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THE UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE HYDRAULIC FRACTURING OF POORLY CONSOLIDATED FORMATIONS: CONSIDERATIONS ON ROCK PROPERTIES AND FAILURE MECHANISMS A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY In partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY by IVAN GIL Norman, Oklahoma 2005 UMI Number: 3152841 UMI Microform 3152841 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 HYDRAULIC FRACTURING OF POORLY CONSOLIDATED FORMATIONS: CONSIDERATIONS ON ROCK PROPERTIES AND FAILURE MECHANISMS A DISSERTATION APPROVED FOR THE MEWBOURNE SCHOOL OF PETROLEUM AND GEOLOGICAL ENGINEERING BY _________________________ Dr. Jean-Claude Roegiers (Chairman) _________________________ Dr. Richard Hughes _________________________ Dr. Roy Knapp _________________________ Dr. Subhash Shah _________________________ Dr. Luther White © Copyright by Ivan Gil, 2005 All Rights Reserved To my parents and unconditional friends, who taught me that anything is possible; thank you Luis and Dora To Sandra, my support and partner in life To a little bundle of energy and source of inspiration called Gabriel To my sister Adriana and my brother Ronald iv Acknowledgements I would like to express my heartfelt appreciation and gratitude to Dr. Jean-Claude Roegiers, my advisor and mentor. His support, guidance, and encouragement made the completion of my studies possible. It was through him that I started enjoying the absorbing world of rock mechanics. I have been honored to receive from Dr. Roegiers, priceless lessons in both technical and personal aspects. Throughout my work with him, I have certainly grown both as a professional and as a human being. I sincerely hope that many more generations of rock mechanics professionals have the opportunity of being inspired by his infectious enthusiasm and generosity. Thanks are also due to Dr. Richard Hughes, Dr. Roy Knapp, Dr. Subhash Shah, and Dr. Luther White for kindly consenting to serve as members of my doctoral advisory committee. I am also deeply indebted to many individuals and institutions, and the contributions of some are mentioned with grateful appreciation. Chyrl Yerdon, Debbie Sipes, Lisa Parks, and Mike Shaw at the MPGE for their friendship and v always welcomed help. The Mewbourne School of Petroleum and Geological Engineering for its financial assistance during the last few years. Last, but certainly not least, I would like to thank my wife, Sandra, and my son Gabriel, for their patience, understanding, and sacrifices, without which the completion of this study would not have been possible. vi Contents 1 Introduction........................................................................1 2 Unconsolidated formations – physical properties .........4 2.1 PORE COMPRESSIBILITY ........................................................................... 4 2.2 POROSITY AND PERMEABILITY ................................................................ 7 2.3 PORE PRESSURE CHARACTERISTICS....................................................... 27 2.4 DEFORMATION BEHAVIOR OF UNCONSOLIDATED ROCKS ...................... 29 2.4.1 Uniaxial Compression Strength........................................................ 30 2.4.2 Strength as function of confining pressure - Triaxial Compression Tests ……………………………………………………………………………….32 2.4.3 Elastic moduli and their dependency on applied stress.................... 36 2.4.4 Shear Strength................................................................................... 46 2.4.5 Creep................................................................................................. 50 2.5 EFFECTS OF CHANGES IN SATURATION ON ROCK MECHANICAL PROPERTIES …………………………………………………………………………56 2.6 COMMENTS ON THE MECHANICAL PROPERTIES OF UNCONSOLIDATED ROCKS …………………………………………………………………………75 3 Reliability of the measurement of mechanical properties in unconsolidated formations ............................86 3.1 CORE DAMAGE CAUSED BY STRESS RELAXATION................................. 88 3.2 CORE DAMAGE INDUCED BY FREEZING ................................................. 96 3.2.1 Background on Soil/Rock Freezing .................................................. 97 3.2.2 General experimental results on the effect of freezing / thawing on rock mechanical behavior.................................………………………………107 3.2.3 Influence of mineralogy on frost alteration of the rock .................. 112 3.2.4 Influence of freezing rate on frost heaving ..................................... 114 3.2.5 Influence of freezing direction on measured rock properties ......... 118 3.3 COMMENTS ON THE RELIABILITY OF THE MEASURED ROCK PROPERTIES FROM UNCONSOLIDATED CORES....................................................................... 124 vii 4 Hydraulic fracturing stimulation in poorly consolidated, highly-permeable formations..............................................129 4.1 OPERATIONAL PROBLEMS COMMONLY ASSOCIATED WITH POORLY CONSOLIDATED FORMATIONS........................................................................... 129 4.1.1 Problems during drilling................................................................. 130 4.1.2 Problems during production........................................................... 139 4.1.3 Problems during stimulation........................................................... 151 4.2 STANDARD HYDRAULIC FRACTURING SIMULATORS ............................. 158 4.2.1 Hydraulic fracturing simulators based on linear elastic fracture mechanics.................................................................................................... 164 4.2.1.1 FracproPT®: ............................................................................ 165 4.2.1.2 MFrac®:................................................................................... 173 4.2.1.3 Stimplan®:............................................................................... 179 4.2.2 Alternative approaches to hydraulic fracture propagation............ 184 4.2.2.1 Continuum Damage Mechanics (Valkó and Economides, 1993): ………………………………………………………………..184 4.2.2.2 Apparent Fracture Toughness (Shlyapobersky et al., 1988):.. 185 4.2.2.3 Crack-Layer and Process Zone Model (Chudnovski et al., 1996): ………………………………………………………………..189 4.2.2.4 Crack Tip Plasticity (Martin, 2000):....................................... 190 4.3 PROPOSED APPROACH .......................................................................... 191 4.3.1 The Discrete Element Method (DEM) ............................................ 192 4.3.2 General formulation in PFC3D........................................................ 196 4.3.2.1 Law of motion......................................................................... 203 4.3.2.2 Contact constitutive method ................................................... 204 4.3.2.3 Bonding models ...................................................................... 204 4.3.2.4 Fluid flow coupling................................................................. 209 4.3.2.5 Advantages of PFC3D .............................................................. 212 4.3.2.6 Limitations of PFC3D .............................................................. 212 3D 5 Hydraulic fracturing modeling using PFC ................214 5.1 OBJECTIVES OF THIS MODELING STUDY................................................ 215 5.2 NATURE OF THE CONSTRUCTED MODELS.............................................. 215 5.3 PROBLEM-SPECIFIC DATA SETS ............................................................ 216 5.3.1 Antler sandstone - Core model ....................................................... 217 5.3.1.1 Model particle size distribution and porosity - Validation ..... 217 5.3.1.2 Mechanical properties of the model - Validation ................... 222 5.3.1.3 Comments on the validation of the model mechanical properties ………………………………………………………………..239 viii 5.3.1.4 Hydraulic properties of the model - Validation ...................... 244 5.3.1.5 Comments of the validation of the model hydraulic properties ………………………………………………………………..251 5.3.2 Antler sandstone - Field model....................................................... 252 5.3.2.1 Testing and results.................................................................. 257 5.3.2.2 Comments on the results obtained from the field model ........ 265 6 Conclusions ...................................................................268 7 Recommendations.........................................................281 References ...........................................................................285 APPENDIX A – Fish routines used during the validation of the model mechanical properties.......................................300 APPENDIX B – Fish routines used during the validation of the model hydraulic properties ..........................................307 APPENDIX C – Fish routines used during the hydraulic fracturing tests.....................................................................335 APPENDIX D – Results of numerical experiments using the field model............................................................................347 ix List of Figures Figure 2-1. Pore volume compressibility vs. applied stress, GOM sample (after Ostermeier, 1993). .........................................................................................