Physics of Fluid Flow and Transport in Unconventional Reservoir Rocks

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