دانلود کتاب Advanced Modelling with the MATLAB Reservoir Simulation Toolbox

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Cover Half-title Title page Copyright information Contents List of Contributors Preface Acknowledgments Navigating the Book and the MRST Modules Part I Grid Generation, Discretizations, and Solvers 1 Unstructured PEBI Grids Conforming to Lower-Dimensional Objects 1.1 Introduction 1.2 Basic Introduction to PEBI Grids 1.2.1 Delaunay Triangulation 1.2.2 PEBI Grids 1.2.3 Clipping PEBI Grids 1.3 Three Approaches for Optimizing PEBI Grids 1.3.1 Background Cartesian Grids 1.3.2 Delaunay Optimization 1.3.3 Minimized Centroidal Energy Function 1.4 Internal Face Constraints 1.4.1 First Method: Simplex Conformity 1.4.2 Configuring the Simplex-Conformity Methods 1.4.3 Second Method: PEBI Conformity 1.5 Adapting Cell Centroids 1.6 Worked Examples 1.6.1 Complex Fault Network in 2D 1.6.2 Statistical Fracture Distribution 1.6.3 Adapting to Permeability (SPE10) 1.6.4 Conforming to Triangulated Surfaces in 3D 1.6.5 Representing a Multilateral Well Path 1.6.6 A More Realistic 3D Case 1.7 Concluding Remarks References 2 Nonlinear Finite-Volume Methods for the Flow Equation in Porous Media 2.1 Introduction 2.2 Model Equations 2.3 Nonlinear Finite-Volume Methods 2.3.1 Construction of One-Sided Fluxes 2.3.2 Harmonic Averaging Point 2.3.3 Nonlinear TPFA 2.3.4 Nonlinear MPFA 2.3.5 Nonlinear Solver 2.4 Numerical Examples 2.4.1 Example 1: Homogeneous Permeability 2.4.2 Example 2: Discontinuous Permeability 2.4.3 Example 3: No-Flow Boundary Conditions 2.5 Concluding Remarks References 3 Implicit Discontinuous Galerkin Methods for Transport Equations in Porous Media 3.1 Introduction 3.2 Model Equations 3.3 Discontinuous Galerkin Methods 3.3.1 Weak Residual Form 3.3.2 Basis Functions 3.3.3 Numerical Integration 3.3.4 Evaluating the Interface Flux 3.3.5 Velocity Interpolation 3.3.6 Limiters 3.4 Numerical Examples 3.4.1 1D Buckley–Leverett Displacement 3.4.2 Smearing of Trailing Waves 3.4.3 Inverted Five-Spot Pattern on a Perpendicular Bisector Grid 3.4.4 Grid-Orientation Errors for Adverse Mobility Ratios 3.4.5 Channelized Medium 3.5 Concluding Remarks References 4 Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids 4.1 Introduction and Background Discussion 4.1.1 Why Do We Need Multiscale Methods? 4.1.2 Basic Flow Model and Abstract Notation 4.1.3 Local Upscaling 4.2 Multiscale Finite-Volume Methods 4.2.1 Geometric Formulation of the Original MsFV Method 4.2.2 Algebraic Formulation of the Original MsFV Method 4.2.3 Deficiencies and Limitations of the Original MsFV Method 4.2.4 The Multiscale Restriction-Smoothed Basis Method 4.2.5 Introduction to the MRST Implementation 4.2.6 Iterative Formulation 4.3 Numerical Examples 4.3.1 Lack of Monotonicity 4.3.2 Grid-Orientation Errors 4.3.3 Coarsening Complex Meshes 4.3.4 Multiscale Methods as an Alternative to Upscaling 4.3.5 Incompressible Multiphase Flow in Fractured Media 4.3.6 Gravity Segregation 4.3.7 Compressible Black-Oil Models: Fully ImplicitMethods and CPR 4.3.8 Compressible Black-Oil Models: Sequential Solution Methods 4.3.9 Compositional Flow 4.4 Concluding Remarks References Part II Rapid Prototyping and Accelerated Computation 5 Better AD Simulators with Flexible State Functions and Accurate Discretizations 5.1 Introduction 5.2 Numerical Models in MRST 5.2.1 A Generic Multicomponent Flow Model 5.2.2 Anatomy of a stepFunction 5.2.3 Validation and Preparation 5.3 StateFunctions: Framework for AD Functions 5.3.1 A Crash Course in State Functions 5.3.2 Evaluation of Properties 5.3.3 Examples of State Functions 5.3.4 The StateFunctionGrouping Class 5.4 Discretization with State Functions 5.4.1 The Simulator as a Graph 5.4.2 The Component Implementation 5.4.3 Temporal Discretizations 5.4.4 Example: Fully Implicit, Explicit, and Adaptive Implicit 5.4.5 Spatial Discretizations 5.5 Concluding Remarks References 6 Faster Simulation with Optimized Automatic Differentiation and Compiled Linear Solvers 6.1 Introduction 6.2 Accelerated Implementation of Automatic Differentiation 6.2.1 Different Backends for Automatic Differentiation 6.2.2 Motivation for Different Types of AD Backends 6.2.3 Sparse AD Backends in MRST 6.2.4 High Performance: DiagonalAutoDiffBackend 6.2.5 Performance of AD Backends 6.3 High-Performance Linear Solvers 6.3.1 Selecting Different Linear Solvers 6.4 Setting Up and Managing Simulation Cases 6.4.1 Packed Problems: Storing and Running Simulation Cases 6.4.2 Automatic Setup of ECLIPSE DataSets 6.5 Numerical Examples 6.5.1 Packed Problems: Simulation of an Ensemble 6.5.2 Bringing It All Together: Running a Big Model 6.6 Concluding Remarks Appendix A Compilation of MRST Extensions Appendix B Output from AD Benchmark References Part III Modeling of New Physical Processes 7 Using State Functions and MRST's AD-OO Framework to Implement Simulators for Chemical EOR 7.1 Introduction 7.2 Effective Modeling Using Black-Oil-Type Equations 7.2.1 Immiscible Flow Models 7.2.2 Physical Effects of Polymer 7.2.3 Physical Effects of Surfactants 7.3 The Surfactant–Polymer Flooding Simulator 7.3.1 Design of Flexible Model Classes 7.3.2 The Full Three-Phase, Five-Component Model 7.3.3 A Generic Surfactant–Polymer Model 7.3.4 Running the Simulator from an Input Deck 7.4 Numerical Examples 7.4.1 Numerical Resolution of Trailing Waves 7.4.2 Subset from SPE10: Conformance Improvement 7.4.3 The Dynamics of Slug Injection 7.4.4 Validation against a Commercial Simulator 7.5 Directions and Suggestions for Future Improvements References 8 Compositional Simulation with the AD-OO Framework 8.1 Introduction 8.2 Governing Equations 8.2.1 Basic Flow Equations 8.2.2 Thermodynamics 8.3 Solving the Flash Problem 8.3.1 Rachford–Rice: Determination of Vapor–Liquid Equilibrium 8.3.2 Updating the Thermodynamic Equilibrium 8.3.3 Phase Stability Testing 8.3.4 Equation of State 8.4 Coupled Flow and Thermodynamics 8.4.1 Overall Composition Formulation 8.4.2 Natural Variables Formulation 8.4.3 Comparison between Different Formulations 8.4.4 Implementation as Generic Models 8.4.5 State Functions for Compositional Models 8.4.6 Limitations and Caveats 8.5 Examples 8.5.1 Validation of MRST’s Simulators 8.5.2 Numerical Accuracy 8.5.3 Surface Volumes and Separators 8.5.4 Miscibility 8.5.5 Performance of Compositional Solvers 8.6 Concluding Remarks References 9 Embedded Discrete Fracture Models 9.1 Introduction 9.2 Fracture Permeability 9.3 Mathematical Formulation 9.4 Hierarchical Fracture Model Module 9.5 Two-Phase Flow through a Simple Fracture Network 9.6 Upscaling a Stochastically Generated Fracture Network 9.7 Simulation of Well Test Response in an Outcrop-Based Fracture Network 9.8 Concluding Remarks References 10 Numerical Modeling of Fractured Unconventional Oil and Gas Reservoirs 10.1 Introduction 10.2 Shale Module 10.3 Compositional Flow and Modeling of Fractured Reservoirs 10.3.1 Governing Equations for Compositional Flowin Conventional Reservoirs 10.3.2 Modeling of Fractured Reservoirs in MRST 10.3.3 The pEDFM Transmissibilities 10.4 EDFM and Compositional Simulation in MRST 10.5 Stochastic Generation of Fractures with Arbitrary Orientations in 3D 10.5.1 Generation of Fracture Sets Using ADFNE 10.6 Applications of 3D pEDFM to Model UOG Reservoirs 10.6.1 Basic Model Parameters Representative of the Eagle Ford Shale 10.6.2 Implementation Steps 10.6.3 Eagle Ford Shale Reservoir Simulation Results 10.7 Modeling Transport and Storage Mechanisms in Organic-Rich Source Rocks 10.7.1 Sorption 10.7.2 Molecular Diffusion 10.7.3 Geomechanics Effect References 11 A Unified Framework for Flow Simulation in Fractured Reservoirs 11.1 Introduction 11.2 Modeling and Simulation Techniques for Fractured Reservoirs 11.2.1 Governing Equations 11.2.2 Multicontinuum Models 11.2.3 Discrete Fracture and Matrix Model 11.3 Implementation in MRST 11.3.1 Multicontinuum and Discrete Fracture and Matrix Models 11.3.2 A Brief Note on Other Methods 11.3.3 Description of the fractures Module 11.4 Applications 11.4.1 Validation of the DFM Implementation 11.4.2 Pressure Buildup in Fractured Aquifers during CO[sub(2)] Storage Operations 11.4.3 A Model with Explicit Fractures and Dual Porosity 11.4.4 Multirate Transfer in Multicontinuum Model 11.5 Summary and Conclusion References 12 Simulation of Geothermal Systems Using MRST 12.1 Introduction 12.2 Governing Equations for Geothermal Applications 12.3 The Geothermal Module 12.3.1 A Simple Worked Example 12.3.2 Utility and State Functions 12.4 Numerical Examples 12.4.1 Benchmark with TOUGH2 12.4.2 Subset of SPE10 Model 2 12.4.3 Enhanced Geothermal System 12.4.4 Thermal Aquifer Energy Storage 12.5 Concluding Remarks References 13 A Finite-Volume-Based Module for Unsaturated Poroelasticity 13.1 Introduction 13.2 Governing Equations 13.2.1 Richards’ Equation 13.2.2 Unsaturated Poroelasticity 13.2.3 Boundary and Initial Conditions 13.3 Discretization and Implementation 13.3.1 MPFA and MPSA 13.3.2 Discretization 13.3.3 Solving the Equations 13.4 Numerical Examples 13.4.1 Numerical Convergence Tests 13.4.2 Water Infiltration in a Column of Dry Soil 13.4.3 Desiccation of a Clayey Soil in a Petri Dish 13.5 Concluding Remarks References 14 A Brief Introduction to Poroelasticity and Simulation of Coupled Geomechanics and Flow in MRST 14.1 Introduction 14.2 Governing Equations 14.2.1 Equations of Linear Elasticity 14.2.2 Equations of Linear Poroelasticity 14.2.3 The Linear Poroelastic Equations 14.3 Moduli, Moduli, Moduli … 14.3.1 The Biot–Willis Coefficient, α 14.3.2 Drained and Undrained Moduli 14.3.3 Specific Storage Coefficients 14.3.4 Geertma's Uniaxial Expansion Coefficient, C[sub(m)] 14.3.5 Automatic Computation of Poroelastic Parameters 14.4 Coupling Strategies 14.4.1 Fully Coupled and Sequentially Split Schemes 14.4.2 The Fixed Stress Split Scheme 14.4.3 The ad-mechanics Module in MRST 14.5 Numerical Examples 14.5.1 Compression of a Dry Sample 14.5.2 Compression of a Wet Sample: The Terzaghi Problem 14.5.3 Mandel’s Problem 14.6 Concluding Remarks References