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 xviiPreface xxiIntroduction 11 Unconventional Reservoirs: Advances and Challenges 3Behzad Ghanbarian, Feng Liang, and Hui-Hai Liu1.1 Background 31.2 Advances 41.2.1 Wettability 41.2.2 Permeability 51.3 Challenges 71.3.1 Multiscale Systems 71.3.2 Hydrocarbon Production 91.3.3 Recovery Factor 91.3.4 Unproductive Wells 91.4 Concluding Remarks 11References 11Part I Pore-Scale Characterizations 152 Pore-Scale Simulations and Digital Rock Physics 17Junjian Wang, Feifei Qin, Jianlin Zhao, Li Chen, Hari Viswanathan, and Qinjun Kang2.1 Introduction 172.2 Physics of Pore-Scale Fluid Flow in Unconventional Rocks 182.2.1 Physics of Gas Flow 182.2.1.1 Gas Slippage and Knudsen Layer Effect 182.2.1.2 Gas Adsorption/Desorption and Surface Diffusion 202.2.2 Physics of Water Flow 222.2.3 Physics of Condensation 232.3 Theory of Pore-Scale Simulation Methods 232.3.1 The Isothermal Single-Phase Lattice Boltzmann Method 232.3.1.1 Bhatnagar–Gross–Krook (BGK) Collision Operator 242.3.1.2 The Multi-Relaxation Time (MRT)-LB Scheme 242.3.1.3 The Regularization Procedure 262.3.2 Multi-phase Lattice Boltzmann Simulation Method 272.3.2.1 Color-Gradient Model 272.3.2.2 Shan-Chen Model 282.3.3 Capture Fluid Slippage at the Solid Boundary 292.3.4 Capture the Knudsen Layer/Effective Viscosity 302.3.5 Capture the Adsorption/Desorption and Surface Diffusion Effects 302.3.5.1 Modeling of Adsorption in LBM 302.3.5.2 Modeling of Surface Diffusion Via LBM 312.4 Applications 322.4.1 Simulation of Gas Flow in Unconventional Reservoir Rocks 322.4.1.1 Gas Slippage 322.4.1.2 Gas Adsorption 332.4.1.3 Surface Diffusion of Adsorbed Gas 352.4.2 Simulation of Water Flow in Unconventional Reservoir Rocks 352.4.3 Simulation of Immiscible Two-Phase Flow 392.4.4 Simulation of Vapor Condensation 432.4.4.1 Model Validations 442.4.4.2 Vapor Condensation in Two Adjacent Nano-Pores 442.5 Conclusion 48References 493 Digital Rock Modeling: A Review 53Yuqi Wu and Pejman Tahmasebi3.1 Introduction 533.2 Single-Scale Modeling of Digital Rocks 543.2.1 Experimental Techniques 543.2.1.1 Imaging Technique of Serial Sectioning 543.2.1.2 Laser Scanning Confocal Microscopy 543.2.1.3 X-Ray Computed Tomography Scanning 553.2.2 Computational Methods 553.2.2.1 Simulated Annealing 563.2.2.2 Markov Chain Monte Carlo 563.2.2.3 Sequential Indicator Simulation 563.2.2.4 Multiple-Point Statistics 573.2.2.5 Machine Learning 583.2.2.6 Process-Based Modeling 583.3 Multiscale Modeling of Digital Rocks 593.3.1 Multiscale Imaging Techniques 603.3.2 Computational Methods 603.3.2.1 Image Superposition 603.3.2.2 Pore-Network Integration 613.3.2.3 Image Resolution Enhancement 633.3.2.4 Object-Based Reconstruction 633.4 Conclusions and Future Perspectives 65Acknowledgments 66References 664 Scale Dependence of Permeability and Formation Factor: A Simple Scaling Law 77Behzad Ghanbarian and Misagh Esmaeilpour4.1 Introduction 774.2 Theory 784.2.1 Funnel Defect Approach 784.2.2 Application to Porous Media 794.3 Pore-network Simulations 804.4 Results and Discussion 814.5 Limitations 864.6 Conclusion 86Acknowledgment 86References 87Part II Core-Scale Heterogeneity 895 Modeling Gas Permeability in Unconventional Reservoir Rocks 91Behzad Ghanbarian, Feng Liang, and Hui-Hai Liu5.1 Introduction 915.1.1 Theoretical Models 915.1.2 Pore-Network Models 925.1.3 Gas Transport Mechanisms 935.1.4 Objectives 935.2 Effective-Medium Theory 935.3 Single-Phase Gas Permeability 955.3.1 Gas Permeability in a Cylindrical Tube 955.3.2 Pore Pressure-Dependent Gas Permeability in Tight Rocks 965.3.3 Comparison with Experiments 965.3.4 Comparison with Pore-Network Simulations 985.3.5 Comparaison with Lattice-Boltzmann Simulations 995.4 Gas Relative Permeability 1005.4.1 Hydraulic Flow in a Cylindrical Pore 1005.4.2 Molecular Flow in a Cylindrical Pore 1015.4.3 Total Gas Flow in a Cylindrical Pore 1015.4.4 Gas Relative Permeability in Tight Rocks 1015.4.5 Comparison with Experiments 1025.4.6 Comparison with Pore-Network Simulations 1075.5 Conclusions 108Acknowledgment 109References 1096 NMR and Its Applications in Tight Unconventional Reservoir Rocks 113Jin-Hong Chen, Mohammed Boudjatit, and Stacey M. Althaus6.1 Introduction 1136.2 Basic NMR Physics 1136.2.1 Nuclear Spin 1146.2.2 Nuclear Zeeman Splitting and NMR 1146.2.3 Nuclear Magnetization 1156.2.4 Bloch Equations and NMR Relaxation 1166.2.5 Simple NMR Experiments: Free Induction Decay and CPMG Echoes 1176.2.6 NMR Relaxation of a Pure Fluid in a Rock Pore 1186.2.7 Measured NMR CPMG Echoes in a Formation Rock 1196.2.8 Inversion 1196.2.8.1 Regularized Linear Least Squares 1206.2.8.2 Constrains of the Resulted NMR Spectrum in Inversion 1206.2.9 Data from NMR Measurement 1216.3 NMR Logging for Unconventional Source Rock Reservoirs 1216.3.1 Brief Introduction of Unconventional Source Rocks 1216.3.2 NMR Measurement of Source Rocks 1226.3.2.1 NMR Log of a Source Rock Reservoir 1226.3.3 Pore Size Distribution in a Shale Gas Reservoir 1246.4 NMR Measurement of Long Whole Core 1256.4.1 Issues of NMR Instrument for Long Sample 1256.4.2 HSR-NMR of Long Core 1266.4.3 Application Example 1286.5 NMR Measurement on Drill Cuttings 1306.5.1 Measurement Method 1316.5.1.1 Preparation of Drill Cuttings 1316.5.1.2 Measurements 1316.5.2 Results 1326.6 Conclusions 133References 1357 Tight Rock Permeability Measurement in Laboratory: Some Recent Progress 139Hui-Hai Liu, Jilin Zhang, and Mohammed Boudjatit7.1 Introduction 1397.2 Commonly Used Laboratory Methods 1407.2.1 Steady-State Flow Method 1407.2.2 Pressure Pulse-Decay Method 1417.2.3 Gas Research Institute Method 1437.3 Simultaneous Measurement of Fracture and Matrix Permeabilities from Fractured Core Samples 1447.3.1 Estimation of Fracture and Matrix Permeability from PPD Data for Two Flow Regimes 1447.3.2 Mathematical Model 1467.3.3 Method Validation and Discussion 1487.4 Direct Measurement of Permeability-Pore Pressure Function 1507.4.1 Knudsen Diffusion, Slippage Flow, and Effective Gas Permeability 1507.4.2 Methodology for Directly Measuring Permeability-Pore Pressure Function 1527.4.3 Experiments 1557.5 Summary and Conclusions 159References 1598 Stress-Dependent Matrix Permeability in Unconventional Reservoir Rocks 163Athma R. Bhandari, Peter B. Flemings, and Sebastian Ramiro-Ramirez8.1 Introduction 1638.2 Sample Descriptions 1648.3 Permeability Test Program 1658.4 Permeability Behavior with Confining Stress Cycling 1668.5 Matrix Permeability Behavior 1708.6 Concluding Remarks 172Acknowledgments 174References 1749 Assessment of Shale Wettability from Spontaneous Imbibition Experiments 177Zhiye Gao and Qinhong Hu9.1 Introduction 1779.2 Spontaneous Imbibition Theory 1789.3 Samples and Analytical Methods 1799.3.1 SI Experiments 1799.3.2 Barnett Shale from United States 1809.3.3 Silurian Longmaxi Formation and Triassic Yanchang Formation Shales from China 1809.3.4 Jurassic Ziliujing Formation Shale from China 1829.4 Results and Discussion 1839.4.1 Complicated Wettability of Barnett Shale Inferred Qualitatively from SI Experiments 1839.4.1.1 Wettability of Barnett Shale 1849.4.1.2 Properties of Barnett Samples and Their Correlation to Wettability 1869.4.1.3 Low Pore Connectivity to Water of Barnett Samples 1879.4.2 More Oil-Wet Longmaxi Formation Shale and More Water-Wet Yanchang Formation Shale 1889.4.2.1 TOC and Mineralogy 1889.4.2.2 Pore Structure Difference Between Longmaxi and Yanchang Samples 1889.4.2.3 Water and Oil Imbibition Experiments 1919.4.2.4 Wettability of Longmaxi and Yanchang Shale Samples Deduced from SI Experiments 1979.4.3 Complicated Wettability of Ziliujing Formation Shale 1979.4.3.1 TOC and Mineralogy 1979.4.3.2 Pore Structure 1979.4.3.3 Water and Oil Imbibition Experiments 2009.4.3.4 Wettability of Ziliujing Formation Shale Indicated from SI Experiments and its Correlation to Shale Pore Structure and Composition 2019.4.4 Shale Wettability Evolution Model 2019.5 Conclusions 204Acknowledgments 204References 20410 Permeability Enhancement in Shale Induced by Desorption 209Brandon Schwartz and Derek Elsworth10.1 Introduction 20910.1.1 Shale Mineralogical Characteristics 20910.1.2 Flow Network 21010.1.2.1 Bedding-Parallel Flow Network 21110.1.2.2 Bedding-Perpendicular Flow Paths 21210.2 Adsorption in Shales 21410.2.1 Langmuir Theory 21410.2.2 Competing Strains in Permeability Evolution 21510.2.2.1 Poro-Sorptive Strain 21510.2.2.2 Thermal-Sorptive Strain 21810.3 Permeability Models for Sorptive Media 21810.3.1 Strain Based Models 21910.4 Competing Processes during Permeability Evolution 22010.4.1 Resolving Competing Strains 22010.4.2 Solving for Sorption-Induced Permeability Evolution 22110.5 Desorption Processes Yielding Permeability Enhancement 22310.5.1 Pressure Depletion 22310.5.2 Lowering Partial Pressure 22410.5.3 Sorptive Gas Injection 22510.5.4 Desorption with Increased Temperature 22510.6 Permeability Enhancement Due to Nitrogen Flooding 22510.7 Discussion 22610.8 Conclusion 228References 22911 Multiscale Experimental Study on Interactions Between Imbibed Stimulation Fluids and Tight Carbonate Source Rocks 235Feng Liang, Hui-Hai Liu, and Jilin Zhang11.1 Introduction 23511.2 Fluid Uptake Pathways 23611.2.1 Experimental Methods 23611.2.1.1 Materials 23611.2.1.2 Experimental Procedure 23711.2.2 Results and Discussion 23711.2.2.1 Surface Characterization 23711.2.2.2 Spontaneous Imbibition Tests 23911.3 Mechanical Property Change After Fluid Exposure 24011.3.1 Experimental Methods 24211.3.1.1 Materials 24211.3.1.2 Experimental Procedure 24211.3.2 Results and Discussion 24311.3.2.1 UCS and Brazilian Test on Cylindrical Core Plugs 24311.3.2.2 Microindentation Test 24311.4 Morphology and Minerology Changes After Fluid Exposure 24511.4.1 Experimental Methods 24711.4.1.1 Materials 24711.4.1.2 Experimental Procedure 24811.4.2 Results and Discussion 24811.4.2.1 SEM and EDS Mapping of Thin-Section Surface before Fluid Treatment 24811.4.2.2 SEM and EDS Mapping of Thin-Section Surface after Fluid Treatment 25111.4.2.3 Quantification of Dissolved Ions in the Treatment Fluids 25611.5 Flow Property Change After Fluid Exposure 25711.5.1 Experimental Methods 25811.5.1.1 Materials 25811.5.1.2 Experimental Procedure 25811.5.2 Results and Discussion 25811.5.2.1 Changes in Flow Characteristics 25811.6 Conclusions 259References 261Part III Large-Scale Petrophysics 26512 Effective Permeability in Fractured Reservoirs: Percolation-Based Effective-Medium Theory 267Behzad Ghanbarian12.1 Introduction 26712.1.1 Percolation Theory 26712.1.2 Effective-Medium Theory 26812.2 Objectives 26912.3 Percolation-Based Effective-Medium Theory 26912.4 Comparison with Simulations 27012.4.1 Chen et al. (2019) 27012.4.1.1 Two-Dimensional Simulations 27112.4.1.2 Three-Dimensional Simulations 27312.4.2 New Three-Dimensional Simulations 27412.5 Conclusion 275Acknowledgment 277References 27713 Modeling of Fluid Flow in Complex Fracture Networks for Shale Reservoirs 281Hongbing Xie, Xiaona Cui, Wei Yu, Chuxi Liu, Jijun Miao, and Kamy Sepehrnoori13.1 Shale Reservoirs with Complex Fracture Networks 28113.2 Complex Fracture Reservoir Simulation 28113.3 Embedded Discrete Fracture Model 28313.4 EDFM Verification 28613.5 Well Performance Study – Base Case 29013.6 Effect of Natural Fracture Connectivity on Well Performance 29413.6.1 Effect of Natural Fracture Azimuth 29413.6.2 Effect of Number of Natural Fractures 29513.6.3 Effect of Natural Fracture Length 29813.6.4 Effect of Number of Sets of Natural Fractures 30113.6.5 Effect of Natural Fracture Dip Angle 30513.7 Effect of Natural Fracture Conductivity on Well Performance 30613.8 Conclusions 311References 31214 A Closed-Form Relationship for Production Rate in Stress-Sensitive Unconventional Reservoirs 315Hui-Hai Liu, Huangye Chen, and Yanhui Han14.1 Introduction 31514.2 Production Rate as a Function of Time in the Linear Flow Regime Under the Constant Pressure Drawdown Condition 31714.3 An Approximate Relationship Between Parameter A and Stress-Dependent Permeability 31814.4 Evaluation of the Relationship Between Parameter A and Stress-Dependent Permeability 32114.5 Equivalent State Approximation for the Variable Pressure Drawdown Conditions 32714.6 Discussions 32814.7 Concluding Remarks 329Nomenclature 329Subscript 330Appendix 14.A Derivation of Eq. (14.22) with Integration by Parts 330References 33115 Sweet Spot Identification in Unconventional Shale Reservoirs 333Rabah Mesdour, Mustafa Basri, Cenk Temizel, and Nayif Jama15.1 Introduction 33315.2 Reservoir Characterization 33415.3 Sweet Spot Identification 33415.3.1 The Method Based on Organic, Rock and Mechanical Qualities 33515.3.2 Methods Based on Geological and Engineering Sweet Spots 33715.3.3 Methods Based on Other Quality Indicators 34015.3.4 Methods Based on Data Mining and Machine Learning 34315.4 Discussion 34515.5 Conclusion 346References 347Index 351