Physics of Fluid Flow and Transport in Unconventional Reservoir Rocks

Behzad Ghanbarian, PhD is Associate Professor of Engineering Geology and Director of the Porous Media Research Lab in the Department of Geology, Kansas State University, Manhattan, Kansas, USA. Feng Liang, PhD is Production Technology Leader at Aramco Research Center Houston, Aramco Americas, Houston, Texas, USA. Hui-Hai Liu, PhD is a Senior Petroleum Engineering Consultant at Aramco Research Center Houston, Aramco Americas, Houston, Texas, USA.

List of Contributors xvii

Preface xxi

Introduction 1

1 Unconventional Reservoirs: Advances and Challenges 3
Behzad Ghanbarian, Feng Liang, and Hui-Hai Liu

1.1 Background 3

1.2 Advances 4

1.2.1 Wettability 4

1.2.2 Permeability 5

1.3 Challenges 7

1.3.1 Multiscale Systems 7

1.3.2 Hydrocarbon Production 9

1.3.3 Recovery Factor 9

1.3.4 Unproductive Wells 9

1.4 Concluding Remarks 11

References 11

Part I Pore-Scale Characterizations 15

2 Pore-Scale Simulations and Digital Rock Physics 17
Junjian Wang, Feifei Qin, Jianlin Zhao, Li Chen, Hari Viswanathan, and Qinjun Kang

2.1 Introduction 17

2.2 Physics of Pore-Scale Fluid Flow in Unconventional Rocks 18

2.2.1 Physics of Gas Flow 18

2.2.1.1 Gas Slippage and Knudsen Layer Effect 18

2.2.1.2 Gas Adsorption/Desorption and Surface Diffusion 20

2.2.2 Physics of Water Flow 22

2.2.3 Physics of Condensation 23

2.3 Theory of Pore-Scale Simulation Methods 23

2.3.1 The Isothermal Single-Phase Lattice Boltzmann Method 23

2.3.1.1 Bhatnagar–Gross–Krook (BGK) Collision Operator 24

2.3.1.2 The Multi-Relaxation Time (MRT)-LB Scheme 24

2.3.1.3 The Regularization Procedure 26

2.3.2 Multi-phase Lattice Boltzmann Simulation Method 27

2.3.2.1 Color-Gradient Model 27

2.3.2.2 Shan-Chen Model 28

2.3.3 Capture Fluid Slippage at the Solid Boundary 29

2.3.4 Capture the Knudsen Layer/Effective Viscosity 30

2.3.5 Capture the Adsorption/Desorption and Surface Diffusion Effects 30

2.3.5.1 Modeling of Adsorption in LBM 30

2.3.5.2 Modeling of Surface Diffusion Via LBM 31

2.4 Applications 32

2.4.1 Simulation of Gas Flow in Unconventional Reservoir Rocks 32

2.4.1.1 Gas Slippage 32

2.4.1.2 Gas Adsorption 33

2.4.1.3 Surface Diffusion of Adsorbed Gas 35

2.4.2 Simulation of Water Flow in Unconventional Reservoir Rocks 35

2.4.3 Simulation of Immiscible Two-Phase Flow 39

2.4.4 Simulation of Vapor Condensation 43

2.4.4.1 Model Validations 44

2.4.4.2 Vapor Condensation in Two Adjacent Nano-Pores 44

2.5 Conclusion 48

References 49

3 Digital Rock Modeling: A Review 53
Yuqi Wu and Pejman Tahmasebi

3.1 Introduction 53

3.2 Single-Scale Modeling of Digital Rocks 54

3.2.1 Experimental Techniques 54

3.2.1.1 Imaging Technique of Serial Sectioning 54

3.2.1.2 Laser Scanning Confocal Microscopy 54

3.2.1.3 X-Ray Computed Tomography Scanning 55

3.2.2 Computational Methods 55

3.2.2.1 Simulated Annealing 56

3.2.2.2 Markov Chain Monte Carlo 56

3.2.2.3 Sequential Indicator Simulation 56

3.2.2.4 Multiple-Point Statistics 57

3.2.2.5 Machine Learning 58

3.2.2.6 Process-Based Modeling 58

3.3 Multiscale Modeling of Digital Rocks 59

3.3.1 Multiscale Imaging Techniques 60

3.3.2 Computational Methods 60

3.3.2.1 Image Superposition 60

3.3.2.2 Pore-Network Integration 61

3.3.2.3 Image Resolution Enhancement 63

3.3.2.4 Object-Based Reconstruction 63

3.4 Conclusions and Future Perspectives 65

Acknowledgments 66

References 66

4 Scale Dependence of Permeability and Formation Factor: A Simple Scaling Law 77
Behzad Ghanbarian and Misagh Esmaeilpour

4.1 Introduction 77

4.2 Theory 78

4.2.1 Funnel Defect Approach 78

4.2.2 Application to Porous Media 79

4.3 Pore-network Simulations 80

4.4 Results and Discussion 81

4.5 Limitations 86

4.6 Conclusion 86

Acknowledgment 86

References 87

Part II Core-Scale Heterogeneity 89

5 Modeling Gas Permeability in Unconventional Reservoir Rocks 91
Behzad Ghanbarian, Feng Liang, and Hui-Hai Liu

5.1 Introduction 91

5.1.1 Theoretical Models 91

5.1.2 Pore-Network Models 92

5.1.3 Gas Transport Mechanisms 93

5.1.4 Objectives 93

5.2 Effective-Medium Theory 93

5.3 Single-Phase Gas Permeability 95

5.3.1 Gas Permeability in a Cylindrical Tube 95

5.3.2 Pore Pressure-Dependent Gas Permeability in Tight Rocks 96

5.3.3 Comparison with Experiments 96

5.3.4 Comparison with Pore-Network Simulations 98

5.3.5 Comparaison with Lattice-Boltzmann Simulations 99

5.4 Gas Relative Permeability 100

5.4.1 Hydraulic Flow in a Cylindrical Pore 100

5.4.2 Molecular Flow in a Cylindrical Pore 101

5.4.3 Total Gas Flow in a Cylindrical Pore 101

5.4.4 Gas Relative Permeability in Tight Rocks 101

5.4.5 Comparison with Experiments 102

5.4.6 Comparison with Pore-Network Simulations 107

5.5 Conclusions 108

Acknowledgment 109

References 109

6 NMR and Its Applications in Tight Unconventional Reservoir Rocks 113
Jin-Hong Chen, Mohammed Boudjatit, and Stacey M. Althaus

6.1 Introduction 113

6.2 Basic NMR Physics 113

6.2.1 Nuclear Spin 114

6.2.2 Nuclear Zeeman Splitting and NMR 114

6.2.3 Nuclear Magnetization 115

6.2.4 Bloch Equations and NMR Relaxation 116

6.2.5 Simple NMR Experiments: Free Induction Decay and CPMG Echoes 117

6.2.6 NMR Relaxation of a Pure Fluid in a Rock Pore 118

6.2.7 Measured NMR CPMG Echoes in a Formation Rock 119

6.2.8 Inversion 119

6.2.8.1 Regularized Linear Least Squares 120

6.2.8.2 Constrains of the Resulted NMR Spectrum in Inversion 120

6.2.9 Data from NMR Measurement 121

6.3 NMR Logging for Unconventional Source Rock Reservoirs 121

6.3.1 Brief Introduction of Unconventional Source Rocks 121

6.3.2 NMR Measurement of Source Rocks 122

6.3.2.1 NMR Log of a Source Rock Reservoir 122

6.3.3 Pore Size Distribution in a Shale Gas Reservoir 124

6.4 NMR Measurement of Long Whole Core 125

6.4.1 Issues of NMR Instrument for Long Sample 125

6.4.2 HSR-NMR of Long Core 126

6.4.3 Application Example 128

6.5 NMR Measurement on Drill Cuttings 130

6.5.1 Measurement Method 131

6.5.1.1 Preparation of Drill Cuttings 131

6.5.1.2 Measurements 131

6.5.2 Results 132

6.6 Conclusions 133

References 135

7 Tight Rock Permeability Measurement in Laboratory: Some Recent Progress 139
Hui-Hai Liu, Jilin Zhang, and Mohammed Boudjatit

7.1 Introduction 139

7.2 Commonly Used Laboratory Methods 140

7.2.1 Steady-State Flow Method 140

7.2.2 Pressure Pulse-Decay Method 141

7.2.3 Gas Research Institute Method 143

7.3 Simultaneous Measurement of Fracture and Matrix Permeabilities from Fractured Core Samples 144

7.3.1 Estimation of Fracture and Matrix Permeability from PPD Data for Two Flow Regimes 144

7.3.2 Mathematical Model 146

7.3.3 Method Validation and Discussion 148

7.4 Direct Measurement of Permeability-Pore Pressure Function 150

7.4.1 Knudsen Diffusion, Slippage Flow, and Effective Gas Permeability 150

7.4.2 Methodology for Directly Measuring Permeability-Pore Pressure Function 152

7.4.3 Experiments 155

7.5 Summary and Conclusions 159

References 159

8 Stress-Dependent Matrix Permeability in Unconventional Reservoir Rocks 163
Athma R. Bhandari, Peter B. Flemings, and Sebastian Ramiro-Ramirez

8.1 Introduction 163

8.2 Sample Descriptions 164

8.3 Permeability Test Program 165

8.4 Permeability Behavior with Confining Stress Cycling 166

8.5 Matrix Permeability Behavior 170

8.6 Concluding Remarks 172

Acknowledgments 174

References 174

9 Assessment of Shale Wettability from Spontaneous Imbibition Experiments 177
Zhiye Gao and Qinhong Hu

9.1 Introduction 177

9.2 Spontaneous Imbibition Theory 178

9.3 Samples and Analytical Methods 179

9.3.1 SI Experiments 179

9.3.2 Barnett Shale from United States 180

9.3.3 Silurian Longmaxi Formation and Triassic Yanchang Formation Shales from China 180

9.3.4 Jurassic Ziliujing Formation Shale from China 182

9.4 Results and Discussion 183

9.4.1 Complicated Wettability of Barnett Shale Inferred Qualitatively from SI Experiments 183

9.4.1.1 Wettability of Barnett Shale 184

9.4.1.2 Properties of Barnett Samples and Their Correlation to Wettability 186

9.4.1.3 Low Pore Connectivity to Water of Barnett Samples 187

9.4.2 More Oil-Wet Longmaxi Formation Shale and More Water-Wet Yanchang Formation Shale 188

9.4.2.1 TOC and Mineralogy 188

9.4.2.2 Pore Structure Difference Between Longmaxi and Yanchang Samples 188

9.4.2.3 Water and Oil Imbibition Experiments 191

9.4.2.4 Wettability of Longmaxi and Yanchang Shale Samples Deduced from SI Experiments 197

9.4.3 Complicated Wettability of Ziliujing Formation Shale 197

9.4.3.1 TOC and Mineralogy 197

9.4.3.2 Pore Structure 197

9.4.3.3 Water and Oil Imbibition Experiments 200

9.4.3.4 Wettability of Ziliujing Formation Shale Indicated from SI Experiments and its Correlation to Shale Pore Structure and Composition 201

9.4.4 Shale Wettability Evolution Model 201

9.5 Conclusions 204

Acknowledgments 204

References 204

10 Permeability Enhancement in Shale Induced by Desorption 209
Brandon Schwartz and Derek Elsworth

10.1 Introduction 209

10.1.1 Shale Mineralogical Characteristics 209

10.1.2 Flow Network 210

10.1.2.1 Bedding-Parallel Flow Network 211

10.1.2.2 Bedding-Perpendicular Flow Paths 212

10.2 Adsorption in Shales 214

10.2.1 Langmuir Theory 214

10.2.2 Competing Strains in Permeability Evolution 215

10.2.2.1 Poro-Sorptive Strain 215

10.2.2.2 Thermal-Sorptive Strain 218

10.3 Permeability Models for Sorptive Media 218

10.3.1 Strain Based Models 219

10.4 Competing Processes during Permeability Evolution 220

10.4.1 Resolving Competing Strains 220

10.4.2 Solving for Sorption-Induced Permeability Evolution 221

10.5 Desorption Processes Yielding Permeability Enhancement 223

10.5.1 Pressure Depletion 223

10.5.2 Lowering Partial Pressure 224

10.5.3 Sorptive Gas Injection 225

10.5.4 Desorption with Increased Temperature 225

10.6 Permeability Enhancement Due to Nitrogen Flooding 225

10.7 Discussion 226

10.8 Conclusion 228

References 229

11 Multiscale Experimental Study on Interactions Between Imbibed Stimulation Fluids and Tight Carbonate Source Rocks 235
Feng Liang, Hui-Hai Liu, and Jilin Zhang

11.1 Introduction 235

11.2 Fluid Uptake Pathways 236

11.2.1 Experimental Methods 236

11.2.1.1 Materials 236

11.2.1.2 Experimental Procedure 237

11.2.2 Results and Discussion 237

11.2.2.1 Surface Characterization 237

11.2.2.2 Spontaneous Imbibition Tests 239

11.3 Mechanical Property Change After Fluid Exposure 240

11.3.1 Experimental Methods 242

11.3.1.1 Materials 242

11.3.1.2 Experimental Procedure 242

11.3.2 Results and Discussion 243

11.3.2.1 UCS and Brazilian Test on Cylindrical Core Plugs 243

11.3.2.2 Microindentation Test 243

11.4 Morphology and Minerology Changes After Fluid Exposure 245

11.4.1 Experimental Methods 247

11.4.1.1 Materials 247

11.4.1.2 Experimental Procedure 248

11.4.2 Results and Discussion 248

11.4.2.1 SEM and EDS Mapping of Thin-Section Surface before Fluid Treatment 248

11.4.2.2 SEM and EDS Mapping of Thin-Section Surface after Fluid Treatment 251

11.4.2.3 Quantification of Dissolved Ions in the Treatment Fluids 256

11.5 Flow Property Change After Fluid Exposure 257

11.5.1 Experimental Methods 258

11.5.1.1 Materials 258

11.5.1.2 Experimental Procedure 258

11.5.2 Results and Discussion 258

11.5.2.1 Changes in Flow Characteristics 258

11.6 Conclusions 259

References 261

Part III Large-Scale Petrophysics 265

12 Effective Permeability in Fractured Reservoirs: Percolation-Based Effective-Medium Theory 267
Behzad Ghanbarian

12.1 Introduction 267

12.1.1 Percolation Theory 267

12.1.2 Effective-Medium Theory 268

12.2 Objectives 269

12.3 Percolation-Based Effective-Medium Theory 269

12.4 Comparison with Simulations 270

12.4.1 Chen et al. (2019) 270

12.4.1.1 Two-Dimensional Simulations 271

12.4.1.2 Three-Dimensional Simulations 273

12.4.2 New Three-Dimensional Simulations 274

12.5 Conclusion 275

Acknowledgment 277

References 277

13 Modeling of Fluid Flow in Complex Fracture Networks for Shale Reservoirs 281
Hongbing Xie, Xiaona Cui, Wei Yu, Chuxi Liu, Jijun Miao, and Kamy Sepehrnoori

13.1 Shale Reservoirs with Complex Fracture Networks 281

13.2 Complex Fracture Reservoir Simulation 281

13.3 Embedded Discrete Fracture Model 283

13.4 EDFM Verification 286

13.5 Well Performance Study – Base Case 290

13.6 Effect of Natural Fracture Connectivity on Well Performance 294

13.6.1 Effect of Natural Fracture Azimuth 294

13.6.2 Effect of Number of Natural Fractures 295

13.6.3 Effect of Natural Fracture Length 298

13.6.4 Effect of Number of Sets of Natural Fractures 301

13.6.5 Effect of Natural Fracture Dip Angle 305

13.7 Effect of Natural Fracture Conductivity on Well Performance 306

13.8 Conclusions 311

References 312

14 A Closed-Form Relationship for Production Rate in Stress-Sensitive Unconventional Reservoirs 315
Hui-Hai Liu, Huangye Chen, and Yanhui Han

14.1 Introduction 315

14.2 Production Rate as a Function of Time in the Linear Flow Regime Under the Constant Pressure Drawdown Condition 317

14.3 An Approximate Relationship Between Parameter A and Stress-Dependent Permeability 318

14.4 Evaluation of the Relationship Between Parameter A and Stress-Dependent Permeability 321

14.5 Equivalent State Approximation for the Variable Pressure Drawdown Conditions 327

14.6 Discussions 328

14.7 Concluding Remarks 329

Nomenclature 329

Subscript 330

Appendix 14.A Derivation of Eq. (14.22) with Integration by Parts 330

References 331

15 Sweet Spot Identification in Unconventional Shale Reservoirs 333
Rabah Mesdour, Mustafa Basri, Cenk Temizel, and Nayif Jama

15.1 Introduction 333

15.2 Reservoir Characterization 334

15.3 Sweet Spot Identification 334

15.3.1 The Method Based on Organic, Rock and Mechanical Qualities 335

15.3.2 Methods Based on Geological and Engineering Sweet Spots 337

15.3.3 Methods Based on Other Quality Indicators 340

15.3.4 Methods Based on Data Mining and Machine Learning 343

15.4 Discussion 345

15.5 Conclusion 346

References 347

Index 351