeling revolution in the early 2000s comprises the incorporation of real-time fracture geometry measurements. By now it should be apparent that best practices in stimulation attempt to obtain the best results from two separate processes: modeling fracture growth and directly measuring fracture growth
behavior.
While, particularly with hydraulic fracture treatments, it is dangerous to generalize, some diagnostics have found that fractures are
approximately five times longer than they are tall (de Pater 2015). This is set against a previous expectation anchored in the theory
of simple models that fractures were not as confined, where fractures had more leverage to create width, as the minimum fracture
dimension was thought to be larger. In general terms, this means that fractures were considered now to be narrower than expected, and
that they are more likely conductivity-impaired. It was also generally observed that fractures are significantly shorter when evaluating dimensions inferred from production-data analysis, which also points to more damage than expected to long-term conductivity.
104 Hydraulic Fracturing: Fundamentals and Advancements
Calibrated modeling, especially where production-data analysis is included (Cipolla and Mayerhofer 1998), can help get closer to
“what is happening down there.”
Use of direct fracture mapping technologies has greatly increased over the last two decades, from the first real-time measurement
of fracture dimensions in 1997 to the routine mapping of fracture dimensions on thousands of fracture treatments. The development
of commercial technologies (Wright et al. 1998a, 1998b, 1998c, 1998d, 1998e) to routinely measure fracture growth has greatly
improved fracture modeling capabilities, enabling practitioners to distill the essential fracture growth behavior in many environments
into calibrated fracture models.
Calibrated fracture models combine complementary strengths and weaknesses of fracture mapping and modeling. Fracture models
provide the ability to predict how changes to a fracturing treatment should alter fracture geometry (Crockett et al. 1986) but suffer
from a tenuous and generally unknown relationship with reality. Fracture mapping provides a direct measurement of fracture geometry from a given treatment but cannot be used to predict what might happen under a different set of conditions. By combining direct
measurements with models, calibrated fracture models can be created with superior predictive capabilities.
4.11.1 Derivation of a 3D Net Pressure and Geometry Feedback Model. While the model that was discussed in Section 4.9.2
is simple and straightforward, two issues fracture modelers encountered in the early 2000s require that this model be slightly more
sophisticated, but more universally applicable.
The first issue is that fractures are not often radial. Direct fracture geometry measurements that proliferated in the early 2000s
show significant height confinement, attributed mostly to layer debonding at layer interfaces. There is a need to account for elliptical
fracture shapes with a length/height ratio obtained from mapping. If it is assumed that fracture mapping provides an independent way
to determine this ratio, the half-length/height aspect ratio α is defined as
α=
L
H
or α =
2 LH
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������(4.32)
H
Second, there is a requirement to incorporate the approximate impact of layer debonding. The assumption of continuous elastic
width displacement along the fracture height is not valid anymore because this width profile likely comprises discontinuities at layer
interfaces. This changes the relationship between fracture width and the pressure distribution along various rock layers across its
height, where the default width coupling coefficient 2/π is replaced for a radial fracture for a more general term γw in Eq. 4.28:
w ≈γw
pnet H
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.33)
2E
Eqs. 4.29 and 4.30 then change in the following way:
1
 3 α 2εVE  3
LH = 
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.34)
 2π γ p 
w
net
1
3
 3 εVE 
H = 2
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������(4.35)
 2π αγ w pnet 
1
3
2
 3 γ w2 εVpnet

w=
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.36)
2
 2π α E 
This simple model now incorporates two big lessons learned from calibrating with direct fracture diagnostics: fractures are more
confined than would normally be assumed on the basis of vertical layer stresses alone because vertical fracture growth causes layer
debonding and a general composite layering effect.
What is now created is a simple system of equations to determine approximate fracture dimensions from four independent measurements that can be obtained from pressure-decline analysis and knowledge about approximate fracture growth from fracture
diagnostics.
In the spreadsheet output shown in Fig. 4.29 these equations have been incorporated and tested against the results from a paper
(Stegent and Candler 2018) with microseismic data in the Wolfcamp Formation in the Permian Basin. They measured fracture
half-lengths of approximately 1,100 ft and fracture heights of 950 ft. For the typical fracture volumes in the jobs and the general net pressures, slurry efficiencies, and rock moduli that prevail in this area, it is possible to obtain match dimensions using a
width coupling coefficient of 0.07. This is significantly lower that the default value of 0.636 (2/π) applicable to pure linear elastic
deformation.
Note that this model cannot determine the extent of the shared width distribution of the fracture network. The cumulative width is
likely distributed over many multiple fractures and other fracture complexities.
4.11.2 Calibrated Power-Law Fracture Models. The equations introduced so far for fracture dimensions can be further simplified
in fracture mapping projects where good data are available to observe the sequential growth of a hydraulic fracture system. Even
without knowledge of all the actual parameters in the main fracture-dimension equations in the previous section, it could be inferred
that growth in dimensions can be expressed in terms of injected volume.
This was done in an example by Weijers et al. (2009), where they provided an extended abstract with results for microseismic mapping of fracture treatments in 5 wells and 40 stages in the Mamm Creek Field in the Piceance Basin in Garfield County, Colorado, as
well as production and reservoir analysis associated with these large-volume fracture treatments.
Hydraulic Fracture Modeling
105
Back-of-the-envelop elliptical frac model*
- Determine net fracture pressure at the end of an injection by picking ISIP and closure stress
- Determine slurry efficiency (very) approximately from the formula in the graph on the right or use Nolte’s equation based on dimensionless closure time
- Obtain calibrated length-height ratio from direct diagnostics; use width coupling coefficient to match both net pressures and length&height
- Enter information for the text in red in the INPUTS for FRAC DIMENSION box
- Obtain end-of-job fracture dimensions in OUTPUT box
INPUTS for FRAC DIMENSIONS
Volume pumped**
10,000 bbl
Slurry efficiency**
95.0 %
Net pressure**
1,000 psi
Young’s modulus
3,000,000 psi
Poisson’s ratio
0.2 Width coupling coeff.
0.07 1.7 Alpha (L/H Ratio)
OUTPUT
Half-length
Height
Cumulative width**
** end of treatment.
CALCULATIONS
Frac volume**
Opening modulus
9,500 bbl
781,250 psi
*Model Assumptions:
- Elliptical fracture growth, using length-to-height ratio from direct fracture diagnostics
- Incorporates mass balance and fracture opening
- Allows for width decoupling when entering gamma coefficient smaller than 2/pi (=0.636)
- Not a predictive tool, as efficiency and net pressures need to be measured
936 ft
1,102 ft
0.5922 in
H=2
εVE
αγ w pnet
3
2π
1
3
w=
3
2π
γ 2w εVp2net
1
3
εVE 2
Fig. 4.29—Fracture dimensions from a simple feedback model as calculated for a typical Wolfcamp fracture treatment in
the Permian Basin (Stegent and Candler 2018). Courtesy of Liberty Oilfield Services.
The thick section of lenticular sands of the Williams Fork Formation in the Piceance Basin in western Colorado requires a special
limited-entry completion strategy for optimal economic development. The Williams Fork is composed of a 2,500+ ft stacked sequence
of fluvial-channel and crevasse-splay sands interbedded with associated overbank and floodplain siltstone and shale deposits. Coals
and tongues of marine sands are also present in the lower part of Williams Fork.
Treatments require an average volume of 8,000 bbl of slickwater and 160,000 lbm of 20/40-mesh Ottawa sand. Resultant fractures
are very long, with an average half-length of 1,200 ft, ranging between 750 for the smaller treatments and 1,600 ft for the largest
treatments. Fig. 4.30 shows that there is, as normally expected for relatively simple fractures, a good correlation between the fracturetreatment volume and fracture half-length. Note that the fracture half-lengths are reported for the fracture wings that could be fully
measured, and that there is an assumption that fractures are symmetric. For purely radial fracture growth without leakoff, the fracture
radius is proportional to the volume pumped to the power 4/9. For perfectly confined fracture growth, half-length becomes proportional to the volume pumped to the power 4/5. In the log-log plot of half-length (in ft) vs. pumped volume (in bbl), the relationship
between half-length and volume is L f = 1.46V 0.74 .
Height, plotted vs. volume, also shows a good correlation between the fracture treatment volume and fracture height. In the
log-log plot of height (in ft) vs. pumped volume (in bbl), the relationship between height and volume is H f = 6.75V 0.51. Note that
the combination of the half-length and height relationships with volume do not comply with the law of conservation of mass,
possibly because half-length and height measurements are underestimated during pumping, when microseismic noise levels were
higher.
1,000
1,000
13A
24D
14D
14C
24B
Lf trendline 13A
Lf trendline 24D
Lf trendline 14D
Lf trendline 14C
Lf trendline 24B
Lf trendline all wells
100
1,000
Volume (bbl)
10,000
Height (ft)
Half-Length (ft)
4.11.3 Net-Pressure-History and Fracture Geometry Matching Example. Now consider the uncalibrated net-pressure match in
Fig. 4.31, and its associated fracture geometry prediction in the top of Fig. 4.32. The uncalibrated match shows a fracture geometry
with significant out-of-zone growth. This match was conducted using the “classical” confinement mechanism of fracture closure
stress contrast. To match the high initial net pressures during the breakdown injection, significant “tip effects” were applied. To match
the increasing net pressure throughout most of the propped-fracture treatment, it was assumed that there was increasing fracture
growth complexity. Even though the barrier/ pay zone closure stress contrast is significant, it is lower than the 2,000 psi of net pressure observed during the propped fracture treatment. Therefore, the net-pressure match using a parameterized fracture model results
in significant out-of-zone growth with fracture half-length and total fracture height of approximately 250 ft, as shown by the top
geometry in Fig. 4.32.
100
1,000
13A
24D
14D
14C
24B
Hf trendline 13A
Hf trendline 24D
Hf trendline 14D
Hf trendline 14C
Hf trendline 24B
Hf trendline all wells
Volume (bbl)
Fig. 4.30—Fracture half-length and height vs. injected volume.
10,000
106 Hydraulic Fracturing: Fundamentals and Advancements
15.00
100.0
2,500
Btm prop conc (lbm/gal)
Slurry efficiency
Slurry rate (bbl/min)
Prop conc (lbm/gal)
Observed net (psi)
Net pressure (psi)
4.000
15.00
2,500
12.00
80.0
2,000
3.200
12.00
2,000
9.00
60.0
1,500
2.400
9.00
1,500
6.00
40.0
1,000
1.600
6.00
1,000
3.00
20.0
500
0.800
3.00
500
0.00
0.0
0 150.0
250.0
350.0
450.0
0.000
0.00
650.0 0
550.0
Time (minutes)
Fig. 4.31—Observed net pressure (black) and match with model net pressure (green). The model net-pressure response
from the un-calibrated model and that from the calibrated model are almost identical. Btm = bottomhole pressure.
Prop conc = proppant concentration.
Logs : well XXI...
TVD(ft) MD(ft)
GR...
Concentration of proppant in fracture (ib/ft2)
Layer properties
Rocktype
Stress (...
Permea...
0
1
Compos...
0
200
750
500
250
0
250
500
Width profil...
750
0
TVD(ft)
Shale 1
2500
1500
2500
Observed net (psi)
Prop conc (ppg)
Net pressure (psi)
Slurry rate (bpm)
Btm prop conc (ppg)
5000
1500
2000
1200
2000
4000
1200
1500
9000
1500
3000
9000
1000
6000
1000
2000
6000
5000
3000
5000
1000
3000
00
00
001500
2500
3500
4500
5500
00
6500 00
7,500 7,500
7,500
Shale 2
Silt
Shale 4
8,000 8,000
Time (minutes)
8,000
Proppant concentration (Ib/ft2)
0
Logs : well XXI...
TVD(ft) MD(ft)
2500
5000
1500
Observed net (psi)
Net pressure (psi)
Slurry rate (bpm)
Prop conc (ppg)
Btm prop conc (ppg) Net pressure (psi)
2500
5000
1500
2000
4000
1200
2000
4000
1200
1500
3000
9000
1500
3000
9000
1000
2000
6000
1000
2000
6000
5000
1000
3000
5000
1000
3000
00
00
001500
2500
3500
4500
Time (minutes)
5500
6500
00
00
00
GR...
Stress (...
0.2
0.3
0.4
0.5
0.6
Concentration of proppant in fracture (ib/ft2)
Layer properties
Rocktype
0.1
Permea... Compos...
750
200
0
0.2 0
500
250
0
250
500
Width Profil...
750
0
TVD(ft)
Shale 1
7,500
7,500 7,500
Shale 2
8,000 8,000
Silt
Shale 4
8,000
Proppant concentration (Ib/ft2)
0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 4.32—Estimated fracture geometry for net-pressure history match using “classical” model assumptions (top) and
matching of both net-pressure history and directly observed fracture geometry using additional containment effects
such as composite layering (bottom). MD = measured depth.
Hydraulic Fracture Modeling
107
However, microseismic mapping showed an actual fracture height of only 130 ft and a fracture half-length of 700 ft—significantly
different from the uncalibrated pressure-matching result. Net-pressure history matching was performed to match the directly observed
geometry. First, it was determined that a closure stress gradient greater than 1 psi/ft was required in the shales around the pay to
obtain the observed confinement using this simulator, and this was considered unrealistic. A composite layering effect was introduced
to match the level of confinement observed. Additional confinement increased net pressures, and both the extent of tip effects and
fracture complexity had to be reduced to maintain a net-pressure match. Also, as the fracture surface area in the pay zone increased
significantly, the reservoir permeability and wall-building coefficient had to be reduced to maintain a net-pressure match of leakoff
behavior. Fig. 4.32 (bottom) shows the final fracture geometry from the calibrated model, which was obtained for an identical netpressure response in Fig. 4.31 as the previous net-pressure match.
Once a calibrated model has been obtained by matching net-pressure response and directly measured fracture dimensions, the
fracture model can then be run in predictive mode to evaluate alternative designs and the effect of the various calibration factors
assessed and optimized. In this example, production data showed that effective propped half-length was far shorter than the 700-ft
propped-hydraulic-fracture half-length, most likely because of insufficient cleanup farther away in the fracture.
4.11.4 Fracture Geometry Database. These types of calibrated model results come in many forms and can incorporate a variety
of anecdotal and more established fracture diagnostic measurements. Numerous commercial fracture mapping projects have been
conducted with the aim to determine fracture dimensions. Out of more than 1,000 mapping treatments, generally conducted with
microseismic mapping and/or downhole tilt mapping in offset wells, fracture pressure analysis and development of a calibrated model
were conducted only on a subset.
As discussed in the previous example, most direct diagnostic measurements show a much smaller fracture height than that predicted by fracture models that solely use the “classical” confinement mechanisms of fracture closure stress contrast and permeability
contrast. Weijers et al. (2005) grouped model calibration parameters for several hundred mapped fractures.
Fig. 4.33 confirms that measured fracture growth is often significantly confined in most environments. The solid black diagonal
line represents perfect radial fracture growth. On average, total fracture heights equal approximately 240 ft, with fracture half-length
of approximately 600 ft (or total fracture lengths of approximately 1,200 ft). This reflects an average fracture length/height ratio of
approximately 5 for these reservoirs.
Fig. 4.34 shows that in the process of matching both net pressure and observed fracture dimensions, the use of a higher fracture
closure stress contrast between pay and neighboring layers is not sufficient to match observed dimensions. This reflects either a
limitation in the ability to estimate closure in the layers outside the pay zone, or that there is another mechanism than just the closure
stress contrast that dominated fracture height confinement. Incorporation of parameters to account for the composite layering effect
was needed in most cases.
Further categorizing these geometry observations, de Pater (2015) captures the fracture geometry with two dimensionless numbers:
height and length normalized by gross reservoir thickness:
H N, f =
Hf
dgross
, LN , f =
Lf
dgross
. ������������������������������������������������������������������������������������������������������������������������������������������������������ (4.37)
When fracture height vs. length is plotted, he observed that there was no correlation (see Fig. 4.34). It makes more sense to look
at normalized dimensions with respect to reservoir thickness. Fig. 4.35 shows that the data points can be grouped in two classes: one
where the fracture height keeps increasing with length (e.g. Green River sandstone) and one where the fracture height is almost
constant. The latter class is mainly coal and the Canadian (shallow gas) cases.
Coal and shallow-gas cases were excluded because it is well-known that coal usually has good containment, and typically there
is an expected strong containment for depleted soft reservoirs. The mechanism in both cases might be related to T-shaped fracture
growth along the various interfaces and joints.
Measured Fracture Height (ft)
1,000
800
600
400
200
0
0
200
400
600
800
1,000
1,200
1,400
Measured Fracture Half-Length (ft)
1,600
1,800
2,000
Fig. 4.33—Measured fracture half-length vs. measured fracture height. The black solid line represents radial fracture
growth. Most of the fracture geometries for which a calibrated model was developed exhibit confined fracture height
growth.
108 Hydraulic Fracturing: Fundamentals and Advancements
Measured Length/Height Ratio
100.0
10.0
1.0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Net Pressure/Closure Stress Contrast
Fig. 4.34—Measured length/height ratio vs. net pressure/closure stress contrast ratio. As the net pressure increases
in comparison to the closure stress contrast between the pay zone and the neighboring layers, fractures are generally
expected to show more out-of-zone growth. Once the net pressure is equal to the closure stress contrast or higher, it
was expected that fractures would grow in a more radial manner. However, the data from calibrated models does not
show this behavior, indicating that there are other mechanisms that result in fracture confinement.
Grouped by: basin
102
CA
Denver
ETX
Green river coal
Green river SS
Mid-continent
OK/anadarko
Piceance
San juan coal
San juan SS
TX permian
WCSB
HN,f (-)
101
100
10–1
100
101
LN,f (-)
102
103
Fig. 4.35—Fracture height normalized by gross reservoir thickness vs. fracture length normalized by gross reservoir
thickness from diagnostics for different basins. CA: California, Denver: Rocky Mountains, ETX: East Texas, OK/Anadarko:
Oklahoma and Anadarko, Piceance: Utah and Colorado, San Juan: New Mexico, TX Permian: West Texas, WCSB: West
Canada Sedimentary Basin.
Fig. 4.36 shows the normalized height vs. length grouped by basin. The fracture geometry falls near a trendline described by the
following equation:
H N , f = 0.2 L1.09
N , f . ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.38)
This implies only a small change in aspect ratio with fracture size. There is certainly a large variation of height vs. fracture length,
but for green field fracture designs it is a good initial guess to use heights equal to approximately 20% of length for an initial fracture
geometry.
Hydraulic Fracture Modeling
109
Grouped by: basin
102
HN,f (-)
101
CA
Denver
ETX
Green river SS
Mid-continent
OK/anadarko
Piceance
San juan SS
TX permian
100
10–1
100
101
LN,f (-)
102
Fig. 4.36—Fracture height normalized by gross reservoir thickness vs. fracture length normalized by gross reservoir
thickness for North American basins. (Data set excluding coal and shallow gas). The solid line represents fractures with
a 1:1 height/length ratio; the dashed trendline of the data is represented by Eq. 4.38.
4.11.5 Case Histories. Case histories discussed here represent those undertaken by funded industry projects where a large amount of
complimentary fracture diagnostic data was collected during fracture treatments. A more detailed description about some of the more
general findings of these joint-industry projects is provided in the Fracture Diagnostics Chapter.
Case History 1 – M-Site, Piceance Basin, Colorado. A complete data set for model calibrations is available from the M-site
experiment, with extensive microfracture tests, core testing, and fracture mapping from microseismic and downhole tiltmeters
(Warpinski et al. 1996, 1997; Engler and Warpinski 1997). It is also a troubling data set because it provides a strong case for very high
net pressure. If one accepts the measured modulus of the rock samples taken, the downhole tiltmeter data confirm the measured net
pressure of approximately 1,300 psi. Some workers have tried to reduce the measured pressure (by shifting the closure, which might
be justified, see more on this in the Fracturing Pressure Analysis Chapter), but then the tiltmeter data were not matched because the
same modulus was used (Gulrajani et al. 1997). Assuming a linearly elastic formation and the validity of the elastic superposition
principle, the measurement of width and height constrains net pressure, independent of the stress on the fracture. Often, the occurrence of net pressure that is higher than predicted by conventional models can be explained by underestimation of modulus. The
correct modulus for fracture opening is the unloading modulus, and in cases where there is anelastic strain, this can be two to three
times higher than the commonly used first-load modulus from multistage triaxial tests (MSTs). However, in the case of the M-site
treatments, the discrepancy in modulus is not able to explain the high net pressure observed.
The data indicate that with higher net pressure significant height growth occurs, but this cannot be explained using the measured
stress profile. Fig. 4.37 shows the strong containment of the water injection and the upward growth of the subsequent gel injection,
which had higher pressure that induced fracture height growth early in the treatment.
The two critical problems of fracture modeling, net-pressure prediction and fracture height growth, have been tackled with
numerical fracture models that can accurately describe the physics of fracture propagation and the subtle balance between fluid
flow toward the tip of the fracture and the top and bottom of the fracture (Smith et al. 2001; Hsu et al. 2012). Older work used
either a boundary-element method or a finite-difference method based on influence functions (Clifton and Abou-Sayed 1979; Lam
et al. 1986; Barree 1983), but these methods are valid only in uniform isotropic media. The modeling of layer effects because of
anisotropy and differences in layer modulus requires a more sophisticated method such as a finite-element model (FEM) model
for the fracture opening.
Laboratory work has shown that the conventional LEFM approach for fracture propagation is invalid and that at least a cohesive
zone mechanism is necessary to obtain an accurate description of fracture propagation (van Dam and de Pater 2001). One apparent
consequence is that effective stress then needs to be considered, so that fracture propagation becomes dependent on the difference
between minimum stress and (local) pore pressure at the fracture tip. This differs from the conventional LEFM criterion. It has been
attempted by some investigators to make toughness dependent on effective stress, but that does not capture the potential effect of
pore-pressure changes.
A fully coupled model was used to simulate the fracture geometry and net pressure of a water injection and crosslinked gel injection into the B sand of the M-site experiment. Fig. 4.37 shows the simulated fracture geometry at the end of pumping compared with
the observed microseismic clouds.
110 Hydraulic Fracturing: Fundamentals and Advancements
GR
20
Stress (psi)
200 2,000
5,000
100
0
300
200
400
4,400
X-link fracture
TVD
(ft)
4,500
4,600
Proppant screenout
Water injection
Fig. 4.37—Comparison of fracture geometry with microseismic clouds for M-site B-sand Injections 3 and 7.
The water injection was readily matched by adjusting the effective permeability of the formation and the tip pore pressure. Because
the net pressure was lower than predicted by the code when pore pressure was at virgin level, the pore pressure had to be increased by
800 psi to match observed net pressure. The containment could be matched without modifying any parameters.
The crosslinked gel injection was growing upward after approximately 15 minutes of pumping. The higher net pressure during the
crosslinked gel injection could not explain the height growth. So, it was assumed that the tip pore pressure was increased in the shale
by 1,300 psi over time, which yielded the correct amount of height growth at the end of the treatment, as shown in Fig. 4.37.
A few microseismic events at a large distance from the well were ignored in the match. Often, a few events can be seen during
treatments that are far from the dominant cloud. It is uncertain what causes such shear events, but it could be because of stringers and
fluid leakoff or perhaps the result of stress changes on supercritical faults or simply because of poor location accuracy. Both fracture
geometry and net pressure were able to be matched in these simulations (Fig. 4.38).
For default settings, the fracture would be contained as shown in the left picture of Fig. 4.39. The right picture shows height growth
that matched the microseismic data; but in this case the match was obtained by incorporating a higher pore pressure at the tip of the
fracture in the top layer.
The same comparison can be made for a parameterized 3D model that yielded significant height growth at top and bottom with
default settings; see the left picture in Fig. 4.40. The right picture shows the matched geometry, which in this case was obtained by
modeling delamination that is assumed to yield a higher tip pressure for propagation, which then can explain more containment in
some layers.
So, the parameterized 3D model yielded too little height containment with default settings, whereas the fully gridded model with
cohesive zone yielded too much containment. The parameterized 3D model is unique because of a sophisticated tip model, but in
general the gridded models yield much more containment than predicted with equilibrium height models. Qualitatively, this containment effect predicted by gridded models agrees with field observations of height growth. However, the M-site data show that neither
approach can be trusted to give an adequate prediction without calibrating for differences in measured fracture height growth. The
observed strong containment can be easily incorporated in the default settings of the parameterized 3D model to obtain a practical
calibration of the predicted geometry. However, it is more difficult to change default settings in a fully gridded model because the
160
140
1,600
400
Hf (ft)
350
Lf (ft)
1,400
120
300
1,200
100
250
1,000
80
Hf
60
Hf-sim
40
200
150
Water
X-Link
800
Pnet
Lf-sim
600
Pnet-Sim
200
50
0
Lf
400
100
20
Pnet (psi)
0
0
Water
X-Link
Water
X-Link
Fig. 4.38—Comparison of observed and simulated fracture height, length, and net pressure for M-site B-sand
Injections 3 (water) and 7 (X-link).
Hydraulic Fracture Modeling
4,500
4,440
4,450
4,500
4,400
4,000
4,000
4,450
3,500
4,500
3,500
4,500
3,000
3,000
4,550
4,550
2,500
4,600
2,000
4,650
1,500
4,700
1,000
4,750
500
4,800
0
50
100
150
200 250
X (ft)
300
350
400
450
0
Depth (ft)
Depth (ft)
111
2,500
4,600
2,000
4,650
1,500
4,700
1,000
4,750
500
4,800
0
50
100
150
200 250
X (ft)
300
350
400
450
0
Fig. 4.39—Fracture height simulated with full 3D FEM fracture model for M-site 7B injection with default stress and tip
pressure (left) and matched geometry using modified tip pressure (right). Color indicates effective stress on the fracture
plane.
Layer properties
Rockt...
Shale
Sandst...
Shale
Stress...
Modul...
Layer properties
Concentration of proppant in fracture (lb/ft²)
Perme... TVD(ft)
0
0.1
50
100
150
200
250
300
350
400
450
500
Rockt...
Shale
4,300
Sandst...
Shale
4,400
Sandst...
Stress...
Modul...
Concentration of proppant in fracture (lb/ft²)
Perme... TVD(ft)
0
0.1
50
100
150
200
250
300
350
400
450
500
4,300
4,400
Sandst...
4,500
4,500
4,600
4,600
4,700
Proppant concentration (lb/ft²)
4,700
Shale
Proppant concentration (lb/ft²)
Shale
0
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.0
0
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.0
Fig. 4.40—Fracture height simulated with parameterized 3D fracture model for M-site 7B injection with default stress and
tip pressure (left) and matched geometry using composite layer effect which modifies the tip pressure (right).
whole philosophy behind these models is that only independently measured, physical inputs should be used. This example of the interpretation of the M-site matching highlights some of the differences between the approaches of using a simplified or a more-detailed
gridded model.
Case History 2—East Texas Cotton Valley (Mayerhofer et al. 2000). The Cotton Valley is a tight gas reservoir with highly
laminated sandstone/shale/lime sequences. The entire Cotton Valley is fractured in multiple stages from vertical wells. This example evaluates the uppermost stage in the Upper Cotton Valley. Well CGU 21-10 was fractured in three stages with 25 lbm/Mgal
crosslinked gel, and a 1- to 5-lbm/gal proppant ramp. Stage 3 used 250,000 gals of crosslinked gel with 504,000 lbm of 20/40 sand
pumped at 45 bbl/min.
Fig. 4.41 shows the stress profile as determined from stress tests and minifracture injection tests. A total of four stress tests were
performed in shale and limestone intervals throughout the Cotton Valley sequence. Shale and limestone closure stresses were determined from the decline of small-volume water injections (1 to 10 bbl). Sandstone stresses were estimated from the minifracture
falloffs. The stress tests showed no significant stress contrasts through the Upper Cotton Valley and provided unique anchor points
for fracture geometry calibration.
Modeling performed before microseismic mapping (Fig. 4.42) indicated that fractures would probably grow in a radial fashion.
Based on the small stress contrasts and net-pressure history, one approach that was taken was to match the level of the net pressure
assuming that excess net pressure was because of fracture complexity effects. Much like Case History 1, if this approach is assumed
this would result in short and unconfined fracture growth. However, the microseismic mapping showed that the fracture was much
longer and much more confined than the initial fracture model evaluation, indicating that this approach was incorrect.
Mechanisms other than fracture closure stress contrast between layers must have caused the observed confinement. Because the
zones consist of highly laminated shale/sand sequences, it was postulated on the basis of microseismic mapping, that a composite
layering effect could inhibit fracture height growth. The subsequent match assumed that, to calibrate the modeling composite, layer
effects would need to be used in the bounding layers. The new matching approach now matched both the net-pressure history and
112 Hydraulic Fracturing: Fundamentals and Advancements
Stress profile
8,300
CGU 22-9 Stress tests
8,500
Minifracture
Stress test
Bodcaw/Vaughn sands 0.55 psi/ft
8,700
Davis shale/Sands 0.57 psi/ft
8,900
Bolinger/Justice/E-sands 0.57 psi/ft
Depth (ft)
9,100
Roseberry/Ardis sands 0.61 psi/ft
9,300
Sexton shale 0.68 psi/ft
C-lime 0.82 psi/ft
9,500
Taylor sand 0.58 psi/ft
9,700
Bossier shale 0.91 psi/ft
9,900
10,100
Permeability
Low
High
10,300
4,000 5,500 7,000 8,500 10,000 1,000 750
500
250
Closure Stress (psi)
Propped Length (ft)
0
250
500
750 1,000
Hydraulic Length (ft)
Fig. 4.41—Stress test in Cotton Valley sandstones and surrounding layers indicate only small stress contrasts. The
fracture treatment was conducted in the Bodcaw/Vaughn Interval.
North (ft)
400
0
–400
–1,200 –800
–400
0
East (ft)
400
800
1,200
–8,400
Fracture model prediction
Depth (ft)
–8,800
–9,200
–9,600
–10,000
–1,200
Calibrated fracture model matches
microseismic mapping results
–800
–400
0
East (ft)
400
800
1,200
Fig. 4.42—Blue ellipse shows fracture geometry inferred from net-pressure match without calibration with direct fracture
diagnostic data for a project in the Cotton Valley Sandstone. Actual fracture growth was measured using microseismic
fracture mapping, showing more confined height growth than the model prediction. Net-pressure data were rematched
to both net-pressure response and actual fracture geometry.
microseismic mapping results. This treatment did also show some fracture asymmetry, which cannot be modeled using this simulator,
so the fracture was shifted to match the total fracture length.
This example demonstrates that fracture modeling using pressure calibration alone can be nonunique because different parameters
might be used to calibrate to these pressure measurements. It is interesting to note that though the net-pressure matches were virtually identical, they resulted in vastly different geometry predictions. This underscores that incorporating fracture geometry data in the
model calibration process is of great importance to obtain a more unique and useful solution.
Hydraulic Fracture Modeling
113
4.12 Complex Fracture Models
4.12.1 Discrete Fracture and Distinct Element Models. Introduction. Fracture geometry is the basic paradigm for fracture modeling. As is often the case in engineering, the paradigm of planar fracture was chosen more for convenience than for an accurate
description of fractures in geological formations. It is true that under ideal conditions fractures can grow like razor sharp planar
discontinuities, but in outcrops fractures appear often as rough, branched systems. In applications such as like geothermal HDR
reservoirs and shale gas formations, it might be essential to describe the fracture systems honoring the true complexity (Dershowitz
1999; Fu et al. 2013; Gan and Elsworth 2016; Sarmadivaeh 2012). Two main sources of complexity are interaction with natural fractures and with laminations (Saffer et al. 1984; Warpinski and Teufel 1987). When a fracture crosses an existing discontinuity, it might
branch because it follows the discontinuity, and then continues in the preferred plane with an offset. In stimulation of conventional
reservoirs, this is seen as a disadvantage because the offsets create obstructions to proppant transport. In shale gas stimulation and
geothermal EGS, fracture branching has the advantage of creating more productive surface area so that the connection between the
well and the reservoir is multiplied by several orders of magnitude.
Predicting fracture geometry has always been an issue because fracture height, length, and width were poorly known even for
single fractures. Fracture mapping has improved insights into fracture height which led to development of calibrated models. That
was an improvement compared with fracture modeling practice where fracture, height estimates were a matter of engineering judgment. The advent of fracture network models means that again engineering judgment is required for height estimation because a
full-3D fracture network model is currently too complex for simulations. Fracture mapping can still be used to guide the height
estimate that is needed, but with fracture network models it is much more difficult to correctly assess height and width of the
various branches.
Modeling of multiple fractures started in the 1980s for near-wellbore fracture complexity but is now much more relevant for
modeling shale gas stimulation and interaction between nearby stages (Lecampion et al. 2015). Indeed, near wellbore effects and
particularly fracture initiation are increasingly seen as necessary areas to investigate to improve shale fracture effectiveness.
In engineering geology, it has always been important to model a rock mass with the relevant fracture sets because at shallow depth
the deformation and fluid flow of rock masses is typically governed by the fractures. So, modeling techniques were developed for those
applications, such as UDEC, Universal Distinct Element Code, and PFC, Particle Flow Code (Cundall and Strack 1971). These techniques attempt to model accurately the fracture opening and propagation based on simple fracture mechanics. An alternative approach
has been followed by researchers who started from the geological complexity of rock formations and then applied simple relations to
model the mechanics of fracture opening and fluid flow in a fracture network, as shown in Fig. 4.43 (Dershowitz and Fidelibus 1999).
Hydraulic fracture modeling has been dominated by the first approach, but giving precedence to geological reality as happens in the
latter approach might be preferred for some applications because correctly represented geological complexity is sometimes a necessity to obtain an accurate estimate of fracture system flow behavior.
For simplicity’s sake, the discrete-fracture-network (DFNs) models typically use a simple rectangular grid: a so-called wire mesh
(Xu et al. 2010). This is often considered good enough to represent and characterize the flow behavior of the system, and their virtue
is that only a few parameters, such as spacing and conductivity, need to be calibrated with observed data such as fracture mapping,
treatment records, and well tests.
Theory. Fluid flow in discrete fracture sets has been approached in two ways: starting from a solid that is then crossed by a set of
fractures or with blocks that are connected by joints that represent the fracture system. The latter approach was chosen for modeling
jointed rock masses, while the former approach has been preferred for hydraulic fracturing because it is based on boundary element
techniques (BEM) that have been popular for modeling hydraulic fractures (Li 2015; Ricois 2017; Wang et al. 2018; Wu 2014; Zhang
et al. 2018; Zhou 2017). BEM models provide accurate solutions for fracture opening and propagation while reducing the dimensionality of a problem that gives efficient codes. Although modeling multiple fractures is feasible, it is difficult to model the entire evolution of a fracture system, including the branching that occurs by interaction with existing joints. However, it is possible to define the
A: (1m,-1m,-1m)
B: (-1m,1m,1m)
+z
B
F9
–x
–y
F16
+y
+x
–z
F8
A
Fig. 4.43—DFN fracture system with many fractures occupying a cubic meter of rock (Dershowitz and Fidelibus 1999).
114 Hydraulic Fracturing: Fundamentals and Advancements
Hk
Trace j
Trace 1
ure K
Fract
Trace i
interaction such that the result resembles observed geological fracture systems, but that is equivalent to constraining
the problem by defining the fracture system at the very start.
The mechanical equilibrium is computed in different
ways in the different methods, but the fluid-flow simulation is similar in the different methods because the flow in a
fracture network is simplified to flow in a connected set of
channels.
Constitutive Equations and Required Inputs. Flow is
described for fracture segments such as these shown in
Fig. 4.44 with
∂p
1 q
= −µ 3
. ������������������������������������������������������(4.39)
∂x
w Hh
Fracture J
Fig. 4.44—Fracture connections in a DFN (Dershowitz and
Fidelibus 1999).
Eq. 4.39 is the equation for Newtonian fluids such as water,
which can be generalized for power-law fluids (Nolte
1988b).
The mass balance is given by continuity:
∂q ∂ H h w
+ q = 0. ������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.40)
+
∂x
∂t
The global mass balance is obtained by integrating this over time and the fracture network, using the connections as shown in
Fig. 4.44 that are applied for a fracture network shown in Fig. 4.43:
∫ Q dt = ∫ Hw d x + ∫ ∫ q dt d x. ������������������������������������������������������������������������������������������������������������������������������������������������(4.41)
t
L
L t

The stress induced by fracture opening can be efficiently computed using influence functions as is commonly done for fractures
described with a set of dislocations:
N
N
j =1
j =1
σ i = ∑ Cijnsγ j + ∑ Cijnnδ j . ������������������������������������������������������������������������������������������������������������������������������������������������������������(4.42)
The influence functions Cns and Cnn are singular, so that when fractures cross, the discretization must be adapted to avoid the singularity (McClure and Horne 2014).
In discrete-element-model (DEM) systems the forces between contacting particles or blocks are computed so that equilibrium can
be obtained. In some cases, the full equation of motion with inertial forces is solved, which is a convenient way to reach equilibrium
after several pseudo-time steps. However, it is more efficient to use directly the static contact forces and iterate toward equilibrium
using the deviation from static equilibrium to obtain new particle positions (Baars 1996).
Discrete-element-simulations use the same flow equations, although the channel network is determined by the pore system between
the particles.
The fluid-flow calculations are performed with an explicit scheme. The flow equation for a contact is
∆p
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.43)
rb1 + rb 2
qc = k f
The pressure change itself is obtained with
n
n
δ p = K f ∆t ∑ qc, i = K f ∆t ∑ k f , i
i =1
i =1
∆pi
( rb1 + rb 2 )i
. ��������������������������������������������������������������������������������������������������������������������������������(4.44)
For pipe flow, the following relation between flow rate and pressure difference is
qpipe =
π D 4 ∆p
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.45)
128 µ 
where D is the pipe diameter,  its length, and μ is the fluid viscosity. Because domain volume is proportional to the pore diameter
cubed, the result is for the flow rate divided by domain volume
qpipe
Vdom
∝
D ∆p
. ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.46)
µ 
Hydraulic Fracture Modeling
115
The pressure change would be
δ p = Kf
∆V K f ∆t n Di
=
∑ ∆pi . ��������������������������������������������������������������������������������������������������������������������������������������������������(4.47)
V
µ i =1  i
The mechanics is based on the forces between the particles, for which Newton’s law is solved.
∑ F = mx
x
contacts
∑ F = my. ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.48)
y
contacts
∑ M = Iφ
contacts
Using a time-stepping algorithm, the positions can be updated from the excess forces, until equilibrium is obtained.
If only static equilibrium is desired, without inertial effects, a more direct approach is to use Newton’s first law:
δ ∑ Fx = 0
contacts
δ ∑ Fy = 0 . ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.49)
contacts
δ ∑ M =0
contacts
Eqs. 4.48 and 4.49 can be solved to obtain the new particle positions, using the forces exerted by nearby particles. Since
all particles will be coupled by their inter-particle forces, this procedure needs to be performed a few times to achieve
equilibrium.
Although the equations for flow and particle contact appear to be based on first principles, the coefficients are empirical in nature.
The contact force can be based on Hertz-Mindlin contact theory, but in practical applications often a linear spring is used. For the
shear forces, a spring is used in combination with Mohr-Coulomb friction.
Applications. Laboratory Tests. Interaction of hydraulic fracture with pre-existing fractures (simulating natural fractures)
has been investigated in scaled laboratory tests (de Pater and
Beugelsdijk 2005); see Fig. 4.45. At low flow rate (and low pressure), the fluid flowed into the natural fractures, while at high
rate a dominant hydraulic fracture was propagated that mostly
crossed the natural fractures. This could be modeled with a DEM
simulation where disc-like particles were bonded into a rock
mass; natural fractures were simulated by breaking the bonds
along the fractures; see Fig. 4.46. The experimental data were
matched by the simulation that showed less interaction with natural fractures at higher pressure (Fig. 4.47), which is important
for mitigating near-wellbore tortuosity (Weijers et al. 2002). It
is remarkable that the opposite conclusion would be reached for
very hard rock where the fluid can only enter the existing joints.
In that case, higher pressure induces a more tortuous fracture
because at high pressure any joint can be opened, irrespective of
orientation. So, for relatively weak rocks, it is essential that the
simulation allows the creation of new fractures to obtain a match
with the experiment.
High-flow Rate-test
Borehole
Low-flow Rate-test
Borehole
Fig. 4.45—The flow from a fracture, K, is computed from
the head, HK and conductivity of the conduits between the
traces that define the fracture connections.
Fracture Network Models. In large-scale fracture simulations, these ideas have been applied with BEM simulations where assemblies
of hydraulic fractures and joints are modeled. The arrest or crossing of hydraulic fractures by natural fractures is represented in these
models, as well as initiation of new fractures; see Fig. 4.48.
With these DFN simulations, the effect of fluid viscosity can be adequately simulated; see Fig. 4.49. Although the effect of fluid
type can be represented to match observed microseismic clouds, it is unclear whether the simulations can also predict productivity of
a fracture system for different stresses. It is observed that almost isotropic stress in the horizontal plane yields a very wide fracture
system, like in the Barnett Shale while larger horizontal stress bias yields much narrower fracture systems, like in the Marcellus. However, larger stress difference will give more fracture roughness (van Dam 1999), which compensates for a narrower fracture system
because the induced fractures will retain higher conductivity. To make productivity forecasts more reliable, it will be necessary to link
the fracture network simulation not only to the observed MS cloud (obtained during pumping), but also to the residual aperture of the
fracture system during production.
Field Case Studies. Most shale stimulation work is done with minimal fracture engineering effort, but some operators have applied
DFNs in designing stimulations. It is of course essential to gather a large quantity of data on the natural-fracture systems that interact
with hydraulic fractures. First, geologic characterization work is needed to determine the parameters that describe natural fractures,
116 Hydraulic Fracturing: Fundamentals and Advancements
Cracks
0.15
0.1
y (m)
0.05
0
–0.05
–0.1
–0.15
–0.15
–0.1
–0.05
0
0.05
0.1
0.15
x (m)
Fig. 4.46—Fracture simulation with DEM. The joints were made by breaking bonds (black). At low rate the fluid flowed
into the joints (blue), while new fractures were propagated (green) that yielded a dominant fracture connected with the
wellbore at high rate and high pressures.
Cracks
0.15
Ball pressure
Ball pressure
x 107
0.1
2.5
5
2
4
0
0
–0.05
0
–0.05
–0.05
–0.1
–0.05
–0.15
–0.15 –0.1 –0.05
0
x (m)
0.05
0.1
0
x (m)
0.05
y
(m)
3
0
1.5
2
1
1
0.5
–0.05
0
x (m)
0.05
y (m)
y (m)
0.05
0.05
0.05
0
–0.05
0.15
Fig. 4.47—Fracture simulation with DEM. The joints were made by breaking bonds (black, left picture). At low rate, the
fluid flowed into the joints (right picture), while at high rate and high pressure, new fractures were propagated (middle)
that yielded a dominant fracture connected with the wellbore.
Hydraulic fracture
Natural fracture
σh
σH
Fig. 4.48—Interaction of hydraulic fractures pumped from a horizontal well with natural fractures as modeled with DFN
simulation (Weng et al. 2011).
Hydraulic Fracture Modeling
117
a
b
Fig. 4.49—DFN simulation using crosslinked fluid (top) and water (bottom) showed quite different geometry, which
agreed with microseismic observations (Weng et al. 2014).
specifically length, spacing, and conductivity. Microseismic mapping is an important tool to determine the geometry of the fracture
stages along a lateral; see Fig. 4.50. Given the calibrated model, the pore-pressure effect can be simulated, which determines the
background stress for subsequent infill wells. Also, fracture hits from other wells might be mitigated. However, it is seen in Fig. 4.50
that even with a calibrated model, it is hard to match the microseismic event cloud with a DFN, and extensive engineering judgment
is needed to obtain a match. Some of the microseismic events might only represent the stress front ahead of the hydraulic fracture tip
or fractures that are propagated during stimulation, but that closes during pressure fall-off and production.
For conventional stimulation, the calibration workflow is rather straightforward because only fracture height growth needs to be
matched. In DFN models, there are many parameters that must be calibrated. If microseismic surveys are available on most of the
stimulations, there is hardly a need for calibration because the observed fracture geometry can be used. However, if only a small number of treatments is surveyed, the natural-fracture network can be assumed fixed, which is often an invalid assumption. Alternatively,
the parameters of the natural-fracture network are modified in the match of treatment data, which is by nature nonunique.
Published field studies of shale stimulation show a complete integration of formation characterization, DFN modeling and observations such as microseismic mapping, and treatment and production data (Ejofodomi et al. 2015). If the most important conclusion
from such modeling work is that placing more sand makes better wells, it is hard to justify the effort because much simpler analysis
will yield the same conclusion (Ely et al. 2019; Weijers et al. 2019).
Perhaps it will become feasible to calibrate DFN models on readily available log measurements because it would then become possible to forecast the fracture geometry for future wells at least after drilling. However, in view of the tight spacing, large fracture size,
and strong heterogeneity of shale formations (based on log data along the laterals), it is unlikely that a reliable prediction of fracture
size for each stage can be made.
Detailed shale stimulation studies with DFN simulations could be useful for characterizing the formations, but it appears more
productive to develop much simpler modeling techniques that can be used for designing routine well stimulations. Fracture network
simulations such as those shown in Fig. 4.51 helps to optimize the number of clusters because more clusters gives better drainage,
but the individual length of fracture stages will be hard to predict, which is important for avoiding fracture hits if the fractures cover a
118 Hydraulic Fracturing: Fundamentals and Advancements
H-1 History match pressure distribution
H1
H12 H5 H6 H7 H8 H9
Geomechanical modeling
H1
H5
–4,700 psi
–6,000 psi
–2,500 psi
Pi–7,500 psi
–8,000 psi
Pore pressure
Shmin
Fig. 4.50—DFN simulation matched to microseismic observations (left) which was used to predict pore-pressure
depletion (middle) and stress (right) so that infill well treatments can be optimized (Lorwongngam et al. 2019).
Number of clusters = 294, slickwater
30 years
Bigger drainage area/volume => more EUR
30 years
Number of clusters = 98, crosslinked-gel
30 years
Less drainage area/volume => less EUR
30 years
Bigger drainage area
Fig. 4.51—Example of different DFN simulation results for increased number of clusters and slickwater (left) vs. designs
with less clusters and viscous gel (Xiong et al. 2019).
larger area. For instance, in a detailed study of fracture hits (Lorwongngam et al. 2019) it was feasible to arrive at general guidelines
for mitigating future fracture hits, which gives a valuable contribution to the project. However, it would be necessary to conduct
real-time fracture mapping to avoid fracture hits in all cases. Perhaps, low-cost surveying methods such as electromagnetic fracture
mapping (Hickey et al. 2019) might be able to provide real-time data of the extent of the fracture system (Hickey et al. 2019), but that
is still an immature technology that will be difficult to apply in many cases.
Conclusions.
• Progress in simulation of multiple fracture systems has delivered useful tools that can be applied in cases where a full suite of
data is obtained.
Hydraulic Fracture Modeling
119
• For a range of rock properties, the creation of fracture networks can be predicted: in case multiple fractures should be avoided
for conventional reservoir stimulation and in reservoirs where a fracture network is necessary for achieving sufficient surface
area of the fracture system.
• DFN models contain many parameters that need to be calibrated on the basis of full reservoir characterization and microseismic mapping and treatment records. Given the large number of input parameters, it is impossible to make reliable, detailed
predictions of fracture geometry in offset wells. At best, an average fracture geometry can be obtained from model calibration.
4.12.2 Nonplanar Fracture Models.
Introduction. Because fractures grow perpendicular to the least principal stress, most hydraulic fractures can be approximated as
planar. However, if a fracture approaches an area with a higher pore pressure that created a large fracture stress nonuniformity, it can
become important because the fracture curves and grows toward areas of larger pore pressure, though at a slower growth rate. Also, at
small scale, near-wellbore fractures will be nonplanar because of the stress concentration at the wellbore and the effect of perforations.
Fracture curvature has been studied for large-scale injection-induced stress and near-wellbore geometry (Weijers 1995; Minner
et al. 2002).
Recently, interest in fracture curvature and interaction has been raised because of very tight well and fracture spacing in shale
reservoirs, so that fractures might grow toward fractures propagated from nearby wells, especially if depletion has occurred and
fracture paths might be influenced by nearby stages (Lecampion et al. 2015).
Theory. Interaction of multiple fractures can be simulated by computing the stress fields induced by the fractures, which are summed
to obtain the stress at each fracture tip. The propagation rate and orientation of fracture extension can be computed with various criteria such as strain energy density and maximum tangential stress. For elastic simulations in uniform media, it is efficient to use the
BEM, while for layered media finite element analysis (FEA) is preferred. Recently, FEA has become more suitable for curved fracture
problems by so-called extended FEA, which introduces additional degrees of freedom that describe the fracture aperture in an element
(Remij et al. 2015, 2018). Some local re-meshing might still be required, but this is much easier compared with the full remeshing that
used to be required with conventional FEA for each subsequent fracture propagation increment.
By contrast, BEM meshing has the virtue that the dimensionality of the problem is reduced, so that for modeling 2D fractures the
mesh consists of a series of dislocation elements along the fracture path. In 3D models, the fracture elements are planar trapezoidal
elements that are connected to form the fracture plane. Especially in 2D modeling, the fracture propagation is easily accomplished by
adding additional elements at the fracture tips, in the direction that is obtained from the computed tip stress.
In view of the singular nature of the influence functions used for the dislocation stress, it is a problem to describe fracture crossing.
That problem is solved by empirical crossing or arrest functions that are matched to physical observations (Gu et al. 2012). Details of
the mathematical formulation of the BEM can be found in Oliveira (1992) and Crouch et al. (1983).
Modeling Laboratory Tests. Near-wellbore fracture tortuosity has been studied extensively with model tests and numerical simulations (Oliveira 1992; Weijers 1995; van de Ketterij 2001). The best mechanism for explaining severe near-wellbore friction pressure is
provided by multiple fracture interaction. This has been modeled in two dimensions with a set of fractures that initiate from a wellbore
that is inclined with respect to the principal stress; see Fig. 4.52. The fractures on the outside of the perforated interval might be free
to grow but might be poorly connected to the well. Fractures in the middle of the perforated interval will be squeezed and attain only
a small width so that the pressure drop is high, and proppant can easily screen out in these fractures.
One way to mitigate tortuosity is to aim for link-up of the fractures that propagate from each perforation. This can be modeled
in three dimensions as shown in Fig. 4.53 for a high stress bias. The individual fractures just continue to grow in the direction of
initiation without much reorientation.
If the stress bias is smaller and the perforations are put in the same plane, the fractures have a good chance to link up; see
Fig. 4.54.
Lf,max = 0.25 cm
1.5 cm
3.0 cm
5.0 cm
6.5 cm
A
σ h,min =
9.7 MPa
α = 45°
B
C
σ h,min = 19.4 MPa
5 cm
Fig. 4.52—Interaction of three fractures initiated from a wellbore that is inclined with respect to the stress field. Fracture
tip A is free to grow, while fracture tips B and C are arrested by interaction with neighboring fractures. This mechanism
explains reduced width at the wellbore, causing high entrance pressure and screenouts.
120 Hydraulic Fracturing: Fundamentals and Advancements
θ = 90°
θ = 0°
Fig. 4.53—At high horizontal stress, contrast fractures
initiate from the base of perforations with little tendency for
link-up (van de Ketterij 2001).
Field Case Studies. In the section on coupled models, simulations were described that applied the curved fracture modeling to field cases where the stress was changed by water
injection (Minner et al. 2002). Recently, most interest in
fracture reorientation came from fracturing shale reservoirs,
where the fracture stages are propagating with a tight spacing
between stages and very close to neighboring wells.
So-called stress shadowing where the stress field from one
stage influences the background stress of a nearby fracture
stage is quite rare in conventional reservoirs. The spacing
of fractures must be smaller than the smallest dimension
(usually the height) to get a significant stress effect. In conventional reservoirs the spacing is normally larger than the
fracture height, giving only a small stress effect. With more
than 40 stages per lateral in tight/shale formations, there is
a bigger stress shadow effect that might harm coverage of
the drainage area targeted by the wells. Another effect might
be because of the common use of multiple perforation clusters per stage. Fig. 4.55 shows a simulation with single and
multiple clusters (Lecampion et al. 2015). Single clusters
yield good coverage of the reservoir, while multiple clusters show a tendency for asymmetric fracture growth. Modeling this effect is useful because the asymmetric fracture
growth should be mitigated (for instance with high wellbore
pressure) so that a better coverage of the drainage area is
obtained.
Conclusions.
• Realistically modeling multiple fracture interactions is
best achieved in two dimensions with the BEM. For
problems that are essentially 3D, it is feasible to use
BEM, but the complexity of such simulations means
that it is currently a tool for research, rather than practical applications.
• Alternative methods such as extended FEA, while still
under development, could become useful tools in the
future.
4.13 Fully Coupled Geomechanical
Fracture Models
Fig. 4.54—With lower stress contrast and zero-phased
perforations fractures can link up nearby perforations (van
de Ketterij 2001).
4.13.1 Introduction. Traditionally, geomechanical modeling has been used by geotechnical specialists for evaluating
subsidence, borehole stability, sand failure, and waterflood
fracturing. More recently, geomechanical models have also
been used to integrate reservoir monitoring with reservoir
simulation. Preferably, monitoring data such as seismic surveys and microseismicity should be used to obtain reservoir
data. However, that is rarely feasible and the best that can
Fig. 4.55—Different fracture lengths because of stress interaction for one fracture per stage (left) or four fractures per
stage (right) (Lecampion et al. 2015).
Hydraulic Fracture Modeling
121
be hoped for is forward modeling where predictions from a reservoir model can be fitted to the observations. So, if a forward geomechanical model is available as a platform for interpreting and integrating all monitoring data, the model should also have the
potential to be used for fracture design optimization and evaluation.
Fully coupled modeling has been applied in waterflood fracturing, gas injection, and steamflooding. These models also have
potential for fracture stimulation. However, it is an open question whether the industry can make the effort to apply coupled models,
since it is labor intensive and requires specialist knowledge of geomechanics on the micro and the macro scale. Although in principle
all reservoir processes are coupled, it might be sufficient to include only a subset of the coupling parameters. Moreover, using only
limited coupling will be more practical in many cases compared with full coupling. For instance, coupling of a fractured well to the
reservoir is now routinely done with explicit fractures in 3D simulation models, but ignoring detailed stress changes. Stress evolution by depletion might be a necessary component to include because depletion tends to give a strong stress effect, and this has a big
influence on fracture geometry. The stress change caused by depletion can deviate significantly from simple 1D assumptions, so it is
then beneficial to make an accurate stress evaluation that considers geometry, rock properties, and pressure distribution. The so-called
coupled simulations incorporate at least a stress simulation with a flow simulation, either during fracture propagation or depletion of
the reservoir. Different levels of coupling can be applied: The simplest way is to couple pressure to stress and displacements, but full
coupling of flow properties (transmissibility) with stress and its impact on flow and pressure can also be performed. Because fracture
propagation yields a huge change in reservoir transmissibility, it is necessary to use full coupling for fracture propagation simulation
when reservoir stress changes are important. This has been performed for poro-elastic and thermoelastic stress during water injections, but might also be necessary in cases where natural fractures dominate hydraulic fracture propagation and production, as studies
by Settari et al. (2009) have shown.
Theory. Compared with a simple geomechanical model that underlies propped-fracture simulation, a coupled model introduces
additional parameters that relate the pore pressure and temperature to stress and relate that stress to fluid content.
In porous rocks, deformation is coupled to pore pressure and, conversely, pressure and flow are coupled to deformation and stress.
Deformation of the rock is computed in the usual way from Newton’s first law, expressed as the equilibrium equations. Pore pressure appears in the equilibrium equations because the gradient of the pressure emanates as a body force on the rock. Looking at a
small scale with an almost uniform pressure, this body force can be neglected. However, with large gradients it becomes important
to consider the coupling force.
The field equations for fluid transport, derived from the mass balances for fluid and solid and Darcy’s law, can be solved for the
pressure and fluid content. The coupling with deformation is obvious but, in most cases, this will contribute little to the pressure field.
Much more significant is the stress dependence of permeability. In tight reservoirs, because of the fracture stimulation of the wells, it
might be important to relate and contrast the behavior of the reservoir during injection, at high injection pressure, with the behavior
during production when the pore pressure is reduced or “drawn down” around the well.
Constitutive Equations and Required Inputs. The constitutive equation for elastic material gives strain ε in terms of stress σ :
ε ij =
ν
1+ν
σ ij − σ kkδ ij . ��������������������������������������������������������������������������������������������������������������������������������������������������������������(4.50)
E
E
Eq. 4.49 can be used for rock, but it has been found that pore pressure is essential for explaining initial rock behavior because a large
part of the overburden load is carried by the fluid pressure. Effective stress governs rock behavior, but it is a different failure compared
with the theory of linear elasticity. Failure in tensile or shear mode depends on the difference between total stress and pore pressure
because it depends on the equilibrium of total load with pore-pressure load in microfractures. For linear elastic behavior, effective
stress depends on the response of the rock skeleton and the rock grains to pore pressure, as follows from elastic superposition. Effective stress is therefore given by the difference between total stress and pore pressure multiplied by Biot’s coefficient, to compensate
for pore pressure effects:
σ ij′ = σ ij − α B pδ ij . ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.51)
With this effective stress, the poro-elastic Hooke’s law can be obtained:
ε ij =
ν
1 + νb
σ ij′ − b σ kk′ δ ij . ������������������������������������������������������������������������������������������������������������������������������������������������������������(4.52)
Eb
Eb
In the original formulation of poro-elasticity theory, the inverse of the storage coefficient was introduced as the Biot modulus.
Another coefficient was also introduced that relates the pore-pressure change with change of stress for undrained behavior, the
so-called Skempton coefficient B.
So, the coupling of pore pressure with deformation introduces three additional parameters: the Biot coefficient, αB, the Skempton
coefficient B, and Biot modulus M. Alternatively, other coefficients can also be defined in the attempt to understand the effect of stress
and strain for the rock, such as the undrained bulk modulus.
The additional coefficients can be expressed in terms of derivatives that can be experimentally measured and properties of the
rock’s constituents. For instance, the Biot coefficient is given by the change of pore volume with volume change:
αB =
∆Vp
∆V
≈1−
Kb
. ��������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.53)
Kg
122 Hydraulic Fracturing: Fundamentals and Advancements
The Skempton coefficient is obtained from the change in pore pressure with average stress:
1
1
+
cb + cg
Kb K g
∆p
B=
≈
=
. ������������������������������������������������������������������������������������������������(4.54)
∆σ φ  c f − cg  +  cb − cg 
 1
1   1
1 
−
φ
−
+

 K f K g   Kb K g 
The Biot modulus gives the change in fluid content ζ with pressure at constant volume:
1
α B2
∂ζ
=S=
= φ c f + (α B − φ ) cs =
. ����������������������������������������������������������������������������������������������������������������������������(4.55)
∂p ε
M
Ku − Kb
In principle, the poro-elastic coefficients can be derived from fundamental properties, but often, there is a significant difference between the measured and expected coefficients derived from the fundamental properties. Moreover, if core-test results
are applied to field behavior it is often observed that the reservoir behaves differently from what is expected from such simple
models. For very large reservoirs, one would expect 1D compaction to be a reasonable assumption, but the expected stress
change might still deviate considerably from 1D predictions. That can be explained using poro-elastic coefficients but also using
reservoir geometry and interaction between the reservoir and nonreservoir rocks, which also plays a role. For better assessment
of stress changes, it is beneficial to measure or determine the poro-elastic parameters in the field and to model the stress changes
with a 3D model that incorporates the geometrical effects in the reservoir and the proper boundary conditions.
The relationship between the stress change and the pressure change depends on the boundary conditions and reservoir geometry.
In general, the ratio of stress change to pressure change is termed the “reservoir stress path” and the literature cites various values
that have been measured in practice (Addis 1998). Often, the minimum stress change is related to pressure change by the stress-path
parameter. Assuming that both horizontal stresses change by the same amount and the vertical stress remains constant, the change in
average stress is two-thirds the change in minimum stress. The stress path is given by the parameter γ:
γ =
∆σ min
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(4.56)
∆p
As with the other poro-elastic parameters for simple 1D models, this can be related to the Biot coefficient and the Poisson ratio,
but in practice the parameter must be measured in the field because it could deviate significantly from the expected theoretical
value.
Coupling Effects. Porosity is often a function of the stress, but more importantly permeability will nearly always exhibit a strong
stress dependency. Fracture propagation by fluid injection will change the permeability in the fracture plane by orders of magnitude
because of fracture opening. Also, permeability might change because of shear strain and compaction that occurs over a large volume.
High-permeability reservoirs show little change of permeability with stress, but in tight reservoirs the permeability can be strongly
dependent on stress and pressure because pore throats often are the porosity. Whether depletion results in decreasing or increasing
permeability depends on the relative effect of shear vs. compaction, as illustrated in Fig. 4.56. Shear strain often leads to enhancement
of permeability because shear-dilated fractures can create permeability. This effect can overwhelm the effect of compaction, which
tends to close pore space and decrease permeability.
Normalized Reservoir Permeability
6
5
4
Shear failure
3
Compactionreduced
permeability
2
1
Shear-enhanced permeability
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Stress
0.8
0.9
1
Fig. 4.56—Stress-dependent permeability as used in a coupled model to capture both the shear enhancement of
permeability and the reduction of permeability by compaction.
Hydraulic Fracture Modeling
123
Numerical Methods. Early fracture modeling work was based on the BEM because this conveniently reduces the dimension of the
problem to be solved: Planar fractures in three dimensions can be described on a 2D surface with only 2D integrations of the fundamental influence functions. Moreover, fracture opening and propagation can be described accurately with solutions that incorporate
the singularity at the tip. The deficiency with this is that the influence functions are only strictly valid in uniform media, so that layering of the rock is only described approximately. If layer properties are quite heterogeneous, it becomes important to model fracture
opening accurately, using finite elements that can describe nonuniform media.
Since hydraulic fracture behavior depends critically on the interaction of fracture opening and propagation because of the fluid
pressure distribution, for simplicity it is necessary to integrate the elastic problem with fluid flow in the fracture and reservoir.
In principle, it is possible to develop an implicit solution for both fracture opening and pressure, which has the benefit of unconditional stability. However, the problem is strongly nonlinear and requires many iterations with updates of the system matrix to
obtain convergence. Therefore, for simplicity in practical simulations, the solution is usually obtained from iterations between the
elastic opening solution (for a given pressure) and the fluid transport problem (for a given fracture opening). This also requires many
iterations, but it can still give a stable solution by remaining close to equilibrium using small propagation steps.
Using a fully gridded FEM gives the best solution to the fracture opening problem and the propagation of the fracture in a heterogeneous formation. In addition, the FEM system can compute the initial stress more accurately, which is important when the rock layers
have different properties and some reservoir compartments or zones are depleted.
Some codes use a combined method of BEM and a gridded solution of the stress contribution from the reservoir pressure. Given
the pressure distribution, it is possible to compute the poro-elastic stress on a fracture plane, so that the total stress can be obtained on
boundary elements, including the tectonic stress, thermo-poro-elastic stress, and the fracture opening stress. The main advantage of
such a method is that the pressure can be obtained from a reservoir simulation using only a reservoir grid, so that the effort of meshing
the nonreservoir layers can be avoided.
Mesh. Both structured and unstructured meshes have been used for fracture propagation modeling. The advantage of a structured
mesh is that the same mesh is used for a series of propagation steps and only the properties of the fracture cells and the boundary conditions on the fracture nodes need to be updated. The disadvantage is that many elements are needed, requiring longer
computational time.
With unstructured meshes only the regions where gradients are large get a refined mesh, so that the number of elements is low;
however, every time step the mesh is updated and the computed variables need to be transferred to the new mesh. Although automatic
remeshing is feasible with modern techniques, it can still yield a poor mesh so that accuracy might be sacrificed. Most applications
use a structured mesh, which is more convenient to use.
Conventional reservoir simulation uses a grid only in the flow units, so that the grid needs to be extended for stress simulation.
Moreover, the finite-difference method is not very restrictive on the mesh quality, but the FEM meshes need to have elements with a
positive Jacobian (also sometimes called the Jacobian ratio—the deviation of a given element from an ideally shaped element) and the
mesh quality needs to be good to avoid singularities in the solution. Although it is feasible to modify and extend a reservoir-simulation
grid for an FEM model, it is better to develop a new model for FEM work starting from the horizons and fault surfaces that were
defined in the geological model of the reservoir and overburden.
Coupling of Fracture to FEM. The fundamental assumption of hydraulic fracture modeling is that the fracture displacement is small,
so that the stress field induced by the fracture can be superposed on the virgin stress state. With a fracture opening only a fraction of
an inch, this condition is always satisfied.
The simplest method to incorporate a fracture into an FEM is the so-called “smeared crack” method. Instead of explicitly modeling
the fracture opening displacement, the element properties are modified to describe the fracture opening. In some models, the opening
is even neglected and only fracture transmissibility is included because that is most important. Fig. 4.57 shows the transmissibility
multiplier for a typical case as a function of the stress on the fracture plane. Because fracture permeability is very high, the multiplier
is very large. Careful numerical methods are required to handle the effect of the resulting transmissibility because there will be a huge
difference between reservoir and fracture transmissibility.
Explicit opening of the fracture can be obtained with an FEM of a half-space with nodes inside the fracture perimeter allowed to
move away from the fracture plane (provided aperture is positive), while the rest is constrained by symmetry on the fracture plane.
This method is used in dedicated fracture simulators that use a fully gridded stress simulation. Such models often incorporate only an
external stress component, which is considered to represent the tectonic stress, but changes in reservoir pressure and temperature can
be added to yield the thermal and poro-elastic stress contributions.
Extended finite-element methods use additional variables (apart from the displacements) in an element that contains a fracture
(Belytschko and Black 1999; Remij et al. 2015). The benefit of such a description is that the mesh can remain the same during fracture
propagation or requires just a minimal refinement around the crack elements. Also, the fracture plane can propagate in any direction,
so that fracture reorientation can be modeled. Extended finite-element methods have been developed for dry crack propagation, but the
method can be extended to fluid-driven cracks (Remij et al. 2018). This method is still in development but could become an important tool
for more-complex fracturing problems where fractures are nonplanar and where there is the propagation of multiple fractures. It is also
possible that computational efficiency would be better, compared with direct methods that use mesh refinement to incorporate a fracture.
4.13.2 Relating Fracture Simulation to Reservoir Simulation. Historically, there have been three basic approaches commonly
used for predicting the production from hydraulically fractured wells. Initially, analytic solutions were most commonly used, based
on an infinite conductivity fracture, which then subsequently developed into a finite-conductivity fracture with a given half-length.
This approach was also extended to cover horizontal multiple fractured wells (Basquet 1999). With the development of reservoir
simulators, two other approaches were developed.
For complicated multiwell, multilayer, multiphase simulations (i.e., full-field models), the fracture stimulation was usually approximated as a negative skin. This is the same as increasing the effective wellbore radius in a reservoir-simulation model. An alternative approach, developed initially for tight gas applications, was to develop a special purpose numerical reservoir simulator that
could explicitly model the flow in the fracture and also consider the special properties of the proppant, such as the stress-dependent
124 Hydraulic Fracturing: Fundamentals and Advancements
10
× 104
Tensile strength
No strength
Fracture Transmissibility Multiplier (–)
9
8
7
6
5
4
3
2
1
0
–500
–450
–400
–350
–300 –250 –200
Stress (psi)
–150
–100
–50
0
Fig. 4.57—Empirical relation of the fracture transmissibility multiplier with stress on the fracture plane for a smearedcrack model.
permeability or the possibility of non-Darcy flow. Such models typically were limited to being run as a single-layer, single-phase (oil
or gas) reservoir simulation.
More recently, with the development of faster computers with sufficient memory, it became feasible to avoid the compromises
that were made in the past when trying to model hydraulic fractures with a normal 3D reservoir simulator. Initially, investigators
manually built grid refinement into their reservoir models to represent a hydraulic fracture (Behr et al. 2006). Although this method
works well, it is very time consuming for the engineer because complicated gridding schemes are necessary to correctly represent
the fracture geometry and subsequent pressure drawdown. In addition, the detailed description of the fracture properties from a
fracture simulation was not usually passed through to the reservoir model, resulting in the assumption of constant properties
(i.e., permeability) for the fracture. This method of simulation is not very efficient and can lead to inconsistencies in the data used
in the different simulations.
New methods have been developed that make detailed production modeling more efficient and consistent than in the past because
it automatically couples the calibrated output of a fracture stimulator with the input into a 3D reservoir simulator (Bennett et al. 1986;
Mayerhofer et al. 2005a).
With the development of these methods, it has now become feasible to routinely run full 3D simulations of multiphase production
from multilayer reservoirs while explicitly modeling hydraulic fracture(s) in the reservoir model. To make this practical, it was necessary to develop tools to interface the hydraulic-fracture-modeling software and the reservoir-simulation software. These new tools
take the results from a fracture growth model, and automatically translate them into the correct format for the reservoir simulator.
Fracture Model Output. The most important outputs for the reservoir simulation are the fracture dimensions and the fracture
conductivity. For both proppant and acid fractures, the conductivity profile varies with respect to the fracture length and height. Various techniques are then used that convert fracture-simulator data for use in the reservoir simulation, acknowledging that the created
fracture length and the productive effective fracture length can be different.
The spatial variation is converted to a gridded rectangular geometry for the reservoir simulator. Of course, because the fracturegridblock width is a constant in the reservoir simulator, the only way to model the varying width (and varying conductivity) of the
fracture is to adjust the permeability of the reservoir gridblocks representing the fracture. By obtaining an equivalent conductivity with
a constant width, a realistic result can be achieved.
Typical values used for the gridblock size in the fracture are 10 × 10 ft or 20 × 20 ft. This grid size gives enough resolution to be
able to effectively represent typical hydraulic fracture dimensions, while optimizing simulation run times.
The fracture growth model tracks the fluid leakoff (filtrate) from the fracture into the formation. There is more filtrate fluid leaking
off near the wellbore than at the fracture tip. In this way, the leakoff history is accurately transferred to the reservoir simulator, by initializing the water saturation in the appropriate gridblocks adjacent to the fracture face. Of course, the fracture gridblocks themselves
are considered to have 100% water saturation at the beginning of production. The capability to accurately include the filtrate fluid in
the reservoir-simulation input is very important when trying to accurately model (or history match) the initial post-fracture cleanup
period, which can be of critical importance especially in tight gas reservoirs.
Fracture conductivity data are very important for accurate predictions from the reservoir simulator. Fracture conductivity decreases
with increasing net stress for both propped and acid fractures, and laboratory measurements of proppant conductivity can be dramatically reduced in field applications because of damage mechanisms. For the case of propped fractures, laboratory data are often published by the proppant-manufacturing companies and can be corrected using various correlations and used in the simulation. For acid
fractures, the Nierode-Kruk (1973) correlation is typically used to estimate the pressure-dependent conductivity of an etched fracture.
Hydraulic Fracture Modeling
125
This correlation can be adjusted on the basis of measured rock data, and then the resulting conductivity data are passed to the reservoir
simulator in the form of a table for pressure-dependent permeability for the gridblocks representing the fracture.
Non-Darcy and multiphase effects in the proppant pack can also be very important in certain situations. For reservoir simulators
that do model non-Darcy flow, the non-Darcy effects can be calculated by the reservoir simulator. Alternatively, approximate fracture
conductivity multipliers can be used that mimic non-Darcy effects.
It is preferred, if possible, to model the non-Darcy effects in the reservoir simulator, by using the first option, so that changing bottomhole pressure can be considered when calculating the non-Darcy pressure drop in the fracture.
Grid Generation. The typical dimensions of the refined region are related to the fracture extent and the trade-off between representative results and reasonable simulation time. Typically, local grid refinement (LGR) extends to three times fracture length along the
fracture and to four times fracture length in the direction normal to the fracture. In the z-direction, the LGR is defined for the host
gridblocks that contain the fracture height and approximately half of the fracture height above and below the fracture itself.
The fracture in the LGR is represented by a planar series of gridblocks. The mesh for the fracture conductivity distribution supplied
by the fracture simulator is considered as a starting point for the discretization within the LGR. In the x–y-plane outside the fracture,
the number of gridblocks increases toward the LGR boundary or to the middle point between fractures (for the horizontal-well case).
A finer grid is built around the well and fracture tips to capture the dominant radial character of the flow in these regions. The gridblocks near the fracture plane have a particularly small width (normal to the fracture plane) to ensure an accurate computation of the
high-rate transient flow during the initial production period.
This example of the type of gridding typically used has been found to allow for an accurate representation of the filtrate fluid
distribution around the fracture that is transferred from the fracture simulator. Note that the typical filtrate leakoff depth varies from
centimeters to tens of centimeters in tight gas reservoirs, or to even greater depths in higher-permeability reservoirs.
Initialization of Grid Properties. Every gridblock in the host grid and the LGR is assigned one value of each distributed reservoir
characteristic: porosity, permeabilities in three directions, phase saturations, and pore pressure. This basic information is taken from
the input to the fracture simulator.
The fracture in the reservoir-simulation model is not modeled with its actual width, but with a fictive width that is the size of the
corresponding fracture gridblock. The fictive width is normally set to a value larger than the actual width to allow for larger timestep
sizes in the reservoir simulation. Because the pore volumes and the transmissibility of the fracture blocks should remain unchanged,
regardless of the width used for the fracture in the reservoir simulator, the fracture porosities and permeabilities are recalculated to
adjust the fracture properties.
In practice, modeling the true pore volume of the propped fracture is only important if the initial fluid recovery needs to be modeled. If this is the case, then a very small timestep is required because the pore volume of the fracture gridblocks is still very small, in
spite of the upscaling of the fracture width. For full-field modeling and long-term modeling, the porosity of the fracture gridblock can
be left unchanged. This results in too much pore volume in the fracture itself, and a slight initial flush production, but allows larger
timesteps to be used, which is necessary for long-term simulations.
The initial water saturation near the fracture plane is calculated from the leakoff depth data calculated by the fracture model, which
is represented as a 2D piecewise constant distribution with its own mesh size and is translated into the reservoir grid using an areal
weighting scheme. In doing so, it is assumed that the filtrate fluid has the same properties as reservoir water when it will be produced
back through the fracture. The porous volume of the fracture is saturated by filtrate (water saturation is taken to be 100%) at the beginning of the simulation of the post-fracturing production.
Propped-Fracture Modeling in Post-Fracturing Production Forecast. After the treatment, production forecasts can be made with a
full-field or sector model that represents the fracture geometry and properties that are based on treatment analysis. Fig. 4.58 shows
how the LGRs are placed in a sector model grid. By modeling the fracture on the basis of the net-pressure analysis, the conductivity,
FR8
FR6
FR7
FR4
FR2
FR5
FR3
FR1
Sector model
Full-field model
Fig. 4.58—Sector model for history matching and production forecast (Shaoul et al. 2005).
126 Hydraulic Fracturing: Fundamentals and Advancements
height, and length of the fractures could be accurately represented and incorporated into the reservoir-simulation model (Shaoul et al.
2005, 2009). Fracture properties for LGR modeling are obtained from the fracture simulations. An example of an LGR with gridblock
permeability is shown in Fig. 4.59. Because the gridblock width representing the fracture is 1 ft wide, the fracture conductivity is the
same value as the permeability presented in the figure, but then in md-ft. The fracture conductivity includes the estimated proppant
damage factor and has been adjusted during the production history matching to match the observed bottomhole flowing pressure and
the change in pressure seen when the well is shut in. A series of LGRs is then added to the host grid so that all fractures in a horizontal
well can be modeled in a sector of a reservoir as shown in Fig. 4.60.
4.13.3 Applications. Stress Evaluation: Differences with 1D Model. Even if only the stress evolution is modeled, this might give a
positive contribution to optimizing fracture design because the actual stress distribution is very important for fracture design and different properties, and structural effects often yield a stress field that differs from the simplistic estimate. In a coupled model, the effect
of depletion should then be coupled to flow/fracturing. Fracture mapping data indicate a strong effect of depletion on stress gradient,
as well as a strong containment effect.
In a depleted reservoir, the stress can usually be estimated with the pressure drop and the poro-elastic coefficient. However,
this is valid only for a layer-cake formation, and with faulting and structural dip the stress will deviate from such a simple
model. Fig. 4.61 shows a stress profile in a 3D geomechanical model of a gas reservoir that was fully depleted, giving lower
stress. In fracture models with a 1D geomechanical model, the reservoir stress would simply be computed with the pressure
change and the poro-elastic coefficient derived from Biot coefficient and Poisson’s ratio. For the reservoir, this appears to
give a satisfactory result compared with the 3D model. However, there is also a significant stress change in the overburden
because of arching, which is hard to estimate analytically. The change in overburden stress might be important for assessing
fracture containment.
D
D
A
A
C
B
B
Permeability
0
5,058
10,116
15,174
20,232
Fig. 4.59—Detail of LGR for the propped fracture.
PERMX (md)
0.0
2,600.0
5,200.0
7,800.0
Fig. 4.60—Simulation grid for horizontal well with five longitudinal fractures, showing permeability values.
Hydraulic Fracture Modeling
127
x=110,937, y=517,323 [G4-EL]
–1,000
σ x,1971
–1,200
σ x,2007
σ x,2007, theory
–1,400
Domain
–1,600
Depth (m)
–1,800
–2,000
–2,200
–2,400
–2,600
–2,800
–3,000
20
30
40
50
Pressure and Stress (MPa)
60
Fig. 4.61—Stress vs. depth computed in an FEM of a depleted reservoir. The largest difference between the 1D prediction
and the FEM stress solution occurs in the overburden.
Stress drop resulting from depletion could also be important in horizontal-well fracturing in tight reservoirs. In such wells, relative
stress variations along the laterals are important, so it is beneficial to model the stress change accurately.
Stress Changes by Depletion and Injection. Fracture containment is likely changing because of preferential depletion of some layers.
This can be beneficial in case of overpressured reservoirs where stress is likely isotropic with small differences between layers in the
virgin state. After depletion, there will be more containment of the fracture because of larger stress differences.
In other cases, vertical coverage will be reduced because the fracture will stay preferentially in the best, depleted layers.
An example of stress simulation that aids stimulation optimization is shown in Fig. 4.62. This is a tight oil reservoir where both
producers and injectors needed propped fractures (Minner et al. 2002). The horizontal stress difference is sufficiently large for the
1,500
Producer
1,250
Injector
1,000
Northing
(ft)
750
500
Reoriented
stress
250
0
0
250
500
750
1,000
1,250
1,500
Easting (ft)
Fig. 4.62—Stress reorientation as indicated with trajectories of maximum horizontal stress. Virgin stress orientation
is indicated by the heavy solid line for producer fractures (black) and injector fractures (blue). At the lines of injector
wells, the stress orientation remains the same, but at producer wells, the stress changes so that later fractures would
be suboptimal.
128 Hydraulic Fracturing: Fundamentals and Advancements
fractures to be well-aligned with the maximum-stress direction. It was observed that infill wells showed variable fracture orientation
leading to poor sweep. Although it would be expected that pore-pressure changes do not change the horizontal stress difference,
that is not true for a line drive. High pressure at the injectors results in rock expansion because of lower effective stress, resulting
in an increase of the horizontal stress contrast. The reverse happens at the producer lines where the horizontal stress difference
disappears.
The solution to such fracture reorientation problems is to drill and stimulate all wells in virgin stress conditions. That is a challenge
if the drainage area is uncertain, but in large field developments it can be assumed that the drainage area is known so that well spacing
can be determined for developing a new field compartment or section.
A similar effect has been observed in recent projects where long laterals were stimulated with many fractures. Local depletion
can lead to stress change that then hampers uniform fracture growth at nearby wells, leading to inefficient stimulation (Jacobs 2018).
Because depletion has a strong effect on stress, it is beneficial to model the stress in conjunction with reservoir simulation and fracture
simulation. Even if the coupling is only one-way, this will yield a better strategy for field development.
Coupled Solutions of Gas Reservoir Stimulation. In some cases, it is necessary to couple the fracture and reservoir simulation to
stress modeling because the critical properties depend strongly on stress. In tight reservoirs, it is difficult to obtain independent estimates of reservoir quality and reservoir pressure. Moreover, the fracture length and conductivity are coupled to the estimated reservoir
quality. The best hope for obtaining both fracture parameters and reservoir quality is to use all data. A fully coupled model offers the
best platform for a full calibration process.
All collected data can be interpreted, such as treatment pressure records, initial water and hydrocarbon rate, and microseismic data.
Production records and pressure-buildup data can be used to calibrate the model and make long-term recovery predictions.
The seminal work on coupled models was conducted by Tony Settari, who published the methodology and several case studies. An
example of an integrated interpretation of a complete data set with treatment data, fracture mapping, cleanup period production, well
tests and long-term production history is presented by Settari et al. (2009).
In tight reservoirs, very long fractures might be induced. In this case, microseismic fracture mapping showed a moderate fracture
half-length of some 450 ft, which could be matched using pressure-dependent permeability; see Fig. 4.63. Opening of fissures at high
fracture pressure is often inferred from a much higher leakoff rate than that expected from matrix permeability. The shorter fracture
can then be used for interpreting the production. Because microseismic data are recorded while injecting into a fracture system at very
high pressure, it is necessary to predict the fracture aperture as a function of pressure to forecast production performance at much
lower pressure.
Most likely, the apparent poor stimulation results were related to damage to the proppant pack by high stress and kill fluid.
However, the well test was not long enough to reach radial flow, so the reservoir permeability had to be obtained from core data.
Unfortunately, in such cases the solution tends to favor high reservoir quality combined with poor fracture length (Shaoul 2015b).
If the reservoir permeability is much lower while the fractures are longer, it leads to a waste of resources when trying to improve
stimulation, which is impossible if the bottleneck in production is the reservoir quality.
The production data in Fig. 4.64 show that the final model matches the production over a long period, so it appears that in this case
the right balance was found between reservoir quality and fracture length.
In very tight reservoirs and shales, it is important to estimate an SRV—and, typically, practitioners have based this on microseismic mapping and pressure interpretation—so that an early evaluation of drainage area can be made, as well as a forecast of
reserves. Studies in shale reservoirs are increasingly looking to see what other diagnostic techniques might provide further insights
into SRVs seen in production. Overall, using coupled models offers the best hope of an accurate analysis, but it is obviously
necessary to obtain long-term measurements in pressure-buildup tests or production data to calibrate these models and properly
determine reservoir quality.
A-13 Stage 1— Final HM, Original Initial Pressures
Promult, wbs, Variable k Matrix, Fracture kr, Variable Tmult in Stages
9,500
80,000
obs BHP SRT+mini at 10,080 ft
obs BHP junk+mini
9,000
70,000
Matrix Permeability Functions—Stage 1 and 3
HM4 final match (higher krw)
50,000
7,500
40,000
7,000
30,000
7,500
20,000
6,000
10,000
5,500
0
0.5
0.1
0.15
0.2
0.25
0.3
0.35
40
Permeability Multiplie
BHP (psia)
8,000
0
45
60,000
Inj rate
Inj Rate (BPD)
8,500
35
Stage 1
Stage 3
30
25
20
15
10
5
0
5,000
6,000
7,000
8,000
9,000
Pressure (psia)
0.4
Time (days)
Fig. 4.63—Stage 1 treatment-pressure match and applied matrix-permeability multiplier to match the leakoff during
high-pressure injection (Settari et al. 2009).
Hydraulic Fracture Modeling
129
1,000
10,000
BHP data
9,000
900
Gas rate data
PLT gas rates
HM6_ws_0.1
BHP (psia)
7,000
HM6_ws_0.1_80ac
800
700
6,000
600
5,000
500
4,000
400
3,000
300
2,000
200
1,000
100
0
0
50
100
150
200
250
300
350
400
Gas Rate (Mscf/D)
8,000
0
450
Time from 5 February (2006)
Fig. 4.64—Production match showing fair agreement between measured and simulated gas rate (Settari et al. 2009).
Conclusions.
• Geomechanical modeling of stress changes in relation to pressure changes requires additional measurements that can be
obtained from specialized core tests.
{{ The poro-elastic parameters can be computed from fundamental properties such as bulk moduli of the rock constituents, but
these could differ from direct measurements.
{{ Field measurement of poro-elastic coefficients can also differ significantly from core-test data.
• Even limited coupling between fluid flow and stress simulation can aid stimulation optimization in cases where stress changes
are important.
• For interpreting treatment and production data in stress-sensitive reservoirs, it is necessary to use a fully coupled model of
stress and fluid flow.
4.14 Further Fracture Model Integration and Novel Developments
4.14.1 Fracture Models Coupled With Reservoir/Production Models. Fracture model calibration can be extended by taking the
analysis “full circle” using production model calibration. The geometry results of a calibrated fracture model can be exported to a
reservoir/production model, where in unconventional plays the geometries for multiple fracture in a horizontal well can be incorporated into the reservoir model. Tweaking reservoir properties can then lead to a match of the actual production data. Once this match
is established, sensitivities to fracture design changes can be explored, as well as a full evaluation of the economics.
Mayerhofer and Cipolla have written a multitude of papers that discuss the integration of direct fracture diagnostics and production
modeling with fracture modeling. Cipolla et al. (1993) and Cipolla (1996) pioneered integration of well testing, production analysis,
and fracture modeling. Cipolla and Mayerhofer (1998) discuss the general benefits and limitations of this approach. Their workflow
was extended to include a calibration step with directly measured fracture dimensions, as detailed in Mayerhofer et al. (2005a, 2006)
and Cipolla et al. (2008).
The evaluation and optimization of hydraulic fracture treatments must always be performed in conjunction with a reservoir/production evaluation. The integration of all results from different technologies such as fracture diagnostics, calibrated fracture modeling,
and production analysis is crucial for hydraulic fracture optimization but also for field-development and well-placement strategies.
Production analysis of fractured wells can be very nonunique with standard daily flow rates and surface flowing pressure information. The reason for this nonunique behavior is that early-time flow data are partly influenced by cleanup of hydraulic fracturing fluid
but also by fracture length, fracture conductivity, and reservoir permeability all impacting the early-time flow behavior in a similar
manner; also real field data cannot be clearly distinguished with commonly available daily flow rates and flowing tubing pressures.
This underlines the importance of using other independent and constraining information such as fracture diagnostics and crosswell
production testing.
While fracture geometries can be estimated with fracture diagnostics, calibrated models provide the important link to fracture conductivity, which currently cannot be measured with any proven fracture diagnostic technology. Post-fracturing pressure-buildup tests
have been used in conventional and tight reservoirs to estimate fracture conductivity in vertical wells. However, in unconventional
reservoirs post-fracturing buildup analysis is impractical, difficult, and nonunique in horizontal wells with multistage fracture treatments. Additionally, oil and gas operators will generally not want to shut-in unconventional wells for long-term pressure buildups
130 Hydraulic Fracturing: Fundamentals and Advancements
lasting several weeks. Currently, calibrated fracture modeling might be the only practical method for providing fracture conductivity
estimates for reservoir modeling purposes. Modeling challenges remain when quantifying the conductivity distribution within the
hydraulic fractures because of uncertainties related to proppant-transport modeling, but advances in that field might provide reasonable starting estimates for reservoir simulation.
Reservoir and production modeling are typically conducted with either analytical or numerical models. Analytical models run very
fast on any type of computer but have less flexibility when it comes to the details of the hydraulic fracture properties. They will typically use average fracture conductivities and have hydraulic fractures defined with generally uniform geometries along a horizontal
well. They are also usually constrained to single-well modeling. Numerical models, while slower, have more flexibility in defining
varying fracture geometries along the horizontal wells, in conductivity distribution within the fractures, and in modeling complex
fracture networks, and they can be set up to perform multwell modeling, which is important for evaluating potential well interaction.
Numerical models are also capable of modeling multphase flow effects, non-Darcy flow, stress-sensitive fracture conductivity and
time-dependent damage mechanisms in the fractures.
4.14.2 Field Statistics and Fracture Models/Production Models. US states require oil and gas operators to provide a range of well
information, which is generally disclosed to the public through state-run websites. Almost all US States require monthly updates of
production response by well (or by production battery in Texas), while some states require access to well logs and completion data, in
some cases including a full completion report. At the same time, federal requirements to disclose all fluid additives through FracFocus
(2019) have also caused a proliferation of well data.
Some companies have used these data for scoping studies and have integrated these capabilities with sensitivity studies that rely
on fracture models and reservoir/production models. As such, this integration provides an additional opportunity to calibrate fracture
models.
One such integration is shown in Fig. 4.65 from Agarwal et al. (2019), which compares the relative increase in 365-day cumulative oil production (bbl/ft) with increasing proppant loading from 500 lbm/ft as predicted by the detailed fracture/reservoir modeling
(blue) and a multivariate analysis (MVA) in orange. Both models agree reasonably well in predicting the change in oil production as
a function of proppant loading, thus increasing confidence in the results of this study because the detailed physics-based modeling is
consistent with big data analytics.
The statistical analysis is intended to be used as a scoping tool for horizontal-well completion optimization in unconventional
reservoirs. These models provide useful conclusions about the relative importance of completion parameters for well performance.
While MVA has been widely used in the industry, statistical models are limited by their inability to provide quantifiable predictive
relationships (as opposed to mostly simple linear regressions that are qualitative in nature and unreliable beyond the data range).
Despite the complexities in the MVA workflow, statistical models only uncover statistical relationships between parameters without
providing physical reasons as to why there might be a relationship. On the other side of the spectrum are “smart” physical models
(calibrated fracture and reservoir models) to estimate how major completion parameters should affect well performance.
The advantage of “big data” statistical models is that information for thousands of wells is readily available and can be screened
quickly, whereas detailed physical modeling is generally performed on a few wells and is very time consuming. Combining the
strengths of both methods and including well-understood physical relationships for common completion parameters will allow the
industry to improve the use of MVA models. The engine of the economic evaluation (Mayerhofer et al. 2017) is a novel hybrid
approach that uses calibrated relationships from physics-based modeling (combination of fracture and numerical reservoir modeling)
between completion parameters and production response as “transformed nonlinear variables” in a multiple linear regression MVA.
This type of methodology should provide a more constrained and physically realistic prediction of production response to suggested
completion changes.
The final step in this workflow is to couple the hybrid MVA model with detailed completion cost models to determine which fracture
design and completion methods are the most effective at lowering USD/BO (well cost per bbl of oil produced in a given time frame).
Change in Norm 365-day Cum Oil (bbl/ft)
Fracture/reservoir modeling
ACE MVA
25
20
15
10
5
0
500
700
900
1,100
1,300
1,500
1,700
1,900
2,100
Proppant Mass (lbm/ft)
Fig. 4.65—Comparison of detailed fracture/reservoir modeling to ACE MVA in predicting the sensitivity of normalized
365-day cumulative oil production to proppant loading (Agarwal et al. 2019).
Hydraulic Fracture Modeling
131
This is then compared with calibrated fracture and reservoir models to determine if sensitivity to a range of fracture completion design
parameters is similar to what has actually been observed over a larger area in a specific shale basin.
Public access to well drilling and completion information has unleashed “big data” MVA as a scoping tool that can be used for production optimization or minimization of the cost to produce a barrel of oil (USD/BO) or barrel of oil equivalent (USD/BOE). These
statistical tools have helped the US shale industry on its path to higher well production and more-economical wells.
4.15 Fracture Modeling Advantages and Challenges
4.15.1 Fracture Modeling Advantages. Pressure matching using routine treatment data with a fracture model has significant advantages over other fracture diagnostic techniques, such as microseismic fracture mapping or fiber-optic temperature measurements.
First, the basic data for fracture treatment data analysis is collected on every fracture treatment pumped. Collecting these data is a
routine part of the process and is relatively inexpensive. As part of the objective to “get the job away,” as mentioned in Section 4.2,
pressure matching can provide a powerful tool for real-time treatment evaluation and help evaluate fracture entry problems. Finally,
it can be a very effective tool for design refinement and overall job design optimization.
Fracture models do not compete with mapping data—instead, they facilitate integration of all data into a comprehensive interpretation of the formation and fracture behavior. Models have the benefit that they can be inexpensive to expand into more widespread
use once key diagnostic data have been collected and the model has been calibrated. Then, alternative designs can be evaluated with
a calibrated model.
Initial model use might be as simple as a power-law model that can be run from a spreadsheet as a function of job volume on
every job.
Another model advantage is that, once calibrated, a different interpretation of fracture closure stress has only a minor impact
on fracture dimensions. Fracture modeling results are therefore somewhat self-correcting and forgiving. One reason for this is
that fracture modeling essentially uses two important parameters that drive fracture dimensions from a single measurement. For
example, if different closure stress picks are evaluated using a “back-of-the envelope” model (Fig. 4.29), it is possible to evaluate how a different closure pick would impact observed net pressure and efficiency, and in turn how that affects created fracture
dimensions. The results of such an exercise are shown in Fig. 4.66, where it can be observed that a ±100-psi change in closure
pick (±10% change in resulting net pressure) results in a 7% change in total fracture width and only a 3% change in length and
height.
The goal of any model is to accurately reflect the way a physical process works, so that the model can be an appropriate analysis
tool for that process. Hydraulic-fracture-growth models were originally designed to reflect an understanding of how it was felt the
process was supposed to occur. Now, fracture growth data are being measured directly, and the model is changed or calibrated to
reflect actual (geometry) results.
The benefit of some of these case histories is that these represent joint industry projects, where a significant budget is available to
investigate many additional and nonroutine measurements. For example, many fracture diagnostics (see Chapter 15 Fracture Mapping and Propagation Analyses) would all be available, where most of these would not be deployed for a typical commercial project.
Commercial fracture projects often suffer from two main problems: fracturing model physics are generally not well understood and
fracture model input parameters are often poorly defined. These issues will be addressed in the next two sections.
1,400
0.7
1,200
0.6
1,000
0.5
800
0.4
600
0.3
400
0.2
200
0.1
0
88
1,200
Fracture Width (in.)
Fracture Half-Length and Height (ft)
4.15.2 Limitations of Fracture Models. It is in the well-monitored joint-industry projects that shortcomings associated with the use
of fracture models become apparent. Even in cases where there is direct measurement of all the critical model input parameters, the
physics of the model are often not consistent with what really happens under in-situ conditions. This is because there is still a lack
of understanding and knowledge of all the mechanisms that are important in hydraulic fracture growth, and particularly what input
parameters should be provided for these unknown mechanisms.
0.0
89
1,100
90
1,000
91
900
92
800
Efficincy (%) and Net Pressure (psi)
Half-length
Height
Cumulative width**
Fig. 4.66—The impact of a different closure pick on the example provided in Fig. 4.29, where a later pick results in a
higher end-of-job net pressure and a lower end-of-job efficiency, on fracture half-length, height, and overall fracture
width.
132 Hydraulic Fracturing: Fundamentals and Advancements
For example, there is not confidence (yet) about the ability to predict in which environments “classical” confinement mechanisms
describe fracture height growth. In most of the examples, it appears that composite layering is the dominant mechanism to control
fracture confinement, but the industry is still learning about when this mechanism is more prevalent and when it is not. For example,
composite layering has been observed to be more important in highly laminated formations (showing a “noisy” gamma ray response),
such as the Atoka Shale. Also, layers with a large mechanical contrast with respect to neighboring layers, such as coal, which has a
much lower modulus and higher Poisson’s ratio than most other rock types, often provide significant confinement. Industry research
should attempt to unravel how to quantify this parameter and effectively incorporate this aspect into hydraulic fracture simulators.
These shortcomings of models can be addressed by calibrating fracture models with direct fracture diagnostics. Although all the
physical mechanisms that play a role in hydraulic fracture growth might not be completely understood, it is possible to use the data
from tiltmeter mapping and microseismic mapping to empirically train fracture models. Even in the absence of a full understanding of
the physics, a fracture design provided with a calibrated model will better reflect what happens during a fracture treatment.
A common misconception is that fracture modeling and fracture mapping compete, but the reality is that they work best in synergy.
Models are predictive, while diagnostics are investigative. By directly measuring geometry data and merging these data with pressure,
rate, and density data, most models can be calibrated to reflect actual geometry for the remainder of the treatment or in a fieldwide
application. A correlation can then be made between actual measured dynamic width, height growth with time, and fluid efficiency
and pressure responses, on the one hand, and production data, on the other. Using direct fracture diagnostics to record fracture geometry during a minifracture and then calibrating the model with these data enables the stimulation engineer to better forecast the success
of proppant placement for optimized reserves recovery.
Models today are significantly more sophisticated than 20 years ago, but they often still do not accurately predict fracture growth.
As discussed, this results from an incomplete understanding of relevant physics. However, poor characterization of rock, reservoir,
and geology provides another challenge.
4.15.3 The Challenge of Poor and Incomplete Model Inputs. In the new world of round-the-clock “factory mode” shale stimulation/fracturing with the associated general focus on pumping efficiency, time for simulation engineering is often limited and
sometimes nonexistent. Prefracturing diagnostic injections, which could easily be conducted when only a single fracturing job had
to be performed during a day, are mostly a thing of the past. Even time for short-time tests, such as step-down test analyses, is often
not available. If modeling is targeting a few stages in a well, some operators do spend a little extra time to collect the necessary
pressure-decline data, and rate stepdown tests might be conducted a few times throughout a fracturing job to look at the completion
(perforation) connectivity/efficiency.
Prefracturing injections in ultratight shale plays are not very useful if not performed correctly because one of the main objectives
of these injections is to observe fracture closure during the pressure decline. Whole fracture closure can be observed within minutes
following a 5-minute water injection into a moderate- to high-permeability conventional reservoir (30 to 70% end-of-job fluid efficiencies), but the closure process might take hours or days in a low-permeability unconventional reservoir (>95% end-of-job fluid
efficiencies). As a practical change, if fracture closure stress (as a bound for net pressure) is required to be measured, the industry
now reverts to the implementation of DFITs. These tests also bring the additional benefit of being able to measure a specific fracture
leakoff mechanism, large-scale reservoir permeability (though at elevated injection pressures), and reservoir pressure. DFITs can be
conducted weeks before the main fracturing job, requiring a fracturing pump on location for only a few hours, and installation of a
pressure gauge at the wellhead. The most practical aspect about DFIT injections is that they do not need to interfere with fracturing
operations, eliminating competition between time for engineering optimization and pump time.
However, even when all these data are properly collected, net-pressure analysis has its limitations. First, direct observations of
pressure are generally conducted at the wellhead and then extrapolated to downhole. Correcting for various friction components
during pumping to determine accurate bottomhole wellbore pressures or bottomhole fracturing pressures can be very problematic,
making it tough to understand what is happening during pumping. In the conventional vertical-well days, this could be addressed with
a deadstring or a bottomhole pressure gauge. In unconventional plays, these are instruments of the past that interfere with efficiency
and heighten risk. In a typical horizontal-well unconventional completion, the only way to obtain an accurate bottomhole pressure is
through a temporary shut-down, where the hydrostatic head becomes the only correction factor required to extrapolate from surface
pressure to bottomhole pressure in the well or fracture.
Should an accurate bottomhole pressure be available, and through it an accurate observed net pressure, there is another problem that
presents itself. This lies in the fact that net-pressure matching using fracture propagation models is an indirect technique. The fracture
geometry is inferred from net pressure and leakoff behavior and is subjected to a range of assumptions associated with rock mechanics and fluid dynamics and many other physical mechanisms. Thus, solutions are often nonunique and only careful and consistent
application can lead to useful results, where trends can be compared. Accurate inference of fracture dimensions, however, is often not
achieved when no other data are available.
The problem of nonexistent or poor input measurements can be addressed by conducting better measurement of these critical input
parameters, but this will be neither easy nor inexpensive. Young’s modulus can be measured from core, but the industry is now routinely measuring dynamic modulus using sonic logging tools, providing a reasonable input for this parameter. The industry has also
made advances in permeability measurements (Mayerhofer and Economides 1997), obtaining better estimates of the permeabilitythickness product using pre- and after-closure fracture analysis. The fracture closure stress profile remains a critical model input
parameter that in general is not known very well.
In general, it is possible to divide the critical fracture model input parameters into four groups, with some of the following parameters as part of each group:
• “Known knowns”—Parameters that are well-defined and considered to be relatively well-understood and that are relatively
inexpensive to measure reliably.
{{ Fluid rheology. Viscosity as a function of shear rate is generally measured on location with a Fann viscometer. In addition,
most oilfield services companies can also provide these data from laboratory measurements at a variety of temperatures
and additive concentrations, and there are research-consortia data available for inclusion in more elaborate-proppant
transport-simulation.
Hydraulic Fracture Modeling
133
Wall-building coefficient. Is generally measured for a fluid system in a fracturing company’s laboratory. Most industry
fracture propagation simulators either calculate values or provide library values for a variety of fluid systems.
{{ Pressure-dependent leakoff. This is generally determined from the type of pressure decline as measured through a minifracture
or a DFIT.
{{ Closure stress in pay interval. Attempts to measure the closure stress through dipole sonic interpretation are notoriously flawed (Wright et al. 1998), and the best method to determine fracture closure is to conduct a pump-in/shut-in
test. The fracture closure stress is now routinely measured in the pay interval using a breakdown injection/pressure
decline before the main fracture treatment, but this provides only a single direct measurement at a certain depth to be
used along the entire length of the well. In shale plays, DFITs are conducted before less than 1% of all treated wells,
with appropriate stage treatment data including longer-than-usual shut-in periods collected on a subset of stages in a
fraction of these wells.
• “Known unknowns”—Parameters that are understood well, but which are harder and more expensive to measure, and that are
therefore less reliable.
{{ Young’s modulus. Can be measured indirectly (dynamic modulus) through a full-waveform dipole sonic log, providing
values as a function of depth. This measurement does require calibration through core tests by subjecting a core sample to
a triaxial test to measure how stress and strain are related.
{{ Permeability and pore pressure. These parameters can be measured in core flow tests, but for low-permeability shales these
methods are often unreliable or take a long time. Therefore, in shale plays these parameters are more reliably obtained
through a DFIT, which effectively “samples” an average permeability and pore pressure for a radius of investigation of tens
to hundreds of feet from the injection point.
{{ Closure stress in neighboring layers. With relatively small DFIT injection volumes, penetration of the initial fracture outside
the zone of interest is expected to be minimal. It is only in joint-industry science projects that there is sometimes the luxury
of measuring the closure stress directly in layers outside the pay zone. For fracture modeling on typical fracture treatments,
practitioners hope to make educated guesses about the closure stress in zones outside the pay through dipole sonic measurements and interpretation of reservoir pore pressure and depletion. However, significant uncertainties remain that can
significantly alter fracture growth in the model.
• “Unknown knowns”—Parameters that are not known and cannot be measured easily and for which the governing physics are
not well-understood.
{{ Fracture complexity. Multiple fracture growth is hard to infer beyond core-through, but sometimes can be inferred from
microseismic mapping. In addition, high levels of net pressure are often inferred from overlap of multiple fractures and
general fracture complexity.
{{ Tip effects. The resistance to growth at the fracture tip.
{{ Composite layering and fracture width coupling.
Because of the unknown nature of these parameters and/or the inability to measure them directly, simulations generally “lock
in” these parameters in a calibrated model—incorporating both net-pressure data and fracture diagnostic data.
• “Unknown unknowns”—Parameters that are not known and cannot appropriately be measured at all required scales.
{{ Formations are nonuniform with fractures and faults at all scales. Therefore, it is possible that a fracture could interact with
sand lenses or faults without a clear pressure signal, so that the fracture system deviates from the expected geometry without
any warning if only routine monitoring data are acquired.
{{
4.15.4 Summary. Even though today’s fracture models can be used to conduct net-pressure history matching, by themselves they
are not reliable predictors of hydraulic fracture growth. Fracture models will always face the challenge of predicting (modeling) a
complex process that is taking place thousands of feet below the Earth’s surface with only poor characterization of the rock, reservoir, and geology on the scale (tens to hundreds of feet) relevant for hydraulic fracture growth. Rock properties are influenced by
microscale layering, but relevant reservoir heterogeneity exists on too large a scale to detect with cores and logs but too small a scale
to be mapped as part of field characterization.
Models are simply tools that can be used like a hammer to build beautiful furniture—or to throw into a window. The usefulness of
a model is dependent not so much on the software brand that is being used, but on the practitioner. Commercial modeling software
often provides a toolkit of various model types, such as 2D and 3D models that can be calibrated with directly observed data and that
are designed for on-site engineering flexibility. The quality of results is more user dependent than model dependent, where making the
right engineering assumptions is key. The general model rule of “garbage in, garbage out” applies, and it is key to honor the observed
data with the most reasonable and relevant assumptions possible.
Do these inherent difficulties mean that fracture modeling is a futile endeavor? No. The fact that engineering hydraulic fractures
is problematic, to say the least, does not detract from the wealth of data that have proved their effective use and the tremendous
opportunity that exists to optimize a process that has a multibillion-USD annual impact. It is a truth that the modeling will be only
approximate and that there will always remain a significant empirical component to the process. But there has been a demonstrably
huge economic benefit from the enhanced understanding of fracture growth achieved in the last 30 years. The coming decades should
see even greater impact from further advancements in the understanding of fracture growth.
4.16 Thoughts on Future Use and Developments of Fracture Growth Models
4.16.1 Future of Hydraulic Fracture Modeling: The Big Picture. Fracture modeling started as a tool for design, using engineering
judgment to determine fracture height and fluid leakoff. With the introduction of MHF in the 1970s, it became necessary to establish
methods to obtain these parameters from field data. From that time, the evolution of fracture modeling has been driven by the desire
to better calibrate models with all available data, which started with pressure analysis and now includes logs, geological modeling,
and fracture mapping.
The workflow of stimulation optimization starts from reservoir characterization, which, in combination with a preliminary well
design, provides the basis for fracture modeling. Calibration of the fracture model is then necessary to finalize the design. The well
134 Hydraulic Fracturing: Fundamentals and Advancements
performance is obtained from reservoir simulation that incorporates the fracture geometry and properties. Comparison of the simulated and observed production is then used for optimizing subsequent stimulation treatments, with respect to both completion and
treatment parameters.
Future development of fracture modeling is expected to improve the quality of the models with better understanding of the physics of fracturing and improved numerical methods. Perhaps even more important is the integration of fracture models with other
disciplines.
On the input side, the relationship between geological modeling and fracture simulation can be improved. Fracture models should
seek to seamlessly link completion choice and the calibration process, using all available monitoring requirements. On the output side,
there is significant scope for improving production simulation for fractured wells, so that it will become easier to make an accurate
production forecast, which is necessary to optimize fracture design for a given reservoir.
The workflow depends on the type of reservoir: conventional vs. shale makes a big difference in view of fracture and well
spacing and level of interaction of hydraulic fractures with natural fractures. Geothermal-reservoir stimulation, which will
become more important in the coming decade, has many similarities with shale reservoir stimulation but targets completely
different rock types.
One overriding issue in fracture modeling is the availability of input parameters. In an ideal world, fracture mapping would be
available in real time for each treatment, but that is impossible for both practical and economic reasons. Because fracture geometry
is poorly known, in most cases the models are only approximate. An appropriate balance needs to be made between available data
and model complexity. Sophisticated 3D models make sense if a full suite of stress and property data is available, but for routine
treatments a complex model is at best a waste of effort and might even deliver worse results compared with a simple model. In recent
decades, sophisticated models have been developed, but it is still uncertain what level of complexity is required and so, in this respect,
the created fracture geometry is still of central importance.
Some practitioners have argued that the planar fracture paradigm has run its course and fracture modeling must embrace the
interpreted geological reality of fracture complexity. It cannot be denied that fractures observed in outcrops and mapped hydraulic
fractures are always branched and show much interaction with natural fractures and bedding interfaces. However, if the true fracture
geometry requires many unknown parameters for its description, it is hard to justify such a complex geometry.
The simple description of a planar fracture, in combination with a very simple wire mesh to describe the unpropped fissures connected to the main fracture or even a simple effective reservoir permeability to capture the effect of the fracture network might be
more appropriate. Fracture engineers should keep in mind what the philosopher Thomas Kuhn suggested about scientific paradigms:
It is not a matter of what the truth is but how convenient a paradigm can be by use in future research.
The paradigm of planar-fracture model application has been stretched over the last 2 decades as insight deepened, but incorporation of calibrated physical phenomena associated with tip effects, multiple fractures, and layer interface effects has not stretched it
beyond the limits of observation. Therefore, many believe that the planar-fracture paradigm is still a good basis-of-design rule that
can be applied for the industry. While its predictions might not fully represent the truth, it is still the most convenient fracture growth
application and the most effective and best overall approximation of the created fracture system.
4.16.2 Input Side of Fracture Modeling From Geology and Completion. Developing a mechanical Earth model is necessary
for any geomechanics analysis, such as borehole stability, sand face failure, and fracture stimulation. Stress, modulus, and strength
must be obtained from log and core data. DFITs, XLOTs, and microfractures are often necessary to obtain reliable stress values. For
stimulation, other petrophysical parameters such as permeability might be even more important, in both the horizontal and the vertical
direction.
Completion design is intimately connected to the formation properties, and all aspects need to be integrated for a successful treatment. Although a major advantage of fracture stimulation is insurance against unknown formation properties, it is still important to
select the best options. For instance, fracture stimulation of horizontal wells helps as insurance against a poor well path, but fracture
initiation might be made still easier by selecting the best landing depth. However, it is still far from easy to incorporate completion
issues such as a well-to-fracture connection into a fracture model, so those aspects need further development.
Integration of all inputs might be the core of the art (and enjoyment) of fracturing, but developing tools to aid the engineering
process is still important for improving efficiency.
4.16.3 Effectiveness of Calibration. Much progress has been made in pressure interpretation, but effective interpretation of techniques such as microseismic mapping is still quite limited. One limitation is that observation wells for microseismic arrays are very
costly, while good data require at least four nearby observation wells. Still, it appears worthwhile to optimize the calibration process,
making sure that the uncertainty in all data is honored, especially in microseismic surveys but also in pressure records. Furthermore,
the fracture models should be tuned to the limitations of calibration data so that the match with data is not simply a curve-fitting
exercise but really provides the engineer with insight into the created fracture system.
A specific application that needs further development is calibration of acid fracturing. It is still difficult to predict effective length of
acid fractures and longevity of the created acid fractures themselves. Another issue is the effective conductivity of propped fractures
during production. Data acquired during a treatment are representative of the fracture system at high pressure, but at drawdown
pressure the fracture conductivity can be dramatically reduced.
The physics of fracture growth along/through layer interfaces is not well-understood and is not captured well in most current
models. Future joint industry projects featuring multiple-diagnostics measurements in shales can steepen the learning curve for the
industry. Past projects with minebacks and core-throughs served to prove up the use of both microseismic and tiltmeter mapping,
including their use as calibration points for models. To some degree, this is happening in the industry today, but bringing the physics
of multilayer and layer interface effects into models has been an elusive goal.
4.16.4 Output Side to Reservoir Simulation. Perhaps the relation between fracture models and reservoir simulation has the greatest potential for improvement. After all, the entire purpose of stimulation is to improve production, which must be quantified with
reservoir simulation. In the past decades, much work has been done to add fracture modeling results to full-field (or sector) simulation
models, but there is still scope for streamlining the process and further developing specific applications. For instance, the modeling
Hydraulic Fracture Modeling
135
of refracturung jobs is often inaccurate and results in inaccurate estimates of refracture effectiveness. Fracture model integration with
reservoir simulation is a development that will benefit optimization of treatments, as well as facilitating more-accurate post-fracturing
analysis of production. It has always been an issue to determine whether poor well performance is caused by poor stimulation and
flowback, or poor reservoir quality; but in the future this will become even more important because projects will increasingly target
marginal reservoirs. Obviously, dramatic improvements can be achieved by hydraulic fracture treatment, even in very tight reservoirs,
but, ideally, effective treatments should be based on a realistic assessment of reservoir quality.
4.17 Conclusions
• Two decades of development have seen models catching up as practical tools. Fully gridded models, parameterized models,
fully coupled models and fracture network models have all reached the stage where they can be applied routinely to
practical cases. Fracture models are now being used to forecast the potential production success and efficiency of hydraulic
fracture treatments. Their ability to improve treatment success and reflect the resulting created fracture geometry is their
most important asset.
• Models and associated assumptions have changed dramatically through model calibration with fracture diagnostics. The
changes to fracture modeling assumptions and strategy have been dramatic and significant since the release of the previous
SPE Monograph (Gidley et al. 1989). The application range of hydraulic fracturing has been extended downward by several
orders of magnitude of rock permeability through design and efficiency improvements of this technique in shale rock. In addition, direct diagnostic observations on thousands of fracture treatments have revealed the surprising complexity and variability
of hydraulic fracturing. Fracture model calibration has proved both heartening and humbling, but those in the industry have
learned how a fracture model can be adjusted to match most diagnostic results and the observed net-pressure behavior. A general trend that has been observed is that fractures show moderate containment and, without any prior knowledge of fracturing
in a new area, a 5/1 length-height ratio appears to be a reasonable suggested initial estimate.
• “New” physical mechanisms have been added to models to reflect improved physical understanding. Fracturing knowledge has
grown by leaps and bounds with wild swings in understanding of fracture geometries. Big changes in implemented physical
processes include effects process zone, multiple fracture growth, and layer interface effects.
• The addition of shale has resulted in two distinct modeling approaches—science vs. engineering. The shale focus on pumping efficiency limits time dedicated to more-sophisticated measurements while fracturing. Measurements vital to fracture
pressure behavior are normally performed before the job, during a DFIT, while some extra time might be dedicated to
more-detailed measurements during some treatment stages. Engineering with a full suite of data is often conducted at the
start of the development program, during a pilot. The balance for completion engineering in low-cost shale wells lies in
the collection of fracture closure, efficiency, and net pressure on a few stages per multiwell pilot, as well as some fracture
mapping and calibrating these data by the collection of production data over a few months or a year. From that, a masscompletion approach follows with minor modifications to fracture designs. With the focus on pump efficiencies and well
cost reduction in shale plays, engineering needs to be cost-effective. For high-cost wells, diagnostic injections will remain
a viable option for evaluation. In conventional reservoir stimulation, a variety of anchor points can be collected during
multiple pre-job injections. Project success hinges on relatively high-cost individual wells, while the cost of engineering
and data collection is relatively small.
• Model selection needs to be matched with calibration data quality and sophistication. As detailed in this chapter, it is expected
that the focus will remain on a “roughly right” fracture growth modeling strategy, with its trade-off between optimized simulation run time and requisite model sophistication. A simple “back-of-the-envelope” model with calibrated parameters can be
much more useful for assessing alternative fracture design predictions than a sophisticated model that is not calibrated.
• Despite the development of complex fracture models, the planar-fracture paradigm remains valid. The paradigm of planarfracture-model application has seemingly been stretched over the last 2 decades as insight deepened, but incorporation of
calibrated physical phenomena associated with tip effects, multiple fractures, and layer interface effects has not stretched it
beyond the limits of usefulness. The planar-fracture paradigm is still an applicable ruling paradigm for the industry. While its
predictions might somewhat average the truth, it is still the most convenient for applications and the best overall approximation
of the created fracture system.
• Mechanisms such as layer interface effects are still not well-understood. This chapter shows many examples of fracture model
development associated with joint-industry projects featuring multiple-diagnostics measurements, which have dramatically
steepened the learning curve for model progress. Past projects with minebacks and core-throughs served to prove up microseismic and tiltmeter mapping, and to suggest methodologies and calibration points for models. Future efforts could help to
better understand rock mechanics and the physics of layer interface effects.
• The industry can adapt again, once it is ready to leave the planar-fracture-model paradigm. In 1989, when the previous hydraulic fracture monograph was published, shale was not a viable commercial target for fracturing. The consensus about created
hydraulic fractures was that they were mostly confined and simple. Fracture diagnostics have changed the view of fracturing
and fracture propagation models in three calibration cycles, and the industry has been very willing to adapt. Further changes
and redirections will occur in the future, and it is important that the industry continues to adapt and adopt the new paradigms.
Because when the facts change, there is a need to change the models.
4.18 Nomenclature
=
gravitational acceleration
Ai
=
time-dependent fracture surface area at time i
g
dgross
=
pay height
H
=
fracture height
=
hydraulic head in fracture K
E
=
Young’s modulus
HK
E
=
E
4 (1 − ν 2
Hh
=
hydraulic height
HNf
=
normalized fracture height
)
136 Hydraulic Fracturing: Fundamentals and Advancements
Hi
=
total height at time i
Vleakoff
=
leakoff volume
ISIP
=
instantaneous shut-in pressure
Vp
=
pore volume
Kb
=
rock bulk modulus
vs
=
unobstructed particle settling velocity
Kf
=
permeability of channel
vx
= local fluid velocity
Kg
=
grain bulk modulus
w
=
fracture width
KI
=
stress intensity factor for Mode I fracture
growth behavior (fracture opening)
wi
=
fracture width at the wellbore
KIc
=
fracture toughness or critical stress intensity
factor of the rock
Kl
=
Carter leakoff coefficient
L
=
tip-to-tip fracture length
LH
=
fracture half length
LNf
=
normalized fracture length
Li
=
total length at time i
nfrac
=
number of fracture strands
pfrac
=
pressure in the main body of the hydraulic
fracture
wx
=
local fracture width
α
=
fracture aspect ratio
βperf
=
perforation friction coefficient
βnwb
=
near-wellbore friction coefficient
γ
=
stress path parameter
γcn
=
fracture-width shape factor
γ1
=
fracture-width shape function
δp
=
pressure drop over distance δx
Δpfriction
=
frictional pressure loss through the wellbore,
perforations, and near-wellbore region of the
fracture
Δphydrostatic
=
hydrostatic head
Δpnwb
=
frictional pressure loss through the near-wellbore region of the fracture
pnet
=
net pressure
pnet,obs
=
observed net pressure
psurface
=
measured surface pressure
q
=
flow rate per unit height Q/h
Δpperf
=
frictional pressure loss through perforations
Q
=
total flow rate
ε
=
fracture efficiency
rb
=
radius of particle (ball)
μ
=
apparent viscosity
Rf
=
Fracture radius
ν
=
Poisson’s ratio
Rp
=
particle radius
ρf
=
s
=
integration variable
specific density of the fluid the particle is
embedded in
tclosure
=
closure time
ρmax
=
tcD
=
dimensionless closure time
maximum specific density of the various slurries pumped during a fracturing job
=
injection time
ρmin
=
tinjection
minimum specific density of the various slurries pumped during a fracturing job
ti
=
injection period
ρp
=
specific density of the particle
V
=
injection volume
σclosure
=
closure stress
Vfracture
=
fracture volume
4.19 References
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Hydraulic Fracture Modeling
137
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Chapter 5
Proppants and Fracture Conductivity
David Milton-Tayler, FracTech Limited; Robert Duenckel, CoreLab
David Milton-Tayler is the technology manager at FracTech Limited, a private firm that offers technology services to the oil and gas
industry in the UK and internationally.
Robert Duenckel is vice president in the Stim-Lab Division of CoreLab. His interests are directed at all aspects of hydraulic
­fracturing. Duenckel is a registered professional engineer and holds a BS degree in petroleum engineering from Missouri University
of Science and Technology.
Contents
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Overview�������������������������������������������������������������������������������������������������������������������������������������������������������������� 144
Introduction���������������������������������������������������������������������������������������������������������������������������������������������������������� 144
Effect of Fracture Conductivity on Well Performance������������������������������������������������������������������������������������������ 145
Commercial Proppants���������������������������������������������������������������������������������������������������������������������������������������� 146
5.4.1 Early History������������������������������������������������������������������������������������������������������������������������������������������ 146
5.4.2 Ottawa or “White” Sands������������������������������������������������������������������������������������������������������������������������ 146
5.4.3 Brady Sands������������������������������������������������������������������������������������������������������������������������������������������ 146
5.4.4 White vs. Brown Sand���������������������������������������������������������������������������������������������������������������������������� 146
5.4.5 Regional Sand Sources������������������������������������������������������������������������������������������������������������������������� 147
5.4.6 Ceramic Proppants�������������������������������������������������������������������������������������������������������������������������������� 148
5.4.7 Resin-Coated Proppants������������������������������������������������������������������������������������������������������������������������ 148
5.4.8 Ultralightweight Proppants��������������������������������������������������������������������������������������������������������������������� 149
5.4.9 Other Proppant Types���������������������������������������������������������������������������������������������������������������������������� 149
5.4.10 Proppant Properties������������������������������������������������������������������������������������������������������������������������������� 149
5.4.11 Sampling������������������������������������������������������������������������������������������������������������������������������������������������ 149
5.4.12 Proppant Grain Size and Distribution����������������������������������������������������������������������������������������������������� 149
5.4.13 Determination of Grain Size������������������������������������������������������������������������������������������������������������������� 149
5.4.14 Proppant Sphericity and Roundness����������������������������������������������������������������������������������������������������� 151
5.4.15 Acid Solubility����������������������������������������������������������������������������������������������������������������������������������������� 151
5.4.16 Turbidity Testing�������������������������������������������������������������������������������������������������������������������������������������� 152
5.4.17 Bulk and Apparent Density��������������������������������������������������������������������������������������������������������������������� 152
5.4.18 Proppant Crush-Resistance Test����������������������������������������������������������������������������������������������������������� 152
5.4.19 Loss on Ignition of Resin-Coated Proppant������������������������������������������������������������������������������������������� 152
Laboratory Measurements of Fracture Conductivity�������������������������������������������������������������������������������������������� 152
Factors Affecting Fracture Conductivity—Proppant Characteristics and Fluids�������������������������������������������������� 154
5.6.1 Fracture Conductivity, Permeability, and Beta Factor����������������������������������������������������������������������������� 154
5.6.2 Proppant Crush and the Effect of Cyclic Stress������������������������������������������������������������������������������������� 155
5.6.3 Fines Migration and Plugging����������������������������������������������������������������������������������������������������������������� 156
5.6.4 Proppant Size Distribution and Shape��������������������������������������������������������������������������������������������������� 157
5.6.5 Proppant Coatings��������������������������������������������������������������������������������������������������������������������������������� 157
5.6.6 Fracturing Fluid Residue������������������������������������������������������������������������������������������������������������������������ 158
Factors Affecting Fracture Conductivity—Interactions with the Reservoir����������������������������������������������������������� 158
5.7.1 Introduction�������������������������������������������������������������������������������������������������������������������������������������������� 158
5.7.2 Closure Stress, Temperature, and Time������������������������������������������������������������������������������������������������� 159
5.7.3 Embedment�������������������������������������������������������������������������������������������������������������������������������������������� 159
5.7.4 Diagenesis��������������������������������������������������������������������������������������������������������������������������������������������� 160
144 Hydraulic Fracturing: Fundamentals and Advancements
5.8
5.9
5.7.5 Proppant Flowback�������������������������������������������������������������������������������������������������������������������������������� 160
5.7.6 Non-Darcy and Multiphase Flow������������������������������������������������������������������������������������������������������������ 161
Nomenclature������������������������������������������������������������������������������������������������������������������������������������������������������ 162
References���������������������������������������������������������������������������������������������������������������������������������������������������������� 162
5.1 Overview
This chapter discusses propping agents (proppants) and their role in the hydraulic fracturing process. It reviews the development of
proppants from the initial application to present-day proppant products and describes the role of proppants in affecting the performance of hydraulically fractured wells. The chapter also addresses specifically the role of fracture conductivity in determining the
outcomes of fracture stimulation, discusses the measurement of proppant pack permeability and conductivity in the laboratory, and
explores factors that can severely limit these properties in the downhole environment.
5.2 Introduction
Proppants are essential components of hydraulic fracturing. Without using proppants in the fracturing process, the fractures that are
created will essentially close, which will severely limit the intended well performance benefit (Howard and Fast 1970). The types
and volumes of proppants used in a fracture stimulation vary widely from high-strength large-mesh ceramic proppants in deepwater frac packs and high-permeability conventional reservoirs to very-fine-mesh natural sand products commonly used in onshore
unconventional well developments in North America. The challenge in choosing the right proppant lies in an understanding of the
reservoir properties and the expected fracture geometry to be created, and then matching that understanding to a selection of proppant
properties and performance. Ultimately, the decision is an economic one—a balance of the cost of application of a particular type and
volume of proppant against the value returned.
The three major types of proppants are naturally occurring fracturing sands, manufactured ceramic proppants, and resin-coated proppants, which can be either sands or
ceramics, but most often are sands. In addition, very-lightweight deformable proppant
products and other similar specialty products are available. The breakdown of volume
Global Proppant Consumption
by proppant type is shown in Fig. 5.1. As is evident from the figure, natural sands
by Type 2018
dominate the proppant market.
The demand for proppants, mainly natural sands, has increased dramatically over the
Ceramic
Resin coated
last decade in North America because of the aggressive development of unconventional
1.9%
1.0%
reservoirs. These reservoirs have been developed using horizontal wells with multiple
stages of fracturing occurring throughout the horizontal section. In addition, horizontal
section lengths have increased in general as have the number of stages and the intensity
to which sand volumes have been applied. This has combined to create a significant
increase in fracturing sand requirements per well. Fracturing sand volumes per well
completion have increased from less than 1 million lbm in 2008 (EIA 2016) to more
than 14 ­million lbm in 2018 (Fig. 5.2).
This combination of length, stages, and proppant volumes per stage has led to growth
in total natural sand proppant volumes pumped in the US from roughly 10.5 billion lbm
in 2006 to 225.4 billion lbm in 2018, as shown in Fig. 5.3.
While uncoated natural sands dominate the proppant type used in unconventional
developments of North America, conventional reservoir development continues in the
deepwater Gulf of Mexico and elsewhere globally where proppants of generally higher
conductivity, such as ceramic proppants, are applied. In addition, resin-coated propSand
pants, which are principally sand, continue to be applied in many cases. The share of
97.0%
proppant consumption represented by ceramics and resin-coated proppants has declined
from nearly 30% in as recently as 2009 to approximately 3% in 2018. Fig. 5.4 shows the
Fig. 5.1—Global proppant market by
proppant type. Courtesy of PropTester volumes of ceramic and resin-coated proppant pumped.
Fig. 5.5 shows total global proppant consumption.
Inc. and Kelrik LLC (2019).
North America—Fracturing Sand/Completion
16
14
Million (lbm)
12
10
8
6
4
2
0
2014
2015
2016
2017
2018
Fig. 5.2—Proppant trends per well completion. Courtesy of PropTester Inc. and Kelrik LLC (2019).
Proppants and Fracture Conductivity
145
Fracturing Sand Consumption
250
Billion (lbm)
200
150
100
50
0
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Fig. 5.3—US Fracturing sand consumption. Courtesy of PropTester Inc. and Kelrik LLC (2019).
Ceramic and Resin-Coated Proppants
18
16
Resin coated
Billion (lbm)
14
Ceramic
12
10
8
6
4
2
18
17
20
16
20
15
20
14
20
13
20
12
20
11
20
10
20
09
20
08
20
07
20
06
20
05
20
04
20
03
20
02
20
01
20
20
20
00
0
Fig. 5.4—Global ceramic and resin-coated proppants pumped. Courtesy of PropTester Inc. and Kelrik LLC (2019).
Proppant Consumption
250
Billion (lbm)
200
Resin coated
150
Ceramic
Total sand
100
50
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
0
Fig. 5.5—Total global proppant consumption. Courtesy of PropTester Inc. and Kelrik LLC (2019).
5.3 Effect of Fracture Conductivity on Well Performance
The goal of a hydraulic fracture well stimulation is to create a conductive propped fracture that will provide an effective connection
from the wellbore to the formation. Proppant selection and placement are then important aspects of a successful stimulation treatment.
Fracture conductivity is traditionally reported as the product of the proppant pack permeability and the propped fracture width, kfw,
and is reported in millidarcy-feet (md-ft).
The potential productivity benefit of the fracture is dictated by the capacity of the formation to deliver fluids to the fracture and
the capacity of the fracture to produce the fluids to the wellbore. This relationship of fracture conductivity to reservoir capacity is
­commonly referred to as dimensionless fracture conductivity and defined as
CfD = kfw/kxf , ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� (5.1)
146 Hydraulic Fracturing: Fundamentals and Advancements
where k is the formation permeability in md, kf is the fracture permeability in md, w is the propped fracture width in ft, and xf is
the fracture half-length in ft. In general, a dimensionless conductivity of 30 or greater is taken to represent an infinite-conductivity
fracture.
It is important to consider that the permeability of a proppant pack kf is typically reported from laboratory testing as described in
Section 5.5 of this chapter. This permeability thus reported is obtained at Darcy flow conditions with a clean, single-phase fluid at
some constant stress and is sometimes considered to be an intrinsic property of the proppant pack, varying only in terms of closure
stress. However, the actual conditions in the downhole environment will significantly alter the laboratory measured ­permeability.
These conditions include the effects of multiphase flow, damage from fracturing fluids, formation fines migration, plugging from scale
and salt formation, and the effects of non-Darcy flow. Because the conditions of flow in the fracture are under constant change as a
result of changes in fluid-flow volumes and closure stress, the permeability of a proppant pack, and its conductivity, should be considered a variable and in terms of effective conductivity—that is, the conductivity specific to the flowing conditions at the time. Effective
pack permeabilities are often less than 5% of the laboratory measured permeabilities (Barree et al. 2019; Duenckel et al. 2017).
5.4 Commercial Proppants
5.4.1 Early History. One of the first proppants used in the initial efforts at hydraulic fracturing in the 1940s was dredged Arkansas
River Sand (Gidley et al. 1995). Later, during the mid-1950s, sand from the Ordovician St. Peter Sandstone Formation near Ottawa,
Illinois, USA, became available. In 1958, sand mines near Brady, Texas, USA, opened producing sand from the Hickory Sandstone
Formation.
The mining process for these naturally occurring sandstone deposits includes disassociation of the sand by crushing, screening, and
washing to separate the sandstone matrix into its independent sand grains. A wide range of particle sizes is found in these deposits,
and they must be screened to achieve the desired sizing.
The growth in the application of hydraulic fracturing in the 1980s led to sand supplies from the Cambrian Jordon, Ironton and
Mt. Simon sandstones of Minnesota and Wisconsin. The development of unconventional reservoirs in North America also led to a
­dramatic increase in requirements for natural fracturing sands. The intensity with which proppant is used on a per-well basis has
further boosted the demand for proppants, primarily natural sands.
This dramatic increase in fracturing sand requirements has contributed to the opening of mines more closely positioned to the
development areas in North America. These “regional sands” have become a significant component of the proppant market. Fracturing
sand mining currently occurs in 17 US states, with Wisconsin, Illinois, and Texas as the dominant producers. More than 75 companies
in the US now engage in providing natural fracturing sands. Canada also has significant fracturing sand mining capacity. A number of
sources supply sand globally, including some in Australia and the Middle East.
5.4.2 Ottawa or “White” Sands. Ottawa or “white” or “northern white” sands (Fig. 5.6) are mined principally from the St. Peter
­(Ordovician), the Jordon and Wonewoc (Cambrian), and equivalent deposits. These deposits are broad in areal extent, being mined in
Wisconsin, Illinois, Minnesota, and nearby states.
White sands are considered the highest-quality fracturing sands. They are monocrystalline (have a single crystal phase), resulting in superior strength properties relative to other sands. These sands are characterized by high purity, generally 99% quartz with
occasional minor clays present, with a high degree of roundness and sphericity. The Ordovician St. Peter is also mined in portions of
Missouri and Arkansas.
5.4.3 Brady Sands. Brady sands, also referred to as “brown” sands, are mined from the Hickory Sandstone (Cambrian) in
­central Texas near the town of Brady (Fig. 5.7). The brown appearance emanates from small amounts of iron oxide. These sands
are ­polycrystalline in nature—each grain is composed of more than one quartz crystal bonded together leaving cleavage planes in
the whole grain. The presence of these cleavage planes gives rise to a performance difference between the white and brown sands.
The brown sands are typically 97+% quartz with minor amounts of clay and feldspars.
5.4.4 White vs. Brown Sand. Because of the monocrystalline structure and generally more spherical shape, the white sands typically
show higher conductivity than brown sands. This difference is demonstrated in the baseline conductivity result shown in Fig. 5.8.
The conductivities are measured per API RP 19D (2008) and are typical for these materials. The less spherical nature of the brown
Fig. 5.6—40/70 White sand.
Fig. 5.7—40/70 Brady sand.
Proppants and Fracture Conductivity
Baseline Conductivity
4,000
Conductivity (md-ft)
147
3,500
30/50 Brown sand
3,000
2,500
30/50 White sand
2,000
1,500
1,000
500
0
0
2,000
4,000
6,000
8,000
10,000
12,000
Closure Stress (psi)
Fig. 5.8—Typical baseline conductivities—white and brown sands.
sands provides for a more porous pack when loading the American Petroleum Institute (API) conductivity cell and is reflected in
higher conductivity for the brown sands at low stress. Closure stress increases the higher strength of the white sands, which then leads
to higher conductivities at elevated stresses.
5.4.5 Regional Sand Sources. As noted earlier, within North America a significant number of new mines have been developed
proximate to drilling activity to meet the growing volume requirements and lower the delivered cost of fracturing sands by reducing
transportation costs. These include aeolian dune sands in west Texas, and sources in south Texas, east Texas, Oklahoma, the northeastern US, and other locations. The combined capacities for these regional sources exceed those of the traditional white and brown
sand mines. The chemistries of these regional sands can vary, and they often, but not always, have lower levels of quartz and a higher
component of impurities. They tend to be less spherical in shape. Each of these deposits will have variations in physical properties and
performance that must be determined to make comparisons to the traditional white and brown sands. Fig. 5.9 is a sand from a dune
deposit in west Texas. Fig. 5.10 is a sand from a Canadian glacial deposit, and Fig. 5.11 is Arkansas River sand. All are sized at 40/70.
Table 5.1 shows the typical mineralogy of these sands, compared with the white and brown sands.
Fig. 5.9—West Texas dune sand.
Fig. 5.10—Canadian glacial sand.
Fig. 5.11—Arkansas River sand.
Regional Sand Mineralogy (wt%)
Quartz
White sand
99
Brown sand
97
Canadian glacial
86
West Texas dune
97
Arkansas River sand
83
Table 5.1—Typical mineralogy.
Plagioclase
K-feldspar
Mica
Total clays
(illite/kaolinite)
1
2
1
4
6
2
2
2
1
4
11
1
148 Hydraulic Fracturing: Fundamentals and Advancements
5.4.6 Ceramic Proppants. Unlike fracturing sands that are naturally occurring, ceramic proppants are manufactured man-made materials. Ceramic proppants were developed in response to a requirement for higher-strength proppants for deep-well applications at high
closure stresses. Ceramic proppants first entered the industry in the late 1970s on the basis of a patent by Cooke et al. (1978). These
proppants were manufactured through the sintering of bauxite—a naturally occurring alumina silicate clay containing more than 80%
aluminum oxide (Al2O3). Ceramic proppants of 80% or more aluminum oxide are commonly referred to as high strength (Fig. 5.12).
The development of these high-strength proppants was followed soon by the introduction of what is commonly referred to as an
intermediate-strength proppant (ISP) in which the starting ore was lower in aluminum oxide, generally 70 to 75% (Fitzgibbon 1984).
The densities of these products were higher than that of natural sands, approximately 3.6 g/cm3 for the high-strength ceramics and
3.3 g/cm3 for the ISPs vs. 2.65 g/cm3 for sands (Fig. 5.13).
Fig. 5.13—ISP ceramic.
Fig. 5.12—High-strength ceramic.
The first lightweight ceramic was introduced in 1985 using an
ore that is principally kaolinite with an l2O3 content of approximately 50% (Lunghofer 1985). Its density was very close to that
of sands (Fig. 5.14).
Ceramic proppants are manufactured by first grinding the ores
very finely (usually < 15 µm), pelletizing, and then sintering at
temperatures near 2,700°F. In the sintering process, the bauxite
and kaolinite clays form into crystalline materials of corundum,
mullite, and christobolite. The higher Al2O3 content in general
leads to high corundum content and greater individual-pellet
strength. Some very high Al2O3 proppants have been introduced
in which the crystalline structure approaches 100% corundum.
Though the manufacturing process is similar among various
­suppliers, the quality and performance of each type of ceramic
proppant can vary significantly. Ceramic proppants generally
have high sphericity and roundness relative to natural sands, but
Fig. 5.14—Lightweight ceramic.
again this can vary from product to product.
Ceramic proppants are commonly referred to as high density
(or high strength), intermediate density, or lightweight (Table 5.2). While ceramic proppants are most generally of a highstrength, intermediate-density, or lightweight category and generally ­spherical, other variations of ceramic proppants are available.
These include high-strength ceramics that are rod shaped rather than spherical and lower-density ceramics (specific gravity of
­approximately 2.0).
5.4.7 Resin-Coated Proppants. Resin coatings of proppants were introduced to provide certain improved performance characteristics. The phenolic resin coatings are offered generally as curable or precured. In the case of curable coatings, the coatings are
­manufactured and added in a manner so that complete curing will occur after placement in the fracture. This final curing is initiated
as a result of reservoir temperature, or the closure stress, or both. The curing process results in creating a bond between the proppant
grains, thus preventing the proppant from flowing back into the wellbore after placement. In the case of precured coatings, there is
little to no adhesion between proppant grains. The resin coating also helps to improve the conductivity performance of sands by better
Type
High Density or
High Strength
Intermediate Density or
Intermediate Strength
Lightweight
Ultralightweight
Specific Gravity, g/cm3
>3.3
>3.0
>2.65
≈2.0
Bulk Density, lbm/ft2
>120
>110
>94
≈70
Table 5.2—Typical ceramic proppant properties.
Proppants and Fracture Conductivity
149
d­ istribution of the closure stress among the proppant grains in a pack, thus reducing somewhat the grain failure, and also by encapsulating fines that are generating by grain failure and preventing this movement in the pack, thus preserving pack permeability (­ Graham et
al. 1975; Johnson and Armbruster 1982). These resin coatings can be applied to any type and size of proppant, whether natural sands
or ceramics. Curable coatings are most prevalent when used with ceramic proppants. Fig. 5.15 demonstrates the effects for resin coating of a 30/50 sand. Conductivity is generally lower for the resin-coated sand at low stress because the coating occludes some of the
intergra­nular porosity. However, at high stresses the conductivity for the resin-coated sand is greater because of the distribution of
closure stress (thus reducing grain failure) and the encapsulation of fines that are generated as grain failure occurs. Encapsulation of
these fines prevents their migration in the proppant pack, which can block pore throats, reducing conductivity.
Baseline Conductivity
Conductivity (md-ft)
4,000
3,500
30/50 sand
3,000
2,500
Resin coated
2,000
1,500
1,000
500
0
0
2,000
4,000
6,000
8,000
10,000
Closure Stress (psi)
12,000
14,000
Fig. 5.15—Conductivity: uncoated vs. resin-coated sand.
5.4.8 Ultralightweight Proppants. Proppants have been introduced with densities less than 2.65 g/cm3 and referred to as ultralightweight proppants. In some cases, these are porous ceramics that have been coated to encapsulate the pores. In other cases, these are
polymeric types of products that deform under stress rather than suffering grain failure. Densities as low as 1.0 g/cm3 have been available to the industry. These products generally offer the potential of improved proppant transport but generally do not offer the same
level of conductivity performance as the higher-density proppants.
5.4.9 Other Proppant Types. Other proppants with specialty characteristics are available in the marketplace. These include porous
ceramic proppants that are infused with certain chemicals such a scale inhibitors, and proppants with coatings that can provide selfsuspending behavior for improved proppant transport.
5.4.10 Proppant Properties. The procedures for determining the physical properties of proppants are set out in API STD 19C (2018)
(Duenckel et al. 2016). These basic physical properties include particle size and distribution, particle sphericity and roundness, acid
solubility, turbidity, density, crush resistance, and loss on ignition for resin-coated proppants.
5.4.11 Sampling. One of the key aspects of measuring proppant properties is sampling to ensure that a representative sample is
tested. Unless the sample tested is truly representative of a total shipment or container, testing and correlation with standards or
expected properties will be difficult at best. API STD 19C (2018) sets out recommendations for the sampling of bulk and bagged
materials, including recommended sampling devices. For the best representation of the product, continuous sampling is ideal, but
this is usually not possible in the field. All samples should be obtained from a flowing stream by a manual or automatic sampler. A
minimum of one sample per 9000 kg should be obtained. Because of forces that lead naturally to segregation of particles of differing
mass and size, samples should not be taken from a static pile.
5.4.12 Proppant Grain Size and Distribution. The grain size of a proppant and the distribution of these grains are key characteristics that determine its performance. These factors will directly influence conductivity performance and placement in the fracture.
5.4.13 Determination of Grain Size. API STD 19C (2018) established a consistent methodology for proppant sieve analysis and
evaluation. Equipment required includes sieves in compliance with the American Society for Testing and Materials series and a
shaker that provides simultaneous rotating and tapping action. Table 5.3 shows the sieve stacks to be used per API STD 19C
(2018).
Table 5.4 shows the equivalent particle diameter in inches, micrometers, millimeters, and centimeters for each US sieve-screen
mesh. Nominal particle diameters are expected to pass through the holes in each sieve screen.
The limitations on sieve distribution for proppant in hydraulic fracturing applications per the specifications in API STD 19C (2018)
follows.
• Most of the material, 90%, must fall between the two mesh sizes.
• No more than 0.1% can be coarser than the next largest mesh size.
• No more than 1% is permitted to fall into the pan.
150 Hydraulic Fracturing: Fundamentals and Advancements
Sieve-Opening Sizes
(μm)
3350/
1700
2360/
1180
1700/
1000
1700/
850
1180/
850
1180/
600
850/
425
600/
300
425/
250
425/
212
212/
106
30/50
40/60
40/70
70/140
Typical Proppant/Gravel-Pack Size Designations
6/12
8/16
12/18
12/20
16/20
16/30
20/40
Stack of ASTM Sievesb
First primary sieve
in bold type
4
6
8
8
12
12
16
20
30
30
50
6
8
12
12
16
16
20
30
40
40
70
8
10
14
14
18
18
25
35
45
45
80
Second primary
sieve in bold type
10
12
16
16
20
20
30
40
50
50
100
12
14
18
18
25
25
35
45
60
60
120
14
16
20
20
30
30
40
50
70
70
140
16
20
30
30
40
40
50
70
100
100
200
pan
pan
pan
pan
pan
pan
pan
pan
pan
pan
pan
a
Sieve series as defined in ASTM E11 (2017).
b
Sieves stacked in order from top to bottom.
Table 5.3—Sieve sizes (API STD 19C 2018 ).
US Mesh
D (in.)
D (µm)
D (mm)
D (cm)
3
0.265
6730
6.73
0.6731
4
0.187
4760
4.76
0.47498
5
0.157
4000
4
0.39878
6
0.132
3360
3.36
0.33528
7
0.111
2830
2.83
0.28194
8
0.0937
2380
2.38
0.237998
10
0.0787
2000
2
0.199898
12
0.0661
1680
1.68
0.167894
14
0.0555
1410
1.41
0.14097
16
0.0469
1190
1.19
0.119126
18
0.0394
1000
1
0.100076
20
0.0331
841
0.841
0.084074
25
0.028
707
0.707
0.07112
30
0.0232
595
0.595
0.058928
35
0.0197
500
0.5
0.050038
40
0.0165
400
0.4
0.04191
45
0.0138
354
0.354
0.035052
50
0.0117
297
0.297
0.029718
60
0.0098
250
0.25
0.024892
70
0.0083
210
0.21
0.021082
80
0.007
177
0.177
0.01778
100
0.0059
149
0.149
0.014986
120
0.0049
125
0.125
0.012446
140
0.0041
105
0.105
0.010414
170
0.0035
88
0.088
0.00889
200
0.0029
74
0.074
0.007366
230
0.0024
63
0.063
0.006096
270
0.0021
53
0.053
0.005334
325
0.0017
44
0.044
0.004318
400
0.0015
37
0.037
0.00381
Table 5.4—US mesh and equivalent particle diameters (D).
Proppants and Fracture Conductivity
151
Fig. 5.16 shows typical distributions for a 30/50- and 20/40-sized proppant meeting the specifications above.
After determination of the sieve distribution, the mean and median particle diameters of the proppant can be calculated as per
API STD 19C, using a variable called phi, ϕ. It is calculated using Eq. 5.2 as one-half the difference in the negative logarithm (Base 2)
of the opening sizes of the sieve of interest and the just previous sieve multiplied by the frequency of that fraction:
ϕ = −1/2 × log2 (Oi −1) + log2 (Oi) × ni , ������������������������������������������������������������������������������������������������������������������������������������������(5.2)
where Oi is the sieve opening of interest in mm and ni is the relative mass retained or frequency of occurrence in mass %.
Median phi, ϕ50, is the sum of those differences divided by the sum of the frequencies and is calculated by Eq. 5.3:
ϕ50 = Σϕi / Σni. �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(5.3)
Median diameter, d50, is the antilogarithm (Base 2) of the median phi, ϕ50, and is calculated using Eq. 5.4:
d50 = 2 −φ50 . ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� (5.4)
5.4.14 Proppant Sphericity and Roundness. This measurement evaluates and reports the shape of the proppant. The determination
is made through use of the Krumbein/Sloss chart (Fig. 5.17). The specifications call for ceramic proppants to have a sphericity of 0.7
or greater and roundness of 0.7 or greater. All other proppants should have sphericity and roundness of 0.6 or greater. The measurement is made by visually examining a large number of individual particles, comparing them to the chart, assigning a roundness and
sphericity value to each particle, and then calculating an arithmetic average to obtain a sphericity and roundness value for the proppant.
5.4.15 Acid Solubility. Acid solubility evaluation provides guidance for proppants that can be used in applications subject to contact
with acid. In this test, the proppant is immersed in a 12:3 hydrochloric/hydrofluoric acid for 30 minutes of 150°F. Proppant weights
before and after acid exposure are measured to determine a percent acid solubility. The API STD 19C (2018) specifications limit acid
solubility to 2% for fracturing sands and resin-coated sands larger than or equal to 30/50-mesh sizes and 3% for smaller mesh sizes.
For ceramic proppant, the maximum solubility is 7%.
30/50
60
50
wt%
wt%
40
30
20
10
0
25
30
35
40
45
US Mesh
50
60
45
40
35
30
25
20
15
10
5
0
20/40
20
25
30
35
40
US Mesh
45
Fig. 5.16—Typical distributions for 30/50- and 20/40-sized proppant.
Y
0.9
0.7
X—Roundness
Y—Sphericity
0.5
0.3
0.1
0.3
0.5
Fig. 5.17—Krumbein/Sloss chart.
0.7
0.9
X
50
152 Hydraulic Fracturing: Fundamentals and Advancements
5.4.16 Turbidity Testing. This procedure determines the amount of suspended particles or other finely divided matter present in the
proppant sample. In general, this test measures an optical property of a suspension that results from the scattering and absorption of
light by the particulate matter suspended in a wetting fluid. The higher the turbidity number, the greater the quantity of suspended
particles are present. A 20-mL sample of proppant is placed in 100 mL of water and shaken. The turbidity of the resulting suspension
is then measured. The turbidity of all proppant should not exceed 250 formazin turbidity units.
5.4.17 Bulk and Apparent Density. The bulk density of the proppant describes the mass of proppant that fills a unit volume and
includes both proppant and porosity. It is measured by pouring the proppant into a calibrated cylinder. The proppant required to fill the
cylinder is weighed and that mass divided by the known volume of the cylinder to determine the bulk density. The apparent density
is measured using a wetting low-viscosity fluid and includes pore space inaccessible to the fluid. It is determined by placing a known
mass of proppant into a calibrated pycnometer, adding the test fluid, and calculating the apparent densities from the weights of the
proppant and the fluid.
5.4.18 Proppant Crush-Resistance Test. Crush-resistance tests are conducted on proppant to measure the degree of proppant grain
failure that is to be expected at a specific stress. The test offers a means of comparing the relative strengths of proppants. These tests
are conducted on proppant products that have been sieved to remove particles that are outside of the stated sieve distribution for
that particular proppant. The procedure involves loading a 2-in.-diameter crush cell with a mass of proppant equivalent to 4 lbm/ft2.
A predetermined stress is then applied and held for 2 minutes. The sample is sieved again, and the amount of material smaller than
the bottom sieve size is weighed to determine the amount of fines that were generated. This is reported as percent crush. Typically,
the highest stress level at which the proppant generates no more than 10% crush material rounded down to the nearest 1,000 psi is
reported. This is often referred to as the “K” value for the proppant. This measurement does not apply to resin-coated proppants
because the resin coating tends to agglomerate the particles.
5.4.19 Loss on Ignition of Resin-Coated Proppant. A simple loss-on-ignition test is used to determine the weight percent of resin
coating present on a resin-coated proppant sample. A predetermined mass of proppant is weighed before and after being placed in a
furnace at 1,700°F for 2 hours. The weight loss is indicative of the percent resin coating.
5.5 Laboratory Measurements of Fracture Conductivity
Interest in the evaluation of proppants arose not long after the introduction and acceptance of hydraulic fracturing as an important
stimulation methodology (Gidley et. al. 1989). This interest developed from a number of factors by operators, service companies, and
proppant suppliers. Operators attempting to relate well production to proppant properties required a reliable determination of proppant performance. In preparing job designs, service companies had a requirement for proppant properties to use in recommending
a specific proppant. Proppant suppliers required proppant data to effectively market their products. Initially, efforts were directed at
using equipment and procedures for measurement of reservoir-core properties. It became apparent, however, that it was necessary to
place a closure stress on the proppant pack to obtain meaningful data on proppant performance. Consequently, a method of placing
the proppant pack under closure during measurement was pursued.
Industry laboratories began work in an attempt to develop equipment and methods directed at more closely simulating the
performance of proppant in a hydraulic fracture. Both radial- and linear-flow cells were evaluated. One such linear device from
Mobil is shown in Fig. 5.18. This approach offered advantages in a linear configuration and the ability to measure fracture widths.
E
C
C
F
B
G
D
A
H
A. Proppant pack 4 in. × 1.5 in. × w
B. Soft metal platen material
C. Test unit body
D. Lower piston/spacer
E. Upper piston
F. Base plate
G. Test fluid entry/exit port
H. O-ring seal gland
Fig. 5.18—Linear-flow-conductivity test unit (Gidley et al. 1989).
Proppants and Fracture Conductivity
Although this design overcame many of the issues associated
with other attempts at measuring proppant properties, it did
not gain widespread acceptance until work using a similar cell
was described by Cooke (1973); see Fig. 5.19.
Following some 8 years of development, API issued the first
industry standard for measuring proppant pack conductivity in
October 1989. API RP 61 (1989), Recommended Practices for
Evaluating Short Term Conducti­vity, provided recommended
procedures for measuring proppant conductivity along with
the apparatus to do so. The conductivity-measuring apparatus
is shown in Fig. 5.20. The procedures and apparatus called for
in API RP 61 included the following:
• Deionized or distilled water
• Conducted at ambient temperature: 75°F +/–5°F
• Proppant loaded at volume equivalent to 0.25-in.
proppant pack width (w) or 2 lbm /ft2
• 10-in.2 flow path (cell is 1.5 in. × 7.0l in. × w)
• Proppant confined between steel platens
• Proppant stressed for 15-minute periods at each stress
• Recommended stresses for varying size and type of
proppant
• Stresses ranging from 1 to 14,000 psi
153
Temperature
probe
∆P
Heated
platens
Cell
Rubber
Proppant
Fig. 5.19—Cooke (1973) conductivity cell.
The API RP 61 document carried the following caution:
“The testing procedures in this publication are not designed to
provide absolute values of proppant conductivity under downhole reservoir conditions.”
The document also recognized some of the deficiencies
in the test apparatus and procedures: “Long-term test data …
E
have shown that time (within a few days), elevated temperature, fracturing fluid residues, embedment, and formation
J
fines may reduce fracture proppant pack conductivity by up
B
to 90% or more. A recommended design procedure to address
A
longer term conductivity reduction may be considered in
B
future API work.”
J
Others had previously recognized the effects of temperature and time at stress (Cooke 1973; McDaniel 1986, 1987)
D
C
and the significant effects these parameters had on the conductivities measured. Much and Penny (1987) evaluated the
replacement of steel platens with moderately hard sandstone
to permit some embedment and reduce the wall-slip region
present with the steel platens. McDaniel (1986) and Penny
(1987) outlined a set of procedures and equipment for obtainF
ing repeatable conductivities and permeabilities of proppant
packs in which the use of the API RP 61 testing apparatus was
GH
retained but with a number of revisions to the testing parameI
ters. This included using Ohio Sandstone core instead of steel
platens and oxygen-free silica saturated 2% KCl instead of
A. Proppant pack (6 in. × 1.5 in. × w)
deionized water, ­testing at elevated temperatures rather than
B. Metal platen
ambient, and maintaining stress for at least 50 hours at each
C. Test unit body
stress level. These procedures, rather than those of API RP 61,
D. Lower piston
were commonly used to establish baseline conductivities
E. Upper piston
for all types of proppants and were the basis of comparison
F. Test-fluid entry/exit port
between ­proppants and were eventually adopted as the indusG. Differential-pressure sensing port
try standard for conductivity testing in ISO 13503-5:2006
H. Porous metal filter
(Kaufman et al. 2007). API has subsequently adopted ISO
I. Set screw
13503-5, now referred to as API RP 19D (2008). API RP 19D
J. Square ring seal
was reaffirmed in 2015 by API and is currently in the process
of update/revision. The process might take years to finalize.
Fig. 5.20—API fracture conductivity unit (API RP 61 1989).
A replacement of the steel platens that are called for in API
RP61 was deemed desirable to provide some modest embedment into the sandstone that was not present with the steel. The effects on conductivity of steel vs. the sandstone are shown in
Fig. 5.21 (Penny 1987). A reduction in conductivity with the Ohio Sandstone as compared to the steel platens was noted across
all stresses tested. This reduction has two aspects: a modest reduction in width and, more importantly, an elimination of the effect
of the high-porosity/high-permeability area at the proppant-pack/steel-core interface. This is often referred to as the “wall effect.”
The conductivity of this pack/core region is much higher than that of the bulk proppant pack alone and significantly influences the
result when using steel. The Ohio Sandstone was chosen to replace the steel because it was readily available and of low permeability
154 Hydraulic Fracturing: Fundamentals and Advancements
Conductivity
Permeability
10,000
Conductivity (md-ft)
30,000
10,000
Monel
8,000
Monel
3,000
800
300
Sandstone
Sandstone
1,000
100
600
60
300
30
100
2,000 4,000 6,000 8,000 10,000 2,000 4,000 6,000 8,000 10,000
125 175 250 275 300
125 175 250 275 300
Closure (psi) / Temperature (F)
10
Permeability (darcies)
30,000
Long-Term Conductivity and Permeability
2 lbm /ft2 20/40 Proppant
Fig. 5.21—Effects on conductivity of steel vs. sandstone (Penny 1987).
Proppant bed
Sandstone cores
Fig. 5.22—API conductivity cell.
Permeability (darcies)
10,000
150 °F-brine
75 °F-brine
250 °F-oil only
250 °F-brine only
150 °F-gas @ I.W
150 °F-oil @ I.W
to allow leakoff and filter-cake development during fracturing-fluid
­studies. Typical properties of the Ohio Sandstone include a porosity
of 19%, 0.2-md permeability, and a Young’s modulus of 5 million psi.
The conductivity cell is shown in Fig. 5.22, with the sandstone cores
replacing the steel platens at the proppant pack/core interface.
Temperature effects on the performance of proppant packs have
been recognized by others, including Cooke (1973) as shown in
Fig. 5.23, and led to the recommendation of testing at temperature.
Time at stress was also shown to be significant (Fig. 5.24) and was
one of the major deficiencies of the API RP 61 procedures. As shown
in Fig. 5.24, proppant conductivity falls significantly over the early
portion of the test and begins to stabilize at approximately 50 hours,
although ongoing deterioration of the conductivity beyond 50 hours
is evident.
The procedures outlined by Penny (1987) and others became
­recognized in the industry as “long-term” conductivity or “reference”
conductivity while the results from the API RP 61 (1989) procedures
were commonly referred to as “short-term” conductivity.
Because of the rapid decrease with time that occurs beyond
the 15-minute stress periods used in the short-term test,
short-term conductivities are of little value. There might be,
however, application in a manufacturing setting where the
short-term test results can be ­correlated to a manufacturing
process change.
1,000
5.6 Factors Affecting Fracture
Conductivity—Proppant Characteristics
and Fluids
Average, all
other fluids
100
10
250 °F Brine
0
2
4
6
8
10
Stres (1,000 psi)
12
Fig. 5.23—Effect of temperature (Cooke 1973).
14
5.6.1 Fracture Conductivity, Permeability, and Beta
Factor. Section 5.6 discusses factors that are related to the
proppant itself rather than its specific i­nteraction with the
reservoir rock or production fluids. To quantify fracture
conductivity, it is necessary to define the key properties
measured in the laboratory and then applied to the field,
interpreting and explaining any discrepancies.
The Forchheimer (1901) equation is given as
µ
−∇P = V + βρ V V, ���������������������������������������������(5.5)
κ 

 
Proppants and Fracture Conductivity
∆P  1  1
= + βρV . ��������������������������������������������������� (5.6)
∆ L  µ V  κ
At low velocity, Forchheimer’s equation reduces to the
familiar Darcy equation:
∆P  1  1
= . ������������������������������������������������������������(5.7)
∆ L  µ V  κ
Conductivity vs. Time at 8,000 psi and 275°F
30,000
Fracture Conductivity (md-ft)
where −∇P is the gradient of the differential pressure, V is the
velocity, μ and ρ are the viscosity and density of the flowing
fluid, κ is the absolute permeability, and β is the Beta-factor or
non-Darcy coefficient, both properties of the porous medium.
The equation can be rewritten as
155
10,000
6,000
2 lbm/ft2 20/40
between monel shim
with 2% KCL
Intermediate strength
proppant
3,000
Precured resin-coated sand
1,000
600
300
Jordan sand
In situations of low velocity, such as those encountered in
conductivity cells flowing brine at only a few milliliters per
100
0
50
100
200
minute, the contribution of non-Darcy flow to the total pressure drop is minimal, and Darcy’s equation provides an accuTime (hours)
rate description. In high-rate gas wells, the non-Darcy flow
term might dominate and can contribute more than 90% of the
Fig. 5.24—Effect of time at stress (Penny 1987).
total pressure drop. Much has been written about the physical
interpretation of non-Darcy flow, and it is often considered to
represent turbulence. However, turbulence in pipe flow, for example, is very distinct and represents a fundamental change in the
flow patterns from laminar flow characterized by stable streamlines to a chaotic rapidly changing form. Non-Darcy effects seen
in porous-media flow appear to be more analogous to inertia (Ruth and Ma 1992) and relate to the work (and hence the associated
forces) required to accelerate and move the fluid mass around the curved grain surfaces. Milton-Tayler (1993a) measured Beta-factors
for gases of varying density and obtained constant non-Darcy or Beta-factor values. Barree and Conway (2004) introduced a Tau (τ)
parameter related to the inverse median diameter of the proppant pack to account for a nonconstant Beta-factor seen in some data sets
at high rates.
The significance of inertial effects in proppant packs can be assessed by considering the ratio of the inertial-to-viscous pressure
losses, which can be defined as a Reynolds number, Re, where the characteristic length of the porous medium is given by the product
of the permeability and the Beta-factor (Geertsma 1974). By measuring the Beta-factor and permeability from multirate laboratory
flow tests and entering fluid velocity for a given density and viscosity, the value of Re can be determined. Clearly, for a value of Re = 1,
the pressure losses associated with the Darcy and non-Darcy terms are equivalent and the effective fracture conductivity is 50% of the
expected value that is based on low-rate brine flow.
It is important to appreciate that much of the published product literature reports long-term fracture conductivities with no
­reference to Beta-factors. Without a consideration of the non-Darcy pressure losses, users might overestimate the effective fracture
conductivity by an order of magnitude in high-rate-well situations. As discussed in Subsection 5.7.6 of this chapter, when these
effects are combined with multiphase flow and other conductivity-impairment mechanisms, achieved fracture conductivities might
be considerably lower than anticipated and might not be optimal for the stimulation design.
5.6.2 Proppant Crush and the Effect of Cyclic Stress. Sand and ceramic proppant tend to fail in a brittle manner when a critical
stress is reached. This is proppant crush and might be accompanied by the release of fragments of various sizes into the proppant
pack. Fines also might be produced, depending on the mechanism of failure, and these potentially can flow and plug remaining pore
spaces. While crush testing does not directly evaluate the flow performance of a given proppant under specific field conditions, it is
a useful tool for quickly and inexpensively assessing potential performance. For example, different sands can be benchmarked at a
certain stress and commonly the so called K-value is provided. The K-value is the maximum closure stress to the nearest 1,000 psi for
which fines produced are less than 10% by mass.
Samples are usually poured into the crush cell using a pluviator. This is supposed to achieve a more reproducible packing and probably a closer packing with lower porosity (Getty and Bulau 2014). Coordination number, the number of contact points between grains,
is strongly dependent on packing. A high coordination number will give lower contact stresses between proppant grains. In the field
situation, where proppant is placed inside a viscous fluid, it is hypothesized that the porosity might be higher and the coordination
number lower, giving significantly higher contact stresses between proppant grains. Therefore, it is important to realize that the crush
test is an index test, and the crush strength might not scale directly to the effective closure stress in the field.
Advanced crush tests are run in modified cells that enable the inclusion of a fluid, temperature variation, different platens, and other
effects (Fig. 5.25). The effect of fluid can be quite pronounced. Cooke (1973) noted that the strength of glass beads in the presence
of brine is decreased greatly. This should give caution to those considering the potential use of recycled glass as proppant. It might
have applications, but it should be carefully evaluated under realistic conditions before being pumped in the field. Other proppants
are also affected. The combination of fluid environment and temperature can increase the impact on crush. For example, 16/20
lightweight ceramic at 10,000 psi with an ambient-temperature API standard crush of 2.6% showed 6.3% at 200oC after 18 hours of
exposure (FracTech ­Consortium 2008).
Investigators have tried to correlate fracture conductivity with crush data. For example, Schubarth and Milton-Tayler (2004)
­correlated the mean proppant diameter from crush tests with fracture conductivity. The cycling of stress, which will occur with
repeated shut-ins, will tend to increase proppant crush and has been shown to reduce fracture conductivity. The reduction in
mean proppant diameter with cycles is shown in Fig. 5.26 for a sand and a lightweight ceramic. The effects of stress cycling are
largely irreversible, and the conductivity performance of a proppant pack will largely be dictated by the maximum stress it has
experienced.
156 Hydraulic Fracturing: Fundamentals and Advancements
Servo-controlled load
frame
Fluid backpressure
syringe pump
Proppant pack
Temperature
control
Hardened-steel
disks
Wrap-around
heater
Brine inlet
Fig. 5.25—Advanced crush-testing cell includes fluid saturation, backpressure, and heating capability to generate crush
data at more-realistic reservoir conditions.
1 Stress cycle
5 Stress cycles
20 Stress cycles
2
2 lbm/ft
0
2,000
4,000 6,000 8,000
Closure Stress (psi)
100%
95%
90%
85%
80%
75%
70%
65%
60%
55%
50%
1 Stress cycle
5 Stress cycles
Retained MPD (%)
Retained MPD (%)
100%
95%
90%
85%
80%
75%
70%
65%
60%
55%
50%
10,000 12,000
20 Stress cycles
2
2 lbm/ft
0
2,000
4,000 6,000 8,000
Closure Stress (psi)
10,000 12,000
Fig. 5.26—Relationships between fracture conductivity and mean proppant diameter (MPD) (Schubarth and MiltonTayler 2004).
By making test conditions realistic, the different responses of the proppants to their environment can be understood clearly and
the right proppant for the right application can be better determined. For crush tests and long-term fracture conductivity tests, it is
essential to test production samples intended for the field under realistic conditions. Correlations previously developed, which might
be field specific, can be used to help ensure timely delivery of proppant quality-assurance/quality-control data when only limited time
is available.
5.6.3 Fines Migration and Plugging. A small quantity of fines can be very effective at plugging a porous medium and impairing
fracture conductivity. The extent of the potential damage depends on the geometry and the location for the source of the fines. Killpill packages can be designed to plug against the face of the proppant pack and seal against fluid losses. The simple trigonometric
relationship shown in Fig. 5.27 indicates that a particle with a diameter of approximately one-sixth the mean proppant pack diameter
will plug the port throat. Hence for a 20/40-proppant pack, particles with a diameter on the order of 100 µm are likely to plug quickly,
and smaller particles down to 50 to 60 µm are likely to be screened off as soon as they encounter a smaller pore throat within the
distribution of pore throats present.
 2

r ≥ R
− 1 ≈ 0.155 R. ��������������������������������������������������������������������������������������������������������������������������������������������������������������(5.8)
 3 
Proppants and Fracture Conductivity
157
While 100 µm would probably not be considered fines,
it might be present from fragmented sand grains. Once the
first particle plugs the pore throat, then the critical size
for plugging rapidly decreases and very quickly fines on
the order of a few micrometers will not be able to pass
the pore throat. Assuming a square function between the
grain size and permeability, the normalized permeability
can fall quickly to <1%. The impact of fines on the fracR
ture conductivity of the pack depends on how extensive
30°
they are and on the flow conditions. If the sand grains
are water-wetting in a gas-producing well, they might
not ­
mobilize during single-phase gas production. With
R
the onset of water production, rapid mobilization might
become ­apparent. Gidley et al. (1995) found at 34-mL/min
r
brine-flow rate evidence for movement and plugging of
fines internally generated from proppant crush. Under
dry gas flow at much higher rates, no movement of fines Fig. 5.27—Estimating the critical particle radius to plug a pore
occurred. It is important to distinguish between a mobile throat.
and an immobile liquid phase. When the liquid phase
is mobile under dual gas and liquid flow, the non-Darcy
relative permeability effects might result in high local brine velocities, which might transport fines.
5.6.4 Proppant Size Distribution and Shape. The fracture conductivity of proppant and how it trends with closure stress is strongly
influenced by proppant size and shape. As proppant size increases, the contact stress, or applied force per unit area of contact, actually
reduces as the square root of the diameter of the proppant. However, the number of contact points between grains decreases as the
square root of the diameter, so the net effect is that larger proppant grains behave as if they are weaker under the same stress conditions. The fracture conductivity increases considerably with proppant size at low stress, and hence a larger competent proppant at
2,000 psi will have substantially greater conductivity than a 30/50 mesh. As the closure stress increases, the fracture conductivity will
trend downward more rapidly for the coarser proppant. A selection of data is given in Fig. 5.28 (Ott and Woods 2019).
Enhancing porosity of the proppant pack will increase fracture conductivity, at least at low stress. Porosity can be increased by
disrupting the packing (Larsen and Smith 1985; McDaniel et al. 2010). For example, fibers tend to pack with porosities approaching
70%. Providing that the fibers are strong enough to sustain the porosity at elevated stress, it would be anticipated that the fracture
conductivity will remain high. Of course, higher porosity and more-angular (or more-elongated) proppant will have fewer contact
points between grains and consequently higher contact stresses at those points.
It will appear stronger but will have lower initial porosity. Conceptually, for a given application, a trade-off is possible between
the benefit of the higher initial porosity and the ability to create a sufficiently strong proppant to maintain this benefit at an affordable
price. Other aspects, such as criteria for perforation and fracture screenout, historically developed for spherical proppant, might need
review.
5.6.5 Proppant Coatings. Proppants might be coated with various resins—for example, phenolic resins, epoxy-based systems, and
hybrid systems, including additives such as plasticizers and other fillers. Coatings might be applied for a number of reasons. Sand
might be coated to improve its performance, reducing crush and maintaining fracture conductivity beyond levels normally achieved
without the coating. The coating might hold fines together and help prevent their movement through the pack, potentially plugging
pore throats. Proppant might also be coated with a reactive curable coat that provides grain-to-grain cohesion in the fracture to help
prevent proppant flowback during well cleanup and later during production. Historically, the focus has been on high-rate conventional
completions in particular gas fields with the potential for harmful erosion of surface facilities. However, unconventional completions
also have issues with proppant flowback, as the industry moves toward finer proppant.
The addition of a coating usually results in a reduction in conductivity at low stress because of the loss of some porosity. Most
coatings are comparatively soft compared to the proppant and tend to yield during stress application. However, as the stress increases,
the two lines might cross and higher conductivity might be achieved at elevated stresses. The coating system must be designed for the
High-Strength Bauxite Data, 250°F
Baseline Long-Term
Conductivity (md-ft)
12,000
10,000
20/40
30/60
40/80
10,000
12,000
8,000
6,000
4,000
2,000
0
2,000
4,000
6,000
8,000
Closure Stress (psi)
Fig. 5.28—Baseline fracture conductivity of the same proppant with different meshes.
158 Hydraulic Fracturing: Fundamentals and Advancements
particular field application, and testing to ensure that the
overall objectives are achieved is essential. Compatibility
with the fracturing fluids should also be considered.
High-energy laboratory-based coaters (Fig. 5.29) are
available to prepare small 10-lbm runs of coatings on
trial sands to quantify the potential for enhancement of a
given sand using a resin. A range of resin types and loadings can be tested, and the resulting improvement in crush
and enhanced fracture conductivity can be assessed before
moving to possible large-scale production.
5.6.6 Fracturing Fluid Residue. The fracturing fluid
has two key requirements in regard to proppants. First, it
must open and maintain an induced fracture network to
allow the placement of proppant. Second, it must transport the pro­
ppant from the wellhead into the fracture
network. In conventional treatments, a crosslinked fluid
would typically be used. This could be an elevated-pH
borate-crosslinked guar or HPG fluid. Other options are
available—for example, zirconate-crosslinked systems—
depending on the temperature applications and particular
reservoir properties. Experimental evaluations relating to
fracture conductivity impairment from fracturing fluids
have been published extensively (Much and Penny 1987;
Penny 1987).
During pumping, the overbalanced fluid pressure inside
the fracture might cause leakoff into the formation and the
Fig. 5.29—High-energy laboratory-based coating facility. Courtesy
concentration of polymer on the face of the created fracof FracTech Laboratories.
ture. With time, and depending on the nature of the core
and the fracturing fluid, significant filter cake can be generated and can reach 0.1-in. thickness and more in some cases. How this filter cake degrades during shut-in is key to the retained fracture
conductivity. Polymer concentrations can reach more than 200 to 300 lbm/1,000 gal during this process and can be very difficult to
clean up. Significant pressure gradients of the post-shut-in fluid can be necessary to initiate flow and even begin the cleanup process.
­ ltrate backMost laboratory tests start with a brine return flow alternating through the rock wafer and the proppant pack to simulate fi
flow before moving to oil or gas as appropriate. Fig. 5.30 shows typical relationships between the flow-initiation pressure/retained
permeability and the concentration of the polymer residue (Duenckel et al. 2017).
Given the infinitesimal size of a standard conductivity cell compared to the field situation, care must be taken in the interpretation
of results. An incompletely broken fluid with a residual viscosity of 100 cp might be driven out of the laboratory test cell but might
not be produced back in the field. Viscous fingering, where the much-lower-viscosity production fluid channels through the unbroken
gel, might occur, especially in gas wells. In low-energy reservoirs, much of the fracturing fluid might never be cleaned up, resulting
in very low retained permeability and restricted contributing fracture length.
5.7 Factors Affecting Fracture Conductivity—Interactions with the Reservoir
5.7.1 Introduction. In Section 5.7, the focus is on factors that are determined more by the specific application than by the proppant
itself. How the proppant responds to these different influences might indeed significantly influence the proppant selection.
Retained Perm. (%)
Pressure Differential (psi/ft)
100
10
1
0.1
0.01
Retained permeability (%)
Pressure differential (psi/ft)
0.001
0.0001
0
50
100
150
200
250
300
350
400
450
Polymer Residue (Ibm/1,000 gal)
Fig. 5.30—Flow-initiation pressure and expected maximum retained permeability as a function of polymer residue
concentration (after Duenckel et al. 2017).
Proppants and Fracture Conductivity
159
5.7.2 Closure Stress, Temperature, and Time. After pumping ceases, the excess fracturing fluid leaks off. This leakoff might be
into the matrix through any filter cake and/or it might be into natural fractures or created-fracture extension. Essentially, as the slurry
defluidizes, the proppant establishes grain-to-grain contact, and stress is transmitted throughout the proppant pack. A balance of forces
is achieved (because the proppant will ultimately not be moving). The rate of stress application to the proppant is interesting and rarely
simulated in the laboratory.
Fig. 5.31 shows how the rates of stress change are different for the various stages of the fracturing and production process. From
a to b, the slurry is fluidized and fluid content is above the critical saturation point. This can be during pumping and also in the early
shut-in period when the fluid pressure is supporting the effective minimum horizontal stress. At point b, the critical saturation point
is reached and the proppant starts to become load bearing. The time from b to c is very short, and the minimum effective stress might
be applied to the proppant locally within the fracture over very short times on the order of minutes or less; c to d relates to shut-in
during which the stress is constant and the fluid might break; d to e corresponds to bringing the well onto production with a more
controlled and gradual rate of change of stress. Finally, with depletion, there might be a gradual stress increase with time. This will
be related to the effective minimum horizontal stress, which will increase at some fraction of the depletion, depending on the Biot’s
coefficient. There is also a stress contribution because of the local compression of the rock near the fracture and the fact that additional
material (the proppant) was introduced into a finite volume. Most long-term conductivity tests do not simulate realistic stress ramps
and are commonly run at 100 psi/min. Crush tests tend to be run at 2,000 psi/min, which is more analogous to the rapid closure during
dehydration of the slurry. The rate of stress application might have different impacts, depending on the specific proppant properties.
Historically, testing was performed at ambient temperature conditions, but the importance of simulating the temperature environment correctly is now much better understood. McDaniel (1986) compared the effects of time and temperature on the fracture conductivity of sand and ceramics. Maintaining a closure stress of 8,000 psi, the percentage of conductivity retained at 275°F was compared
to the ambient-temperature value. This ranged from 75% for the high-strength bauxite to 35 to 36% for a sand. At lower stresses,
the percentage retained is higher. For example, at 4,000 psi it is 68% for the sand. Including the effect of extended time out to 10 to
14 days, McDaniel (1986) recorded retained conductivities as low as 7% of the short-term, ambient-temperature values.
In terms of time, the industry has settled on a 50-hour period at each stress typically running through a 2,000-psi to 12,000-psi stress
ramp at 2,000-psi increments. Such a test runs over approximately 2 weeks. It is known that fracture conductivity can continue to
decline after 50 hours to a greater or lesser extent, depending on other conditions (Much and Penny 1987; McDaniel 1986). O
­ bviously,
it is important to understand that the measurement process itself might impact the long-term conductivity trend. For example, there
are difficulties in achieving 100% silica saturation of the 2% KCl brine test fluid. If the saturation is too high (this might occur when
the saturation vessel is heated to greater than the test-cell temperature in a vessel designed for high silica contact), then silica precipitation might occur in the proppant pack, reducing the porosity and impacting conductivity. If silica saturation is too low, dissolution
of the Ohio Sandstone platens might occur, causing weakening and propensity for greater embedment. This will also tend to reduce
the conductivity. Clearly, extended testing might introduce artifacts, and any decline might not entirely reflect field processes. When
designing tests, it is critical to recognize these effects and ensure that time-dependent processes are reflecting degenerative processes
that will also apply in situ.
In summary, it is important for the data user to understand that 50 hours is an arbitrary time reference and is unlikely to reflect
field performance a number of years into the future. What is critical when selecting proppant is for the engineer to identify the key
mechanisms that are expected to have the greatest impact on the achievable fracture conductivity.
5.7.3 Embedment. Embedment refers to the process by which the proppant indents into the rock face under stress. The effect of
embedment is to reduce the open fracture width by the embedment itself and also through occlusion of the proppant pack from
material spalled into the pore spaces. Indentation mechanics can be used as a guide to estimate embedment, although the situation
is more complex with proppant packs. Primarily, this appears to be because of the proximity of adjacent proppant. For single-point
indentations, the depth of invasion is related to the applied force and the diameter of the indenter. The Brinell hardness value links
these variables together for a spherical indenter. When proppants are bounded by other proppants, the spalled material has to flow into
Rate of Stress Change Applied to Proppant Pack
6,000
f
e
Closure Stress (psi)
5,000
4,000
c
d
3,000
2,000
1,000
a
0
0
b
5
10
15
20
25
Time (hours)
30
35
Fig. 5.31—Rate of stress change applied to proppant pack.
40
45
160 Hydraulic Fracturing: Fundamentals and Advancements
Fig. 5.32—Image showing unconsolidated sand excluded using
a sized proppant.
the limited pore spaces. Depending on the extent of spalling and the grain size of the rock, it is possible for debris
to screen off inside these pore throats and restrict embedment. In many cases, embedment is restricted to one grain
radius per formation face, hence a one-proppant-diameter
loss of useful fracture width. In soft coarse-grained sands,
it might be important to size the proppant to exclude reservoir sand from entering. Historically, this was based on
Saucier’s criterion (Saucier 1974), although more-recent
models are now used (Tiffin et al. 1998). Fig. 5.32 shows
an unconsolidated sand successfully excluded with a lightweight ceramic proppant (FracTech Consortium 2007).
In some cases, uncontrolled influx of reservoir material
might occur into the proppant pack, with a potentially serious negative impact for fracture conductivity. For example,
in soft chalks, material might continue to creep and flow
into the pack. This effect might be exacerbated by water.
Shale formations that are water sensitive might soften and
intrude into the proppant pack. Techniques to avoid these
issues include reducing proppant size to lower the contact stress and restricting the pore throat size, and using
­compatible fluids to avoid weakening of the formation.
5.7.4 Diagenesis. Geochemical reactions between the proppant and the formation face were suggested to explain field differences
between surface-modification (SMA) and non-SMA treated proppants (Weaver 2005). Closer examination of laboratory tested proppant packs indicated that small crystals growing on the proppant surface were aluminosilicate-mineral based, suggesting that chemical reactions can occur at a relatively low temperature when subjected to high contact stress. The process is analogous to a pressure
solution in rock formation, although the process appears to occur over weeks rather than millions of years. Proppant-filled hydraulic
fractures, with stress-enhanced reactions, can undergo a significant degree of diagenesis-type reactions within fractions of a year
(Raysoni and Weaver 2013).
Duenckel et al. (2017) comments that zeolite precipitation has been identified in several studies, but its occurrence is strongly
dependent on the level of saturation of the fluids present and the requirement for surfaces to act as seeds to initiate crystallization.
In silica-alumina under saturated dynamic systems, zeolite precipitation might not be observed. Multiple static tests showed that under
certain conditions, precipitants might form and that these can occur on ceramics, natural sands, and resin-coated sands as well as inert
materials. Zeolites appear only to form in alkaline environments and then with poor reproducibility (Duenckel et al. 2012).
5.7.5 Proppant Flowback. Proppant flowback refers to the back production of proppant during post-treatment cleanup and/or
longer-term production. With the placement of high proppant loadings in the 1980s to achieve sufficient fracture conductivity contrast
with the formation, in particular in high-rate gas wells where the effects of non-Darcy flow dominate, proppant flowback became an
issue (Clayton and Gordon 1990). In the North Sea, the back production of potentially erosive proppant in the gas stream represented
a serious potential hazard to the infrastructure. Wells would often be choked back until a proppant-free operating window could be
defined. This was restricting the effective conductivity of the fracture in the sense that the achievable production was being limited
because of proppant flowback.
Proppant flowback was also common in Prudhoe Bay, Alaska, USA, where aggressive fracture designs would give ­high ­fracture
apertures. However, for these oil wells, the associated erosion was much less than for the high-rate offshore gas wells in the
North Sea, and operators would frequently accept 10 to 20% back production of proppant for the increased production it gave
(Martins et al. 1992).
A laboratory-based test program was performed to
determine the factors that affect proppant pack production
(Milton-Tayler et al. 1992). Using a bespoke testing cell
(see Fig. 5.33), the factors affecting proppant pack stability
inside a stressed fracture were evaluated. The data were 6
mm (0.024 in.) interpreted in terms of the ratio between the
fracture aperture and the mean proppant d­ iameter. Dependent on other more subtle conditions, the pack transitions
from stable to unstable as this ratio increases to greater
than approximately 4.5. For example, for a 20/40-proppant pack with a mean diameter of 0.6 mm (0.024 in.),
the transition occurs at ≈3 mm (≈0.1 in.), or an approximately 1-lbm/ft2 proppant loading. The results suggest that
for larger proppant, the stable transition occurs at a higher
proppant ­loading. The results did suggest that for most
conventional high-conductivity designs of the time, 3 to
4 lbm/ft2 of 16/20 with 12/18 tail-ins would have a tendency
to flow back, which is consistent with field experience.
Resin coating of the proppant to provide a consolidated
pack was used to minimize the risk of flowback. Initial
Fig. 5.33—A flowback cell designed to investigate back systems with highly reactive resins set up in the perforation tunnels, and this caused high near-wellbore pressure
production. Courtesy of FracTech Laboratories.
Proppants and Fracture Conductivity
161
losses. Subsequent systems were designed to set up only under
stress, enabling the perforation tunnel to be flowed clear while
maintaining the proppant in place in the fracture. Early-time
flowback could be managed with separators, and once proppant free, the well could be left on production. A small amount
of proppant production during post-fracturing cleanup might
help increase the well productivity (Shaoul et al. 2018).
Today, resin coatings are used to control flowback of proppant in many applications. Their success depends on ensuring
that the product is designed and tuned to work for ­specific field
applications. There is no one-solution panacea. Consideration
has to be given to the development of sufficient compressive
strength of the pack taking into account the journey the proppant experiences during placement. This experience includes
possible inter­actions with fracturing fluid, shear in the pumps
and in pipe, and partial curing. Success depends on having
sufficient bond strength between proppant grains and also
between the resin and the proppant. In some cases, failure can
occur at the resin/proppant interface (Fig. 5.34). This is not
always the case, and it depends on the surface chemistry of the Fig. 5.34—Proppant recovered from flowback cell showing
subs­trate, the quantity of silane used to promote the resin bond resin detachment from the substrate.
to the substrate, and operational conditions.
Challenges remain today in the attempt to manage and control proppant flowback. Providing flowback prevention assurance in low-temperature and low-stressed conventional stimulations is
difficult. Resins tend to work best in the higher-temperature applications where they develop more strength. And as operators move
toward finer-mesh proppant for unconventional shale gas treatments, proppant flowback issues are becoming evident. Similarly to the
experience with conventionals, a control system that prevents any proppant from producing back might restrict production. Some high
near-wellbore conductivity will likely be advantageous but has to be balanced against the risk of pinch-off between the fracture and
the wellbore because of excessive back production, which risks losing connectivity with the fracture.
5.7.6 Non-Darcy and Multiphase Flow. The equations relating to non-Darcy flow were discussed in Section 5.6.1. In this section,
the focus is on influences the reservoir might have on the achieved fracture conductivity. Under conditions of very-high-rate gas,
especially in a convergent flow close to the wellbore, the non-Darcy pressure losses will dominate. The measured pressure losses
are proportional to the product of the velocity squared and the density. For compressible flow, higher line pressures will reduce this
value. Hence, for a given mass flow rate, non-Darcy pressure losses are lower at higher operating line pressure (as for Darcy flow).
Most laboratory testing is run at a few hundred psi, considerably less than typical field values.
While it is implicit in the Forchheimer equation (Eq. 5.5) under ideal-gas conditions that Beta-factor itself is independent of line
pressure, it is important to understand that the pressure drops in the field at the much higher line pressures will be lower, given otherwise ­com­parable conditions. This also has a bearing on cleanup and multiphase flow.
When two phases are flowing, there will be competition between them for pore space. The total pressure drop across the system
is measured and can then be expressed as a ratio of the expected pressure drop if either liquid or gas were flowing as a single phase
occupying 100% of the pore space. The tests are usually run on single-phase gas followed by single-phase brine after pack saturation. Saturated gas can then be flowed at a low rate with brine flowing in parallel. These conditions might approximate to early gas
20/40 Resin-Coated Sand; 200°F; 4 lbm/ft2: Gamma-Factor vs. Gas-Flow Rate
Line Pressure: 3,000 psi; Closure Stress: 2,000 psi
120
Gamma-Factor
100
80
60
40
20
0
0
200
400
600
800
1,000
1,200
1,400
Gas-Flow Rate (s/t/min)
DGWR 20,000
DGWR 2,000
DGWR 200
Fig. 5.35—Gamma-factors as a function of gas-flow rate for various dimensionless gas/water ratios (DGWRs).
162 Hydraulic Fracturing: Fundamentals and Advancements
breakthrough during cleanup. The pressure losses are heavily dominated by the mobile brine flow, and the ratio of the pressure gradient, measured relative to that expected if the same rate of gas was flowing as a single phase, will be very large. This ratio, the so-called
Gamma-factor, provides an easy frame of reference for estimating multiphase-flow effects (Milton-Tayler 1993b). Fig. 5.35 shows
Gamma-factors for different dimensionless gas/water ratios under a constant gas-flow rate. A value of 100 implies a relative permeability of 1% of the single-phase value.
Equations have been developed in terms of relative permeability to liquid and gas with regard to gas-flow rate for various saturations (Barree and Conway 2007; Duenckel et al. 2017). It is clear that a small mobile water saturation can have a significant impact
on pressure losses of the system. From multiple sets, Duenckel et al. (2017) collapsed the data down to a single set of relative permeability curves based on the Corey functions:
K rw = Sw5.5 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(5.9)
K rnw = (1 − Sw ) , �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(5.10)
2.7
where Sw is the wetting-phase saturation, Krw is the relative permeability of the wetting phase, and Krnw is the relative permeability of
the nonwetting phase. It is clear that saturation is a key variable, and it is important to aim to determine the saturations of the phases
while flowing. These cannot be determined from the flow rates but must be established either by having a closed system or by using
some form of gamma ray saturation monitoring system.
Fracture conductivity loss can be greater than 90% of the single-phase value uncorrected for non-Darcy or multiphase-flow effects.
There are further corrections for gel damage, time-dependent decline, diagenesis, scale, fines, asphaltenes, salt precipitation, and
other factors. These considerations inform that it is essential to design the fracturing treatment and pumping schedule not on the
basis of idealized published baseline conductivity data, but by using data that take into account the realistic operating conditions for
the well.
5.8 Nomenclature
Cfd
= dimensionless fracture conductivity
d50
= median diameter, the antilogarithm of the median phi, ϕ50
k
= formation permeability, L2, md
kf
= fracture permeability, L2, md
Krw
= relative permeability of the wetting phase
Krnw
= relative permeability of the nonwetting phase
ni
= relative mass retained or frequency of occurrence in mass %
Oi
= sieve opening of interest in mm
Sw
= wetting-phase saturation
V
= velocity
w
= proppant pack width, L, ft
Xf
= fracture half-length, L, ft
β
= Beta-factor or non-Darcy coefficient
κ
= absolute permeability
μ
= viscosity and density of the flowing fluid
ρ
= viscosity and density of the flowing fluid
ϕ
= variable in Eq. 5.2
ϕ50
= median phi, the sum of differences divided by the sum of the frequencies
−∇P
= gradient of the differential pressure (add the symbol underneath the nabla as shown in figure Eq. 5.5)
5.9 References
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API RP 61, Recommended Practices for Evaluating Short Term Conductivity. 1989. Washington, DC: API.
ASTM E11, Standard Specification for Woven Wire Test Sieve Cloth and Test Sieves, 2017. West Conshohocken, Pennsylvania:
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Barree, R. D and Conway, M. W. 2004. Beyond Beta Factors: A Complete Model for Darcy, Forchheimer and Trans-Forchheimer
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Proppants and Fracture Conductivity
163
Barree, R. D., Duenckel, R. J., and Hlidek, B. T. 2019. The Limits of Fluid Flow in Propped Fractures- the Disparity Between Effective
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164 Hydraulic Fracturing: Fundamentals and Advancements
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in Horizontal Wells with Transverse Fractures. Presented at the SPE International Hydraulic Fracturing Technology Conference
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Chapter 6
Fracturing Fluids and Additives
John W. Ely and Raymond A. Herndon, Ely and Associates Corp.
John W. Ely is the founder and chief operating office of Ely and Associates, Inc. He has more than 50 years of experience in the
oil and gas industry, having started his career with Halliburton in 1965. Ely holds a BS degree in chemistry from Oklahoma State
­University. He is a member of SPE and the American Chemical Society, and is a fellow of the American Institute of Chemistry.
Raymond A. Herndon is a fracturing consultant, currently working with Ely and Associates, Inc. He has more than 30 years of
experience in fracturing stimulation, having started his career with Halliburton in 1980. Herndon holds a BS degree in engineering
from the University of Texas at Austin.
Contents
6.1
6.2
6.3
Overview���������������������������������������������������������������������������������������������������������������������������������������������������������������� 166
Properties of a Viscous Fracturing Fluid���������������������������������������������������������������������������������������������������������������� 166
Water-Based Fracturing Fluids������������������������������������������������������������������������������������������������������������������������������ 167
6.3.1 Linear Fracturing Fluids����������������������������������������������������������������������������������������������������������������������������� 167
6.3.2 Viscoelastic Surfactant Fluids�������������������������������������������������������������������������������������������������������������������� 170
6.3.3 Polyacrylamides����������������������������������������������������������������������������������������������������������������������������������������� 171
6.3.4 Crosslinked Fracturing Fluids��������������������������������������������������������������������������������������������������������������������� 172
6.3.5 Delayed-Crosslink Systems����������������������������������������������������������������������������������������������������������������������� 173
6.4 Oil-Based Fracturing Fluids����������������������������������������������������������������������������������������������������������������������������������� 174
6.5 Alcohol-Based Fracturing Fluids���������������������������������������������������������������������������������������������������������������������������� 174
6.6 Emulsion Fracturing Fluids������������������������������������������������������������������������������������������������������������������������������������ 174
6.7 Foam-Based Fracturing Fluids������������������������������������������������������������������������������������������������������������������������������ 176
6.8 Energized Fracturing Fluids����������������������������������������������������������������������������������������������������������������������������������� 178
6.9 Fracturing Fluid Additives�������������������������������������������������������������������������������������������������������������������������������������� 178
6.9.1 Biocides����������������������������������������������������������������������������������������������������������������������������������������������������� 178
6.9.2 Breakers����������������������������������������������������������������������������������������������������������������������������������������������������� 178
6.9.3 Buffers�������������������������������������������������������������������������������������������������������������������������������������������������������� 180
6.9.4 Surfactants and Nonemulsifiers����������������������������������������������������������������������������������������������������������������� 180
6.9.5 Nanosurfactants����������������������������������������������������������������������������������������������������������������������������������������� 180
6.9.6 Fluorocarbon Surfactants��������������������������������������������������������������������������������������������������������������������������� 180
6.9.7 Clay Stabilizers������������������������������������������������������������������������������������������������������������������������������������������ 181
6.9.8 KCl Substitutes������������������������������������������������������������������������������������������������������������������������������������������ 181
6.9.9 Fluid-Loss Additives����������������������������������������������������������������������������������������������������������������������������������� 181
6.9.10 Foamers����������������������������������������������������������������������������������������������������������������������������������������������������� 182
6.9.11 Friction Reducers��������������������������������������������������������������������������������������������������������������������������������������� 182
6.9.12 Temperature Stabilizers����������������������������������������������������������������������������������������������������������������������������� 183
6.9.13 Diverting Agents����������������������������������������������������������������������������������������������������������������������������������������� 183
6.10 Waterfracs������������������������������������������������������������������������������������������������������������������������������������������������������������� 184
6.10.1 The Dominant Fracturing Fluid Today�������������������������������������������������������������������������������������������������������� 184
6.10.2 Rationale for Small and Substandard Propping Agents����������������������������������������������������������������������������� 184
6.10.3 Using or Not Using Surfactants in Waterfracs�������������������������������������������������������������������������������������������� 185
6.10.4 Summary���������������������������������������������������������������������������������������������������������������������������������������������������� 185
6.11 References������������������������������������������������������������������������������������������������������������������������������������������������������������ 185
6.12 Recommended Reading List��������������������������������������������������������������������������������������������������������������������������������� 191
166 Hydraulic Fracturing: Fundamentals and Advancements
6.1 Overview
This chapter covers the various fracturing fluids and additives necessary to achieve certain attributes that allow for successful stimulation. Included is a discussion of the properties desired in an ideal viscous fracturing fluid. This is fol­lowed by a discussion of the
numerous fluids available, including water-based fluids, oil-based fluids, alcohol-based fluids, emulsion fluids, and foam-based fluids.
The use of various additives in the fracturing fluid systems is also detailed. Because of the tremendous change that has occurred in the
last few years relating to the use of slickwater and hybrid treatments, a large section on these types of fluids is included. The information should provide the design engineer with the basic knowledge needed to choose a base fluid and the important additives.
6.2 Properties of a Viscous Fracturing Fluid
Fracturing fluids are pumped into underground formations to stimulate oil and gas production. To achieve successful stimulation, the
viscous fracturing fluid must have certain physical and chemical prop­erties.
• It should be compatible with the formation material and fluids.
• It should be capable of suspending proppants and transporting them deep into the fracture.
• It should be capable, through its inherent viscosity, to develop the necessary fracture width to accept proppants or to allow
deep acid penetration.
• It should be an efficient fluid (i.e., have low fluid leakoff).
• It should be easy to remove from the formation.
• It should have low friction pressure.
• It should be simple and easy to prepare in the field.
• It should be stable so that it will retain its viscosity throughout the treatment.
• It should be cost-effective.
The first characteristic listed might be the most critical. If the chem­ical nature of the fracturing fluid causes swelling of naturally
occur­ring clays in the formation thereby plugging pore channels, the treatment will be a failure. If the fracturing fluid causes migration
of fines and/or clays, the success of the treatment will be nulli­fied (Smith et al. 1964; Reed 1972; Monaghan 1959; Jones 1964; Hewitt
1963; Hower 1974; Mungan 1965; Peters and Stout 1977; Bates et al. 1946; Coulter et al. 1983). It cannot be overemphasized that
where matrix permeability of the formation is extremely low (i.e., less than 10 μd), disallowing penetration of fluids into the matrix,
clay control is not required.
If the fracturing fluid creates emulsions and/or sludging of the crude oil from the formation, then plugging rather than stimulation can oc­cur (Hawsey et al. 1964; Tannich 1975; Clark et al. 1982; Allen and Roberts 1978; API RP 42 1977; Graham et al. 1959;
Penny et al. 1983). If the fracturing fluid dissolves the cementing material that holds the grains of the sandstone together, spalling
of the for­mation can occur and failure could result. The fracturing fluid should not cause scaling or paraffin problems (Featherston
et al. 1959; Knox et al. 1962; Sloat 1963; Bauer and Bezemer 1967; Tinsley 1967; McCall and Johnson 1984; Stiff and Davis 1952).
Compatibility is therefore a critical and necessary characteristic of a fracturing fluid. Since SPE Monograph 12 (Gidley et al. 1989)
was published, field experience has shown that water, properly treated, has by far been proved to be less damaging than had been predicted by previous authors. In fact, the trend now in the industry of water fracturing (waterfracs) being the vast majority of treatments
pumped bears this out with field results. A separate section is devoted to nonviscosified fracturing fluids (i.e., waterfracs).
Another important characteristic of a viscous fracturing fluid is its ability to transport the proppants down the tubulars through
perfo­rations and deep into the fracture (Novotny 1977; Daneshy 1978; Clark et al. 1977; Hannah and Harrington 1981; Shah 1982;
Ford 1960; Clark and Guler 1983; Harris et al. 2009; Shah et al. 2001; Harris 1996; Brannon and Ault 1991; Gdanski et al. 1991).
Depending on the nature of the fracturing fluid, it might perfectly suspend the proppant or, as is the case of lower-viscosity linear
fluids, allow for some settling and banking of the proppant in the fracture. Large viscosities are needed to transport proppants and
develop the fracture width needed to create and prop long fractures. It is well-known that insufficient fracture width from insufficient
viscosity will not allow proppants to be transported very far into the fracture. There is a great deal of controversy in the industry in
relation to the minimum viscosity required for perfect proppant transport in non-Newtonian fluids. The industry has used a minimum
viscosity of 1,000 cP at 37-reciprocal-seconds shear. Because of the availability of many delayed breaker systems, this viscosity is
achievable in the fracture for fairly long pump times at temperatures below 300°F. For the higher bottomhole temperature where
perfect proppant transport is needed, the industry has had to compromise to a minimum of 500 cP at 37-reciprocal- seconds shear.
The recent dominance of waterfracs in the industry and their widespread success have created a vacuum of knowledge in design
and implementation of fracturing fluids, which basically follow Stokes’ law in relation to proppant settling. The use of proppants that
do not meet American Petroleum Institute (API) quality standards and the dominance of very small low-conductivity proppants have
created the need for a better understanding of how waterfracs create the conductivity to produce high-rate oil and gas with a propping
agent with little effective conductivity at the depth at which these treatments are conducted (Dayan et al. 2009). A significant portion
of the chapter covers waterfracs (fluids with no viscosity enhancement) and the additives used in these treatments.
The ideal fracturing fluid should be moderately efficient. A high percentage of the fluid should remain in the fracture and not be lost to
the formation. Fluid efficiency is normally attained by com­bining high fluid viscosity with fluid-loss additives (Stewart and Coulter 1959;
Hall and Dollarhide 1964, 1968; Hawsey and Jacocks 1961; Gatlin and Nemir 1961; Pye and Smith 1973; King 1977; Shumaker et al.
1978; Settari 1985; Harris 1985, 1987; McDaniel et al. 1985; Zigrye et al. 1985). These fluid-loss additives might consist of plastering
agents, bridging agents, microemulsions, or emulsified gas. A low-efficiency fracturing fluid would not create the desired fracture volume,
carry the proppant, or achieve the desired formation penetration if most of the frac­turing fluid leaks off during treatment. It is believed the
success of waterfracs is because of little or no leakoff in the matrix allowing creation of massive surface area open to production.
Another important characteristic of a fracturing fluid is its ability to revert from high viscosity to low viscosity upon residing in the
formation. Viscosity reduction is necessary so that the treating fluid can be removed from the formation easily. High fluid vis­cosities
in the fracture or in the formation near the fracture can reduce hydrocarbon production. Fracturing fluid viscosity is normally reduced
by thermal degradation in high-temperature wells or by controlled degradation through the use of breaking agents such as enzymes,
oxidizers, or weak acids. Controlled degradation is es­sential for the fluid to maintain its viscosity during the treatment but to degrade
and lose its viscosity after the treatment.
Fracturing Fluids and Additives
167
Many fracturing fluid systems used during the 1950s and 1960s had high viscosity and the ability to degrade; however, they were
extremely difficult to pump down small tubulars. Modern fracturing fluid systems have been developed that allow for high viscosity
but have reduced friction properties. In fact, most of these fluids will pump at pressures lower than low-viscosity base fluids, such as
water or oil, through turbulence suppression by long-­chain-polymer systems. If a fluid cannot be pumped easily, it nor­mally is not
acceptable as a fracturing fluid. Exceptions to this are high-viscosity crude oils used in shallow casing jobs. These high-viscosity,
Newtonian fluids, however, are not applicable for pumping down small tubulars.
Fracturing fluid stability at a high temperature is a critical aspect of any fluid. A fluid that rapidly loses its viscosity because of
thermal thinning or degradation is not applicable for treatment of high-temperature permeable-matrix-dominant wells. A fracturing
fluid should be able to maintain the designed viscosity with minimal viscosity loss vs. time at bot­tomhole temperature (BHT).
Finally, fracturing fluids should be cost-effective and easy to mix in the field. One of the most important and realistic selection
criteria for a fracturing fluid is cost-effectiveness in treating the formation under study. Quite obviously, a fluid that has all these
attributes but will not yield cost-effective stimulation will not be an ideal fluid (Powell 1999; Taylor et al. 2006; Cawiezel et al. 2007;
Lawrence et al. 2009; Samuel et al. 1999; Nolte and Plahn 1993; McGowen et al. 1993; Palmer et al. 1991; Brannon and Ault 1991;
Leopoldo 2010; Funkhouser et al. 2010; Wheaton et al. 1991; Li et al. 2009; Mirakyan et al. 2009; Gupta 2009; Jennings 1996).
6.3 Water-Based Fracturing Fluids
Water-based fracturing fluids are used in the majority of hydraulic fracturing treatments today. This was not the case in the early days
of fracturing, when oil-based fluids were selected for vir­tually all the treatments. Water-based fracturing fluids have many advantages
over oil-based fluids.
•
•
•
•
•
Water-based fluids are economical. The base fluid, water, costs less than oil, condensate, methanol, or acid.
Water-based fluids yield increased hydrostatic head compared to oil, gases, and methanol.
Water-based fluids are incombustible; hence they are not a fire hazard.
Water-based fluids are readily available.
This type of fluid is easily viscosified and controlled.
In the early days of fracturing, there was a great deal of reluc­tance to pump water into an oil-bearing formation. In retrospect, many
of the early water-based fracturing treatments were conducted on formations that were not very water-sensitive. Also, the numerous
waterfloods being performed in the 1950s and 1960s added confidence that a water-based fluid could be used as a stimu­lation fluid.
Again, the widespread success of large volume waterfracs now being conducted daily in the industry has placed more emphasis on
the viability of water as the fluid of choice.
The availability, cost-effectiveness, hydrostatic head, and lack of fire danger provided incentives for the service companies to de­velop
such additives as potassium chloride, clay stabilizers, sur­factants, and nonemulsifiers that make water-based fluids more versatile.
Although many improvements have been made in oil-based fluids, most recent technical development has occurred in water-based
fluid technology, partly because of the recognition that water-based fluids are chosen for fracturing the vast majority of reservoirs.
6.3.1 Linear Fracturing Fluids. The need to thicken water to help transport proppant, decrease fluid loss, and increase fracture
width was apparent to early investigators. The first water viscosifier was starch, which had been used to thicken and decrease the
fluid loss in drilling mud. This particular fluid was short-lived be­cause of shear sensitivity, lack of temperature stability, and bacterial
degradation. In the early 1960s, guar gum was found to be a ready replacement. Guar polymer is derived from a bean, and when added
to water it thickens and viscosifies the fluid. Guar is a naturally occurring polymer that undergoes hydration upon contact with water.
The polymer uncoils, with water molecules attaching them­selves to the polymer chain. This creates a viscous fluid by inter­action of
the polymer coils, one to another, in the water-based system (Kostenuk and Gagnon 2008; Terracina et al. 2001; Weinstein et al. 2009).
The first types of guar polymer developed in the early 1960s are still in use today. Some of the suppliers have improved the product
by removing more of the hulls and inert material to give a lower-residue material, but the product remains basically the same as that
used in the early days of fracturing. Guar and crosslinked guar have once again become the fluids of choice for bottomhole temperature up to 300°F. The guar molecule and derivatives thereof, as a point of reference, are widely used in viscosifying such things as ice
cream and other food items.
Other linear gels used today as fracturing fluids are hydroxypropyl guar (HPG), hydroxyethyl cellulose (HEC), carboxymethyl
hydroxypropyl guar (CMHPG), carboxymethyl guar (CMG), xanthan gum, and in some rare cases, polyacryl­amides (Tiner 1976;
Chatterji and Borchardt 1981; Ely 1981). Of late, the use of polyacrylamides, high-molecular-weight material, has increased dramatically as a friction reducer in waterfracs. The most recent use of polyacrylamide is in creating linear viscosity in slickwater fracturing.
Although this technology is dated, the high-volume usage of acrylamide has lowered the cost such that it is competitive with guar gum.
Developed in the early 1970s, HPG was the most widely used viscosifier for water-based fracturing treatments for a significant
time. HPG is obtained by the reaction of propylene oxide with the guar molecule, creating a polymer with a more stable temperature
and somewhat higher viscosity. It was developed primarily to reduce the residue from guar gum and to achieve greater temperature
stability. The reasons for HPG’s decline as a dominant fracturing fluid polymer are multifaceted. The introduction of CMHPG, which
is a more versatile fluid in crosslinking, is one facet. Others include the high cost compared to guar and improvements to guar in relation to viscosity development and lower residue. The large success of guar borate systems combined with lower cost has negated the
use of HPG other than for special applications such as seawater fracturing fluids.
The residue after degradation of a particular viscosifying polymer is defined as the material that remains as an insoluble product
upon complete degradation of the polymer. Guar products typically vary in nondegradable residue from 4 to 6%. HPG will vary from
1 to 4% residue. This residue was construed as extremely important to some within the industry who believed that the residue could
act as a plugging agent in the fracture system or fracture proppant pack or as a plugging material in the formation pore spaces. The
argument for lower-residue fluids becomes moot when taking into account the positive benefits of the residue active as colloidal solids
that help control leakoff and minimize filter cake.
Early on there was significant work showing enhanced stability at temperature with HPG vs. guar, but with modern-day fluids
guar borate has been used for wells with BHTs up to and slightly above 300°F. Virtually all of the fluids for use above 300°F are now
CMHPG based, with some newer fluids for extreme temperatures (i.e., above 375°F) using acrylamide-based polymers.
168 Hydraulic Fracturing: Fundamentals and Advancements
A further derivative of guar gum, CMHPG is formed by the reaction of HPG with sodium monochloroacetate. This double­derivatized product is used typically in crosslinked-gel applications. CMHPG has little application in linear-gel systems because it is even
higher in cost (Table 6.1) than HPG. As discussed earlier, CMHPG has totally replaced HPG in the vast majority of applications for
BHTs above 300°F. This product has somewhat lower residue than HPG.
Comparative Costs of Polymers
Service Company
A
B
C
D
E
Guar
1.13
0.93
0.94
1.04
1.00
HPG
1.41
1.31
1.18
1.35
1.29
CMHPG
–
–
1.41
–
1.40
HEC
1.50
1.65
1.38
1.85
1.62
CMHEC
1.59
1.44
–
–
1.62
Xanthan
2.62
2.35
–
2.43
2.65
Relative costs are shown based on the average price for guar gum. Since service company E's published price for guar was the exact average,
they would have an index of 1.0 for quar. All other polymer prices are then based on relative costs.
Table 6.1—Comparative costs of polymers.
Certain service companies use a high-temperature fracturing fluid with CMG. This proprietary product is anionic in character and is not
compatible with salts such as KCl. It has been widely used in higher-temperature applications using a KCl substitute. Other viscosifiers
used in linear- gel systems include HEC, car­boxymethyl cellulose (CMC), and carboxymethyl hydroxyethyl cel­lulose (CMHEC). These
cellulose polymers are usually considered synthetics; guar is usually considered a natural polymer. Cellulose derivatives are formed
by reacting natural cellulose from cotton or wood products to form the derivative. HEC is formed by treating cellulose with sodium
hydroxide and reacting it with ethylene oxide. Hydroxyethyl groups are introduced to yield hydroxyethyl ether. CMC is produced by
reacting alkali cellulose with sodium mono­chloroacetate under very controlled conditions. Again, CMHEC is created by a double
derivatization, combining the reactions men­tioned earlier for the creation of HEC, followed by the reaction of sodium monochloroacetate
with HEC. These products yield high-viscosity polymers (Figs. 6.1 through 6.5) that have no residue what­soever upon degradation.
They form clear fluid solutions (Figs. 6.6 through 6.8) that show the turbidity of HPG vs. the nearly opaque nature of guar and the
very clean, clear solutions of cel­lulose derivatives. These relatively high-viscosity synthetic polymers are also high in cost (Table 6.1);
therefore, use of HEC is somewhat limited. HEC has relatively low cost-effectiveness com­pared with guar and HPG. Also, HEC suffers
from extreme difficulty in crosslinking; few metal or metal-chelant techniques are currently available to crosslink HEC.
HEC was used widely in the late 1960s and early 1970s, but the primary use for HEC today has been in gravel-pack appli­cations,
where a non-residual, high-viscosity fluid is required. The use of a retarded (glyoxylated) secondary gel of HEC allowed a large
number of high-temperature fracturing treatments to be con­ducted with relatively high concentrations of HEC in the late 1960s and
well into the 1970s (Fig. 6.4).
CMC has little or no use today in hydraulic fracturing applications because of its sensitivity to salt concentrations. It was used
briefly in the mid-1970s as a crosslinked fluid because of the ease of crosslinking the carboxymethylene group with heavy metals. Its
high cost (Table 6.1) and sensitivity to salts have basi­cally eliminated it from the product line of most fracturing service companies.
CMHEC is an improvement on CMC. The CMHEC product, while retaining the ease in crosslinking ability, does not have CMC’s
sensitivity to salt. CMC was used in applications calling for very-low-residue products, but because of low usage, it has not been
offered in the oil field for some time.
Viscosity of Nonderivatized Guar
Fann 35, R1B1, 2% KCI, pH 5.8
Fann Viscosity at 511 sec-1 (cp)
70
50 lbm/1,000 gal
40 lbm/1,000 gal
30 lbm/1,000 gal
60
50
40
30
20
10
0
60
80
100
120
140
Temperature (°F)
160
Fig. 6.1—Viscosity of nonderivatized guar.
180
200
Fracturing Fluids and Additives
High-Viscosity HPG
Fann Viscosity vs. Temperature
for Various Concentrations
of Polymer (2% KCI)
130
80 lbm/1,000 gal
50 lbm/1,000 gal
30 lbm/1,000 gal
Fann Viscosity at 511 sec-1 (cp)
120
110
60 lbm/1,000 gal
40 lbm/1,000 gal
20 lbm/1,000 gal
100
90
80
70
60
50
40
30
20
10
0
60
40
80
100
120
140
160
180
Temperature (°F)
Fig. 6.2—High-viscosity HPG (Based on Ely 2014).
CMHPG Viscosity vs. Temperature
Fann 35, 2% KCI, pH 6.5
60
Fann Viscosity at 511 sec-1 (cp)
50
40
60-1
60-2
50-1
50-2
40-1
30
40-2
30-1
20
30-2
1 = High-viscosity
CMHPG
2 = Conventional
CMHPG
10
0
60
80
100
120
140
Temperature (°F)
160
180
Fig. 6.3—CMHPG viscosity vs. temperature (Based on Ely 2014).
200
169
170 Hydraulic Fracturing: Fundamentals and Advancements
High-Viscosity HEC
Fann Viscosity vs. Temperature
for Various Concentrations
of Polymer (2% KCI)
200
Fann Viscosity at 511 sec-1 (cp)
180
80 lbm/1,000 gal
60 lbm/1,000 gal
50 lbm/1,000 gal
160
40 lbm/1,000 gal
20 lbm/1,000 gal
140
120
100
80
60
40
20
0
60
50
70
80
90
100 110 120 130 140 150 160 170 180 190
Temperature (°F)
Fig. 6.4—High-viscosity HEC (Based on Ely 2014).
High-Viscosity CMHEC
Fann Viscosity vs. Temperature
for Various Concentrations
of Polymer (2% KCI)
110
80 lbm/1,000 gal
60 lbm/1,000 gal
50 lbm/1,000 gal
Fann Viscosity at 511 sec-1 (cp)
100
90
80
40 lbm/1,000 gal
20 lbm/1,000 gal
70
60
50
40
30
20
10
0
40
60
80
100
120
140
160
180
200
220
240
Temperature (F)
Fig. 6.5—High-viscosity CMHEC (Based on Ely 2014).
Another viscosifier finding some use as a thickener for fracturing fluids is xanthan gum, which is used both as a linear-gel system
and as a crosslinked fluid. It is used as a thickener more often in drilling fluids than in fracturing fluids. Xanthan is a relatively high­cost product (Table 6.1). Its major use in stimulation during the past few years has been as a thickener for hydrochloric acid. Its use
is limited to acid concentrations up to 15% and temperatures of 200°F (93°C) or less.
6.3.2 Viscoelastic Surfactant Fluids. Viscoelastic surfactant (VES) gel systems have been described in the patent literature for
friction reduction and as well-treatment fluids. It has had uses in everyday life for some time. Early use of the product was as a
viscosifying acid and also as a viscous diverting agent in acid treatments. Its use in fracturing fluids is a relatively new phenomenon,
but the patent literature has expanded greatly in this area in the last few years.
Principally, these fluids use surfactants in combination with inorganic salts or other surfactants to create ordered structures, which
result in not only increased viscosity but also elasticity. These fluids have very high zero-shear viscosity without undue increase in
Fracturing Fluids and Additives
high-shear viscosity. Thus, they tend to be shear-degradable
fluids. They also have high elasticity. Zero-shear viscosity
has been found to be an essential parameter in evaluating
proppant transport. Therefore, these fluids can, with lower
loading, transport proppant without the comparable viscosity requirements of conventional fluids (Yu and Nasr-El-Din
2009). The technology of VES systems can be broken down
into several categories based on the structure of the ordered
structures or micelles.
As the concentration of surfactant increases in water,
micelles start to form. Further increasing the concentration
exceeds the critical micelle concentration for the surfactant
in water; these molecules start interacting with each other.
These interactions are based on ionic forces and can be
amplified by adding electrolytes (salts) or other ionic surfactants. Depending on the ionic charges and the size and shapes
of the surfactants and these counter ions, ordered structures
start to form, which increase viscosity and elasticity. The
reverse mechanism is true for breaking these systems. The
structures can be disrupted by adding other surfactants, ionic
additives, and hydrocarbons (from the formation or mutual
solvents or other solvents) or can be diluted by additional
formation water. The most common commercial systems
use cationic surfactants with inorganic salts or with anionic
surfactants. Anionic surfactants with inorganic salts are also
common. Zwitterionic and amphoteric surfactants in combination with inorganic salts have been used.
The common VES fluids have a temperature limit ambient to approximately 300°F. The use of surfactant gels has
been extremely limited because of high costs compared to
conventional systems. Comparative tests have been run in
field operations using the surfactant gels vs. conventional
guar borate. There was no apparent difference in performance of the wells. There has been abundant work by
service companies in developing non-residual gel systems
to fracture with. It is apparent that the development of
high-quality breakers has made the conventional fracturing fluids perform just as well as the fluids containing residue. Users should always keep an open mind in relation to
these fluids because they are excellent fracturing systems
but suffer from exorbitant costs compared to conventional
fluids.
6.3.3 Polyacrylamides. The last linear viscosifiers to be
discussed are polyacrylamides. There are many examples of
polymers and copolymers of acrylamides. The primary use
for acrylamides historically was not as a linear-gel viscosifier but as a friction reducer; these products yield excellent
friction reduction at very low concentrations. The temperature stability of acrylamides is usually adequate, but the cost
has been prohibi­tive. Acrylamides also are somewhat difficult to degrade controllably under low-temperature conditions (Gardner and Eikerts 1982). Typically, these products
are readily crosslinkable but, because of their very high cost
compared with guar or cellulose derivatives, have found
limited use in the oil field other than as friction reducers for
water and acid. Copolymers of acrylamide are finding fairly
wide usage as stable linear and crosslinked gels in fractureacidizing applications. With the trend to deeper drilling
and higher BHTs, crosslinked acrylamides are being used
to allow for viscosity development where the typical limit
of CMHPG zirconium systems fails in the range of 375°F.
Preliminary data on crosslinked acrylamide gels indicates
temperature stability in excess of 450°F.
The introduction of high-viscosity friction reducers
(HVFRs) is a relatively new phenomenon, although the
technology has been around for more than 50 years. The
high-volume use of the product has dramatically reduced
the cost, and it is not uncommon for these products to be
171
Fig. 6.6—Opaque nature of viscosified guar gel.
Fig. 6.7—Turbid nature of viscosified derivatized guar gel.
172 Hydraulic Fracturing: Fundamentals and Advancements
used in slickwater fracturing. It is strongly recommended
to compare viscosity numbers reported with accompanying shear rates. The typical shear-rate viscosity for guar and
derivatives is at 511 reciprocal seconds; always compare
HVFR numbers at a comparable shear rate. Again, acrylamides should have more temperature stability and also
require external breakers to negate any damage to the productivity because of excessive viscosity.
6.3.4 Crosslinked Fracturing Fluids. Linear gels are
relatively simple fluids to use and to control. Ex­cellent
reproducible data are available on the viscosity of these
fluids. The problem with linear fluids is their poor proppant suspension capability. Also, the linear gel has less
temperature stability than a similar crosslinked fluid. If
designing a damage-removal treatment or banking-type
proppant pack for high fracture conductivity near the
wellbore, then a linear gel might be the ideal fluid. Factors to consider include cost-ef­fectiveness, amount of
proppant placed, and type of proppant pack needed. If
trying to achieve deep penetration of proppant or of acid
away from the wellbore, then choose the higher-viscosity
crosslinked fracturing fluids.
Crosslinked fracturing fluids, first used in the late
1960s, were considered a major advancement in hydraulic fracturing technology. With linear gels, the only
means to obtain increased viscosity is to increase the
polymer concentration. Often, 80 to 150 lbm/1,000 gal
of water is needed to yield the viscosities necessary to
Fig. 6.8—Clear nature of viscosified derivatized cellulose gel.
­fracture treat a well successfully with linear-gel systems.
Adding proppant and dispersing fluid-loss additives into such concentrated solutions of linear fluids is difficult.
The development of crosslinked fluids eliminated many of the problems that occurred when linear gels were used to fracture
treat deep, hot reservoirs. The crosslinking reaction is one where the molecular weight of the base polymer is substantially
increased by tying together the various molecules of the polymer into a structure through metal or metal-chelate or borate
crosslinkers.
The earliest crosslinkers were borate and antimony metal. The metals or boron are dispersed between the polymer strands, and an
attraction occurs between the metals and the hydroxyl groups, or in the case of carboxymethyl derivatives, the carboxyl groups. This
interaction takes a gel system from a true liquid (Fig. 6.9) to a pseudoplastic fluid (Fig. 6.10).
The first crosslinked fluid was a guar gum system. A typical cross­linked gel in the late 1960s consisted of 60 to 80 lbm of guar
per 1,000 gal of water crosslinked with antimony or borate. The an­timony system was a relatively low-pH fracturing fluid. The
borate fracturing fluid was a high-pH system, typically in the pH 10 range, while the antimony was approximately pH 3 to 5.
These early cross­linked fracturing fluid systems suffered from some distinct disad­vantages relating to pumpability because of
Fig. 6.9—True-liquid gel system (linear gel).
Fracturing Fluids and Additives
173
Fig. 6.10—Pseudoplastic gel system (crosslinked gel) (Based on Ely 2014).
the rapid crosslink reaction and the high base-gel viscosity. Both the antimony- and borate-crosslinked systems suffered a few
field problems with incomplete gel degradation.
Incomplete gel degradation after fracturing treatments would result, at the very least, in producing back viscous gel that
could possibly carry proppant back out of the fracture. The worst scenario could result in a temporarily, or perhaps, permanently plugged fracture proppant pack. The antimony system experienced fewer gel degradation problems than the borate system because the operating pH range was such that enzyme breakers would function. Field personnel typically did not account
for the effects of formation fluids in raising the pH, which necessitated higher loadings of enzyme breakers.
In the early days, borate systems had degradation problems in low-temperature wells [i.e., below 125°F (52°C)]. In the high
pH range of the borate crosslinked gel, the standard enzyme breaker systems available at that time simply did not function. Many
treatments were overflushed with acid in an attempt to break the borate crosslink. Catalyzed, oxidizer breaker systems can controllably
degrade borate-crosslinked fluids. Antimony crosslinking is used with both guar and HPG through higher loadings of the enzyme
breakers, taking into account any increase in the pH resulting from formation-water contamination. In the present day, guar/borate
fluids are the dominant crosslinked system used for BHTs up to 300°F. This is because of their low cost, lack of shear sensitivity, and
the development of a great many breakers to controllably degrade the gels back to water.
Many other crosslink systems have been developed, such as aluminum, chromium, copper, and manganese. Additionally, in
the late 1960s and early 1970s, crosslinked CMC and some cross­linked HEC were used, although the difficulty in crosslinking HEC limited its use. With the development of the HPG and CMHEC polymers, a new generation of crosslinkers was also
developed. The first and most widely used of the new crosslinkers were the titanium chelates and aluminum compounds in the
case of the CMHEC polymer. The use of titanium chelates was initiated in the early 1970s with HPG. Through the early 1980s,
titanium chelates were the most widely used crosslinkers. Today the vast majority of crosslinked fluids are borate/guar systems
and zirconium-crosslinked CMHPG (England and Parris 2010; Dawson 1991; Cameron et al. 1990).
Crosslinking the polymer molecule tends to increase the temper­ature stability of the base polymer. It is theorized that this temper­
ature stability is derived from less thermal agitation of the molecule because of its rigid nature and some shielding from hydrolysis,
or ox­idation.
Crosslinking of the polymer, although increasing the apparent viscosity of the fluid by several orders of magnitude, does not nec­
essarily cause friction pressures to increase to any degree in the pumping operation (Keck 1991; Shah et al. 1992). It was originally
theorized that the ease in pumping crosslinked fluids was caused by the formation of a water ring similar to that physically prepared
for the super fracturing process (Kiel 1970; Engel 1970). This hypothesis was disproved by observing cross­linked fluids pumped
down test wells and back up to the surface.
Even though crosslinked-guar and guar-derivative systems crosslinked with metals can be pumped into deep, hot reservoirs, severe
shear degradation occurs if the fluid is cross­linked at the surface and pumped at high rates down the tubulars and through the perforations.
Because of this tendency with metallic-crosslinked gels to lose viscosity permanently as a result of high shear rates, the use of instantaneous crosslinked-gel systems has declined dramatically. These systems were replaced by delayed-crosslink-fracturing fluid systems.
6.3.5 Delayed-Crosslink Systems. Many of the early crosslinked fluids thickened instantly or without noticeable time delay.
A noteworthy development of the 1980s was the use of fracturing fluids with a controlled or delayed-crosslink reaction time.
Crosslink time is de­fined as the time for the base fluid to take on a rigid structure. This is evaluated in the field by many techniques. Some visually observe the fluid in a blender. The crosslink time occurs when the vortex in the blender disappears under
a set shear rate. Others simply collect a sample and observe the fluid until it becomes rigid enough to become unpourable (i.e.,
lipping out of a jar and coming back into the jar) (Fig. 6.10). Obviously, crosslink time is the time re­quired to observe a very
large increase in viscosity as the fluid becomes rigid.
A significant amount of research has been performed to under­stand the importance of using the delayed-crosslink fluid
systems. Recent research results indicate that a delayed-crosslink system allows better dispersion of the crosslinker, which
yields more viscosity and improves fracturing fluid temperature stability. Although dis­persion is believed to be a major factor
in stabilizing crosslinked gels, further research (Conway and Harris 1982) has proved that the final stability of the cross­linked
174 Hydraulic Fracturing: Fundamentals and Advancements
gel is directly related to the shear history of the metallic-crosslinked gel at the time of crosslinking. The gel stability is a direct
function of cross­linking at low shear rates. The popular explanation is that at low shear rates the polymer strands are uniformly
laid out and cross­linking actually occurs in a very uniform, structured manner, yielding ultimately much higher viscosities and
better stability to temperature, hydrolytic, and oxidative degradation (Fan and Holditch 1993; Le et al. 2010; Mayerhofer et al.
1991; Sporker et al. 1991; Shah et al. 1992; Al-Mohammed et al. 2007).
Another advantage of delayed-crosslink systems is lower pumping friction because of lower viscosity in the tubulars.
Although the crosslinked gels are pumpable down tubulars, a certain amount of energy is required to shear the crosslink back
toward the base gel. This viscosity is exhibited as higher pumping friction; therefore, the use of delayed-crosslink fluids yields
a higher ultimate viscosity downhole and gives much more efficient use of available horsepower on location. As a result,
delayed-crosslink systems are used more than conventional crosslink systems. The main advantages of using a crosslinked fluid
vs. a linear fluid are summarized below.
• A much higher viscosity in the fracture can be achieved with a comparable gel loading.
• The system is more efficient from the standpoint of fluid-loss control.
• A delayed-crosslink fluid has better proppant-transport capabilities, has better temperature stability, and is more cost-effective
per pound of polymer.
If there is a requirement for high viscosity and deep penetration into the fracture in temperatures approaching 375°F, the
ideal fluid has proved to be a zirconium delayed-crosslink system. If working with small zones, low pressure, and low temperature, however, then consider the use of linear fluids. The most cost-effective approach must be used to obtain the needed
fracture width and to stay within the productive zone. For stable fluids at temperatures above 375°F, the use of crosslinked
acrylamide systems is a must.
6.4 Oil-Based Fracturing Fluids
The most common oil-based fracturing gel available today is a reaction product of aluminum phosphate ester and a base, typically
sodium aluminate or sodium hydroxide. Certain service companies have developed a proprietary system not containing phosphate.
Reaction of the ester and the base creates an association reaction, which in turn creates a gel that yields vis­cosity in diesels or moderateto high-gravity crude systems. The aluminum phosphate ester gels have been improved to gel more crude oils and to enhance temperature stability. The earliest viscosi­fied oils were napalm-type fluids of aluminum octoate. Aluminum phosphate esters can be used to
create fluids with enhanced stability at a high temperature and good proppant­-carrying capacity for use on wells with BHTs in excess
of 260°F (127°C) (Maberry et al. 1998). Using gelled hydrocarbons is advantageous in certain situations to avoid formation damage to
water-sensitive, oil-producing forma­tions that could be caused by the use of water-based fluids. If the produced crude has high enough
gravity, typically above 35°F (0.85 g/cm3), then produced crude oil can be used to fracture the for­mation. The primary disadvantage
of using gelled oil systems is the fire hazard.
In most cases, the pumping friction of an oil-based fluid is higher than a delayed-crosslink water-based fluid system. Pumping pressures are also higher because of a lack of hydrostatic head of the hydrocarbon compared with water. Additionally, when fracturing a
high-temperature well [above 260°F (127°C)], the tem­perature stability of a delayed-crosslink water-based system is more predictable, and such a system is less costly than the typical oil-based fluid system.
It should also be mentioned that preparation of oil-based frac­turing fluids requires a great deal of technical capability and quality
control (Ely 1985). The preparation of water-based fracturing fluids is rela­tively straightforward by comparison.
By way of editorial comment it has been found that virtually all formations that were deemed “water sensitive” have been successfully
treated with water-based fluids. It is believed that by proper treatment of the water, or accepting some formation damage, the waterbased fluids are virtually always more successful compared to oil-based treatments. This movement away from oil-based fluid has been
enhanced by the high cost of oil, environmental considerations, and the very real lack of proper equipment to pump flammable fluids.
6.5 Alcohol-Based Fracturing Fluids
Methanol and isopropanol have been used for many years either as a component of water- and acid-based fracturing fluids or, in some
cases, as the sole fracturing fluid. Alcohol, which reduces the surface tension of water, has frequently purported to have been used to
remove water blocks. In fracturing fluids, alcohol has found wide use as a temperature stabilizer because it acts as an oxygen scavenger. Polymers are available that will viscosify pure methanol or isopropanol. These polymers include hydroxypropylcellulose and
HPG, with a very high molar substitution of propylene oxide. Guar gum will viscosify up to 25% methanol or isopropanol, but above
this, the guar will precipitate. Common HPG and CMHPG will gel up to approximately 60% methanol.
In water-sensitive oil reservoirs, hydrocarbon-based fluids are generally preferred over alcohol-based fluids. Use of alcohol-based
fluids creates several drawbacks, especially the inherent danger to personnel who breathe alcohol fumes and the ever-present danger
of combustion. As fracturing fluids, methanol-based fluids, par­ticularly at higher concentrations, present difficulty in the controlled
degradation of the base fluid. Very high concentrations of any type of breaker are required for complete degradation. Tables 6.2 and
6.3 illustrate the necessary breaker concentrations of a typical cross­linked fluid.
Numerous papers have described the benefits of methanol in water-based linear and crosslinked fracturing fluids and in acid-based
fracturing fluids (Tindell et al. 1974; McLeod and Coulter 1966; Smith 1973; Keeney and Frost 1975; Sinclair et al. 1974). The primary benefits relate to low surface tension, miscibility with water, removal of water blocks, and compatibility with formations that
are water sensitive. Although these types of fluids have been tried several times in many different areas, they have always ceased to be
used because of high costs and little benefit compared to much-lower-cost water-based systems.
6.6 Emulsion Fracturing Fluids
Emulsion fracturing fluids have been used for many years. In fact, some of the first oil-based fluids were oil-external emulsions. These
products had many drawbacks, and their use was greatly limited because of extremely high friction pressure resulting from their
high inherent viscosity and lack of friction reduction. Water-external-emulsion fracturing fluids were introduced in the mid-1970s
Fracturing Fluids and Additives
175
Hpg Gelling Agent
Temperature
20 lbm/1,000
30 lbm/1,000
40 lbm/1,000
50 lbm/1,000
°F
E*
O*
HTO*
E
O
HTO
E
O
HTO
80
0.50
–
–
0.75
–
–
1.00
–
100
0.30
–
–
0.40
–
–
0.60
–
120
0.25
–
–
0.35
–
–
0.50
140
–
0.30
–
0.30
–
–
160
–
0.15
–
–
<0.20
180
–
0.05
–
–
0.10
200
–
<0.05
–
–
220
–
–
–
240
–
–
–
260
–
–
–
60 lbm/1,000
E
O
HTO
E
O
HTO
–
4.00
–
–
<4.00
–
–
–
<2.00
–
–
<2.50
–
–
–
–
0.50
–
–
2.00
–
–
0.15
0.50
–
–
0.50
–
1.00
1.00
–
–
–
0.30
–
–
0.50
–
–
0.60
–
–
–
0.10
–
–
0.20
–
–
<0.20
–
0.05
–
–
0.05
–
–
0.10
–
–
0.15
–
–
–
<0.40
–
–
<0.5
–
–
>0.5
–
–
<0.75
–
–
–
–
–
0.25
–
–
>0.25
–
–
<0.20
–
–
–
–
–
0.20
–
–
0.15
–
–
<0.10
* E = Enzyme breaker, O = Oxidizer breaker, HTO = High temperature oxidizer breaker. All breaker loadings are in either gals/1,000 gallons or
lbm/1,000 gallons of base fluid.
Table 6.2—Four-hour breaker data for batch-mixed crosslinked gel using 1% KCl water.
Hpg Gelling Agent
Temperature
20 lbm/1,000
30 lbm/1,000
40 lbm/1,000
50 lbm/1,000
60 lbm/1,000
°F
E*
O*
HTO*
E
O
HTO
E
O
HTO
E
O
HTO
E
O
HTO
80
<1.50
–
–
<1.50
–
–
2.00
–
–
<2.25
–
–
<4.00
–
–
100
1.15
–
–
<1.00
–
–
1.85
–
–
<2.00
–
–
<3.00
–
–
120
<1.25 <3.00
–
0.75
5.00
–
<0.75 <7.00
–
1.75
5.00
–
<3.00 <6.00
140
<1.25 <2.00
–
<0.75 <3.00
–
1.00
5.00
–
<1.75 <5.00
–
<3.00 <5.00
–
–
3.00
–
–
3.50
–
–
160
–
2.00
–
–
<2.00
–
–
3.00
–
180
–
0.85
<3.00
–
1.00
–
–
2.50
–
–
200
–
–
<1.00
–
–
<4.00
–
–
<7.00
–
2.50
–
–
1.50
–
–
<7.00
–
–
<7.00
220
–
–
0.75
–
–
<1.00
–
–
<1.50
–
–
<4.00
–
–
<2.00
240
–
–
–
–
–
0.75
–
–
<1.00
–
–
<1.25
–
–
<1.50
260
–
–
–
–
–
<0.25
–
–
<0.30
–
–
<0.50
–
–
<0.60
* E = Enzyme breaker, O = Oxidizer breaker, HTO = High temperature oxidizer breaker. All breaker loadings are in either gals/1,000 gallons or
lbm/1,000 gallons of base fluid.
Table 6.3—Four-hour breaker data for batch-mixed crosslinked gel using 20% methanol in 1% KCl water.
(Sinclair et al. 1974). These fracturing fluids, although yielding somewhat higher friction pressure than comparable water-based gels,
were indeed a break­through in the industry and were used for a very long time as a very cost-effective, functional fracturing system.
These water-external emulsions require only one-third the quantity of gelling agent, sur­factant, and other additives, with two-thirds
oil making up the bulk of fluid. The cost-effectiveness of an oil emulsion implies that the load oil can be produced back and sold.
A water-external emulsion was a very popular fluid in the mid-1990s when crude oil and condensate sold for $3 to $5/bbl ($19 to
$31/m3). The use of oil-in-water emulsions has virtually ceased with the increased cost of crude oil. An oil-in-water emulsion has
good fluid-loss control, exhibits excellent proppant-carrying capacity, and tends to clean up well.
The emulsion is broken in the formation when the surfactant that created the emulsion is absorbed into the formation. Waterexternal emulsions are relatively simple fracturing fluids that are easy to mix and pump into most reservoirs.
The two basic types of oil/water emulsions are oil external and water external. An oil-external emulsion is a two-phase system in
which oil is the continuous phase and water is emulsified in the oil. A water-external emulsion is one in which water is continuous
176 Hydraulic Fracturing: Fundamentals and Advancements
and oil is the discontinuous phase. In an oil-external emulsion, the fluid has viscous properties similar to the base oil. As a result, oilexternal emulsions yield high friction pressures related to high oil viscosity.
On the other hand, because of the low viscosity of water com­pared with oil, water-external emulsions have lower friction pressures. Also, there is some tendency to achieve friction reduction with the polymers in the water phase of water-external emulsions.
Attempts have been made to place friction reducers in the oil phase of an oil-external emulsion, but these efforts have met with little
or no success. The pumping pressures of the water-external emulsions, however, are somewhat higher than for typical, con­ventional
crosslinked fracturing fluids but much lower than for the oil­-external emulsions. The water-external-emulsion friction properties seem
to lie between the friction properties of linear gels and cross­linked fluids.
Fig. 6.11 presents a comparison of the viscosities of linear gels, emulsion fluids, and crosslinked fluids at various times. The waterexternal emulsions are relatively cost-effective fluids for use when good viscosity is needed but the temperature stability or the ultrahigh viscosity of crosslinked fracturing fluids is not. It is necessary to consider the possibility that the load oil might not be recovered
in very-low-pressure or depleted reservoirs and that pumping any oil-based system has potential hazards. Today, there is virtually no
use of the water-external emulsions primarily because of the high cost of crude.
Viscosity vs. Time at 250F
Viscosity (cp)
A. Crosslinked gel
B. Water external emulsion
C. Linear gel
A
B
C
1
2
3
4
Time (hours)
Fig. 6.11—Comparison of viscosities of linear gels, emulsion fluids, and crosslinked fluids.
6.7 Foam-Based Fracturing Fluids
The introduction of foam fracturing fluids was a significant achievement in fluid technology (Bernard et al. 1965; Blauer and Kohlhaas
1974; Holcomb and Blauer 1975; Plummer and Holditch 1976; Harris and Reidenbach 1987; Holcomb et al. 1980; Ford 1981; Lord
1981; Holcomb 1977; Holcomb and Wilson 1978; Scherubel and Crowe 1978; Gaydos and Harris 1980; Grundmann and Lord 1983;
Reidenbach et al. 1986; David and Marsden 1969; Holcomb et al. 1981; Ely 1981; Harris 1985). But foam was not widely used as a
fracturing fluid until the mid-1970s. Foam fracturing fluids are simply a gas-in-liquid emulsion. The gas bubbles provide high viscosity and moderate proppant-transport capabilities (Wheeler 2010; Friehauf and Sharma 2009; Tudor et al. 1994; Tan and McGowen
1991).
Stable foam has viscous properties similar to a gelled, water-based fluid. Fig. 6.12 illustrates that the volume of gas necessary to
create a stable foam is approximately 60 to 90% of the total volume at a given pressure and temperature. As Fig. 6.12 shows, foam sta­
bility and viscosity increase as foam quality increases from 60 to 90%. The foam reverts to a mist above 90%. It is extremely im­portant
to stay within the stable foam-quality range during treatment. Typical fracturing treatments are designed to achieve a 70-75-80 quality
foam. This means that 70, 75, or 80% of the fracturing fluid is gas.
Gas bubbles are created by turbulence when liquid and gas are mixed. The bubbles emulsified in the liquid create foam that will
break out slowly with time. The half-life of foam is the time nec­essary for one-half of the liquid used to generate the foam to break
out of the foam under atmospheric conditions.
The gas-in-water emulsion can be stabilized by adding a surfactant to coat the gas bubbles. The addition of polymers to the liquid
also affects foam stability.
Foam mixed to a quality of 70 to 80% with a good-quality foamer but without such stabilizers as guar, HPG, or xanthan generally
yields a half-life of 3 to 4 minutes. Many early fracturing treatments, and some current treatments, were conducted with this type of
foam. The addition of polymer stabilizers increases half-life to 20 to 30 minutes. Half-life measurements are used only as qualitative
indicators of foam stability in the laboratory. In the fracture and under high pressure, foam half-life is much longer than measured at
atmospheric conditions. It should be carefully noted that the addition of polymer (Fig. 6.13) dramatically changes the relationship
between viscosity and foam quality. It is possible to have a “linear-gel” type fluid that has proppant transport characteristics with
quality as low as 30%. Without polymer stabilizers, the fracturing fluid effectively becomes a mist with no viscosity at qualities less
than 60%.
When carbon dioxide (CO2) is used as the energizing medium for foam, liquid CO2 is pumped instead of dry N2 gas. What is formed
at the point of intersection is not true gas/liquid foam. The resulting emulsion turns into foam only if the liquid CO2 turns into a gas
at reservoir conditions (Tudor et al. 1994).
Fracturing Fluids and Additives
Foam Viscosity vs. Quality
100
Shear rate
500
1,500
3,000
∞
90
80
Effective Foam Viscosity (cp)
177
70
Shear rate
sec−1
60
50
40
30
20
10
0
0
0.1
0.2
0.3
0.6
0.4
0.5
Foam Quality
0.7
0.8
0.9
1
Fig. 6.12—Foam viscosity vs. quality (Based on Ely 2014).
Viscosity vs. Quality
400
40-lbm/1,000 US gal HPG
solution foamed with N2
at 75°F
Viscosity (cp)
300
100 s-1
200 s-1
1,000 s-1
200
100
0
0
0.2
0.4
Quality
0.6
0.8
Fig. 6.13—Effect of quality and shear rate on the viscosity of a 40-lbm/1,000 gal HPG solution foamed with
N2 at 75°F (Ely 2014).
Using foam as a fracturing fluid has several advantages. The two most obvious are minimizing the amount of fluid placed on the
for­mation and improving recovery of fracturing fluid by the inherent energy in the gas. In preparing foam, typical use is 65 to 80%
less water than in conventional treatments. The inherent ener­gizing capabilities of the fluid caused by entrained gas assist in rapid
cleanup or simply promote cleanup in low-pressure formations.
However, using foam as a fracturing fluid has several disad­vantages. Much more care must be taken in running a foam frac­turing
treatment from a mechanical point of view. Small variations in the water or gas mixing rates can cause the loss of foam sta­bility in
nonstabilized foam fracturing. N2 foam is not very dense; therefore, pumping pressures will be large compared with gelled water.
Another disadvantage of foam is that it is difficult to get high sand concentrations in foam fracturing. Typically, the highest achievable
sand concentration downhole is approximately 8 lbm/gal (957 kg/m3) because all the sand must be added to approximately one-quarter
of the fluid. For example, to run a 75-quality foam, proppant concentration of 20 lbm/gal (2397 kg/m3) in the liquid phase is needed to
achieve a 5-lbm/gal (599-kg/m3) slurry con­centration. In recent years, the “constant internal phase” concept has been introduced. The
theory proposed is that the proppant becomes part of the internal phase allowing for placement of much higher sand concentrations.
This technique or variations of the constant-internal-phase concept are widely used in foam-fracturing stimulation.
178 Hydraulic Fracturing: Fundamentals and Advancements
Virtually any liquid can be foamed, including methanol, methanol/water mixtures, hydrocarbons, and water. Foam fracturing is a
technique that has many inherent advantages and disadvantages; therefore, it is the ideal fluid in certain formations, while it should
not even be considered in others. Recent improvements in equipment to handle high sand concentrations and in metering capabilities
of gas and liquid have made foam fracturing more controllable. The greatest application for foam fracturing is probably in shallow,
low­-pressure wells that require an energized fluid or in those wells that are so water sensitive that foam must be used.
The addition of a high-quality gaseous phase to fracturing fluids does degrade the proppant-transport capability, putting virtually
all foamed fluids into the category of banking fluids—i.e., these fluids allow for significant proppant settling, and in some cases do
not achieve significant propped length. These fluids have historically given high initial production with rapid decline in productivity,
indicating very short propped length. In low-permeability formations, consideration should be given to using nonenergized systems
with excellent proppant-transport capability and simply swab or pump the load fluid off of the reservoir. Harris and Reiderbach (1987)
and Harris (1985) indicate that if one does not exceed 30% quality foam in crosslinked-gel treatments, the proppant support is not
compromised. This allows for excellent proppant transport while still using N2 for lift assistance.
6.8 Energized Fracturing Fluids
The use of high-pressure hydrocarbon gases to assist in acid­-treatment flowback is documented as far back as the 1950s. The use of
CO2 and N2 was initiated in the late 1960s (Foshee and Hurst 1965; Moran and Horton 1963; Crawford et al. 1983; Hurst 1972; Boren
and Johnson 1965; Shouldice 1966; Black and Langsford 1982; Justice and Nielsen 1952). The ad­vantages of energizing fracturing
fluids are obvious, particu­larly for a formation with low bottomhole pressure. The energy imparted by the gases enables more-rapid
removal of the stimu­lation fluid and might be cost-effective compared with long-term swabbing or pumping operations. Previous
research has shown that entrained gas is also beneficial for fluid-loss control. The incorpo­ration of inert gases into a fracturing fluid
will yield proportionally better fluid efficiency than the same fluid without the entrained gases.
The type of gas used for energizing a fracturing fluid should be considered carefully. N2 is, of course, an inert gas. When N2 is added
in small amounts and without a surfactant, the result is an additive that is totally inert and relatively immiscible in water-based fluids.
The use of CO2, however, introduces a reactive component to the fracturing fluid, and CO2 is soluble in water. CO2 can be converted
to carbonic acid, which is typically incompatible with fracturing fluids.
The solubility of CO2 in treating fluids and reservoir fluids can be advantageous when this gas is used in a stimulation treatment.
Much of the CO2 will go into the solution at typical reservoir conditions. Also, dissolved gas does not easily dissipate into the formation, as might be the case with a less-soluble gas, such as N2.
It is, therefore, imperative that a fluid commingled with a gas should be flowed back as quickly as possible. The flowback equipment should be rigged such that immediate flowback following shutdown of the fracturing treatment can occur, to negate losing much
of the functionality of the energized treatment. The obvious advantages and disadvantages to using CO2 and N2 should be weighed
and the relative cost-effectiveness compared before their use. The use of foamed or energized fluids has dramatically decreased as the
trend toward slickwater application has occurred. The realization that properly treated water does not yield destruction of the reservoir
and that dramatic decrease in cost accompanies elimination of gases has had great consequence.
Where water availability is low, either foam or stabilized foam can be used. It is important to take into account treating pressure and
cost. There are also very-low-pressure reservoirs in which the only option is to energize the treating fluid.
6.9 Fracturing Fluid Additives
The first fracturing treatments contained only gasoline, napalm, and sand. Modern conventional viscous fracturing fluids are more
complex. It is not un­common today in conventional crosslinked systems to have as many as seven or eight different additives in a typical fracturing fluid. These additives, depending on reservoir characteristics, might or might not be needed. It is important, however,
to verify the relative compatibility of the various additives. Fig. 6.14 graphically shows chemical incom­patibility of two additives.
By not having the proper additives present, one or both additives can be lost and the treatment or the well could be endangered.
6.9.1 Biocides. Unless the bottomhole temperature exceeds 240°F, no water-based fracturing fluid containing guar or guar derivatives
should be pumped into a formation without some type of biocide present. Biocides are used to eliminate surface degradation of the
polymers in the tanks. A more important purpose is that properly designed biocides will stop the growth of anaerobic bacteria in
the formation. Many formations have turned sour because of the growth of Desul­fovibrio bacteria, which create hydrogen sulfide
and turn the forma­tion crude sour. Biocides should be added to fracturing fluids to maintain gel stability on the surface and to protect
the formation from bacterial growth. The proper procedure for adding biocides for batch mixed treatments is to add at least half of the
biocide into the tank before it is filled with water. This will give a rapid kill or a concentrated kill of any bacteria in the tank. When the
tank is full, the rest of the biocide should be added, and then approximately 6 to 8 hours should be allowed before gelling up with
the selected polymer. Most biocides require some time to achieve a kill. Biocides are discussed further in the waterfrac section because
the function has nothing to do with protecting gel systems, and the need for and type of biocides in waterfracs are somewhat controversial.
6.9.2 Breakers. A breaker is an additive that enables a viscous fracturing fluid to be degraded controllably to a thin fluid that can be
pro­duced back out of the fracture (Clark and Skelton 1978; Tannich 1975). All breakers used today are internal breakers (i.e., they are
incorporated into the fracturing fluid at the surface). In the early days of fracturing, some attempts were made to break a viscous fluid with
external means. These attempts were unsuccessful because the viscous fluids themselves act as di­verting agents. Currently used breaker
systems include enzymes and catalyzed oxidizer breaker systems for low-temperature [70 to 130°F (21 to 54°C)] applications. Conventional
oxidizer breaker systems are used for a temperature range of 130 to 200°F (54 to 93°C), and delayed-activation oxidizer systems are
applicable for temperatures from 180 to 320°F (82 to 160°C). Weak organic acids are sometimes used as breakers at temperatures above
200°F (93°C) (Terracina et al. 1999; Tayal et al. 1997; Brannon and Pulsinelli 1992; Gulbis et al. 1992; Elbel et al. 1991).
All the breaker systems are used to degrade the polymers in water-­based fracturing gels. Examples of breaker-loading schedules for
enzymes, oxidizers, and controlled oxidizer systems are shown in Tables 6.2 through 6.4. Note that one of the most critical factors
relating to breaker mechanisms is the pH of the fracturing fluid. Most enzyme breakers will function only between pH 3 and 9, with
an optimum at pH 5. Below pH 3 and above pH 8, the effectiveness of a conventional enzyme breaker is greatly reduced. If enzyme
breakers are used in high-pH or very-low-pH fluids, there will be a serious problem with gel degradation. Specialty enzymes work
Fracturing Fluids and Additives
179
Fig. 6.14—Example of chemical incompatibility of two additives (Ely 2014).
Hpg Gelling Agent
Temperature
20 lbm/1,000
40 lbm/1,000
50 lbm/1,000
60 lbm/1,000
°F
E*
O*
HTO*
E
O
HTO
E
O
HTO
E
O
HTO
60
0.400
–
–
0.700
–
–
1.200
–
–
3.000
–
–
80
0.100
–
–
0.200
–
–
0.400
–
–
1.000
–
–
100
0.060
–
–
0.100
–
–
0.250
–
–
0.500
–
–
120
0.060
–
–
0.100
–
–
0.175
–
–
0.300
–
–
130
0.060
0.250
–
–
0.500
–
0.175
0.800
–
0.250
1.000
–
140
0.060
0.175
–
0.100
0.375
–
0.150
0.375
–
0.200
0.550
–
160
0.060
0.080
–
0.100
0.200
–
0.150
0.375
–
0.200
0.550
–
180
–
0.075
–
–
0.150
–
–
0.275
–
–
0.425
–
200
–
0.075
–
–
0.150
–
–
0.200
–
–
0.300
–
* E = Enzyme breaker, O = Oxidizer breaker, HTO = High temperature oxidizer breaker. All breaker loadings are in either gals/1,000 gallons or
lbm/1,000 gallons of base fluid.
Table 6.4—Linear-gel break schedule for 24-hour shut-in time for various guar and cellulose systems. Break data
­applicable for guar, HPG, HEC, CMC, and CMHEC.
outside these pH ranges, but these typically have distinct temperature ranges in which they function. Enzyme breakers actually break
the molecular chains and effectively lower the molecular weight. Oxidizer breaker systems will function from pH 3 through 14.
Oxidizer systems also work by breaking the molecular structure of the polymer. A large amount of literature has covered
the use of enzyme breakers. Enzyme breakers do work well in their specific pH and temperature ranges. There has been a
number of cases in which a combination of oxidizer and enzyme breakers has been used synergistically. Weak organic acids
have also been used, but if the acid contacts carbonate in the reservoir, the breaker will react with the formation rather than
with the fluid.
In oil-based gel systems, typical breakers are bicarbonate, lime, and/or water solutions of amines. Weak acids have been used
with limited success to degrade the system. The oil-gel breaker works with the addition of an acid or a base that dissolves slowly in
the fluid such that the reaction is forced one way or the other, breaking the gel system. The amine system is a proprietary technique
180 Hydraulic Fracturing: Fundamentals and Advancements
in which free-­radical generation occurs. Water at low concentrations must be present. It is an extremely critical reaction used only in
low-temperature applications.
Pilot tests on breakers should be conducted before they are in­corporated into a fracturing treatment. Omission of breakers in
the early stages of fracturing treatments, because they lower the sta­bility of the gel and might cause a screenout, could result in an
un­broken gel that will plug off the fracture system. This is particularly the case if the temperature is inadequate to cause gel degradation. It is imperative that breakers be included throughout a treatment in such reservoirs. Breakers can be run at low concen­trations in
the early stages of a treatment and increased at later stages to enhance breaking and flowback.
6.9.3 Buffers. Common buffering agents are used in fracturing fluids to control the pH for specific crosslinkers and crosslink
times (Ely 1985). They also speed up or slow down the hydration of certain polymers. Typical products are sodium bicarbonate, fumaric acid, combi­nations of monophosphate and disodium phosphate, soda ash, sodium acetate, and combinations
of these chemicals. Another and perhaps more important function of a buffer is to ensure that the fracturing fluid is within
the operating range of the breakers or degrading agents. As mentioned earlier, some breakers simply do not function outside
specific pH ranges. By applying a buffer rather than a strong acid or strong base, a pH range can be maintained even though
con­taminants from formation water or other sources tend to change the pH. Other instances in which buffers are useful include
counteracting fracturing-fluid-tank contamination or compensating for water deliv­ered to the location that has a high concentration of carbonate, bicarbonate, or other minerals that affect the pH. The use of buffers helps prepare quality fracturing fluids
that will hydrate and degrade properly.
A commonly used product for pH control in high-pH fluids is sodium hydroxide. The product is low in cost but is a strong base and
has little or no buffer capacity. Fracturing fluids such as borates might look good in surface testing in blenders and beakers, but once
into the formation, they most probably lose their pH control and the fracturing fluid reverts to linear gel.
6.9.4 Surfactants and Nonemulsifiers. A surfactant (surface-active agent) can be defined as a molecule that seeks out an interface and
has the ability to alter the prevailing conditions (Tannich 1975; Boyer et al. 1981; Cawiezel et al. 2010). A surfactant is almost always
composed of two parts: a long hydrocarbon chain that is virtually insoluble in water but soluble in oil and a strongly ­water-soluble tail.
Because there is partial solubility in oil and water, the surfactant will tend to accumulate at the interface of these fluids.
The water-soluble portion of the molecule might be ionically positive (cationic), negative (anionic), or mixed (amphoteric). The
ionic charge of the various surfactants used in oilfield stimulation is important in terms of wettability imparted to a given formation. The
inherent ionic characteristics of particular formations cause cat­ionic surfactants to leave carbonates water-wet and sandstones oil­-wet.
Anionic surfactants tend to leave sandstones water-wet and limestones oil-wet. Amphoteric surfactants are organic molecules of
which ionic charges depend on the pH of the fluid. Almost all for­mations are naturally water-wet, which favors oil movement through
the rock. Because the water-wet condition is preferred, the ionic nature of the surfactant is an important consideration, and the design
engineer should be aware of the charge of a surfactant in its selection. It is generally inadvisable to mix cationic with anionics because
of the possibility of forming precipitates. Because a large number of formations throughout the world are heterogeneous, limy sands
or sandy limes, it is often useful to select a nonionic surfactant, provided that it meets certain nonemulsification criteria.
An emulsion consists of two immiscible fluids in which one phase exists as fine droplets dispersed throughout the other phase.
Oil­field emulsions are either oil in water (in which oil droplets exist in the continuous water phase) or water in oil (in which oil is
the con­tinuous phase). The viscosity of an emulsion can vary from several hundred to several thousand centipoise. If an emulsion is
created near the wellbore, severe production blockage could occur.
Because of their surface-active nature, surfactants can act as de­-emulsifiers or as emulsifiers. Effectiveness of a surfactant as a
de-­emulsifier in a particular crude-oil/water system must be determined experimentally. Tests should be run according to specifications set out in API RP 42 (1977) to determine the proper type and concentration of surfactants required to prevent emulsification of
a particular crude with a treating fluid. The surfactant should maintain its surface ac­tivity at reservoir temperatures and should not be
easily stripped out of solution by adsorption from contact with the reservoir rock.
As discussed earlier, some fracturing fluids are composed of hydrocarbon and water that are emulsified to build fluid viscosity.
When emulsified fluids are used, it is desirable for the surfactant to adsorb on the formation so that the emulsion will break.
Surfactants are also used to prevent or treat near-wellbore water blocks. Although not as severe as emulsions, a water block can
impair production. Surfactants lower the surface tension of the water and reduce capillary pressure, which results in lower energy
re­quired to move the water across boundaries and through the for­mation matrix.
Another form of well damage that might be treated by surfactants is blockage by fines. Fines can be silts, clay minerals, or drillingfluid solids. If a surfactant that wets the individual fine particles is used in the fracturing fluid, the particles can be removed from the
formation more easily when the broken fracturing fluid is produced back.
There is considerable controversy over the use of common surfactants in slickwater fracturing, and hundreds of treatments are
conducted without any surfactant. Many commonly available surfactants do plate out fairly quickly in the formation leaving the fluid
at in-situ surface tension. Standard tests should be followed for the possibility of emulsions forming because of fluid incompatibility.
6.9.5 Nanosurfactants. In the last few years, there has been a movement toward the use of nanosurfactants, very-low-molecular-weight
surfactants dissolved in an environmentally friendly solvent made with byproducts of oranges. Like other surfactants, this type can be anionic,
cationic, or amphoteric. It has been used successfully in many areas. Although the product has been around for some time, a great deal of
research into application and results continues. Many publications (Tannich 1975) have focused recently on microemulsion surfactants and
their purported benefits. Arguments have been made, both pro and con, relating to the ultimate benefits of the products. Recent studies have
shown significant benefits. There have been successful applications in the Permian, DJ basin and in the Scoop Stack plays (Zelenev 2011; Jin
2016; Alsobaidi et al. 2018). More studies should be undertaken to evaluate the applicability of the products before use. A significant amount
of research is under way to quantify applications and optimize usage.
6.9.6 Fluorocarbon Surfactants. Fluorocarbon surfactants have been used in oilfield treatments for many years (Clark et al. 1982).
Fluorocarbon sur­factants are similar to hydrocarbon surfactants, except that in the oil-soluble half of the molecule, hydrogen atoms
attached to the carbon chain are replaced by fluorine atoms.
Fracturing Fluids and Additives
181
For the most part, fluorocarbon surfactants have been eliminated from service company product lines. This is related to high cost
and the perception that fluorocarbon use destroys the ozone layer.
In recent years, the use of commonly available surfactants, particularly in waterfracs, has dropped dramatically. Field experience
has shown no benefit from adding surfactants, and in some cases negative effects have resulted. A theory suggests that the negative
effects have been related to the low-surface-tension fluid penetrating extremely small pore throats and microfractures and the subsequent plating out of the surfactants, creating a problem in potentially plugging the tiny flow paths. This is a controversial notion
but one that has been widely implemented in thousands of wells, eliminating the cost of surfactants in the large fracture treatments.
6.9.7 Clay Stabilizers. Laboratory studies and field results have indicated that clays and fines present in producing formations can
reduce stimulation success. The percentage of clays present might not be as important as the type and location of clays. Kaolinite,
illite, and chlorite are the most common types found in sandstone reservoirs. These clays are typically nonswelling, particularly in the
presence of potassium chloride water. Often, however, they are inter­spersed with lesser amounts of smectite and mixed-layer clays that
are not particularly stable. The introduction of fracturing fluids or a change in temperature, pressure, or ionic environment could cause
the clays to become dislodged and to migrate through the pore system of the rock (Himes and Vinson 1991; Ghalambor and Guo 2010).
As the particles migrate, they might bridge in narrow pore throats and seriously reduce permeability. Once permeability is impaired,
specific steps must be taken to repair the damage.
Another form of permeability impairment is clay swelling, which reduces the per­meability in a formation. Susceptibility of a formation to damage by clay swelling and particle migration appears to depend on the following characteristics: clay content, clay type,
clay distribution, pore-size and grain-size distribution, and the amount and location of cementing materials such as calcite, siderite,
or silica. Susceptibility to damage can be evaluated through X-ray diffraction, a scanning electron microscope, and thin-section point
counting. Damage can be mitigated through the use of clay­-stabilizing agents. The following are common clay-stabilizing agents.
• Potassium chloride (KCl) prevents the dispersion of clay particles by providing sufficient cation concentration to prevent
leaching of the exchangeable cations present and keeps individual platelets of the stacked clay particles in a coagulated or condensed state. KCl does little to prevent migration and provides no residual pro­tection against dispersion by subsequent contact
with low-salinity water. KCl is the most commonly used antiswelling agent in conventional fracturing treatments (Black and
Hower 1965; Smith et al. 1964). Virtually all treatments in permeable sandstone reservoirs are de­signed to contain KCl, and it
is even used in limestone reservoirs with sandstone intervals containing clays.
• Ammonium chloride behaves like KCl in preventing clay swelling. It typically is not used in fracturing operations because of
high cost but finds some use in hydrofluoric acid treatments.
• Calcium chloride also functions like KCl and ammonium chloride. It readily forms precipitates in the presence of high-sulfate
or high-­alkalinity formation water; however, it appears to be useful in high­methanol/water solutions where KCl and ammonium chloride have limited solubility.
• Upon dilution in water, zirconium salts, particularly zirconium chloride, form a complex inorganic polymer containing
hydroxyl bridging groups (Clarke and Nasr-El-Din 2015). The highly charged nature of these polymers causes them to adsorb
onto the clay surfaces in an irrever­sible fashion, and they might bond the clay particles to the sand-grain surfaces. This particular clay stabilizer might be applicable in preflushes ahead of fracturing treatments.
• Polymeric clay stabilizers are cationically charged high-molecular-­weight polymers that tend to adsorb onto the surface of
clays tena­ciously, tying them down and negating any fines migration or swelling (McLaughlin et al. 1976; Anderson and Kannenberg 1979; Williams and Underdown 1981; Young et al. 1980). They need to be applied with care because over­treatment
can plug the pore spaces. They are relatively permanent once in place, and some success has been achieved with these products, particularly when they are combined with KCl.
• Polymeric solutions of hydroxyaluminum when adsorbed tightly onto clay mineral surfaces might be useful in negating particle migration or clay swelling (Reed 1971, 1972; Blevins et al. 1973; Coppel et al. 1973; Haskin 1976). The requirements of
particle overflush and a somewhat lengthy curing time have limited its use in stimulation applications.
6.9.8 KCl Substitutes. Certain modified polyamines perform two functions: they enhance the clay-swelling control obtained with
KCl and prevent the migration of fines (Clementz 1977). These products chemically adsorb onto clay particles and thereby keep them
in a compact or undispersed state. They might be useful in preventing sloughing and fines generation of the fracture faces during high
flow rates in fracturing and flow­back. These products lack the duration of protection of polymeric clay stabilizers, but they do not plug
pore spaces the way high­-molecular-weight polymeric clay stabilizers do.
These KCl substitutes have gained widespread use in the last few years because of ease in handling compared to KCl. Typical loadings are in the range of 1 to 2 gal per 1,000 gal. The major use has been in relatively low-permeability formations, and in every case
capillary suction tests should be conducted to evaluate the proper clay-control additive.
In recent times, a substantial amount of treatments have been performed using NaCl as a clay stabilizer. The high cost of KCl and
KCl substitutes has caused operators to look hard at compatibility of produced brines and simple NaCl solutions to reduce the cost
of fracture treatments. Field experience and laboratory capillary suction tests have shown that these types of fluids in some cases
outperform KCl and KCl substitutes in controlling clay swelling and migration, but certainly they are much more economical to use.
It is believed that many times fresh water or water treated with minimal amounts of formation brine are the fluids of choice in tight
conventional reservoirs and in almost-impermeable shale.
6.9.9 Fluid-Loss Additives. In the early days when oil-based fluids were normally used, an excellent fluid-loss additive was developed (Hawsey and Jacocks 1961). This additive, a tall oil derivative (Adomite Mark II), gives excellent fluid-loss control when used
with soap-type fluids or an oil-based fluid without viscosifier. It cannot be used in the napalm or aluminum phosphate ester­type gels
because of incompatibility problems. The Adomite Mark II is no longer available. The only fluid-loss additives for oil-based fluids are
water-based systems such as silica flour or starch.
One of the most common water-based fluid-loss additives consists of very finely ground silica flour. A related product uses nonswelling clays mixed with silica fines. Mixtures of vegetable compounds, talc, silica flour, and guar gum are used in another product
182 Hydraulic Fracturing: Fundamentals and Advancements
(Haskin 1976; Penny et al. 1985; Penny 1982; Williams 1970). Many
fluid-loss additives for fracturing were available 15 to 20 years earlier.
Oil base
Water base
There were mixtures of karaya gum with oil-soluble resin, slowly soluble
soap, and many other solids that combined with the colloidal solids in
Silica flour
Silica flour
guar to create a minimal filter cake on the face of the fracture.
Starch blends
Starch blends
The fluids with the best fluid-loss control were the early guar gums,
Lime powder
3% diesel
which had high residues combined with silica flour. Also used successfully was a combination of talc and swellable gums with guar. This
Sodium bicarbonate powder
Nitrogen - CO2
mixture provided an excellent fluid efficiency almost independent of
Nitrogen - CO2
100-mesh sand
permeability. Clean fluids, such as HEC = CMHEC, cannot be treated
100-mesh salt or sand
adequately to give excellent fluid-loss control in high-permeability
formations. In fact, many formations of moderate permeability can be
Table 6.5—Common fluid-loss additives.
severely damaged by the use of such clean fluids. To achieve excellent
fluid loss-control, the design engineer should have not only a bridging
material but also a wall-building material. Nonresidue frac­turing fluids generally do not have wall-building properties.
More-recent efforts to control fluid loss have involved either diesel fuel at concentrations up to 5% or lesser concentrations of aro­matic
hydrocarbons with surfactants that yield a micro­emulsion (Zigrye et al. 1985; Penny 1982). This technique appears to give better fluidloss efficiency for fracturing fluids used in formations with permeabilities less than 1 md. The fluid-loss control achieved by microemulsions
with diesel oil or aromatic hydrocarbons is less efficient in moderate-­to high-permeability reservoirs. The US government has banned use of
diesel in fracturing fluids. Crude oils can be used if permitted before the treatment.
Use of very clean fluids (the HPG, CMHPG, or cellulose derivatives) for moderately permeable reservoirs often entails adding
large concentrations of fluid-loss additives to achieve even moderate fluid-loss control. Because fluid-loss control is a requisite for
effective fracturing, use of such clean fluid appears to be somewhat self-defeating.
For many applications, conventional guar gum systems with in­expensive silica flour could be the most cost-effective fluid-loss ad­ditive to
achieve efficient fracturing fluids. Table 6.5 illustrates many common fluid-loss additives.
Fluid-Loss Additives
6.9.10 Foamers. In the early days of foam fracturing, commercial products that had been used as sudsing agents were used as foam
stabilizers and performed adequately. As the industry moved toward higher-temperature formations, higher sand concentrations, and
larger job sizes, efforts were made to create much more efficient and more-cost-effective foaming equipment and agents (Harris and
Reidenbach 1987). Foaming agents are now available for virtually any base fluid, from fresh water to high-brine fluids contaminated
with large amounts of hydrocarbons to water/alcohol mixtures varying from 0 to 100% methanol.
Virtually any base fluid can be foamed with a temperature-stable foaming agent. However, nonionic water-soluble surfactants often
suffer from cloud­point problems at elevated temperatures. Thus, it is desirable to determine that there is no problem with stability of
the foamer during the treatment. A foam-stability test should be conducted before using any foamer.
Common stabilizers for foaming treatments include the basic guar, HPG, and xanthan gums. Such materials are added to the fracturing fluid to increase the foam half-life, particularly at elevated tem­peratures. In this application, the stabilizer must be relatively
immune to thermal degradation at BHTs. In systems that use delayed crosslinkers, it is not uncommon to crosslink the gelling agents
used as stabilizers for the foam. Researchers report enhanced stability and viscosity and longer half­-lifes for such systems under ambient conditions than normally seen when the gelling agents are not crosslinked (Watkins et al. 1983).
Although foam is nowhere near a perfect proppant-transport fluid, it does create viscosity to place and transport proppant. The
addition of gelling agents does make treatments much less susceptible to screenout because the foam quality can drop quite low while
still maintaining linear viscosity. Note Fig. 6.14. Typical foam half-lifes for nongelled foams are in the range of 2 to 5 minutes, while
gelled or crosslinked foams can have half-lifes in excess of 20 minutes. Fracture treatments can be and are still conducted with highquality foams without gel but must remain above 60% quality to maintain stability.
The use of foam and energized fluid has greatly decreased in the last few years because of the dominance of slickwater and the
realization that water properly treated is not particularly damaging to low-permeability reservoirs.
6.9.11 Friction Reducers. Virtually all polymers act as turbulence-­suppression agents in the presence of low-viscosity base fluids.
When pumped at high rates down small tubulars, low-viscosity water or hydrocarbon fluids tend to achieve high turbulence, which
translates into high friction pressure (Bundrant and Matthews 1955; Lord et al. 1967; Savins 1964; Hoover and Padden 1967; Clark
1979; Rogers et al. 1984; Sinclair 1970; Cloud and Clark 1985; Govier and Aziz 1972; Dodge and Metzner 1959; Conway et al. 1983;
Buechley and Lord 1973; Pruitt 1965; White 1964; Sitaramaiah and Smith 1969). When high-molecular-­weight polymers are added
to these fluids, dramatic decreases in pumping friction are seen because of turbulence suppression.
Turbulence suppression is thought to be achieved by an ordering of the fluid through the use of the high-molecular-weight polymer chain and its inherent affinity for water molecules. The long-chain polymer deters turbulence by controlling migration of the
individual water molecules, thereby eliminating much of the disorder and tur­bulence. Its effect is dramatic when the very efficient
polyacrylamide materials with friction reduction are used in highly turbulent flow. Low concentrations of guar or CMHPG [10 to
20 lbm/1,000 gal (1198 to 2397 g/m3)] are used commonly in fracturing systems today be­cause of their relatively low cost and accessibility. The most-effi­cient and most-cost-effective friction reducers used for fracturing fluids are low concentrations of polymers and
copolymers of acrylamide. These friction reducers are applicable in water and acid systems. Of course, it is necessary to select the
properly charged acrylamide for water- and acid-based systems.
Cationically charged species are typically used for acid and high-brine systems because of the presence of posi­tively charged
cations. In fresh or low-salinity water, negatively charged species function with high efficiency. The key to the selection of
polymer charge is to test the friction reducer in the fluid to be pumped. It must have functionality and be com­patible with all
additives present. Because of the huge increase in waterfracs, the use of polyacrylamide friction reducers has increased exponentially. This has led to abundant work by service company researchers to develop friction reducers to function in a broad
Fracturing Fluids and Additives
183
range of salinity. The huge push to recycle fracturing fluid has led to drag reducers that can be used to lower friction in fluids
that have salinity in excess of 160,000 ppm. Consideration should be given to the drawbacks of using heavy brines from the
standpoint of potential problems with producing the heavy water back and the standpoint of potential compatibility problems
with formation brines.
Recently, higher-viscosity polyacrylamide friction reducers have been used. The volume has dramatically reduced the cost
of the material and made it competitive with guar and guar derivatives. Although this technology is not new, much researchand-development work is going on because of the possibility of using one product to achieve both turbulence suppression
and viscosity to carry proppant and as a tool to combat tortuosity. This is a challenging problem because viscosity actually
decreases friction reduction.
Friction is often reduced in oil-based systems with a high­-molecular-weight polyisodecylmethacrylate. This friction reducer for
oil-based systems is readily available. Although functional, it will seldom achieve friction reduction higher than 70%. Another
way to reduce friction in hydrocarbon fluids is to use low concen­trations of an aluminum phosphate ester gel [e.g., 2 gal/1,000 gal
(0.002 m3/m3)] and a sodium aluminate or other caustic activator.
Friction reducers offer no advantage unless the fluid to be trans­ported is in turbulence. Thus, a fairly viscous oil to be pumped down
casing at a low rate offers little opportunity for friction reduction. Similarly, an already-viscosified fracturing fluid can seldom have
its friction reduced further by addition of an acrylamide friction reducer. High turbulence must be achieved for the friction reducer to
be advantageous, and neither the low-rate casing treatment nor the viscous fluid can be assisted by friction reducers.
6.9.12 Temperature Stabilizers. Temperature stability of fracturing fluids is a result of the stability of the base chain polymer,
the pH of the fracturing fluid, and/or the presence of oxidizing agents. CMHPG and HPG are more stable than guar, and some of
the acrylamides are more stable than the guar derivatives. None of these products is particularly stable in acid media because of
hydrolytic degradation. Therefore, one means of stabi­lizing a fracturing fluid is to increase the pH into the basic range. Typical pHs
for many fracturing fluids are from 8 to 13. The higher pH yields enhanced stability by eliminating hydrogen ion in the fluid. Initial
pH for high-temperature fracturing fluids could exceed 13 at ambient temperature conditions. Most strong bases and buffers lose
solubility at higher temperatures, and it might be necessary for fluid stability to have excess base addition to allow for optimal pH
at in-situ conditions.
Another basic use for temperature stabilization is to remove free oxygen from the system. A temperature stabilizer commonly used
for this purpose is sodium thiosulfate (Thomas and Elbel 1979). It is used as an oxygen scavenger to remove oxidative degradation
as a means of breaking down the fracturing fluid. Another temperature stabilizer with the same function is methyl alcohol. Methanol
becomes an oxygen scavenger at high temperatures and functions in a solvent-change relationship to give a temperature-stabilizing
effect. Methanol is not as cost-effective an oxygen scavenger as sodium thiosulfate.
6.9.13 Diverting Agents. A partial listing of diverting agents (Table 6.6), shows that a diverting agent is typically a graded material
that is insoluble or slowly soluble in fracturing fluids but eventually soluble in produced water or formation fluids. Also included are
slurries of resins, viscous fluids, and crosslinked fluids. Resins, although highly used previously, are not typically available today.
There has been limited success with viscosity as a diversion mechanism.
Diverting Agents
Chemical
Course rock salt
Mixture of karaya and oil soluble resin*
Graded rock salt
Karaya powder*
Graded parfaormaldehyde
Grada naphthalene
Solution of benzoic in alcohol or hydrocarbon*
Oil external emulsion
Flake benzoic acid (fine and course)
High-concentration linear gel
Graded oil soluble resin (low temperature)
Oyster shells
Graded oil soluble resin (high temperature)
Polymer coated sand
Unibeads (wax beads)
Buoyant particles
Crosslinked polymers
High-quality foams
Slurries of oil soluble resings*
Flake boric acid
Physical
Ball sealers
Selective treating with packers and bridge plugs
Ball and baffle technique
Composite bridge plugs
Pine Island procedure
Packer sleeve completions
*These products only function in matrix applications. Schumberger and Halliburton have had some success with fiber and bridging agents.
Table 6.6—Partial listing of diverting agents.
184 Hydraulic Fracturing: Fundamentals and Advancements
Another product is water- or oil-soluble fibrous materials. These products have been used successfully in openhole completions in
fractured reservoirs.
The major purpose of a diverting agent is to divert flow of the fracturing fluid to an alternative zone being treated by plugging off
either the perforation (if a casedhole completion) or some part of the formation (if an openhole completion). Some of the products on
the list are more applicable to matrix diversion but have been used in fracturing situations.
The most effective diversion is by ball sealers or zone isolation through packers. Particulate diverters, such as flake benzoic acid,
rock salt, or other materials, have apparently been used with success in some areas (Hannah et al. 1978). The concentration and the
type of diverting agent are critical. A major consideration is for the diverting agent to be compatible with the fracturing fluid or for the
diverting agent to be run in a spacer fluid between the stages of the fracturing treatment. The industry has many effective mechanical
techniques that achieve a much higher success ratio than the flake or granular materials.
In the past few years, service companies have introduced a large number of specialty diverting agents to be used in the restimulation
of horizontal laterals with large numbers of perforations. These products appear to have had little success, but the same materials have
been used successfully during proppant stages to increase diversion and complexity of slickwater fracturing treatments. The use of
these products to increase complexity is a new application, but a fairly high degree of success has been reported.
6.10 Waterfracs
6.10.1 The Dominant Fracturing Fluid Today. Low-viscosity treatments have been conducted almost since the inception of
hydraulic fracturing. They are defined as treatments using water and no significant amount of thickening agent where surface viscosities at ambient temperatures are less than 10 cP measured at 511-reciprocal-seconds shear. In fact, in the San Juan Basin, slickwater
treatments were the prevailing type of treatment before 1968 and have continued up to today. Before the introduction of crosslinked
gels in 1968, low-viscosity treatments were a large segment of fracturing treatments. With the development of crosslinked fracturing
fluids and all their attributes, low-viscosity fracturing came to be considered low technology and became a small segment of treatments pumped. Over the past several years, there has been a huge movement toward nonviscosified fluids containing small proppants.
This was led initially by the early efforts of the Union Pacific Resources Company with their paper on the lack of need for proppants
and early treatments in tight-sandstone reservoirs such as the Cotton Valley, Travis Peak, Bossier, and many tight sands in the Rocky
Mountains area. (Mayerhofer et al. 1997; Walker et al. 1998; Britt et al. 2006).
With the beginning of source rock stimulation in the Barnett and other shale plays, the use of waterfracs has virtually exploded. The
success of these types of treatments has shaken fracturing theory to the core. Tremendously successful stimulation has been achieved
using propping agents, which, based on conventional thinking, have virtually no conductivity at downhole conditions. Remarkably,
the use of larger, more-conductive proppants in this 1-cP fluid has not only not improved stimulation results, but has been shown to
be detrimental far beyond the problem of potential screenouts because of poor transport.
Overflushing has become the norm, and pumping alternating sand-laden and neat fluid has improved results instead of
yielding the expected decrease because of a lack of effective conductivity. Conventional requirements for net pressure gain
to achieve good conductivity have been replaced with the need to show no net pressure gain on properly designed treatments.
Net pressure gain is indicative of packing proppant. Some believe that the small proppants used in waterfracs do not function
in a pack but rather act as bridging and diverting agents and/or nonfunction as a mechanism to hold the fracture open akin to
partial monolayer theory (Warpinski 2009). This translates into using low concentrations of proppant and designing in terms
of sweeps, to be sure that no packing occurs.
The use of viscous fluids in the vast majority of shales has been counterproductive. It is believed that the high-viscosity
fluids tend to create a dominant hydraulic fracture that is counterproductive in naturally fractured reservoirs. Where production
comes mainly from natural fractures, it is wise not to parallel the fracture systems, which is the natural course of events when
using viscous fluids. This phenomenon has been observed during microseismic work in which a multitude of seismic events
occurred at great distances from the wellbore while thin fluid was being pumped. When starting to pump viscous fluid, such
as a hybrid treatment, all seismic events cease from the wellbore and a dominant narrow fracture pattern is generated near the
wellbore. Low-viscosity fluid tends to follow the natural fracture plane allowing for much improved stimulation compared to
a dominant fracture paralleling these same fractures. Some authors have hypothesized that the success of waterfracs in stacked
sand/shale sequences such as the Granite Wash, Cotton Valley, Olmos, and others relates to differential width between the
sands and shale and the small proppant bridges holding open infinitely conductive fractures. Another mechanism, perhaps more
acceptable, is that many of the so-called microdarcy formations are dominated by natural fractures in the reservoir and the
matrix permeability is too low to produce hydrocarbons in geologic time. This is borne out by the huge success of waterfracs
in many reservoirs where crosslinked gels have been unsuccessful.
An interesting fact is that more and more “conventional reservoirs” have achieved better results with waterfracs compared to the
conventional proppant-pack treatments using crosslinked gels. Examples of these reservoirs are the Cleveland Formation and the deep
Morrow Formation in the Texas Panhandle, the Olmos Formation in South Texas, the Cotton Valley and Travis Peak formations in
northeast Texas, the Mesaverde Formation in Colorado, and many others. There has been great success with crosslinked-gel systems
in many reservoirs, but the question to consider is what a properly designed waterfrac would do in these same reservoirs. Almost all
of the deep high-temperature reservoirs were being treated with slickwater, or certainly systems with no stable viscosity before 1968,
but the treatments were typically small and used large proppants.
6.10.2 Rationale for Small and Substandard Propping Agents. In the early stages of the “waterfrac boom,” operators were
having screenout problems while using 20/40 or larger proppants. To alleviate the screenouts, operators switched to smaller
40/70 proppant and were able to place the proppants at concentrations exceeding 2 lbm/gal. Surprisingly, not only were they
able to place the proppant, they achieved better stimulation results compared with wells where larger proppant had been placed.
Following the same thinking, operators in the Barnett Shale started using 100-mesh sand as the primary proppant. With the
huge number of treatments and the extraordinary volumes of proppant pumped, there was simply not enough Ottawa-quality
sand available, and operators started pumping much-lower-quality 100-mesh sand. This proppant was available close to the
Fracturing Fluids and Additives
185
Barnett Shale play, and remarkably the wells responded equally as well as they had with the Ottawa 100-mesh sand and the
Ottawa 40/70 sand.
Success has been noted in using sand as proppant in deeper shale such as the Haynesville, Woodford, and Eagle Ford where,
because of the basis of the fracturing gradient, ceramic proppants should be used. The initial thought to explain the phenomena was
the speculation that since the shale in many cases does not have a dominant stress, the closure would be less. Perhaps a more believable explanation for the shale is that since there is virtually no permeability in the matrix of the rock, there is no mechanism for the
pressures to be drawn down to crush the proppant. Needless to say, this use of weak proppant should not necessarily be transferred
to conventional reservoirs where there is measurable permeability in the matrix. In a nonpublished work, one operator has reported
success in waterfracs in a South Texas conventional reservoir using 100-mesh Ottawa sand. The depths are within the range of Ottawa
but belie the need for a conductive proppant pack in the tight reservoir.
6.10.3 Using or Not Using Surfactants in Waterfracs. Several years ago, a frugal operator decided to remove surfactants from his
fracture treatment in the Cotton Valley Sand. This move was contrary to conventional wisdom at the time, and observers believed that the
high-surface-tension fluids would not clean up. The well was closely monitored; surprisingly, it cleaned up quite well and appeared to be
better than offsets. It was hypothesized that perhaps it is not a good idea to pump low-surface-tension fluids into very-low-permeability
reservoirs allowing water to penetrate into tiny pore throats and hairline fractures where the surfactant would inevitably plate out, leaving high-surface-tension fluid in the pore spaces and creating damage. Since that time, many major and independent operators have not
recommended the use of conventional surfactants in waterfracs and have seen no ill effects because of the omission.
Several water-recovery products have been introduced to the industry over the history of fracturing, and intuitively many believed
that better water recovery would achieve better production. In reality, it has been determined that enhanced water recovery has little
or no effect on production (Kabir 2001). Many combinations of conventional surfactants and some relatively expensive fluorocarbon
surfactants have been used in fracturing and have indeed yielded enhanced flowback but with no real effect on productivity. It has
been noted in some cases in extremely tight rock that particular surfactant formulations have in fact damaged the rock to the extent
that an interval would not build up pressure after previous production. There is a correlation between load recovery and productivity,
but the correlation is inverse—i.e., production and the quality of the well are better with minimal load recovery, and very poor wells
recover very large percentages of the load.
In recent years, a significant amount of microemulsion or nanosurfactant products have been used in waterfracs with significant
improvements in productivity. Although not functional in every formation, it does appear that with continuous research and studies
into applicability these products will become a major additive in slickwater and other applications.
6.10.4 Summary. The tremendous success of waterfracs has indeed shaken the foundations of conventional hydraulic-fracturing
theory, especially when compared to much of what was discussed in the predecessor to this monograph, SPE Monograph 12 (Gidley
et al. 1989). It is interesting to observe many continue to use conventional high-viscosity gels and high-strength proppant in unconventional rock and, even with obvious failure to achieve success compared to waterfracs, persist in their thinking and procedures.
Although the mechanisms leading to the success of waterfracs are not fully understood, at the same time, the obvious results should
not be overlooked. What is most encouraging for the future is that a process has been identified that appears to be unlocking previously
nonaccessible hydrocarbon reserves.
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Williams, L. H. Jr. and Underdown, D. R. 1981. New Polymer Offers Ef­fective Permanent Clay Stabilization Treatment. J Pet
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Young, B. M., McLaughlin, H. C., and Borchardt, J. K. 1980. Clay Stabili­zation Agents—Their Effectiveness in High-Temperature
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Yu, M. and Nasr-El-Din, H. A. 2009. Quantitative Analysis of Viscoelastic Surfactants. Presented at the SPE International Symposium
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Zelenev, A. S. 2011. Surface Energy of North American Shales and its Role in Interaction of Shale with Surfactants and Microemulsions.
Presented at the SPE International Symposium on Oilfield Chemistry, The Woodlands, Texas, USA, 11−13 April. SPE-141459-MS.
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Zigrye, J. L., Whitfill, D. L., and Sievert, J. A. 1985. Fluid-Loss Control Differences of Crosslinked and Linear Fracturing Fluids.
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Barron, A.N., Hendrickson, A.R., and Wieland, D.R.: “The Effect of Flow on Acid Reactivity in a Carbonate Fracture,”
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192 Hydraulic Fracturing: Fundamentals and Advancements
42. Roberts, L.D. and Guin, J.A.: “The Effect of Surface Kinetics in Fracture Acidizing,” SPEJ (Aug. 1974) 385-95; Trans.,
AIME, 257.
43. Coulter, A.W. et al.: “Alternate Stages of Pad Fluid and Acid Provide Improved Leak-Off Control for Fracture Acidizing,” paper
SPE 6124 presented at the 1976 SPE Annual Technical Conference and Exhibition, New Orleans, Oct. 3-6.
44. Knox, J.A., Lasater, R.M., and Dill, W.R.: “A New Concept in Acidizing Utilizing Chemical Retardation,” paper SPE 975
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45. Carpenter, N.F. and Ernst, E.A.: “Acidizing: With Swellable Polymers,” JPT (Sept. 1962) 1041-47; Trans., AIME, 225.
46. Crowe, C.W., Martin, R.C., and Michaelis, A.M.: “Evaluation of Acid-Gelling Agents for Use in Well Stimulation,” SPEJ (Aug.
1981) 415-24.
47. Norman, L.R., Conway, M.W., and Wilson, J.M.: “Temperature-Stable Acid-Gelling Polymers: Laboratory Evaluation and Field
Results,” JPT (Nov. 1984) 2011-18.
48. Norman, L.R.: “Properties and Early Field Results of a Liquid Gelling Agent for Acid,” paper SPE 7834 presented at the 1978
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49. Pabley, A.S. and Holcomb, D.L.: “A New Method of Acidizing or Acid Fracturing: Crosslinked Acid Gels,” Proc, Southwestern
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52. Williams, B.B., Gidley, J.L., and Schechter, R.S.: Acidizing Fundamentals, Monograph Series, SPE, Richardson, TX (1979) 6.
53. Holtmyer, M.D. and Githens, C.J.: “Field Performance of a New High Viscosity Water Base Fracturing Fluid,” paper
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54. Free, D.L., Frederick, A.F., and Thompson, J.E.: “Fracturing With a High-Viscosity, Crosslinked Gel—Continuous Fracturing
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55. Holtmeyer, M.D., Githens, C.J., and Tinsley, J.M.: “Fracturing Well Formations,” British Patent No. 1,337,651 (1973).
56. Holtmeyer, M.D., Githens, C.J., and Tinsley, J.M.: “Compositions for Fracturing Well Formations,” U.S. Patent No. 4,021,355
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59. Hannah, R.R. and Matson, W.G.: “A Family of Viscous Gelled Water Systems Featuring Moderate Polymer Loadings and Low
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60. Hannah, R.R. and Baker, J.R.: “A New Nondamaging, Aqueous Cross-Linked Gel with Improved Fracturing Properties and
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61. Lescarboura, J.A., Sifferman, T.R., and Wahl, H.A.: “Evaluation of Fracturing Fluid Stability by Using a Heated, Pressurized
Flow Loop,” SPEJ (June 1984) 249-55.
62. Gardner, D.C. and Eikerts, J.V.: “The Effects of Shear and Proppant on the Viscosity of Crosslinked Fracturing Fluids,” paper
SPE 11066 presented at the 1982 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 26-29.
63. Craigie, L.J.: “A New Method for Determining the Rheology of Cross-linked Fracturing Fluid Using Shear History Simulation,”
paper SPE 11635 presented at the 1983 SPE/DOE Low-Permeability Gas Reservoirs Symposium, Denver, March 13-16.
64. Harms, S.D., Goss, M.L., and Payne, K.L.: “New Generation Fracturing Fluid for Ultrahigh-Temperature Application,” paper
SPE 12484 presented at the 1984 SPE Formation Damage Control Symposium, Bakersfield, Feb. 13-14.
65. Baumgartner, S.A. et al.: “High Efficiency Fracturing Fluids for High Temperature Reservoirs,” paper SPE 11566 presented at
the 1983 SPE Production Operations Symposium, Oklahoma City, Feb. 27-March 1.
66. Lagrone, C.C., Baumgartner, S.A., and Woodroof, R.A. Jr.: “Chemical Evolution of a High-Temperature Fracturing Fluid,”
SPEJ (Oct. 1985) 623-28.
67. Payne, K.L. and Harms, S.D.: “Chemical Processes for Controlling Crosslinking Reaction Rates,” paper presented at the 1984
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68. Rummo, G.J.: “Crosslinking Delay Achieved with Gel Additive,” Oil AGasJ. (Sept. 13, 1982) 84.
69. Harris, P.C.: “Influence of Temperature and Shear History on Fracturing Fluid Efficiency,” paper SPE 14258 presented at the
1985 SPE Annual Technical Conference and Exhibition, Sept. 22-26.
70. Kucera, C.H., Smith C.F., and Braunlich, F.H.: “New Oil Gelling Systems Prevent Damage in Water-Sensitive Sands,” paper
SPE 3503 presented at the 1974 SPE Annual Meeting, New Orleans, Oct. 3-6.
71. Burnham, J.W. et al.: “Developments in Hydrocarbon Fluids for High-Temperature Fracturing,” JPT (Feb. 1980) 217-20.
72. Hendrickson, A.R., Nesbitt, E.E., and Oaks, B.D.: “Soap-Oil Systems for Formation Fracturing,” Pet. Eng. (May 1957) B-58.
73. Malone, W.T. and Anderson, T.O.: “Gelled Crude for Formation Fracturing,” Oil & Gas J. (Feb. 1956) 117.
74. Kalish, P.J. et al.: “The Effect of Bacteria on Sandstone Permeability,” JPT (July 1964) 805-14; Trans., AIME, 231.
75. Muecke, T.W.: “Formation Fines and Factors Controlling Their Movement in Porous Media,” JPT (Feb. 1979) 144-50.
76. Veley, CD.: “How Hydrolyzable Metal Ions React With Clays to Control Formation Water Sensitivity,” JPT (Sept. 1969)
1111-18.
77. Dayan, A., Stracener, S.M. and Clark, P.E. “Proppant Transport in Slick-Water Fracturing of Shale-Gas Formations,” paper
125068-MS, presented at the SPE Annual Technical Conference and Exhibition, 4-7 October 2009, New Orleans, Louisiana
78. Goel, N. Shah, S.N. and Asadi, M., “New Empirical Correlation to Predict Apparent Viscosity of Borate-Crosslinked Guar Gel
in Fractures,” paper 63011-PA, SPE Production & Facilities, Volume 15, Number 2 (May 2000) 90-95
79. Harris, P.C., Heath, S.J., “Rheological Properties of Low-Gel-Loading Borate Fracture Gels,” paper 52399-PA, SPE Production
& Facilities, Volume 13, Number 4, (November 1998) 230-235.
80. Harris, P.C., Klebenow, D.E., Kundert, P.D., “Constant Internal Phase Design Improves Stimulation Results,” paper 17532-PA,
SPE Production Engineering, Volume 6, Number 1 (February 1991) 15-19.
Fracturing Fluids and Additives
193
81. Alharbi, A., Liang, F, Al-Muntasheri, G. A., Li, L., “Nanomaterials-Enhanced High-Pressure Tolerance of Borate-Crosslinked
Guar Gels,” paper 188817-MS, presented at the SPE Abu Dhabi International Petroleum Exhibition & Conference, November,
2017.
82. Quintero, H. J., Mattucci, M., O’Neil, B., Folkes, G., Zhang, K., Wang, C. Z., Lu, W., “Enhanced Proppant Suspension in a
Fracturing Fluid Through Capillary Bridges,” paper 190055-MS, presented at the SPE Western Regional Meeting, April, 2018.
83. Vernigora, D., Olennikova, O., Parkhonyuk, S., Fedorov, A.,Belyakova, L., Velikanov, I., Konchenko, A., “Unveil the Unknown:
Combining the Laboratory Study of Fracturing Fluids at High Pressure with a State-of-the-Art Hydraulic Fracturing Simulator,”
paper 189518-MS, presented at the SPE International Conference and Exhibition on Formation Damage Control, February,
2018.
84. Aliu, A. O., “Rheology, Regain Fracture Conductivity and Viscous Fingering Phenomenon for Proppant Suspension in CMC
Hydraulic Fracturing Fluid, paper 189278-STU, presented at the SPE Annual Technical Conference and Exhibition, October,
2017.
85. Al-Muntasheri, G. A., Liang, F., Hull, K. L., “Nanoparticle-Enhanced Hydraulic-Fracturing fluids: A Review,” paper 185161PA, SPE Production & Operations Journal, May 2017.
86. Sanchez Reyes, J., Hutchins, R. D., Parris, M. D., “Experimental Determination of the Effect of Pressure on Fluid Loss for
Linear and Crosslinked Fracturing Fluids,” paper 168161-PA, SPE Production & Operations Journal, August, 2015.
87. Gupta, D. V. S., Jackson, T. L., Hlavinka, G. J., Evans, J. B., Le, H. V., Batrashkin, A., Shaefer, M. T., “Development and Field
Application of a Low pH, Efficient Fracturing Fluid for Tight Gas Fields in the Greater Green River Basin, Wyoming,” paper
116191-PA SPE Production & Operations Journal, November, 2009.
88. Wang, X., Qi, Q., “Development of a Nonresidue Polymer-Based Fracturing Fluid,” paper 80227-MS, presented at the
International Symposium on Oilfield Chemistry, February, 2003.
89. Holtsclaw, J., Rocio Montenegro Galindo, G., Chopade, P., “Next-Generation Boron-Crosslinked Fracturing Fluids: Breaking
the Lower Limits on Polymer Loadings,” paper 174988-PA,, SPE Production & Operations Journal, February, 2017.
90. Fischer, C. C., Navarrete, R. C., Constien, V. G., Coffey, M. C., Asadi, M., “Novel Application of Synergistic Guar/
Non-Acetu;ated Xanthan Gum Mixtures in Hydraulic Fracturing,” paper 65037-MS, presented at the SPE International
Symposium on Oilfield Chemistry, February, 2001.
91. Huang, F., Gundewar, R.S., Loughridge, B.W., Steed, D.L., “Feasibility of Using Produced Water for Crosslinked Gel-Based
Hydraulic Fracturing,” paper 94320-MS, presented at the SPE Production Operations Symposium, April, 2005.
92. Prabhu, R., Hutchins, R., Makarychev-Mikhailov, S., “Evaluating Damage to the Proppant Pack from Fracturing Fluids Prepared
with Saline Water,” paper 179029-MS, presented at the SPE International Conference and Exhibition on Framation Damage
Control, February, 2016.
93. Lopez, E., Nelson, T., Bishop, D.M., “Achieving a Stable Native Guar Boron Crosslink in 100% Produced Water,” paper 173735-MS,
presented at the SPE International Symposium on Oilfield Chemistry, April, 2015.
94. Cikes, M., Cubric, S., Moylashov, M.R., “Formation Damage Prevention by Using an Oil-Based Fracturing Fluid in Partially
Depleted Oil Reservoirs of Western Siberia,” paper 39430-MS, presented at the SPE Formation Damage Control Conference,
February, 1998.
95. Brannon, H.D., Wood, W.D., Wheeler, R.S., “The Quest for Improved Proppant Placement: Investigation of the Effects of
Proppant Slurry Component Properties on Transport,” paper 95675-MS, presented at the SPE Annual Technical Conference and
Exhibition, October, 2005.
96. Bannon, H.D., Wood, W.D., Wheeler, R.S., “Large Scale Laboratory Investigation of the Effects of Proppant and Fracturing
Fluid Properties on Transport,” paper 98005-MS, presented at the SPE International Symposium and Exhibition on Formation
Damage Control, February, 2006.
97. Li, W., Oliveira, H.A., Maxey, J.E., “Invert Emulsion Acid for Simultaneous Acid and Proppant Fracturing,” paper 24332-MS,
presented at the Offshore Technology Conference, OTC Brasil, October, 2013.
98. Schols, R.S., Visser, W., “Proppant Bank Buildup in a Vertical Fracture Without Fluid Loss,” paper 4834-MS, presented at the
SPE European Spring Meeting, May, 1974.
99. Gomaa, A.M., Hudson, H., Nelson, S. Brannon, H., “Improving Fracture Conductivity by Developing and Optimizing Channels
within the Fracture Geometry: CFD Study,” paper 178982-MS, presented at the SPE International Conference and Exhibition
on Formation Damage Control, February, 2016.
100. Sierra, L., Sahai, R. Mayerhofer, M.J., “Quantification of Proppant Distribution Effect on Well Productivity and Recovery
Factor of Hydraulically Fractured Unconventional Reservoirs,” paper 171594-MS, presented at the SPE/CSUR Unconventional
Resources Conference - Canada, September, 2014.
101. Jackson, K., Orekha, O., “Low Density Proppant in Slickwater Applications Improves Reservoir Contact and Fracture
Complexity – A Permian Basin Case History,” paper 187498-MS, presented at the 2017 SPE Liquids-Rich Basins Conference –
North America, September, 2017.
102. Al-Muntasheri, G.A., “A Critical Review of Hydraulic Fracturing Fluids over the Last Decade,” paper 169552-MS, presented at
the SPE Western North American and Rocky Mountain Joint Meeting, April, 2004.
103. Kim, J., Zhang, H., Sun, H., Li, B., Carman, P., “Choosing Surfactants for the Eagle Ford Shale Formation: Guidelines for
Maximizing Flowback and Initial Oil Recovery,” paper 180227-MS, presented at the SPE Low Perm Symposium, May, 2016.
104. Aften, C.W., “Study of Friction Reducers For Recycled Stimulation Fluids In Environmentally Sensitive Regions,” paper
138984-MS, presented at the SPE Eastern Regional Meeting, October, 2010.
105. Khan, R., Al-nakhli, A.R., “An Overview of Emerging Technologies and Innovations for Tight Gas Reservoir Development,”
paper 155442-MS, presented at the SPE International Production and Operations Conference & Exhibition, May, 2012.
106. Baudendistel, T.A., Farrell, J.W., Kidder, M.F., “To Treat or Not to Treat? Optimized Water Decisions Throughout the ProducedWater Management Cycle,” paper 178698-MS, presented at the Unconventional Resources Technology Conference, July, 2015.
107. King, S.R., Worley, H.W., “Have We Forgotten Oil is Not Inert? Guidelines for Enhancing Stimulation Success,” paper 59541MS, presented at the SPE Permian Basin Oil and Gas Recovery Conference, March, 2000.
194 Hydraulic Fracturing: Fundamentals and Advancements
108. Walters, H.G., Morgan, R.G., Harris, P.C., “Kinetic Rheology of Hydraulic Fracturing Fluid,” paper 71660-MS, presented at the
SPE Annual Technical Conference and Exhibition, September, 2001.
109. Al-Driweesh, S.M., Dashash, A.A., Malik, A.R., Leal, J., Soriano, E., Lopez, A., “Overcoming Hydraulic Fracturing Challenges
in High Temperature and Tight Gas Reservoirs of Saudi Arabia with an Enhanced Fracturing Fluid System,” paper IPTC-17686MS, presented at the International Petroleum Technology Conference, January, 2014.
110. Christiawan, A.B., Buelvas, M.L., Shukla, S., “Innovative multi Technologies Collaboration for Ultra-HP/HT Offshore
Fracturing Stimulation,” paper 26663-MS, presented at the Offshore Technology Conference Asia, March, 2016.
111. Esmaeilirad, N., Terry, C., Kennedy, H., Prior, A., Carlson, K., “Recycling Fracturing Flowback Water for Use in Hydraulic
Fracturing: Influence of Organic Matter on Stability of Carboxyl-Methyl-Cellulose-Based Fracturing Fluid,” paper 179723-PA,
SPE Journal, August , 2016.
112. Cadix, A., Wilson, J., Carouhy, T., Harrisson, S., Guichon, H., “A New Class of Associative Polymer for Hydraulic Fracturing
Applications,” paper 174210-MS, presented at the SPE European Formation Damage Conference and Exhibition, June, 2015.
113. Morvan, M., Moreau, P., Degre, G., Leng, J., Masselon, C., Bouillot, J., Zaitoun, A., “New Viscoelastic Fluid for Chemical
EOR,” paper 121675-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2009.
114. Gomaa, A.M., Gupta, D.V.S., Carman, P., “Viscoelastic Behavior and Proppant Transport Properties of a New High-Temperature
Viscoelastic Surfactant-Based Fracturing Fluid,” paper 173745-MS, presented at the SPE International Symposium on Oilfield
Chemistry.
115. Van Zanten, R., “Stabilizing Viscoelastic Surfactants in High Density Brines,” paper 141447-MS, presented at the SPE
International Symposium on Oilfield Chemistry, April, 2011.
116. Whitlock, L., Sanders, A., Knox, P., “The Evaluation of Polycationic, Carbohydrate-Based Surfactants as Viscoelastic (VES)
Fracturing Fluids,” paper 173791-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2015.
117. Crews, J.B., “Internal Phase Breaker Technology For Viscoelastic Surfactant Gelled Fluids,” paper 93449-MS, presented at the
SPE International Symposium on Oilfield Chemistry, February, 2005.
118. Hull, K.L., Sayed, M., Al-Muntasheri, G.A., “Recent Advances in Viscoelastic Surfactants for Improved Production from
Hydrocarbon Reservoirs,” paper 173776-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2015.
119. Reddy, B.R., Eoff, L.S., Crespo, F., Lewis, C.A., “Recent Advances in Organically Crosslinked Conformance Polymer Systems,”
paper 164115-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2013.
120. Swiecinski, F., Reed, P., Andrews, W., “The Thermal Stability of Polyacrylamides in EOR Applications,” paper 179558-MS,
presented at the SPE Improved Oil Recovery Conference, April, 2016.
121. Ferreira, V.H.S., Moreno, R.B.Z.L., “Polyacrylamide Mechanical Degradation and Stability in the Presence of Iron,” paper
27953-MS, Offshore Technology Conference, OTC Brasil, October, 2017.
122. Mohammed, M.N., Mahmoud, M., Elkatatny, S., “Development of a Smart Fracturing Fluid for Tight and Unconventional
Reservoirs,” paper 187125-MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2017.
123. Tomson, R.C., Guraieb, P., Graham, S., Yan, C., Ghorbani, N., Hanna, T., Cooper, C., “Development of a Universal Ranking
for Friction Reducer Performance,” paper 184815-MS, presented at the SPE Hydraulic Fracturing Technology Conference and
Exhibition, January, 2017.
124. Ibrahim, A.F., Nasr-El-Din, H.A., Rabie, A., Lin, G., Zhou, J. Qu, Q., “A Non-Damaging Friction Reducing Agent for SlickWater Fracturing,” paper 180436-MS, presented at the SPE Western Regional Meeting, May, 2016.
125. Ibrahim, A.F., Nasr-El-Din, H.A., Rabie, A., Lin, G., Zhou, J. Qu, Q., “A New Friction-Reducing Agent for Slickwater Fracturing
Treatments,” paper 180245-MS, presented at the SPE Low Perm Symposium, May, 2016.
126. Rodvelt, G., Yuyi, S., VanGilder, C., “Use of a Salt-Tolerant Friction Reducer Improves Production in Utica Completions,” paper
177296-MS, presented at the SPE Eastern Regional Meeting, October, 2015.
127. Chung, H.C., Hu, T., Ye, X., Maxey, J.E., “A Friction Reducer: Self-Cleaning to Enhance Conductivity for Hydraulic Fracturing,”
paper 170602-MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2014.
128. Zelenev, A.S., Gilzow, G.A., Kaufman, P.B., “Fast Inverting, Brine and Additive Tolerant Friction Reducer for Well Stimulation,”
paper 121719-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2009.
129. Wilson, A., “New Salt-Tolerant Friction-Reducer System Enables 100% Reuse of Produced Water,” 1217-0076-JPT, Journal of
Petroleum Technology, December, 2017.
130. Xu, L., Lord, P., Riley, H., Koons, J., Wauters, T., Weiman, S., “Case Study: A New Salt-Tolerant Friction Reducer System
enables 100% Re-use of Produced Water in the Marcellus Shale,” paper 184052-MS, presented at the SOE Eastern Regional
Meeting, September, 2016.
131. Inyang, U., Cortez, J., Singh, D., Orth, J., Fontenelle, L., Kishore, T., “Investigating the Dominant Factors Influencing Well
Screenouts for Crosslinked Fracturing Fluids in Shale Plays,”, paper IPTC-18252-MS, presented at the International Petroleum
Technology Conference, December, 2015.
132. Putzig, D.E., St. Clair, J.D., “A New Delay Additive for Hydraulic Fracturing Fluids,” paper 105066-MS, presented at the SPE
Hydraulic Fracturing Technology Conference, January, 2007.
133. Zhang, B., Huston, A., Whipple, L., Urbina, H., Barrett, K., Wall, M., Hutchins, R.D., Mirakyan, A.L., “A Superior Highperformance Enzyme for Breaking Borate Cross-linked Fracturing Fluids under Extreme Well Conditions,” paper 160033-MS,
presented at the SPE Annual Technical Conference and Exhibition, October, 2012.
134. Reddy, B.R., Eoff, L., Dalrymple, E.D., Black, K., Brown, D., Rietjens, M., “A Natural Polymer-Based Crosslinker System for
Conformance Gel Systems,” paper 75163-MS, presented at the SPE/DOE Improved Oil Recovery Symposium, April, 2002.
135. Saini, D., Mezei, T., “Potential Use of Oil-Field Produced Water as Base Fluid for Hydraulic Fracturing Operations: Effect
of Water Chemistry on Crosslinking and Breaking Behaviors of Guar Gum-Based Fracturing Fluid Formulations,” paper
185693-MS, presented at the 2017 SPE Western Regional Meeting, April, 2017.
136. Khamees, T., Flori, R.E., Wei, M., “Simulation Study of In-Depth Gel Treatment in Heterogeneous Reservoirs with Sensitivity
Analyses,” paper 185716-MS, presented at the 2017 SPE Western Regional Meeting, April, 2017.
137. Wheeler, R., Williams, V., Mayor, J., Khan, S., Everson, N., Steinhardt, A., “Gelled Isolation Fluid Makes Refracturing Well
Feasible,” paper 185622-MS, presented at the 2017 SPE Western Refional Meeting, April, 2017.
Fracturing Fluids and Additives
195
138. Aldawsari, M.A., Al-Sagr, A.M., Al-Driweesh, S.M., Al-Shammari, N.S.,Altammar, A.H., Atayev, N., Melo, A., “HT Fracturing
Fluid in Stimulating Saudi HTHP Gas Wells: Lab Results and Field Cases,” paper 185340-MS, presented at the SPE Oil and Gas
India Conference and Exhibition, April, 2017.
139. Harry, D.N., Mallory, M., Tucker, S., “Method for Estimating and Analyzing for TOC of Hydraulic Fracturing Fluids,” paper
184531-MS, presented at the SPE International Conference on Oilfield Chemistry, April, 2017.
140. Liang, F., Al-Muntasheri, G., Ow, H., Cox, J., “Reduced-Polymer-Loading, High-Temperature Fracturing Fluids by Use of
Nanocrosslinkers,” 177469-PA, SPE Journal, April, 2017.
141. Almubarak, T., Ng, J.H., Nasr-El-Din, H., “Chelating Agents in Productivity Enhancement: A Review,” paper 185097-MS,
presented at the SPE Oklahoma City Oil and Gas Symposium, March, 2017.
142. Liang, F., Li, L., Al-Muntasheri, G.A., “A Non-Damaging Fracturing Fluid system for High-Temperature Unconventional
Formations,” paper 183673-MS, presented at the SPE Middle East Oil & Gas Show and Conference, March, 2017.
143. Song, L., Yang, Z., “Synthetic Polymer Fracturing Fluid for Ultrahigh Temperature Applications,” paper IPTC-18597-MS,
presented at the International Petroleum Technology Conference, November, 2016.
144. Al-Hylail, I.A., Karadkar, P., Al-Janabi, Y.H., Al-Khabaz, H., Khalifa, M., “The Future of Fracture Acidizing: A Low pH,
Robust, and Residue-Free Crosslinked Fracturing Fluid,” paper 182891-MS, presented at the Abu Dhabi International Petroleum
Exhibition & Conference, November 2016.
145. Prakash, C., Raykov, T., Koalsa, B., Belakshe, R., Janiczek, P., “Hydraulic Fracturing Application of New Seawater-Based Clean
Fluid,” paper 183024-MS, presented at the Abu Dhabi International Petroleum Exhibition & Conference, November, 2016.
146. Jiang, Q., Jiang, G, Wang, C., Zhu, Q., Yang, L., Wang, L., Zhang, X., Liu, C., “A New High-Temperature Shear-Tolerant
Supramolecular Viscoelastic Fracturing Fluid,” paper 180595-MS, presented at the IADC/SPE Asia Pacific Drilling Technology
Conference, August, 2016.
147. Cramer, D.D., Dawson, J., Ouabdesselam, M., “An Improved Gelled Oil System for High-Temperature Fracturing Applications,”
paper 21859-MS, presented at the Low Permeability Reservoirs Symposium, April, 1991.
148. Maberry, L.J., McDonnell, S.B., Hinkel, J.J., “New Complexation Chemistry Provides Improved Continuous-Mix Gelled Oil,”
paper 37227-MS, presented at the International Symposium on Oilfield Chemistry, February, 1997.
149. McCabe, M.A., Terracina, J.M., Kunzi, R.A., “Continuously Gelled Diesel Systems For Fracturing Applications,” paper 21586MS, presented at the CIM/SPE International Technical Meeting, June, 1990.
150. Li, C., Carman, P.S., Davis, B.J., “Modern Fracturing Revitalizes Dormant Technologies: A Case History,” paper 189482-MS,
presented at the SPE International Conference and Exhibition on Formation Damage Control, February, 2018.
151. Alzate, G.A., Franco, C.A., Restrepo, A., Del Pino Castrillon, J.J., Escobar Murillo, A.A., “Evaluation of Alcohol-Based
Treatments for Condensate Banking Removal,” paper 98359-MS, presented at the SPE International Symposium and Exhibition
on Formation Damage Control, February, 2006.
152. Pandya, N., Wadekar, S., “A Novel Emulsified Acid System for Stimulation of Very High-Temperature Carbonate Reservoirs,”
IPTC-16452-MS, presented at the International Petroleum Technology Conference, March, 2013.
153. Rahim, Z., Al-Anazi, H., Al-Kanaan, A., “Selecting Optimal Fracture Fluids, Breaker System, and Proppant Type for Successful
Hydraulic Fracturing and Enhanced Gas Production – Case Studies,” paper 163976-MS, presented at the SPE Unconventional
Gas Conference and Exhibition, January, 2013.
154. Quintero, L., Jones, T.A., Pietrangeli, G.A., “Proper Design Criteria of Microemulsion Treatment Fluids for Enhancing Well
Production,” paper 154451-MS, presented at the SPE Europec/EAGE Annual Conference, June, 2012.
155. Rabie, A.I., Gomaa, A.M., Nasr-El-Din, H.A., “HCl/Formic In-Situ-Gelled Acids as Diverting Agents for Carbonate Acidizing,”
140138-PA, SPE Production & Operations Journal, May, 2012.
156. Sayed, M.A., Assem, A.I., Nasr-El-Din, H.A., “Effect of Oil Saturation on the Flow of Emulsified Acids in Carbonate rocks,”
152844-PA, SPE Production & Operations Journal, February, 2014.
157. Sayed, M.A., Nasr-El-Din, H.A., De Wolf, C.A., “Emulsified Chelating Agent: Evaluation of an Innovative Technique for High
Temperature Stimulation Treatments,” paper 165120-MS, presented at the SPE European Formation Damage Conference &
Exhibition, June, 2013.
158. Gomaa, A.M., Nasr-El-Din, H.A., “New Insights Into the Viscosity of Polymer-Based In-Situ-Gelled Acids,” 121728-PA, SPE
Production & Operations Journal, August, 2010.
159. Mahmoudkhani, A., O’Neil, B., Wylde,, J.J., Kakadjian, S., Bauer, M., “Microemulsions as Flowback Aids for Enhanced Oil
and Gas Recovery after Fracturing, Myth or Reality: A Turnkey Study to Determine the Features and Benefits,” paper 173729MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2015.
160. Sayed, M.A.I., Nasr-El-Din, H.A., “Reaction Rate of Emulsified Acids and Dolomite,” paper 151815-MS, presented at the SPE
International Symposium and Exhibition on Formation Damage Control, February, 2012.
161. Al-Mutairi, S.H., Nasr-El-Din, H.A., Hill, A.D., “Droplet Size Analysis of Emulsified Acid,” paper 126155-MS, presented at the
SPE Saudi Arabia Section Technical Symposium, May, 2009.
162. Maheshwari P., Maxey, J.E., Balakotaiah, V., “Simulation and Analysis of Carbonate Acidization with Gelled and Emulsified
Acids,” paper 171731-MS, presented at the Abu Dhabi International Petroleum Exhibition and Conference, November,
2014.
163. AlDuailej, Y.K., AlOtaibi, F.M., AlKhaldi, M.H., “ CO2 Emulsified Fracturing Fluid for Unconventional Applications,” paper
177405-MS, presented at the Abu Dhabi International Petroleum Exhibition and Conference, November, 2015.
164. Edrisi, A.R., Kam, S.I., “A New Foam Rheology Model for Shale-Gas Foam Fracturing Applications,” paper 162709-MS,
presented at the SPE Canadian Unconventional Resources Conference, October, 2012.
165. Li, H, Lau, H.C., Huang, S., “Coalbed Methane Development in China: Engineering Challenges and Opportunities,” paper
186289-MS, presented at the SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition, October, 2017.
166. Letichevskiy, A., Nikitin, A., Parfenov, A., Makarenko, V., Lavrov, I., Rukan, G., Ovsyannikov, D., Nuriakhmetov, R.,
Gromovenko, A., “Foam Acid Treatment – The Key to Stimulation of Carbonate Reservoirs in the Depleted Oil Fields of the
Samara Region,” paper 187844-MS, presented at the SPE Russian Petroleum Technology Conference, October, 2017.
167. Singh, R., Mohanty, K.K., “Nanoparticle-Stabilized Foams for High-Temperature, High-Salinity Oil Reservoirs,” paper 187165MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2017.
196 Hydraulic Fracturing: Fundamentals and Advancements
168. Beck, G., Nolen, C., Hoopes, K., Krouse, C., Poerner, M., Phatak, A., Verma, S., “Laboratory Evaluation of a Natural Gas-Based
Foamed Fracturing Fluid,” paper 187199-MS, presented at the SPE Annual Technical Conference and Exhibition, October,
2017.
169. Nath, F., Xiao, C., “Characterizing Foam-Based Frac Fluid Using Carreau Rheological Model to Investigate the Fracture
Propagation and Proppant Transport in Eagle Ford Shale Formation,” paper 187527-MS, presented at the SPE Eastern Regional
Meeting, October, 2017.
170. Ibrahim, A.F., Emrani, A., Nasraldin, H., “Stabilized CO2 Foam for EOR Applications,” paper 186215-MS, presented at the
Carbon Management Technology Conference, July, 2017.
171. Emrani, A.S., Ibrahim, A.F., Nasr-El-Din, H.A., “Mobility Control using Nanoparticle-Stabilized CO2 Foam as a Hydraulic
Fracturing Fluid,” paper 185863-MS, presented at the SPE Europec featured at 79th EAGE Conference and Exhibition, June,
2017.
172. King, B., Wang, S., Chen, S., “Minimize Formation Damage in Water-Sensitive Montney Formation With Energized Fracturing
Fluid,” 179019-PA, SPE Reservoir Evaluation & Engineering Journal, May, 2017.
173. Ribeiro, L.H., Sharma, M.M., “Multiphase Fluid-Loss Properties and Return Permeability of Energized Fracturing Fluids,”
139622-PA, SPE Production & Operations Journal, August, 2012.
174. McAndrew, J.J., Fan, R., Sharma, M., Ribeiro, L., “Extending the Application of Foam Hydraulic Fracturing Fluids,” paper
urtec-2014-1926561, presented at the Unconventional Resources Technology Conference, August, 2014.
175. Williams-Kovacs, J.D., Clarkson, C.R., “Modeling Two-Phase Flowback From Multi-Fractured Horizontal Tight Gas Wells
Stimulated with Nitrogen Energized Frac Fluid,” paper 167231-MS, presented at the SPE Unconventional Resources Conference
Canada, November, 2013.
176. Corrin, E., Harless, M., Rodriguez, C., Degner, D.L., Archibeque, R., “Evaluation of a More Environmentally Sensitive Approach
to Microbiological Control Programs for Hydraulic Fracturing Operations in the Marcellus Shale Using a Nitrate-Reducing
Bacteria and Nitrate-Based Treatment System,” paper 170937-MS, presented at the SPE Annual Technical Conference and
Exhibition, October, 2014.
177. Blauch, M.E., “Developing Effective and Environmentally Suitable Fracturing Fluids Using Hydraulic Fracturing Flowback
Waters,” paper 131784-MS, presented at the SPE Unconventional Gas Conference, February, 2010.
178. Carpenter, J.F., Nalepa, C.J., “Bromine-Based Biocides for Effective Microbiological Control in the Oil Field,” paper 92702MS, presented at the SPE International Symposium on Oilfield Chemistry, February, 2005.
179. Dao, H., “A Hygienic, Safe and Powerful Solution to Control Problematic Microorganisms,” NACE International, NACE-20144144, presented at the CORROSION 2014 Conference, March, 2014.
180. Wentworth, C.C., Srivastava, A., Kramer, J.F., “Comparative Hydrothermal Stability of Biocides Used in the Oil and Gas
Industry,” NACE International, NACE-2016-7671, CORROSION 2016 Conference, March, 2016.
181. Summer, E.J., Duggleby, S., Janes, C., Liu, M., “Microbial Populations in the O&G: Application of this Knowledge,” NACE
International, NACE-2014-4376, CORROSION 2014 Conference, March, 2014.
182. Yin, B., Enzien, M., Love, D., “Biocide Formulations With Enhanced Performance On Sessile And Planktonic Bacteria control,”
NACE International, NACE-2012-1398, CORROSION 2012 Conference, March, 2012.
183. Houston, N.A., Blauch, M.E., Weaver, D.R., Miller, D., O’Hara, D., “Fracture-Stimulation in the Marcellus Shale-Lessons
Learned in Fluid Selection and Execution,” paper 125987-MS, presented at the SPE Eastern Regional Meeting, September, 2009.
184. Norman, L., Vitthal, S., Terracina, J., “New Breaker Technology for Fracturing High-Permeability Formations,” paper 30097MS, presented at the SPE European Formation Damage Conference, May, 1995.
185. Harris, P.C., Sabhapondit, A., “Chemistry Applied to Fracture Stimulation of Petroleum Wells,” paper 120029-MS, presented at
the SPE Middle East Oil and Gas Show and Conference, March, 2009.
186. Holditch, S.A., Tschirhart, N., “Optimal Stimulation Treatments in Tight Gas Sands,” paper 96104-MS, presented at the SPE
Annual Technical Conference and Exhibition, October, 2005.
187. El Shaari, N.A., Minner, W.A., “Northern California Gas Sands: Hydraulic Fracture Stimulation Opportunities and Challenges,”
paper 114184-MS, presented at the SPE Western Regional and Pacific Section AAPG Joint Meeting, March, 2008.
188. Vezza, M., Martin, M., Thompson, J.E., DeVine, C., “Morrow Production Enhanced by New, Foamed, Oil-Based Gel Fracturing
Fluid Technology,” paper 67209-MS, presented at the SPE Production and Operations Symposium, March, 2001.
189. Lim, K.S., Ravitz, R., Patel, A.D., Martens, H., Luyster, M.R., Kuck, M.D., “Specially Formulated Delayed-Breaker Systems
for Water-Sensitive Formations,” paper 144136-MS, presented at the SPE European Formation Damage Conference, June, 2011.
190. Elgassier, M.M., Stolyarov, S.M., “Reasons for Oil-Based Hydraulic Fracturing in Western Siberia,” paper 112092-MS,
presented at the SPE International Symposium and Exhibition on Formation Damage Control, February, 2008.
191. DeVine, C.S., Wood, W.D., Shekarchian, M., Hunnicutt, B.R., “New Environmentally Friendly Oil-Based Stimulation Fluids,”
paper 84576-MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2003.
192. Nimerick, K.H., Temple, H.L., Card, R.J., “New pH-Buffered Low-Polymer Borate-Crosslinked Fluids,” 35638-PA, SPE Journal,
June, 1997.
193. Legemah, M., Sun, H., Carman, P., Mayor, J., “A Novel Approach to Crosslink Delay of Low-pH Fracturing Fluid,” paper
173752-MS, presented at the SPE International Symposium on Oilfield Chemistry, April, 2015.
194. Elsarawy, A.M., Nasr-El-Din, H.A., Cawiezel, K.E., “Laboratory Study on Using Produced Water in High pH Borate Gels Used
in Hydraulic Fracturing,” paper 179553-MS, presented at the SPE Improved Oil Recovery Conference, April, 2016.
195. Elsarawy, A.M., Nasr-El-Din, H.A., Cawiezel, K.E., “Compatibility and Rheology of High-pH Borate Gels Prepared With
Produced Water for Hydraulic-Fracturing Applications,” 185953-PA, SPE Production and Operations Journal, April, 2017.
196. Yue, Z., Peng, Y., He, K., Xu, L., “Multifunctional Fracturing Additives as Flowback Aids,” paper 181383-MS, presented at the
SPE Annual Technical Conference and Exhibition, September, 2016.
197. Bose, C.C., Alshatti, B., Swartz, L., Gupta, A., Barati, R., “Dual Application of Polyelectrolyte Complex Nanoparticles as
Enzyme Breaker Carriers and Fluid Loss Additives for Fracturing Fluids,” paper 171571-MS, presented at the SPE/CSUR
Unconventional Resources Conference – Canada, September, 2014.
198. Walker, M.L., Shuchart, C.E., Yaritz, J.G., Norman, L.R., “Effects of Oxygen on Fracturing Fluids,” paper 28978-MS, presented
at the SPE International Symposium on Oilfield Chemistry, February, 1995.
Fracturing Fluids and Additives
197
199. Mumallah, N.A., “Do Fluid Loss Control Additives Perform As Claimed In Acid-Fracturing Treatments,” paper 39581-MS,
presented at the SPE Formation Damage Control Conference, February, 1998.
200. Huang, J., Safari, R., Fragachan, F.E., Smith, C., “Improving Diversion Efficiency in Re-Fracturing by Using Engineered Solid
Particulate Diverters,” paper 190023-MS, presented at the SPE Western Regional Meeting, April, 2018.
201. Oort, E.V., “How to Test for Compatibility Between Fluids and Shales,” paper 189633-MS, presented at the IADC/SPE Drilling
Conference and Exhibition, February, 2018.
202. Sanaei, A., Shakiba, M., Varavei, A., Sepehrnoori, K., “Mechanistic Modeling of Clay Swelling in Hydraulic-Fractures
Network,” 180372-PA, SPE Reservoir Evaluation & Engineering Journal, February, 2018.
203. Ely, J.W., Jacoby, M.A., “Utilization of Simple Fluids and Proppant Combined with Design Optimization Yields Outstanding
Results in New Mexico Yeso-San Andrew Oil Play,” paper 146523-MS, presented at the SPE Annual Technical Conference and
Exhibition, October, 2011.
204. Johnson, R.L., Brown, T.D., “Large-Volume, High-Rate Stimulation Treatments in Horizontal Wells in the Niobrara Formation,
Silo Field, Laramie County, Wyoming,” paper 25926-MS, presented at the Low Permeability Reservoirs Symposium, April,
1993.
205. Grieser, B., Hobbs, J., Hunter, J., Ables, J., “The Rocket Science Behind Water Frac Design,” paper 80933-MS, presented at the
SPE Production and Operations Symposium, March, 2003.
206. Palisch, T.T., Vincent, M.C., Handren, P.J., “Slickwater Fracturing: Food for Thought,” paper 115766-MS, presented at the SPE
Annual Technical Conference and Exhibition, September, 2008.
207. Denney, D., “Slick-Water and Hybrid Fracturing Treatments: Lessons Learned,” 0305-0038-JPT, Journal of Petroleum
Technology, March, 2005.
208. Ilk, D., Rushing, J.A., Sullivan, R.B., Blasingame, T.A., “Evaluating the Impact of Waterfrac Technologies on Gas Recovery
Efficiency: Case Studies Using Elliptical Flow Production Data Analysis,” paper 110187-MS, presented at the SPE Annual
Technical Conference and Exhibition, November, 2007.
209. Woodworth, T.R., Miskimins, J.L., “Extrapolation of Laboratory Proppant Placement Behavior to the Field in Slickwater
Fracturing Applications,” paper 106089-MS, presented at the SPE Hydraulic Fracturing Technology Conference, January, 2007.
210. Coronado, J.A., “Success of Hybrid Fracs in the Basin,” paper 106758-MS, presented at the Production and Operations
Symposium, March, 2007.
211. Jennings, A.R., Westerman, C., Westerman-Tadlock, D., Westerman, R., Anderson, M., “A Systematic Approach to Improved
Success With Hydraulic Fracturing Applications,” paper 101837-MS, presented at the SPE Annual Technical Conference and
Exhibition, September, 2006.
212. Ghanbari, E., Xu, M., Dehghanpour, H., Bearinger, D., “Advances in Understanding Liquid Flow in Gas Shales,” paper 171653-MS,
presented at the SPE/CSUR Unconventional Resources Conference – Canada, September, 2014.
213. Inyang, U., Fontenelle, L, Schultheiss, N., “Proppant Pack Permeability: Does it Matter? Field Case Histories of a Nearly
Residue-Free Crosslinked Fluid System,” paper 168159-MS, presented at the SPE International Symposium and Exhibition on
Formation Damage Control, February, 2014.
214. Flowers, J.R., Guetta, D.R., Stephenson, C.J., Jeremie, P., d’Arco, N., “A Statistical Study of Proppant Type vs. Well Performance in
the Bakken Central Basin,” paper 168618-MS, presented at the SPE Hydraulic Fracturing Technology Conference, February, 2014.
215. Das, P., Achalpurkar, M.P., “Impact of Rock Mechanics and Formation Softening Analysis in Shale Fracturing Fluid Design,”
paper 167336-MS, presented at the SPE Kuwait Oil and Gas Show and Conference, October, 2013.
216. Bhattacharya, S., Nikolaou, M., “Analysis of Production History for Unconventional Gas Reservoirs With Statistical Methods,”
147658-PA, SPE Journal, October, 2013.
217. Agrawal, S., Sharma, M.M., “Liquid Loading Within Hydraulic Fractures And Its Impact on Unconventional Reservoir
Productivity,” paper URTEC2013-115, presented at the Unconventional Resources Technology Conference, August, 2013.
218. Durst, D., Vento, M.C., “Unconventional Shale Play Selective Fracturing Utilizing Multilateral Technology,” paper 163959-MS,
presented at the SPE Unconventional Gas Conference and Exhibition, January, 2013.
219. Brake, A.C., “Fracture Optimization in a Giant Gas Field, Wamsutter, Wyoming, USA,” paper 164029-MS, presented at the SPE
Unconventional Gas Conference and Exhibition, January, 2013.
220. Owolabi, O.O., Volz, R.F., Smith, P.S., “Can Shale-Like Stimulations Unlock the Potential of Extremely Low Permeability Tight
Gas Reservoirs?,” paper 164001-MS, presented at the SPE Unconventional Gas Conference and Exhibition, January, 2013.
221. Rylance, M., “Optimising Remote Unconventional Gas Exploration,”, paper 163987-MS, presented at the Unconventional Gas
Conference and Exhibition, January, 2013.
222. Yu, S., “The Optimal Completion Techniques for Horizontal Gas Wells in the Cadomin Formation, Northeastern British
Columbia,” paper 162575-MS, presented at the SPE Canadian Unconventional Resources Conference,” October, 2012.
223. Massaras, L.V., Mcnealy, T.R., “Highly Accurate Prediction of Screenouts in the Eagle Ford Shale with the Screenout Index,”
paper 157613-MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2012.
224. Shelley, R.F., Guliyev, N., Nejad, A., “A Novel Method to Optimize Horizontal Bakken Completions in a Factory Mode
Development Program,” paper 159696-MS, presented at the SPE Annual Technical Conference and Exhibition, October, 2012.
225. Van Gijtenbeek, K.A.W., Shaoul, J.R., De Pater, H.J., “Overdisplacing Propped Fracture Treatments-Good Practice or Asking
for Trouble?,” paper 154397-MS, presented at the SPE Europec/EAGE Annual Conference, June, 2012.
226. Arogundade, O., Sohrabi, M., “A Review of Recent Developments and Challenges in Shale Gas Recovery,” paper 160869-MS,
presented at the SPE Saudi Arabia Section Technical Symposium and Exhibition, April, 2012.
227. Ramurthy, M., Barrree, R.D., Kundert, D.P., Petre, J. E., Mullen, M.J., “Surface-Area vs. Conductivity-Type Fracture Treatments
in Shale Reservoirs,” 140169-PA, SPE Production & Operations Journal, November, 2011.
Chapter 7
Fluid Leakoff
Ghaithan A. Al-Muntasheri and Msalli A. Al-Otaibi, EXPEC Advanced
Research Center, Saudi Aramco, Dhahran, Saudi Arabia
Ghaithan A. Al-Muntasheri is the chief technologist of the Production Technology Team in the EXPEC Advanced Research Center
of Saudi Aramco in Dhahran, Saudi Arabia. He holds bachelor’s and master’s degrees in chemical engineering from King Fahd University of Petroleum and Minerals, Saudi Arabia, and a PhD degree in petroleum engineering from Delft University of Technology.
Al-Muntasheri is an SPE Distinguished Member.
Msalli A. Al-Otaibi is the drilling fluid and cementing unit supervisor with the EXPEC Advanced Research Center of Saudi Aramco.
His interests include hydraulic fracturing, proppant transport in complex fractures, and drilling fluids. Al-Otaibi holds a BS degree in
chemical engineering from Louisiana State University, an MS degree in chemical engineering from King Fahd University of Petroleum and Minerals, and a PhD degree in petroleum engineering from Colorado School of Mines.
Contents
7.1
7.2
7.3
Overview���������������������������������������������������������������������������������������������������������������������������������������������������������������� 199
Introduction������������������������������������������������������������������������������������������������������������������������������������������������������������ 200
Fluid-Leakoff Equation������������������������������������������������������������������������������������������������������������������������������������������� 200
7.3.1 Filter-Cake Leakoff Coefficient������������������������������������������������������������������������������������������������������������������� 200
7.3.2 Relative Permeability Leakoff Coefficient �������������������������������������������������������������������������������������������������� 201
7.3.3 Reservoir-Fluid Leakoff Coefficient������������������������������������������������������������������������������������������������������������ 201
7.3.4 Combined Leakoff Coefficient�������������������������������������������������������������������������������������������������������������������� 202
7.3.5 Sample Calculations���������������������������������������������������������������������������������������������������������������������������������� 203
7.4 Modeling of Leakoff Coefficient����������������������������������������������������������������������������������������������������������������������������� 210
7.5 Laboratory Measurements of Fluid-Loss Parameters�������������������������������������������������������������������������������������������� 216
7.6 Effect of Key Parameters on Leakoff����������������������������������������������������������������������������������������������������������������������� 219
7.6.1 Pressure-Drop Effect���������������������������������������������������������������������������������������������������������������������������������� 219
7.6.2 Temperature Effect������������������������������������������������������������������������������������������������������������������������������������� 221
7.6.3 Shear-Rate Effect��������������������������������������������������������������������������������������������������������������������������������������� 221
7.6.4 Formation Permeability Effect�������������������������������������������������������������������������������������������������������������������� 223
7.7 Advances in Fluid-Loss Additives�������������������������������������������������������������������������������������������������������������������������� 223
7.7.1 Additives for Polymer-Based Fluids����������������������������������������������������������������������������������������������������������� 223
7.7.2 Additives for Other Fracturing Fluids���������������������������������������������������������������������������������������������������������� 225
7.8 Pressure-Dependent Leakoff��������������������������������������������������������������������������������������������������������������������������������� 225
7.9 Nomenclature�������������������������������������������������������������������������������������������������������������������������������������������������������� 227
7.10 References������������������������������������������������������������������������������������������������������������������������������������������������������������ 228
7.1 Overview
This chapter introduces fluid leakoff during the hydraulic fracturing process. It includes both modeling of the leakoff coefficients
and their experimental measurements. First, the chapter presents the fundamental equations governing fluid leakoff and then advanced
models that capture the dynamic conditions for calculating leakoff coefficients. The applications and limitations of these models
are illustrated by comparative experimental data and sample calculations. After that, advances in the design of experimental setups
to measure fluid leakoff are presented. Here, the chapter includes new designs of various fluid-loss cells and shares new limits of
experimental conditions that can be applied in the laboratory. In specific, experimental parameters such as absolute pressures, pressure
drops, and shear rates are highlighted, with the support from experimental data in the literature. Then, the impact of pressure drop,
temperature, shear, and formation permeability on the leakoff coefficient is discussed. Next, a review of fluid-loss additives is shared
for all fracturing fluids, including materials such as nanoparticles, organic acids, and fibers. The chapter concludes with the impact of
pressure on fluid leakoff coefficient in naturally fractured reservoirs.
200 Hydraulic Fracturing: Fundamentals and Advancements
7.2 Introduction
Hydraulic fracturing fluids are pumped underground at high pressures to initiate and propagate fractures. During this process, part
of the pumped fluid is lost into the formation as leakoff. The leakoff volume should be accounted for in the fracturing design, as
it plays a critical role in achieving desired fracture lengths and needed channels for fluid flow. Moreover, excessive fluid leakoff
­volume could negatively impact the proppant distribution in created fractures and result in formation damage and higher costs in both
pumping and materials. To predict the fluid leakoff, reservoir rock properties, pumping conditions, reservoir fluids, and fracturing
fluid properties are all considered.
7.3 Fluid-Leakoff Equation
During fracturing operations, the injected fluid fills the volume of the created fractures and part of it leaks off into the formation.
This can be mathematically represented by Eq. 7.1 below (Howard and Fast 1957):
Vi = VL + V f , ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.1)
where Vi is injected fluid volume (gal), VL is volume of the fluid leaking off into the formation (gal), and V f is volume of the created
fractures (gal).
The fluid leakoff volume per unit fracture area (VL′) at a given time is found by integrating the fluid flow velocity with respect to
time at a constant area. For a Newtonian fluid with a constant viscosity flowing through a porous medium under linear conditions,
Eq. 7.2 is used to compute fluid velocity. Integrating Eq. 7.2 with respect to time at a constant area obtains Eq. 7.3, which predicts VL′
with key assumptions such as a uniform fracture width, linear fluid flow perpendicular to the fracture face, and no change in pressure
(Howard and Fast 1957; Penny and Conway 1989; Valko and Economides 1999).
v(t ) =
C
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.2)
t
where v is fluid velocity (ft/min), t is time (minutes), and C is leakoff coefficient ft/(min)1/2.
V L′ = 2 × C × t − ts + V s′ , ��������������������������������������������������������������������������������������������������������������������������������������������������������������(7.3)
where VL′ is volumetric flow rate per fracture unit area at any given time (ft3/ft2), C is leakoff coefficient (ft/min0.5), t is fluid
­exposure time to the fracture face (minutes), ts is time duration of the spurt loss (minutes), and Vs′ is spurt loss per fracture unit
area (ft3/ft2).
The fluid-leakoff coefficient in Eq. 7.2 combines three independent leakoff mechanism effects, namely, reservoir fluids displacement, fracturing fluid filtrate invasion into the reservoir rock, and filter-cake wall effects. Each of these factors presents a resistance
to the fracturing-fluid leakoff into the reservoir matrix, while their magnitudes differ on the basis of fracturing-fluid type, reservoir
fluids, and pumping conditions. The next subsections describe these leakoff coefficients and how they are used to calculate the overall
leakoff coefficient of the fracturing fluid.
7.3.1 Filter-Cake Leakoff Coefficient. During the leakoff process, a filter cake develops presenting a resistance to the fluid flow into
the formation. The filter-cake resistance is represented by a leakoff coefficient, Cw. For fluids with no bridging materials, there will be
no filter cake and, hence, this coefficient is neglected. Cw is
defined by Eq. 7.4 as
Cumulative Filtrate Volume (gal)
Cw =
Slope m = Cw*area /0.0164
Intercept = spurt volume;
rate controlled by Cvc
÷ Time (minutes)
Fig. 7.1—Cumulative filtration volume is plotted as function of
t-1/2 to calculate Cw; from Penny and Conway (1989).
0.0164 m
, ��������������������������������������������������������(7.4)
A
where m is slope of the line of the filtrate volume vs.
t1/2 plot and A is area of core sample used in the filtration
test (cm2).
Eq. 7.4 assumes that the cake thickness is ­proportional
to the fluid leakoff volume; the cake permeability
is ­independent of its thickness; Darcy’s law is followed
by the leakoff fluid through the cake; and there is no pressure change across the cake (Howard and Fast 1957). The
leakoff coefficient of the filter cake is determined experimentally through the measurement of the cumulative
leakoff volume as a function of time. Then, the data are
plotted vs. the square root of time under static conditions.
The slope of the linear portion of this relationship, m,
and the area of the core sample, A, are used to calculate
Cw. The intercept of the linear portion with the y-axis
represents the spurt ­
volume, which is defined as the
fluid volume lost before the filter cake develops. Fig. 7.1
shows a typical example of experimental data plotted to
calculate Cw.
Fluid Leakoff
201
7.3.2 Relative Permeability Leakoff Coefficient. The fracturing fluid invading the formation experiences a resistance to flow
because of the relative permeability of the reservoir rock and the viscosity of the fluid. This resistance is represented by the filtrate
leakoff coefficient, Cv, which can be calculated using Eq. 7.5. This equation assumes constant pressure drop across the invaded zone
and full displacement of the mobile phase(s) by the filtrate, resulting in 100% filtrate saturation; it also assumes that the fluid and rock
are incompressible (Howard and Fast 1970).
Cv = 0.0469
k f φ∆p
µf
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.5)
where k f is relative permeability of formation to the leakoff filtrate (darcies), φ is formation porosity fraction, ∆p is pressure drop
between fluid at the formation face and pore pressure (psi), and µ f is leakoff filtrate viscosity at bottomhole conditions (cp).
When the filter cake is developed for low-permeability formations (<0.1 md), the filtrate viscosity during spurt is similar to
the base-fluid viscosity. This happens when the gelling agent is trapped at the filter cake or cannot ­penetrate a tight formation.
For high-permeability formations, the filtrate viscosity increases with increasing permeability during the spurt loss, as shown
in Table 7.1, while the filtrate lost after spurt has the same viscosity as the base fluid (Penny and Conway 1989). This was verified by Vitthal and McGowen (1996) as shown in Fig. 7.2. However, this increase does not affect the total leakoff coefficient, Ct ,
because the spurt loss is small relative to the total ­leakoff volume. For that, most simulators use the base-fluid viscosity for the
filtrate viscosity.
Average Permeability (md)
Filtrate viscosity (10 sec−1)
0.015 to 0.093
0.3
0.187
0.3
0.37
0.3
0.75
1.7
1.5
2.4
Table 7.1—Filtrate-viscosity during spurt increase with increasing
permeability (Penny and Conway 1989).
Apparent Viscosity @ 170
(sec–1)
70
Base gel
60
2,000 psi
1,000 psi
50
500 psi
40
30
20
10
0
0.0
50.0
100.0
150.0
200.0
Permeability (md)
250.0
300.0
Fig. 7.2—Effluent viscosity during spurt increases with permeability and pressure drop; from Vitthal and McGowen
(1996).
7.3.3 Reservoir-Fluid Leakoff Coefficient. The displaced reservoir fluid imposes flow resistance on the leakoff fluid, which is a
­function of the reservoir-fluid viscosity and formation compressibility. Such resistance (leakoff mechanism) is captured through
the reservoir-fluid leakoff c­ oefficient and is defined by Eq. 7.6. This equation assumes constant pressure drop between the filtrate/­
reservoir interface and the reservoir, compressible flow, constant f­ormation total compressibility, an unbounded reservoir, and
­relatively slow fluid invasion. For gas reservoirs, this ­coefficient can be neglected (Howard and Fast 1970).
Cc = 0.0374 ∆p
krφ ct
, ����������������������������������������������������������������������������������������������������������������������������������������������������������������(7.6)
µr
where kr is relative permeability of formation to the reservoir fluid (darcies), ct is formation total compressibility (psi−1), and µr is
reservoir-fluid viscosity at bottomhole conditions (cp).
202 Hydraulic Fracturing: Fundamentals and Advancements
7.3.4 Combined Leakoff Coefficient. Industry literature and practice have various proposed methods to select or combine the leakoff coefficient(s) that will be used in the prediction of the fluid-leakoff volumes and to design the fracturing treatments. The simplest
method is to assume that the filter-cake leakoff coefficient will dominate and use Cw. Nolte (1988) showed that the leakoff is limited
either by the reservoir or by the filter cake. For that, he proposed to select the lower between the filter-cake coefficient, Cw, and the
combined filtrate/reservoir leakoff coefficient, Cvc. The combination of the Cc and Cv coefficients was developed by Williams (1970)
as shown in Eq. 7.7:
Cvc =
2Cv Cc
Cv + Cv2 + 4 Cc2
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������(7.7)
The other method for calculating an overall leakoff coefficient was developed by Williams et al. (1979), which simultaneously measures the three leakoff coefficients. This is accomplished by assuming negligible spurt volume and time while using the relationship
between each coefficient and the pressure drop to combine their effects under a total pressure drop for the overall coefficient. Eq. 7.8
shows the effect of the combined three coefficients:
Ct =
2Cv Cc Cw
(
Cv Cw + Cw2 Cv2 + 4 Cc2 Cv2 + Cw2
)
. ����������������������������������������������������������������������������������������������������������������������������������������(7.8)
Eq. 7.8 requires calculating each coefficient separately while using the pressure drop as an overall pressure drop for all the
leakoff coefficients. The calculated total coefficient can then be used in Eq. 7.3 to calculate the leakoff volume loss rate at a
­specific time. Because the leakoff spurt volume is controlled by Cvc, the spurt time can then be calculated using Eq. 7.9 (Penny
and Conway 1989).
2
 V′ 
t s =  S  . ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.9)
 2Cvc 
There are published experimental data for spurt losses from common fluids as shown in Fig. 7.3. The figure defines the spurt-loss values
for different complexed hydroxypropyl guar (HPG) loadings and permeabilities at 125°F. The obtained values can be corrected for
different temperatures as shown in Fig. 7.4. Most of the fluid-leakoff volume can be attributed to the spurt loss for high-permeability
1
LEGEND
20 lbm gel/Mgal
40 lbm gel/Mgal
50 lbm gel/Mgal
60 lbm gel/Mgal
80 lbm gel/Mgal
Spurt (gal/ft2)
0.1
0.01
0.001
0.1
1
10
100
Permeability (md)
Fig. 7.3—Spurt-loss values for different concentrations of complexed HPG as a function of rock permeability measured
at 125oF; from Penny and Conway (1989). Mgal = 1,000 gal.
Fluid Leakoff
203
3
Spurt Factor
2
1
0
50
150
250
Temperature (F)
350
Fig. 7.4—Temperature correction factors for spurt-loss values of complexed fluids; from Penny and Conway (1989).
formations, despite any filtration-control additives. On the other hand, the spurt-loss effect can be neglected for low-permeability
formations.
7.3.5 Sample Calculations. The following example demonstrates how the leakoff coefficients, Cc, Cv, Cw, and Ct, are calculated using both field and laboratory data. The parameters used
in this example, which analyzes a gas-producing reservoir, are
shown in Table 7.2.
1. Calculation of the Formation Total Compressibility,
cr . The total compressibility of a formation can be calculated by combining the individual compressibilities of
the rock and all fluids: water, oil, and gas. The total compressibility is derived from Eq. 7.10.
ct = So co + Sw cw + Sg cg + cr. ������������������������������������ (7.10)
ct = 0 + 0.32 × 3 × 10 −6 + 0.68 × 222 × 10 −6 + 5 × 10 −6.
ct = 1.57 × 10 −4 psi−1.
So is oil saturation [fraction (0)], co is oil compressibility [psi (can
be found from Fig. 7.5], Sw is water saturation [fraction (0.32)],
cw is water compressibility [psi−1 (from Fig. 7.6, for bottomhole
treating pressure (BHTP) of 4,600 psi at 200°F, cw is 3 × 10−6
psi−1)], Sg is gas saturation [fraction (0.68)], cg is gas compressibility [psi−1 (cg = 222 × 10−6 psi−1, see calculation below)], and cr is
rock compressibility [psi−1 (from Fig. 7.7, for consolidated sandstone at 11% porosity, cr = 5 × 10−6 psi−1)].
−1
2. Calculation of Gas Compressibility, cg.
Parameter
Value
Net perforation interval
57 ft
Gross interval
100 ft
Bottomhole pressure
(BHP)
3,600 psi
Bottomhole treating
pressure (BHTP)
4,600 psi
Reservoir temperature
200oF
Porosity
11%
Oil saturation
0%
Residual oil saturation
0%
Water saturation
32%
Residual water saturation
32%
Chlorides
36,500 ppm
Permeability
0.28 md
Fracturing fluid, HPG
40 lbm/1,000 gal,
2% KCl water
Gas specific gravity
0.65
Table 7.2—Example parameters for a gas-producing
reservoir.
• Pseudoreduced pressure ( ppr) is equal to the reservoir pressure divided by the pseudocritical pressure Ppc):
p pr =
p
3600
=
= 5.39.
Ppc 668 (from Fig. 7.8)
204 Hydraulic Fracturing: Fundamentals and Advancements
• The pseudoreduced temperature (Tpr) is equal to the reservoir temperature divided by the pseudocritical temperature (Tpc):
(200 + 460) R
T
=
= 1.76.
T pc 375 R (from Fig. 7.8)
T pr =
• The gas pseudoreduced compressibility (Cpr) is calculated by
C pr =
C prT pr
T pr
=
0.26(from Fig. 7.9)
= 0.148.
1.76
• Finally, the gas compressibility (cg) is calculated by
C pr
Ppc
=
0.148
= 2.22 × 10 −4 psi −1.
668
Avg. Compressibility Factor ¥ 106
cg =
20
15
10
5
0
0.5
0.6
0.7
0.8
Specific Gravity of Oil at Saturation Pressure
Fig. 7.5—Average values of oil compressibility as a function of specific gravity; from Calhoun (1953).
Temperature (C)
10
20
30
40
50
60
70
80
90
100
110
4.00
Average Compressibility (×104 psi-1)
54
3.80
Compressibility
distilled water
3.70
3.60
52
26 kg/cm2 50
3.50
3.40
3.30
P=
369.8 psi
100 ”
3.20
3.10
3.00
2.90
2.80
2.70
200 ”
300 ”
400 ”
475 ”
1422.3 ”
2844.7 ”
4267.0 ”
5689.4 ”
6756.1 ”
48
46
44
42
40
38
2.60
36
2.50
40
60
80
100
120
140
160
Temperature (F)
180
200
220
Fig. 7.6—Average values for compressibility of distilled water; from Long and Chierici (1961).
240
Average Compressibility [×104 (kg/cm3)-1]
56
3.90
Fluid Leakoff
205
Pore Volume Compressibility (¥ 10-6 psi-1) @ 75% Lithostatic Pressure
100
Unconsolidated
sandstones
friable sandstones
10
Total all samples
Hall’s
correlation
Limestones
Consolidated
sandstones
1.0
0
5
10
15
20
25
30
Initial Porosity at Zero Net Pressure (%)
35
Fig. 7.7—Rock compressibility for different rock types as a function of porosity; from Newman (1973).
3. Calculation of Rock Permeability by Filtrate Fluid, KL. The formation rock permeability in this example of 0.28 md represents the formation permeability to gas measured at 100 psi. This value is then converted into an equivalent liquid permeability using Eq. 7.11.
kL =
kg

ba  , ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.11)
 1 + p 
where kL is relative formation permeability to the liquid filtrate, (md); kg is relative formation permeability to gas, measured, (md); p is
average pressure drop at the point of measurement (50 psi); ba is gas slippage factor, given in Fig. 7.10; and
kL =
0.28
(1 + 1.350 )
= 0.272 (md). ��������������������������������������������������������������������������������������������������������������������������������������������������������(7.12)
4. Calculation of Gas Viscosity at Bottomhole Temperature (BHT), ur:
• Using molecular weight and BHT, the gas viscosity at 1 atm is determined from Fig. 7.11, µ1 = 0.0125 cp.
• The viscosity ratio,
µr
= 1.6, is determined from Fig. 7.12 using Tpr = 1.76, and ppr = 5.39.
µ1
Gas viscosity is calculated as:
µr = µ1 × 1.6 = 0.0125 × 1.6 = 0.02 cp.
206 Hydraulic Fracturing: Fundamentals and Advancements
800
Pressure Correction (psi)
700
Pressure Correction (psi)
Ppc Pseudocritical Pressure (psia)
750
0
G = 0.6 − 1.5
G = 2.0
−50
0
5
10
G = 0.6 − 2.0
0
−100
15
Mol % N2
100
Pressure Correction (psi)
100
50
0
5
10
0
−100
15
Mol % CO2
G = 0.6 − 2.0
0
5
10
Mol % H2S
15
Miscellaneou
s gases
650
Conde
nsate
well fl
uid
s
600
0
G = 0.6 − 2.0
−50
0
5
10
Mol % N2
15
0
G = 0.6 − 2.0
−50
0
5
10
15
s
ou
s
se
ga
e
an
ell
sc
Mi
Mol % CO2
450
nsa
nde
Co
400
ell
te w
350
ds
flui
50
Temperature Correction (F)
Tpc Pseudocritical Temperature (R)
500
50
Temperature Correction (F)
550
Temperature Correction (F)
50
G = 0.6 − 1.5
G = 2.0
0
−50
0
5
10
15
Mol % H2S
300
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Gas Gravity, Air = 1
Fig. 7.8—Pseudocritical pressure and temperature values for natural gases; from Brown et al. (1948) and Carr et al.
(1954).
5. Calculation of the Filter-Cake Leakoff Coefficient, Cw. The value of Cw was determined experimentally for different concentrations of silica flour as a function of the gelling agent concentration, as shown in Fig. 7.13. For a silica flour concentration of zero, with a 40 lbm/1,000 gal dosage of HPG, Cw is shown on the graph as 0.0028 ft/min1/2 at a temperature of 125°F.
The reservoir temperature in the example is 200°F, so the value should be corrected using Fig. 7.14.
Cw = 1.3 × 0.0028 = 0.0036 ft / min 0.5 .
Fluid Leakoff
207
10
Cpr Tpr
1
0.1
0.01
Tpr
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
0.1
1
10
Reduced Pressure (Ppr )
100
Fig. 7.9—Pseudoreduced compressibility, Cpr , and temperature, Tpr , values as function of pseudoreduced pressure for
natural gases; from McCain (1990).
Gas Slippage Factor, b (psi)
10
1
0.1
0.01
0.01
0.1
1
10
100
Permeability to Nonreacting Liquid “kL” (md)
1,000
Fig. 7.10—Gas slippage factor as a function of liquid permeability; from API RP 27 (1952).
6. Calculation of the Relative Permeability Leakoff Coefficient, Cv . Because this is a low-permeability reservoir, the
effluent viscosity was assumed to be that of water. The viscosity of water at a temperature of 200°F, derived from
Fig. 7.15, is 0.3 cp.
Cv = 0.0469
k f φ∆p
µf
= 0.0469
(0.000272 darcies)(0.11)(1,000 psi)
= 0.1484 ft /min 0.5.
0.3 cp
N2
CO2
0 .0015
1.
0
γ g = 0.6
0
5
10
1.5
1.0 .0005
0
15
Mole % H2S
5
=0
10
5
1.
1.0
2.
.0005
0
15
γ g=
0
Mole % N2
5
0.6
10
15
Mole % CO2
Gas-Specific Gravity
1.0
1.5
0.5
.016
.6
γg
0
.0010
=
.0010
γg
γg
.0005
.0
=2
=
.0010
0
2.
0
.0015
1.
5
H2S
.0015
γg
Correction Added
to Viscosity (cp)
208 Hydraulic Fracturing: Fundamentals and Advancements
2.0
.015
Viscosity at 1 atm, m g1 (cp)
.014
.013
.012
400 °F
.011
.010
300 °F
.009
200 °F
.008
100 °F
.007
.006
.005
.004
10
20
30
40
50
Molecular Weight
60
Fig. 7.11—Viscosity values for gases at atmospheric pressure; from McCain (1990).
6.0
5.0
Viscosity Ratio, m /m 1
4.0
3.0
20
15
10
Ps
eu
do
red
uce
dt
8
2.0
em
pe
rat
u
6
re,
P
pr
4
3
2
1
1.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Pseudoreduced Temperature (Tpr)
2.6
2.8
3.0
Fig. 7.12—Viscosity conversion factor from the atmospheric conditions, based on pseudoreduced temperature and
pressure; from Carr et al. (1954).
Fluid Leakoff
209
3
0.01
Legend
0-lbm Silica flour/Mgal
Cw (ft /min1/2)
50-lbm Silica flour/Mgal
0.001
10
100
Gelling Agent Concentration (lbm/Mgal)
Fig. 7.13—Filter-cake leakoff coefficients for different
concentrations of gelling agent and silica flour measured
at 125°F; from Penny and Conway (1989).
Cw Correction Factor
25-lbm Silica flour/Mgal
2
1
0
50
150
250
Temperature (F)
350
Fig. 7.14—Correction factor for Cw as a function of
temperature; from Penny and Conway (1989).
7. Calculation of the Reservoir Leakoff Coefficient, Cc.
krφ ct
(0.000272 darcies)(0.11)(1.57 × 10 −4 psi−1 )
= 0.0374 (1, 000 psi)
.
µr
0.02 cp
Cc = 0.0374 ∆p
Cc = 0.0184 ft /min 0.5.
8. Calculation of the Combined Filtrate and Reservoir Leakoff Coefficients.
Cvc =
Cvc =
2Cv Cc
Cv + Cv2 + 4 Cc2
.
2 × 0.1484 × 0.0184
0.1484 + (0.1484)2 + 4 × (0.0184)2
.
Cvc = 0.01811 ft/min 0.5 .
9. Calculation of the Combined Leakoff Coefficient.
Ct =
Ct =
2Cv Cc Cw
(
Cv Cw + C Cv2 + 4 Cc2 Cv2 + Cw2
2
w
)
.
2 × 0.1484 × 0.0184 × 0.0036
0.1484 × 0.0036 +
( 0.0036 )2 × ( 0.1484 )2 + 4 × ( 0.0184 )2 × [( 0.1484 )2 + ( 0.0036 )2 ]
.
Ct = 0.00326 ft /min 0.5.
10. Calculation of the Leakoff Volume per Area Over 60-Minute Exposure. The leakoff volume per unit area is calculated
using Eq. 7.3. The spurt-loss volume is set to zero because none is anticipated at a permeability of 0.28 md (refer to Fig. 7.3).
That makes the spurt time zero also.
VL′ = 2 × Ct × t − t s + VS′.
VL′ = 2 × 0.00326 × 60 − 0 + 0 = 50.5 × 10 −3 ft 3 /ft 2 .
VL′ = 50.5 × 10 −3 ft 3 /ft 2 × 7.48 gal/ft 3 = 0.3778 gal/ft 2 .
210 Hydraulic Fracturing: Fundamentals and Advancements
2.1
1.14
Estimated max. error
Temp
µ*
f
40° – 120°
1%
5%
120° – 212° 5%
5%
212° – 400° 10%
5%
1.8
1.12
1.10
si
1.9
1.7
0p
2.0
Viscosity, m* (cp)
f
10
,00
1.08
1.6
1.06
1.5
1.04
1.4
1.02
1.3
1.00
1.2
i
0
00
ps
8,
i
ps
00
6,0
i
0 ps
4,00
i
ps
2,000
0
100
200 300
T (F)
400
Pressure correction factor (f )
for water vs. T, °F
Presumed applicable to brines but
not confirmed experimentally
Viscosity at elevated pressure
µp,T = µ* T − fp,T
1.1
1.0
0.9
0.8
0.7
20
16
12 %
8 %
4 %%
0
%
0.6
0.5
26
24 %
% NaC
%
l
Viscosity (µ*) at 1 atm pressure below 212°
at saturation pressure of water above 212°
0.4
0.3
0.2
0.1
0
40
60
80
100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
T (F)
Fig. 7.15—Water viscosity values as a function of temperature and salinity; from Matthews and Russell (1967).
7.4 Modeling of Leakoff Coefficient
The simple model presented in Eq. 7.3 to calculate the fluid-loss volume works well only when the fracture propagation rate is large
relative to the fluid-leakoff rate (i.e, in low-permeability formations). This is attributed to the model not accounting for dynamic
­conditions, changing fracturing pressure, radial flow, or nonlinear behavior with time. These factors limit the application of Eq. 7.3,
and can yield either large over or under estimations in mid- to high-permeability formations. Several studies (Gulbis 1983; Penny
et al. 1985; and Roodhart 1985) showed experimentally that there is a significant difference between fluid leakoff in static conditions
and that in dynamic conditions. This has led to the development of new models that have better leakoff volume prediction capability,
as will be discussed in the below paragraphs.
Gulbis (1983) developed one of the earliest models for predicting leakoff volume under dynamic conditions, as shown in
Eq. 7.12. He found that at shear rates below 80 sec−1, the cumulative leakoff volume follows a linear trend of VL′ vs. t−1. However,
above this value, the dynamic test leakoff volume was higher than that of the static test for crosslinked fluids, and approached a
linear relationship with t. Eq. 7.12 requires obtaining the spurt-loss volume under dynamic conditions and calculating the dynamic
leakoff coefficient, Cd. The dynamic leakoff coefficient is determined using Eq. 7.13, where m′ refers to the linear slope of VL′ vs. t,
then Eq. 7.12 is used to predict the leakoff volume per area at the exposure time, t. In another study by Crawford (1983), the dynamic
condition effect on increasing the leakoff coefficient was estimated to be 50%; the study recommended a factor of 1.5 to correct the
leakoff coefficient obtained from static conditions.
Fluid Leakoff
211
V L′ = Vs′+ Cd × t ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.13)
Cd =
m′
, ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.14)
A
Cd is dynamic leakoff coefficient (ft/min), m′ is slope of plot of fluid loss vs. time (ft3/min), A is core area (ft2), and t is exposure time
(minutes).
Penny et al. (1985) confirmed the effect on fluid loss under dynamic conditions and showed that for a shear rate of 40 sec−1,
titanate-complexed HPG followed the linear trend of VL′ vs. t 0.5. However, above this shear rate, the linear relationship takes
the form VL′ vs. tn, while n (defined in Eq. 7.15) ranges from 0.5 to 1.0. Fig. 7.16 shows experimental data for shear rates of 40 and
100 sec−1.
Penny et al. (1985) developed a new model to predict fluid-leakoff volume under dynamic conditions, as shown in Eq. 7.15.
The values for m″ and n can be determined from a least-squares fit of the fluid-leakoff volume vs. time in a log-log plot. The
intercept of the linear relationship represents the value of m″ while its slope represents the value of n. The spurt loss is calculated
using Eq. 7.16.
VL′ = Vs′+ m ″ × t n , ������������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.15)
m″ is y-intercept of leakoff volume vs. time in a log-log plot (cm/minn), n is slope of the leakoff volume vs. time in a log-log
plot (0.5 ≤ n ≤ 1.0 ), and t is exposure time (minutes).
Vs′ = V i′ − m ″ × (ti )n, ������������������������������������������������������������������������������������������������������������������������������������������������������������������������� (7.16)
where ti is early time of leakoff, taken at 2 minutes, and Vi′ is initial leakoff volume per area at ti.
Ford and Penny (1988) established that the values of n and m″ are not only functions of the shear rate but also of the pressure drop. Figs. 7.17 and 7.18 show the slopes and intercepts varying with pressure drop and shear rates. Because the shear
rate changes during pumping, the equation can be used to calculate the volume at different shear rates. These volumes are then
added to give the total leakoff volume. Then, the effective leakoff coefficient, Cw_eff, is calculated using the total leakoff volume
in Eq. 7.17.
VL′ − Vs′
. ����������������������������������������������������������������������������������������������������������������������������������������������������������������������(7.17)
2 × t 0.5
Fluid = 40-lbm Titanate Complexed HP Guar
0.4 md 175°F Hollow Core
101
Dynamic leakoff data
100 sec−1 n = 0.61
40 sec−1 n = 0.5
Leakoff Volume (mL/cm2)
Cw _ eff =
100
10−1
100
101
102
Time (minutes)
Fig. 7.16—Shear-rate effect on leakoff volume vs. time linear relationship; from Penny et al. (1985).
212 Hydraulic Fracturing: Fundamentals and Advancements
Leakoff Volume (mL/cm2)
Fluid: 40-lbm/1,000-gal HP Guar Complexed With Delayed Titanate
@ 175°F; Permeability: 0.1 md; Shear Rate: 40 sec −1
101
∆p
30
100
300
500
1,000
100
n
1.00
0.73
0.70
0.64
0.59
10−1
10−2
100
101
Time (minutes)
102
Leakoff Volume (mL /cm2)
Fig. 7.17—Pressure-drop effect on the linear relationship of leakoff vs. time at a shear rate of 40 sec−1; from Ford and
Penny (1988).
Fluid: 40-lbm/1,000-gal HP Guar Complexed With Delayed Titanate
@ 175°F; Permeability: 0.1 md; Shear Rate: 102 sec −1
101
∆p
n
30
1.04
100
0.73
300
0.64
500
0.62
100
1,000 0.65
10−1
10−2
10−3
100
101
Time (minutes)
102
Fig 7.18—Shear-rate effect on leakoff volume vs. time linear relationship at shear rate of 102 sec−1; from Ford and
Penny (1988).
Roodhart (1985) described the leakoff mechanism in three stages: spurt loss, building of the filter cake, and fluid erosion of the filter
cake. He developed a model with three terms, each describing one of the stages. As shown in Eq. 7.18, Vs represents the spurt-loss
volume, and 2(CW) t A0.5 is the fluid loss during the buildup of the filter cake. The third term, Cd tB, describes the erosional effect, which
is a function of the shear rate of the fluid. Note that when Cd = 0, Eq. 7.18 reduces to the fluid loss in the static condition. Eq. 7.18,
developed using experimental data from dynamic conditions, matches well with the dynamic experimental data presented in Fig. 7.19a.
Fluid Leakoff
213
Poor prediction by the static model, Eq. 7.3, is illustrated in Fig. 7.19b. The variations in Cw between Roodhart’s model and the static
model increase with increasing shear rate and can even double, as shown in Table 7.3.
VL′ = Vs′× 2Cw × t A0.5 + Cd × t B , ��������������������������������������������������������������������������������������������������������������������������������������������������� (7.18)
where tA is time duration of wall building (minutes), tB is time duraCw (ft/min0.5)
Shear rate
tion of leakoff after wall building (tB = ttotal – tA) (minutes), and Cw
-1
(sec )
Roodhart model
Static model
is filter-cake-building coefficient, estimated from static leakoff data
−0.5
(ft/min ).
0
0.30
0.31
Clark and Barkat (1990) evaluated the accuracy and limitations of
109
0.51
0.395
predictions from earlier models using data published by McDaniel
611
0.62
0.35
et al. (1985). The data include four cases with variable shear rates,
as presented in Table 7.4. As for the static model, it is not applicable
Table 7.3—The leakoff coefficient calculated by the
for dynamic fluid loss because it gives negative spurt loss. This can
static model showed more than a 100% increase in
be seen in Fig. 7.20, where using the last data points would give an value relative to the Roodhart model (1985).
intercept with a negative value.
The limitation of the Penny et al. (1985) equation is that spurt loss is a function of time. Also, Clark and Barkat showed that fluidloss data does not always form a straight line when plotted on a log-log scale, as shown in Fig. 7.21. Another element to consider is
that toward the last data points of the plot, it is not clear which data points should form the straight line, affecting the slope and the
intercept. The Penny et al. (1985) model had lower error values in estimating the leakoff volume but exhibited negative spurt lossvalues, as shown in Table 7.5. The Roodhart model provided a good fit to experimental data but showed negative spurt loss as shown
in Fig. 7.22 and Table 7.6.
(a)
Vol. filtrate
Area rock
2.0
V'L = V's + 2Cw √t + Cd
 cm3
V'L
 cm2
Shear rate
611 s−1
109 s−1
1.0
0 s−1
0
(b)
0
2,000
4,000
6,000
8,000
t (s)
2.0
V = V's + m√t
 cm3
V'L
 cm2
Shear rate
611 s−1
109 s−1
1.0
0 s−1
Spurt loss
0
0
20
40
60
80
√t (√s)
Fig. 7.19—Roodhart model showing (a) good fit for different shear rates, while the static model shows (b) poor fit to the
dynamic leakoff data; from Roodhart (1985).
Case
McDaniel et al. (1985)
Shear Rate (sec−1)
Pressure Drop (psi)
Core Length (cm)
Permeability (md)
1
O
123
300
2
0.19
2
Δ
82
300
2
0.21
3
◊
41
300
2
0.15
4
□
0
300
2
0.21
Table 7.4—Experimental leakoff data from McDaniel et al. (1985).
214 Hydraulic Fracturing: Fundamentals and Advancements
2.0
Volume (mL)
1.5
1.0
0.5
0.0
0
1
2
3
4
5
6
7
(Time)1/2
Fig. 7.20—The static model yields a negative spurt-loss value for dynamic leakoff data; from Clark and Barkat (1990).
Volume (mL)
10
8
7
6
5
4
3
2
1
8
7
6
5
4
0.01
0.1
1
Time (minutes)
10
100
Fig. 7.21—Dynamic leakoff data plotted in a log-log scale showing nonlinear behavior; from Clark and Barkat (1990).
Curve
V s′
1
4.07 x 10
2
6.65 x 10−2
3
4
n
2.0 x 10−3
8.74 x 10−2
7.68 x 10−1
2.7 x 10−3
4.85 x 10
6.65 x 10
7.70 x 10
−1
2.4 x 10−3
−1.49 x 10−2
1.40 x 10−1
4.57 x 10−1
1.0 x 10−3
−2
1.04 x 10
Estimated Error
m″
−1
−2
−1
−2
7.74 x 10
Table 7.5—Leakoff prediction from model by Penny et al. (1985) showing low estimated errors but a negative volume
of spurt loss (Clark and Barkat 1990).
Clark and Barkat (1990) modified the original equation (Eq. 7.3) by inserting a parameter that describes the initial leakoff data
points and at the same time develops their equation for dynamic conditions. Their model is shown in Eq. 7.19. The parameters are
determined using computer programs to give the best fit. Data shown in Fig. 7.23 fit this model well, and Table 7.7 presents values
of spurt loss and estimated error.
(
)
VL′ = Vs′× 1 − e− cb × t + m ′ × t , ������������������������������������������������������������������������������������������������������������������������������������������������(7.19)
where m′ is slope of the straight-line portion of the VL′ vs. t curve, cb is cake-buildup constant (minutes–0.5), and Vs′ is spurt loss determined at the intercept, at t is 0.
Fluid Leakoff
215
6
Volume/Area (mL/cm2)
5
Curve 1
Curve 2
Curve 3
Curve 4
4
3
2
1
0
0
50
100
150
200
250
300
Time (minutes)
Fig. 7.22—Roodhart model predicts the dynamic experimental data with high accuracy but yields negative spurt losses
in Curves 1 and 2; from Clark and Barkat (1990).
Curve
V′s
2Cw
1
−3.37 x 10
1.68 x 10
2
−5.99 x 10
1.11 x 10
3
2.70 x 10−3
4
3.80 x 10
−2
−3
−3
Estimated Error
Cd
2.20 x 10
−2
4.5 x 10−3
1.24 x 10
−2
3.2 x 10−3
1.42 x 10−1
1.63 x 10−2
2.4 x 10−3
1.21 x 10
−7.84 x 10
8.3 x 10−4
−1
−1
−1
−2
Table 7.6—Leakoff prediction from the Roodhart (1985) model (Eq. 7.17) showing low estimated errors but negative
spurt loss volumes (Clark and Barkat 1990).
6
Volume /Area (mL/cm2)
5
Curve 1
Curve 2
Curve 3
Curve 4
4
3
2
1
0
0
50
100
150
200
250
300
Time (minutes)
Fig. 7.23—Clark and Barkat model (1990) shows good prediction of experimental data with positive spurt-loss values.
Curve
V′s
1
9.45 x 10
2
7.19 x 10−1
3
6.36 x 10
−1
4
7.07 x 10
−1
2.74 x 10
Estimated Error
cb
m″′
−1
−2
5.1 x 10−3
2.32 x 10−2
6.17 x 10−2
5.1 x 10−3
1.72 x 10
−2
4.39 x 10
−2
6.0 x 10−3
4.12 x 10
−3
5.50 x 10
−2
6.7 x 10−3
−2
4.30 x 10
Table 7.7—Leakoff prediction by Clark and Barkat model (1990) showing low estimated errors and positive spurt-loss
volume.
216 Hydraulic Fracturing: Fundamentals and Advancements
7.5 Laboratory Measurements of Fluid-Loss Parameters
Both dynamic and static laboratory tests have been used to measure the leakoff coefficient, Cw, and spurt loss, Vs, and compare the
effects of various additives on fluid leakoff. Penny and Conway (1989) discussed key laboratory testing methods and apparatus.
Table 7.8 provides a summary of these methods. Key points from the information presented by these authors will be reported
before proceeding to new advances in this topic. In all of these setups, the pressure drop is maintained anywhere from 1,000
to 1,500 psi, depending on the system being used. There are key differences between dynamic and static tests. First, dynamic
tests are reported to provide larger leakoff rates compared with static tests, and the data analysis/processing of the leakoff volume
as a function of time is performed differently. During static tests, the cumulative volume is plotted vs. the square root of time;
dynamic tests, however, are plotted as a function of time. The experimental procedure is to add fluid to the cell, then heat it to the
desired temperature. When the temperature is reached, nitrogen is used to apply the required pressure differential (1,000 psi in most
cases). Then, the outlet valves are opened to allow filtrate collection, which is collected while the time is recorded (McGowen and
Vitthal 1996).
Huang and Crews (2009) have reported the use of ceramic disks in leakoff experiments. Although these materials lack the rock/
fluid interaction (Penny and Conway 1989), they still provide comparisons between different fluid-loss additives. In addition, Huang
and Crews (2009) have optimized the pressure differential at 300 psi instead of 1,000 psi, which is the most commonly used. Although
this pressure drop might not represent the actual field conditions, it can still give comparative answers when testing the performance
of different fluid additives under the same conditions.
To better simulate the pressure drops that occur during fracturing treatments, McMechan (1991) developed a design that can handle
higher injection pressures while keeping the backpressure the same. The need for this type of testing arose as a result of depleted
gas wells. Once depleted, the producing reservoirs of these wells provide a large pressure differential between the fracture-treating
­pressure and the reservoir pressure. Hence, the standard 1,000 psi of pressure drop used in most tests does not mimic field conditions.
A schematic of the design is given in Fig. 7.24. The backpressure was kept constant at 250 psi, with the injection pressure exceeding
9,000 psi, to achieve pressure drops as high as 9,000 psi.
This setup used a modified Halliburton static loss cell. A 1-in. length of core with a 1.75-in. diameter was placed on a pedestal
base. The temperature was 250°F in most runs. The base permeability of the core was established by using 2% KCl. Then, the brine
was removed from the cell and the fracturing fluid was placed in the cell while heating and pressurization commenced. The fluids
Testing Apparatus
Testing Condition
Target Application
Reference
Standard fluid-loss cell (Halliburton and Baroid designs)
Static
Matrix
Long and Chierici (1961)
Impinging flow
Dynamic
Matrix
Harris (1987)
Fluid stirring in a standard fluid-loss cell
Dynamic
Matrix
Penny et al. (1985)
Slot device
Dynamic
Matrix
Penny et al. (1985)
Hollow core
Dynamic
Matrix
Hall and Dollarhide (1964)
Modified API conductivity cell
Dynamic
Matrix
Penny (1987)
Fractured hollow core
Dynamic
Fracture
Hall and Houk (1983)
Tapered slot
Dynamic
Fracture
Woo and Cramer (1984)
Table 7.8—Summary of the testing apparatus reported by Penny and Conway (1989).
Water
Drain
Nitrogen
Valve block
Pump
Pressure
chamber
Fluid-loss
cell
Heating
jacket
Core
Pedestal
base
Ruska pump
Graduated
cylinder
Fig. 7.24—Fluid-loss system with a high pressure drop; from McMechan (1991).
Fluid Leakoff
217
tested included HPG crosslinked with titanium, carboxymethyl hydroxypropyl guar (CMHPG) crosslinked with zirconium, and HPG
linear gels. A water pump was used to pressurize the nitrogen chamber. Then, after heating, the pressure drop is applied with nitrogen
gas. Samples are collected as a function of time. Although this setup has pushed the limit for the testing conditions, variations in the
backpressure were observed. The pumps used for maintaining the pressure drop probably caused these variations.
McGowen and Vitthal (1996) compared various dynamic setups for testing fluid loss. Their experiment was run at 180°F, with a
pressure differential of 1,000 psi. A schematic is shown in Fig. 7.25. Five different cells were used and compared: an American Petroleum Institute (API) conductivity cell, a modified API conductivity cell, a dynamic fluid loss (DFL) cell, a high-temperature/high pressure static fluid-loss (HPHT FL) cell, and a Hassler-sleeve static cell. Schematics of the various setups are shown in Figs. 7.26 through
Fig. 7.29. Preconditioning of the fluid is achieved by flowing it through three shear loops with outside diameters (ODs) of 0.25, 0.5,
and 0.75 in. This configuration made it possible to produce a wide range of shear rates. For example, the maximum shear rates were
reported to be 1,902, 207, and 56 sec−1 through the 0.25-, 0.5-, and 0.75-in. loops, respectively. When the flow rate is lowered, shear
rates can be lowered to a minimum of 173, 19, and 5 sec−1, respectively. The simulators were equipped with valves along different
s