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 |  موضوع: كتاب Mechanics of Hydraulic Fracturing - Experiment, Model, and Monitoring الأحد 12 مارس 2023, 10:32 pm | |
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أحضرت لكم كتاب
Mechanics of Hydraulic Fracturing - Experiment, Model, and Monitoring
Edited by
Xi Zhang
China University of Geosciences
Wuhan, China
Bisheng Wu
Tsinghua University
Beijing, China
Diansen Yang
Wuhan University
Wuhan, China
Andrew Bunger
University of Pittsburgh
Pittsburgh, PA, USA
و المحتوى كما يلي :
Contents
List of Contributors xiii
Foreword xv
Preface xvii
1 Hydraulic Fracture Geometry from Mineback Mapping 1
R. G. Jeffrey
1.1 Introduction 1
1.2 Summary of Mapped Fracture Geometries 1
1.2.1 Fractures in Coal 1
1.2.1.1 DHM-7 Fracture 2
1.2.1.2 DDH 190 Fracture 2
1.2.2 Fractures in Hard Rock 5
1.2.2.1 Northparkes E48 Mapped Fractures 5
1.2.3 Other Mapped Fractures 7
1.3 Comparison of Mapped Fracture Geometries 7
1.3.1 Dimensionless Parameters 7
1.4 Fracture Geometry Summary 8
1.5 Conclusions 9
References 9
2 Measurements of the Evolution of the Fluid Lag in Laboratory Hydraulic Fracture Experiments in Rocks 11
Dong Liu and Brice Lecampion
2.1 Introduction 11
2.2 Materials and Methods 12
2.2.1 Materials and Experimental Set-up 12
2.2.2 Methods 12
2.2.3 Experimental Design 13
2.3 Results 14
2.3.1 MARB-005 – A HF Growth with a Fluid Lag 14
2.3.2 MARB-007 – A HF Growth during and after the Injection 15
2.3.3 GABB-002 – A Point-Load Like HF Growth 16
2.4 Discussions and Conclusions 18
2.4.1 Resolution of the Fluid Front Location 18
2.4.2 Quasi-Brittle Effects 18
2.4.3 Hydraulic Fracture Surfaces 19
2.4.4 Conclusions 21
Data Availability 21
Appendix A Determination of the Time of Fracture Initiation 21
References 22
v3 Mapping Hydraulic Fracture Growth Using Tiltmeter Monitoring Technique 25
Z. R. Chen and R. G. Jeffrey
3.1 Introduction 25
3.2 Forward Problem Formulation 26
3.2.1 Forward Model Definition 26
3.2.2 Forward Model 27
3.2.2.1 Point Source Dislocation Singularity Model 28
3.2.2.2 A General Distributed Dislocation Model 29
3.3 Bayesian Inversion Method 30
3.4 Field Applications 31
3.4.1 Inversion Results Using the Point Source Forward Model 31
3.4.2 Inversion Results Using the General Planar Forward Model 31
3.5 Conclusions 34
Acknowledgments 34
References 34
4 Experimental Observations of Hydraulic Fracturing 37
Guangqing Zhang and Dawei Zhou
4.1 Introduction 37
4.2 Experimental Setup on Laboratory-Scale 37
4.3 Laboratory Investigation of Fluid-Driven Fractures in Various Applications 38
4.3.1 Hydraulic Fracturing in Oil and Gas Reservoirs 38
4.3.1.1 Basic Issues of Breakdown Pressure and Fracture Geometry 38
4.3.1.2 Multiple Hydraulic Fracture Growth 39
4.3.1.3 Interactions Between Hydraulic Fractures and Natural Fractures 40
4.3.1.4 Fracture Propagation Through the Layered Formation 41
4.3.1.5 Nonlinear Fracturing in the Deep Reservoir 42
4.3.1.6 Cyclic Fracturing 43
4.3.2 Environmental Fracturing in a Shallow Formation 44
4.3.3 Hydraulic Stimulation in EGS 44
4.4 Conclusions and Future Work 45
References 46
5 First Field Trail and Experimental Studies on scCO2 Fracturing 51
Haiyan Zhu, Lei Tao, Shouceng Tian, and Haizhu Wang
5.1 Introduction 51
5.2 Review on scCO2 Fracturing 52
5.2.1 Shale and scCO2 Interaction 52
5.2.1.1 Microscale Physical Changes 52
5.2.1.2 Microscale Chemical Changes 52
5.2.1.3 Macroscale Mechanical Changes 53
5.2.1.4 Conclusions on the Experiments on Shale and scCO2 Interaction 54
5.2.2 Experiments and Numerical Simulations on scCO2 Fracturing 54
5.2.2.1 Experiments on scCO2 Fracturing 54
5.2.2.2 Numerical Simulations on scCO2 Fracturing 57
5.3 A Field Trail on scCO2 Fracturing of Continental Shale in Yanchang Oil Field 57
5.3.1 scCO2 Fracturing Technology 57
5.3.2 scCO2 Fracturing Field Test 58
5.3.2.1 Reservoir Properties of Test Wells 58
5.3.2.2 Fracturing Process and Operation Parameters 58
5.3.3 Field Test Results and Analysis 59
5.3.3.1 Microseismic Monitoring and Inversion of Fracture Geometry 59
vi Contents5.3.3.2 Production Data 60
5.4 Challenges in scCO2 Fracturing 60
5.4.1 scCO2 Fracturing Mechanism Is Still Not Clear 60
5.4.2 Challenges in Proppants Carrying 60
5.4.3 Challenge on the Predicting and Monitoring CO2 Phase 61
5.4.4 Lack of Specialized Equipment for scCO2 Fracturing 61
5.5 Conclusions 61
Acknowledgments 61
References 61
6 An Unstructured Moving Element Mesh for Hydraulic Fracture Modeling 65
John Napier and Emmanuel Detournay
6.1 Introduction 65
6.2 Discrete Model of a Planar Hydraulic Fracture 65
6.2.1 Unstructured Mesh 66
6.2.2 Discrete Elasticity Equation 66
6.2.3 Discretized Lubrication Equations for Channel Elements 67
6.2.4 Tip Elements 67
6.3 Time-Marching Algorithm 67
6.3.1 Iteration Loops 68
6.3.2 Local Front Update 68
6.3.3 Generation of a New Ring of Tip Elements 68
6.3.4 Crack Surface Remeshing 69
6.3.5 General Solution Algorithm Logic 69
6.4 Numerical Simulations: Stress Barriers 70
6.4.1 Description of Experiment 70
6.4.2 Numerical Simulations (no Remeshing) 70
6.4.3 Comparison with Experimental Results and Other Simulations 71
6.4.4 Illustration and Assessment of the Element Re-Meshing Strategy 71
6.5 Conclusions 73
Acknowledgments 73
References 73
7 Study of Hydraulic Fracture Interference with a Lattice Model 75
C. Detournay, B. Damjanac, M. Torres, and Y. Han
7.1 Introduction 75
7.2 XSite Code Overview 75
7.3 Numerical Studies of Fracture Interference 75
7.3.1 Interaction of a Hydraulic Fracture with a Natural Fracture 76
7.3.2 Interaction of Two Hydraulic Fractures 76
7.3.2.1 Numerical Study 76
7.3.2.2 Interpretation of Results 78
7.3.3 Interaction of Hydraulic Fractures in Injection of Multiple Clusters 79
7.3.4 Interaction of Hydraulic Fractures in Fractured Medium 81
7.3.5 Interaction of Hydraulic Fractures in Zipper-Stage Injection 83
7.4 Afterword 83
References 85
8 The Tipping Point: How Tip Asymptotics Can Enhance Numerical Modeling of Hydraulic Fracture Evolution 87
A. Peirce
8.1 Introduction 87
8.2 Mathematical Model 87
Contents vii8.2.1 Assumptions 87
8.2.2 Governing Equation 88
8.2.2.1 Elasticity 88
8.2.2.2 Fluid Transport 88
8.2.2.3 Boundary and Propagation Conditions 88
8.2.2.4 Tip Asymptotics, Vertex Solutions, and Generalized Asymptotes 89
8.3 Discretization, Coupled Equations, and the Multiscale ILSA Scheme to Locate the Free Boundary 91
8.3.1 Discretization 91
8.3.1.1 Displacement Discontinuity Formulation for Planar Fractures 91
8.3.2 Locating the Free Boundary Using the Implicit Level Set Algorithm (ILSA) 92
8.4 Numerical Results 95
8.4.1 Symmetric Stress Barrier: m-Vertex Solution vs Experiment and the Effect of Toughness 95
8.4.2 A Stress Drop: Distinct Propagation Regimes Along the Periphery 95
8.5 Conclusions 95
8.6 Acknowledgment 97
References 97
9 Plasticity: A Mechanism for Hydraulic Fracture Height Containment 99
Panos Papanastasiou
9.1 Introduction 99
9.2 The Dependence of the Effective Fracture Toughness on Propagation Direction 100
9.3 Effective Fracture Toughness vs. Closure Stress 101
9.4 A New Brittleness Index Defines Fracture Containment 102
9.5 Conclusions 103
Acknowledgments 104
References 104
10 Turbulent Flow Effects on Propagation of Radial Hydraulic Fracture in Permeable Rock 107
E.A. Kanin, D.I. Garagash, and A.A. Osiptsov
10.1 Introduction 107
10.2 Model Formulation 108
10.2.1 Problem Definition 108
10.2.2 Governing Equations 109
10.2.2.1 Crack Elasticity 109
10.2.2.2 Fluid Flow 109
10.2.2.3 Fracture Propagation 110
10.2.2.4 Boundary Conditions 110
10.2.2.5 Global Fluid Volume Balance 110
10.3 Solution Approach 111
10.4 Solution Examples for Typical Field Applications 112
10.5 Limiting Propagation Regimes 115
10.6 Normalization of the Governing Equations 118
10.7 Problem Parameter Space Analyses 119
10.7.1 Zero Leak-Off Case (Impermeable Rock) 120
10.7.2 Nonzero Leak-Off Case (Permeable Rock) 121
10.8 Conclusions 122
Acknowledgments 124
References 125
11 Analysis of a Constant Height Hydraulic Fracture 127
E.V. Dontsov
11.1 Introduction 127
viii Contents11.2 Governing Equations 128
11.3 Tip Region 129
11.4 Vertex Solutions 132
11.4.1 Storage Viscosity 132
11.4.2 Leak-off Viscosity 133
11.4.3 Storage Toughness 133
11.4.4 Leak-off Toughness 133
11.5 Full Solution 134
11.6 Application Examples 136
11.7 Summary 137
References 137
12 Discrete Element Modeling of Hydraulic Fracturing 141
Mengli Li and Fengshou Zhang
12.1 Introduction 141
12.2 Discrete Element Modeling of Hydraulic Fracturing 142
12.3 Hydraulic Fracture Interacting with Natural Fractures 142
12.3.1 Hybrid Discrete-Continuum Method 143
12.3.2 Model Calibration for a Hydraulic Fracture in Intact Rock 144
12.3.3 Orthogonal Crossing 145
12.3.3.1 Effects of Stress Ratio and Friction of Natural Fractures 145
12.3.3.2 Effect of Strength (Toughness) Contrast 147
12.3.3.3 Effect of Stiffness (Modulus) Contrast 149
12.3.4 Non-Orthogonal Crossing 150
12.3.5 Fracturing Complexity 151
12.4 DEM Modeling of Supercritical Carbon Dioxide Fracturing 153
12.4.1 New Algorithm for the Toughness-Dominated Regime 153
12.4.2 Numerical Model Setup 154
12.4.2.1 Model Description 154
12.4.2.2 Model Verification 156
12.4.3 Hydraulic Fracturing in Intact Rock Sample 157
12.4.4 Hydraulic Fracturing in Fractured Rock Sample 161
12.5 DEM Modeling of Fluid Injection into Dense Granular Media 163
12.5.1 Background and Experimental Motivation 163
12.5.2 Model Setup 165
12.5.3 Effect of the Injection Rate 166
12.5.4 Dimensionless Time Scaling 168
12.5.5 Energy Partition 170
12.6 Discussion 171
12.7 Conclusions 171
References 172
13 Interaction of a Hydraulic Fracture with Natural Fractures of Lesser Height and Weak Bedding Interfaces as a
Possible Mechanism for Fracture Swarms 177
Xiaowei Weng and Olga Kresse
13.1 Introduction 177
13.2 Possible Mechanisms for Fracture Bifurcation 179
13.3 Interaction of Closely Spaced Parallel Fractures 182
13.3.1 Fracture Tip Extension in Overlapped Region 182
13.3.2 Instability of Closely Spaced Parallel Hydraulic Fractures – Shared Inlet 183
13.3.3 Instability of Closely Spaced Parallel Hydraulic Fractures – Separate Inlets 184
13.4 Possible Mechanisms for Creating Fracture Swarms 185
Contents ix13.5 Conclusions 188
References 189
14 Hydraulic Fracturing Mechanisms Leading to Self-Organization Within Dyke Swarms 193
Andrew. P. Bunger, D. Gunaydin, S. T. Thiele, and A. R. Cruden
14.1 Introduction 193
14.2 Swarm Morphology and Fundamental Drivers 193
14.3 Dyke Swarm Model and Energetics 194
14.4 Alignment 196
14.5 Avoidance 197
14.6 Stress Shadow 197
14.7 Stress Plugs 199
14.8 Attraction 199
14.9 Emergent Spacing 200
14.10 Simulating Dyke Swarm Assembly 201
14.11 Conclusions 202
Acknowledgments 203
References 203
15 Numerical Simulation of Thermal Fracturing During Heat Extraction from a Closed-Loop Circulation Enhanced
Geothermal System 207
Z. Lei, Bisheng Wu, and Z. Chen
15.1 Introduction 207
15.2 Mathematical Formulation 208
15.2.1 Problem Description 208
15.2.2 Governing Equations of Coupled Thermoelastic Model 209
15.2.2.1 Fluid Flow 209
15.2.2.2 Rock Deformation 209
15.2.2.3 Fracture Initiation and Propagation 210
15.2.2.4 Thermal Transport Through Fluid Flow 211
15.2.2.5 Heat Transfer in Rock Matrix 211
15.2.3 Boundary and Initial Conditions 211
15.3 Solution Methodology and Computational Procedures 211
15.3.1 Coupled Fluid-Fracture Solver 211
15.3.1.1 Weak Form and FEM Discretization 211
15.3.1.2 Extended Finite Element Approximation 212
15.3.2 Coupled Fluid-Thermal Solver 213
15.3.3 Solution Strategy 213
15.4 Numerical Results 214
15.4.1 Fluid Flow and Production Temperature 214
15.4.2 Temperature Distribution in Rock Formation 216
15.4.3 Fracture Propagation 216
15.4.3.1 Single Fracture Case 216
15.4.3.2 Double Fracture Case 220
15.5 Conclusions 221
References 221
16 Multiple Hydraulic Fractures Growth from a Highly Deviated Well: A XFEM Study 225
Yun Zhou and Diansen Yang
16.1 Introduction 225
16.2 Problem Formulation 227
16.2.1 Governing Equations 228
x Contents16.2.1.1 Solid Deformation 228
16.2.1.2 Fluid Flow in Matrix 229
16.2.1.3 Fluid Flow in Fractures 229
16.2.1.4 Flow Rate Division to Multiple Fractures 229
16.2.1.5 Fracture Propagation 229
16.2.2 Weak Forms 230
16.3 Numerical Method 230
16.3.1 XFEM Approximation of u(x, t) and p(x, t) 230
16.3.2 Spatial and Time Discretization 231
16.3.3 Solution Strategy 231
16.3.3.1 Solution of HM-Coupled Equations 231
16.3.3.2 Solution of Flow Rate Division 231
16.4 Numerical Results 232
16.4.1 Verification of the Model 232
16.4.2 Multi-Cluster Hydraulic Fracturing in High-Angle Well 233
16.4.2.1 Model Set-up 234
16.4.2.2 Operational Parameters 235
16.4.2.3 Deviation Angle 236
16.4.2.4 Fracture Spacing 239
16.4.2.5 Fracture Placement 240
16.4.2.6 Fracture Number 241
16.5 Discussion 245
16.6 Conclusions 245
Appendix 16.A Dimensionless Toughness κ 245
Appendix 16.B Dimensionless Parameter Gm 246
Appendix 16.C Dimensionless Variability Coefficient Cv 246
References 246
17 Hydraulic Fracturing-Induced Slip on a Permeable Fault 251
Xi. Zhang, R. G. Jeffrey, and J. Yang
17.1 Introduction 251
17.2 Model Setup 252
17.3 Summary of Modeling Results 254
17.3.1 Fully Closed Fractures 254
17.3.1.1 Constant Fault Permeability 254
17.3.1.2 Enhanced Fault Permeability 254
17.3.1.3 Fault Permeability Reduction 255
17.3.2 Partially Opened Fracture 256
17.3.2.1 Planar Fault 256
17.3.2.2 Nonplanar Fault 256
17.4 Radiated Energy 256
17.5 Conclusions and Future Work 258
Acknowledgment 259
References 259
Index 263
Index
Note: Page numbers in italics refer to figures; page numbers in bold refer to tables.
a
ABAQUS 208–209, 212–213, 221
acoustic emission (AE) 38–39, 45
acoustic imaging system 12
AE, see acoustic emission
alignment, dyke swarms 196–197
ANSYS 207
attraction, dyke swarms 199–200
avoidance, dyke swarms 197
b
Bayesian inversion method,
tiltmeter 30–31
bedding interfaces, fracture
swarms 182
BEM, see boundary element method
bifurcation, fracture
swarms 179–182, 180
boundaries, geothermal 211
boundary conditions 88–89
constant height fracture 129–131
HW, HAW 228
radial hydraulic fracture 110
seismic events 253–254
boundary element method 73, 185,
208, 254
breakdown pressure 38, 38–39
brittleness index 102–103, 103
c
carbon dioxide fracturing, DEM
modeling 153–163
Carrara marble 12, 12, 13
channel elements, unstructured
mesh 66, 66–67
China University of Petroleum at
Beijing 38
closed fractures 254–256
closure stress 101–102
coal 1
coalbed methane 1
coalescent fluid 89
coal fractures 1–5, 2
complex fracture model,
Kresse 177–178, 178
COMSOL Multiphysics 207
constant height 127–139, 128
boundary condition 129–131
leak-off, dimensionless 136
leak-off toughness 133–134
leak-off viscosity 133
linear elastic fracture mechanics
(LEFM) 127
parametric space 130, 135
PKN fracture 128–130, 130, 134–136
plane strain 127
storage toughness 133
storage viscosity 132
tip region 129–131, 130
transitions 131
vertex solutions 132–134, 136
containment, fracture 102–103
CO2 phase, scCO2 fracturing 61
coupled fluid-thermal
solver 213–214, 214
crack elasticity equation 109
crack surface remeshing 69
crystalline rock 1
cyclic fracturing 43, 43
d
DDH 190 fractures 2–5, 4, 5, 8
DDM, see displacement discontinuity
method
degrees of freedom 213, 226, 230
DEM 141–175
carbon dioxide fracturing, DEM
modeling 153–163
discrete/continuum modeling 143,
143–144
discrete element modeling 142
energy components 170–171,
170–171
Fast Lagrangian Analysis of Continua
(FLAC) 143
fluid injection, DEM
modeling 163–171
fluid viscosity 164
fractured rock 161–163, 162,
163, 172
friction 145–147
glycerin solutions 164
granular media 141, 163–171
injection rate 166, 166–168,
167–168, 172
material inhomogeneity 172
natural fracture
intersections 151–153,
152–153, 172
natural fractures 142–153, 144, 144,
147, 155, 171
non-orthogonal
crossing 150–151, 151
numerical model 154–157, 155–156,
157, 160
offset crossing 148
orthogonal crossing 145–146, 146,
148, 172
orthogonal natural
fractures 145–146, 146–147
particle flow code (PFC) 143–144,
144, 144
Contents
List of Contributors xiii
Foreword xv
Preface xvii
1 Hydraulic Fracture Geometry from Mineback Mapping 1
R. G. Jeffrey
1.1 Introduction 1
1.2 Summary of Mapped Fracture Geometries 1
1.2.1 Fractures in Coal 1
1.2.1.1 DHM-7 Fracture 2
1.2.1.2 DDH 190 Fracture 2
1.2.2 Fractures in Hard Rock 5
1.2.2.1 Northparkes E48 Mapped Fractures 5
1.2.3 Other Mapped Fractures 7
1.3 Comparison of Mapped Fracture Geometries 7
1.3.1 Dimensionless Parameters 7
1.4 Fracture Geometry Summary 8
1.5 Conclusions 9
References 9
2 Measurements of the Evolution of the Fluid Lag in Laboratory Hydraulic Fracture Experiments in Rocks 11
Dong Liu and Brice Lecampion
2.1 Introduction 11
2.2 Materials and Methods 12
2.2.1 Materials and Experimental Set-up 12
2.2.2 Methods 12
2.2.3 Experimental Design 13
2.3 Results 14
2.3.1 MARB-005 – A HF Growth with a Fluid Lag 14
2.3.2 MARB-007 – A HF Growth during and after the Injection 15
2.3.3 GABB-002 – A Point-Load Like HF Growth 16
2.4 Discussions and Conclusions 18
2.4.1 Resolution of the Fluid Front Location 18
2.4.2 Quasi-Brittle Effects 18
2.4.3 Hydraulic Fracture Surfaces 19
2.4.4 Conclusions 21
Data Availability 21
Appendix A Determination of the Time of Fracture Initiation 21
References 22
v3 Mapping Hydraulic Fracture Growth Using Tiltmeter Monitoring Technique 25
Z. R. Chen and R. G. Jeffrey
3.1 Introduction 25
3.2 Forward Problem Formulation 26
3.2.1 Forward Model Definition 26
3.2.2 Forward Model 27
3.2.2.1 Point Source Dislocation Singularity Model 28
3.2.2.2 A General Distributed Dislocation Model 29
3.3 Bayesian Inversion Method 30
3.4 Field Applications 31
3.4.1 Inversion Results Using the Point Source Forward Model 31
3.4.2 Inversion Results Using the General Planar Forward Model 31
3.5 Conclusions 34
Acknowledgments 34
References 34
4 Experimental Observations of Hydraulic Fracturing 37
Guangqing Zhang and Dawei Zhou
4.1 Introduction 37
4.2 Experimental Setup on Laboratory-Scale 37
4.3 Laboratory Investigation of Fluid-Driven Fractures in Various Applications 38
4.3.1 Hydraulic Fracturing in Oil and Gas Reservoirs 38
4.3.1.1 Basic Issues of Breakdown Pressure and Fracture Geometry 38
4.3.1.2 Multiple Hydraulic Fracture Growth 39
4.3.1.3 Interactions Between Hydraulic Fractures and Natural Fractures 40
4.3.1.4 Fracture Propagation Through the Layered Formation 41
4.3.1.5 Nonlinear Fracturing in the Deep Reservoir 42
4.3.1.6 Cyclic Fracturing 43
4.3.2 Environmental Fracturing in a Shallow Formation 44
4.3.3 Hydraulic Stimulation in EGS 44
4.4 Conclusions and Future Work 45
References 46
5 First Field Trail and Experimental Studies on scCO2 Fracturing 51
Haiyan Zhu, Lei Tao, Shouceng Tian, and Haizhu Wang
5.1 Introduction 51
5.2 Review on scCO2 Fracturing 52
5.2.1 Shale and scCO2 Interaction 52
5.2.1.1 Microscale Physical Changes 52
5.2.1.2 Microscale Chemical Changes 52
5.2.1.3 Macroscale Mechanical Changes 53
5.2.1.4 Conclusions on the Experiments on Shale and scCO2 Interaction 54
5.2.2 Experiments and Numerical Simulations on scCO2 Fracturing 54
5.2.2.1 Experiments on scCO2 Fracturing 54
5.2.2.2 Numerical Simulations on scCO2 Fracturing 57
5.3 A Field Trail on scCO2 Fracturing of Continental Shale in Yanchang Oil Field 57
5.3.1 scCO2 Fracturing Technology 57
5.3.2 scCO2 Fracturing Field Test 58
5.3.2.1 Reservoir Properties of Test Wells 58
5.3.2.2 Fracturing Process and Operation Parameters 58
5.3.3 Field Test Results and Analysis 59
5.3.3.1 Microseismic Monitoring and Inversion of Fracture Geometry 59
vi Contents5.3.3.2 Production Data 60
5.4 Challenges in scCO2 Fracturing 60
5.4.1 scCO2 Fracturing Mechanism Is Still Not Clear 60
5.4.2 Challenges in Proppants Carrying 60
5.4.3 Challenge on the Predicting and Monitoring CO2 Phase 61
5.4.4 Lack of Specialized Equipment for scCO2 Fracturing 61
5.5 Conclusions 61
Acknowledgments 61
References 61
6 An Unstructured Moving Element Mesh for Hydraulic Fracture Modeling 65
John Napier and Emmanuel Detournay
6.1 Introduction 65
6.2 Discrete Model of a Planar Hydraulic Fracture 65
6.2.1 Unstructured Mesh 66
6.2.2 Discrete Elasticity Equation 66
6.2.3 Discretized Lubrication Equations for Channel Elements 67
6.2.4 Tip Elements 67
6.3 Time-Marching Algorithm 67
6.3.1 Iteration Loops 68
6.3.2 Local Front Update 68
6.3.3 Generation of a New Ring of Tip Elements 68
6.3.4 Crack Surface Remeshing 69
6.3.5 General Solution Algorithm Logic 69
6.4 Numerical Simulations: Stress Barriers 70
6.4.1 Description of Experiment 70
6.4.2 Numerical Simulations (no Remeshing) 70
6.4.3 Comparison with Experimental Results and Other Simulations 71
6.4.4 Illustration and Assessment of the Element Re-Meshing Strategy 71
6.5 Conclusions 73
Acknowledgments 73
References 73
7 Study of Hydraulic Fracture Interference with a Lattice Model 75
C. Detournay, B. Damjanac, M. Torres, and Y. Han
7.1 Introduction 75
7.2 XSite Code Overview 75
7.3 Numerical Studies of Fracture Interference 75
7.3.1 Interaction of a Hydraulic Fracture with a Natural Fracture 76
7.3.2 Interaction of Two Hydraulic Fractures 76
7.3.2.1 Numerical Study 76
7.3.2.2 Interpretation of Results 78
7.3.3 Interaction of Hydraulic Fractures in Injection of Multiple Clusters 79
7.3.4 Interaction of Hydraulic Fractures in Fractured Medium 81
7.3.5 Interaction of Hydraulic Fractures in Zipper-Stage Injection 83
7.4 Afterword 83
References 85
8 The Tipping Point: How Tip Asymptotics Can Enhance Numerical Modeling of Hydraulic Fracture Evolution 87
A. Peirce
8.1 Introduction 87
8.2 Mathematical Model 87
Contents vii8.2.1 Assumptions 87
8.2.2 Governing Equation 88
8.2.2.1 Elasticity 88
8.2.2.2 Fluid Transport 88
8.2.2.3 Boundary and Propagation Conditions 88
8.2.2.4 Tip Asymptotics, Vertex Solutions, and Generalized Asymptotes 89
8.3 Discretization, Coupled Equations, and the Multiscale ILSA Scheme to Locate the Free Boundary 91
8.3.1 Discretization 91
8.3.1.1 Displacement Discontinuity Formulation for Planar Fractures 91
8.3.2 Locating the Free Boundary Using the Implicit Level Set Algorithm (ILSA) 92
8.4 Numerical Results 95
8.4.1 Symmetric Stress Barrier: m-Vertex Solution vs Experiment and the Effect of Toughness 95
8.4.2 A Stress Drop: Distinct Propagation Regimes Along the Periphery 95
8.5 Conclusions 95
8.6 Acknowledgment 97
References 97
9 Plasticity: A Mechanism for Hydraulic Fracture Height Containment 99
Panos Papanastasiou
9.1 Introduction 99
9.2 The Dependence of the Effective Fracture Toughness on Propagation Direction 100
9.3 Effective Fracture Toughness vs. Closure Stress 101
9.4 A New Brittleness Index Defines Fracture Containment 102
9.5 Conclusions 103
Acknowledgments 104
References 104
10 Turbulent Flow Effects on Propagation of Radial Hydraulic Fracture in Permeable Rock 107
E.A. Kanin, D.I. Garagash, and A.A. Osiptsov
10.1 Introduction 107
10.2 Model Formulation 108
10.2.1 Problem Definition 108
10.2.2 Governing Equations 109
10.2.2.1 Crack Elasticity 109
10.2.2.2 Fluid Flow 109
10.2.2.3 Fracture Propagation 110
10.2.2.4 Boundary Conditions 110
10.2.2.5 Global Fluid Volume Balance 110
10.3 Solution Approach 111
10.4 Solution Examples for Typical Field Applications 112
10.5 Limiting Propagation Regimes 115
10.6 Normalization of the Governing Equations 118
10.7 Problem Parameter Space Analyses 119
10.7.1 Zero Leak-Off Case (Impermeable Rock) 120
10.7.2 Nonzero Leak-Off Case (Permeable Rock) 121
10.8 Conclusions 122
Acknowledgments 124
References 125
11 Analysis of a Constant Height Hydraulic Fracture 127
E.V. Dontsov
11.1 Introduction 127
viii Contents11.2 Governing Equations 128
11.3 Tip Region 129
11.4 Vertex Solutions 132
11.4.1 Storage Viscosity 132
11.4.2 Leak-off Viscosity 133
11.4.3 Storage Toughness 133
11.4.4 Leak-off Toughness 133
11.5 Full Solution 134
11.6 Application Examples 136
11.7 Summary 137
References 137
12 Discrete Element Modeling of Hydraulic Fracturing 141
Mengli Li and Fengshou Zhang
12.1 Introduction 141
12.2 Discrete Element Modeling of Hydraulic Fracturing 142
12.3 Hydraulic Fracture Interacting with Natural Fractures 142
12.3.1 Hybrid Discrete-Continuum Method 143
12.3.2 Model Calibration for a Hydraulic Fracture in Intact Rock 144
12.3.3 Orthogonal Crossing 145
12.3.3.1 Effects of Stress Ratio and Friction of Natural Fractures 145
12.3.3.2 Effect of Strength (Toughness) Contrast 147
12.3.3.3 Effect of Stiffness (Modulus) Contrast 149
12.3.4 Non-Orthogonal Crossing 150
12.3.5 Fracturing Complexity 151
12.4 DEM Modeling of Supercritical Carbon Dioxide Fracturing 153
12.4.1 New Algorithm for the Toughness-Dominated Regime 153
12.4.2 Numerical Model Setup 154
12.4.2.1 Model Description 154
12.4.2.2 Model Verification 156
12.4.3 Hydraulic Fracturing in Intact Rock Sample 157
12.4.4 Hydraulic Fracturing in Fractured Rock Sample 161
12.5 DEM Modeling of Fluid Injection into Dense Granular Media 163
12.5.1 Background and Experimental Motivation 163
12.5.2 Model Setup 165
12.5.3 Effect of the Injection Rate 166
12.5.4 Dimensionless Time Scaling 168
12.5.5 Energy Partition 170
12.6 Discussion 171
12.7 Conclusions 171
References 172
13 Interaction of a Hydraulic Fracture with Natural Fractures of Lesser Height and Weak Bedding Interfaces as a
Possible Mechanism for Fracture Swarms 177
Xiaowei Weng and Olga Kresse
13.1 Introduction 177
13.2 Possible Mechanisms for Fracture Bifurcation 179
13.3 Interaction of Closely Spaced Parallel Fractures 182
13.3.1 Fracture Tip Extension in Overlapped Region 182
13.3.2 Instability of Closely Spaced Parallel Hydraulic Fractures – Shared Inlet 183
13.3.3 Instability of Closely Spaced Parallel Hydraulic Fractures – Separate Inlets 184
13.4 Possible Mechanisms for Creating Fracture Swarms 185
Contents ix13.5 Conclusions 188
References 189
14 Hydraulic Fracturing Mechanisms Leading to Self-Organization Within Dyke Swarms 193
Andrew. P. Bunger, D. Gunaydin, S. T. Thiele, and A. R. Cruden
14.1 Introduction 193
14.2 Swarm Morphology and Fundamental Drivers 193
14.3 Dyke Swarm Model and Energetics 194
14.4 Alignment 196
14.5 Avoidance 197
14.6 Stress Shadow 197
14.7 Stress Plugs 199
14.8 Attraction 199
14.9 Emergent Spacing 200
14.10 Simulating Dyke Swarm Assembly 201
14.11 Conclusions 202
Acknowledgments 203
References 203
15 Numerical Simulation of Thermal Fracturing During Heat Extraction from a Closed-Loop Circulation Enhanced
Geothermal System 207
Z. Lei, Bisheng Wu, and Z. Chen
15.1 Introduction 207
15.2 Mathematical Formulation 208
15.2.1 Problem Description 208
15.2.2 Governing Equations of Coupled Thermoelastic Model 209
15.2.2.1 Fluid Flow 209
15.2.2.2 Rock Deformation 209
15.2.2.3 Fracture Initiation and Propagation 210
15.2.2.4 Thermal Transport Through Fluid Flow 211
15.2.2.5 Heat Transfer in Rock Matrix 211
15.2.3 Boundary and Initial Conditions 211
15.3 Solution Methodology and Computational Procedures 211
15.3.1 Coupled Fluid-Fracture Solver 211
15.3.1.1 Weak Form and FEM Discretization 211
15.3.1.2 Extended Finite Element Approximation 212
15.3.2 Coupled Fluid-Thermal Solver 213
15.3.3 Solution Strategy 213
15.4 Numerical Results 214
15.4.1 Fluid Flow and Production Temperature 214
15.4.2 Temperature Distribution in Rock Formation 216
15.4.3 Fracture Propagation 216
15.4.3.1 Single Fracture Case 216
15.4.3.2 Double Fracture Case 220
15.5 Conclusions 221
References 221
16 Multiple Hydraulic Fractures Growth from a Highly Deviated Well: A XFEM Study 225
Yun Zhou and Diansen Yang
16.1 Introduction 225
16.2 Problem Formulation 227
16.2.1 Governing Equations 228
x Contents16.2.1.1 Solid Deformation 228
16.2.1.2 Fluid Flow in Matrix 229
16.2.1.3 Fluid Flow in Fractures 229
16.2.1.4 Flow Rate Division to Multiple Fractures 229
16.2.1.5 Fracture Propagation 229
16.2.2 Weak Forms 230
16.3 Numerical Method 230
16.3.1 XFEM Approximation of u(x, t) and p(x, t) 230
16.3.2 Spatial and Time Discretization 231
16.3.3 Solution Strategy 231
16.3.3.1 Solution of HM-Coupled Equations 231
16.3.3.2 Solution of Flow Rate Division 231
16.4 Numerical Results 232
16.4.1 Verification of the Model 232
16.4.2 Multi-Cluster Hydraulic Fracturing in High-Angle Well 233
16.4.2.1 Model Set-up 234
16.4.2.2 Operational Parameters 235
16.4.2.3 Deviation Angle 236
16.4.2.4 Fracture Spacing 239
16.4.2.5 Fracture Placement 240
16.4.2.6 Fracture Number 241
16.5 Discussion 245
16.6 Conclusions 245
Appendix 16.A Dimensionless Toughness κ 245
Appendix 16.B Dimensionless Parameter Gm 246
Appendix 16.C Dimensionless Variability Coefficient Cv 246
References 246
17 Hydraulic Fracturing-Induced Slip on a Permeable Fault 251
Xi. Zhang, R. G. Jeffrey, and J. Yang
17.1 Introduction 251
17.2 Model Setup 252
17.3 Summary of Modeling Results 254
17.3.1 Fully Closed Fractures 254
17.3.1.1 Constant Fault Permeability 254
17.3.1.2 Enhanced Fault Permeability 254
17.3.1.3 Fault Permeability Reduction 255
17.3.2 Partially Opened Fracture 256
17.3.2.1 Planar Fault 256
17.3.2.2 Nonplanar Fault 256
17.4 Radiated Energy 256
17.5 Conclusions and Future Work 258
Acknowledgment 259
References 259
Index 263
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