"Computational Methods for Multiphase Flows in Porous Media" by Zhangxin Chen, Guanren Huan, Yuanle Ma (Repost)

This book offers a fundamental and practical introduction to the use of computational methods, particularly finite element methods, in the simulation of fluid flows in porous media. It covers a wide variety of flows, including single-phase, two-phase, black oil, volatile, compositional, nonisothermal, and chemical compositional flows in both ordinary porous and fractured porous media.

This book can be used as a textbook for graduate or advanced undergraduate students in geology, petroleum engineering, and applied mathematics, and as a reference book for professionals in these fields, as well as scientists working in the area of petroleum reservoir simulation. It can also be used as a handbook for employees in the oil industry who need a basic understanding of modeling and computational method concepts and by researchers in hydrology, environmental remediation, and some areas of biological tissue modeling.

Contents
List of Figures
List of Tables
Preface
1. Introduction
1.1 Petroleum Reservoir Simulation
1.2 Numerical Methods
1.3 Linear System Solvers
1.4 Solution Schemes
1.5 Numerical Examples
1.6 Ground Water Flow Modeling
1.7 Basin Modeling
1.8 Units
2. Flow and Transport Equations
2.1 Introduction
2.2 Single Phase Flow
2.2.1 Single Phase Flow in a Porous Medium
2.2.2 General Equations for Single Phase Flow
2.2.3 Equations for Slightly Compressible Flow and Rock
2.2.4 Equations for Gas Flow
2.2.5 Single Phase Flow in a Deformable Medium
2.2.6 Single Phase Flow in a Fractured Medium
2.2.7 Non-Darcy’s Law
2.2.8 Other Effects
2.2.9 Boundary Conditions
2.3 Two-phase Immiscible Flow
2.3.1 Basic Equations
2.3.2 Alternative Differential Equations
2.3.3 Boundary Conditions
2.4 Transport of a Component in a Fluid
2.5 Transport of Multicomponents
2.6 The Black Oil Model
2.7 A Volatile Oil Model
2.8 Compositional Flow
2.9 Nonisothermal Flow
2.10 Chemical Compositional Flow
2.11 Flows in Fractured Porous Media
2.11.1 Dual Porosity/Permeability
2.11.2 Dual Porosity Models
2.12 Concluding Remarks
2.13 Bibliographical Information
Exercises
3. Rock and Fluid Properties
3.1 Rock Properties
3.1.1 Capillary Pressures
3.1.2 Relative Permeabilities
3.1.3 Rock Compressibility
3.2 Fluid Properties
3.2.1 Water PVT Properties
3.2.2 Oil PVT Properties
3.2.3 Gas PVT Properties
3.2.4 Total Compressibility
3.2.5 Equations of State
3.3 Temperature-dependent Properties
3.3.1 Rock Properties
3.3.2 Fluid Properties
3.4 Bibliographical Information
Exercises
4. Numerical Methods
4.1 Finite Difference Methods
4.1.1 First Difference Quotients
4.1.2 Second Difference Quotients
4.1.3 Grid Systems
4.1.4 Treatment of Boundary Conditions
4.1.5 Finite Differences for Stationary Problems
4.1.6 Finite Differences for Parabolic Problems
4.1.7 Consistency, Stability, and Convergence
4.1.8 Finite Differences for Hyperbolic Problems
4.1.9 Grid Orientation Effects
4.2 Standard Finite Element Methods
4.2.1 Finite Element Methods for Stationary Problems
4.2.2 General Domains
4.2.3 Quadrature Rules
4.2.4 Finite element methods for transient problems
4.3 Control Volume Finite Element Methods
4.3.1 The Basic CVFE
4.3.2 Positive Transmissibilities
4.3.3 The CVFE Grid Construction
4.3.4 The Upstream Weighted CVFE
4.3.5 Control Volume Function Approximation Methods
4.3.6 Reduction of Grid Orientation Effects
4.4 Discontinuous Finite Element Methods
4.4.1 DG Methods
4.4.2 Stabilized DG Methods
4.5 Mixed Finite Element Methods
4.5.1 A One-dimensional Model Problem
4.5.2 A Two-dimensional Model Problem
4.5.3 Extension to Boundary Conditions of Other Kinds
4.5.4 Mixed Finite Element Spaces
4.5.5 Approximation Properties
4.6 Characteristic Finite Element Methods
4.6.1 The Modified Method of Characteristics
4.6.2 The Eulerian–Lagrangian Localized Adjoint Method
4.7 Adaptive Finite Element Methods
4.7.1 Local Grid Refinement in Space
4.7.2 Data Structures
4.7.3 A Posteriori Error Estimates
4.7.4 The Eighth SPE Project: Gridding Techniques
4.8 Bibliographical Remarks
Exercises
5. Solution of Linear Systems
5.1 Tridiagonal Systems
5.2 Gaussian Elimination
5.3 Ordering of the Nodes
5.4 CG
5.5 GMRES
5.6 ORTHOMIN
5.7 BiCGSTAB
5.8 Preconditioned Iterations
5.8.1 Preconditioned CG
5.8.2 Preconditioned GMRES
5.9 Preconditioners
5.9.1 ILU(0)
5.9.2 ILU(l)
5.9.3 ILUT
5.10 Practical Considerations
5.10.1 Decoupling Preconditioners
5.10.2 COMBINATIVE Preconditioners
5.10.3 Bordered Systems
5.10.4 Choice of Initial Solutions
5.11 Concluding Remarks and Comparisons
5.12 Bibliographical Remarks
Exercises
6 Single Phase Flow
6.1 Basic Differential Equations
6.2 One-dimensional Radial Flow
6.2.1 An Analytic Solution
6.2.2 Numerical Comparisons
6.3 Finite Element Methods for Single Phase Flow
6.3.1 Linearization Approaches
6.3.2 Implicit Time Approximations
6.3.3 Explicit Time Approximations
6.4 Bibliographical Remarks
Exercises
7 Two-phase Flow
7.1 Basic Differential Equations
7.2 One-dimensional Flow
7.2.1 An Analytic Solution
7.2.2 An Example
7.3 IMPES and Improved IMPES
7.3.1 Classical IMPES
7.3.2 The Seventh SPE Project: Horizontal Well Modeling
7.3.3 Improved IMPES
7.4 Alternative Differential Formulations
7.4.1 Phase Formulation
7.4.2 Weighted Formulation
7.4.3 Global Formulation
7.4.4 Numerical Comparisons
7.5 Numerical Methods for Two-phase Flow
7.5.1 Mixed Finite Element Methods
7.5.2 CVFE Methods
7.5.3 Characteristic Finite Element Methods
7.5.4 Comparison between Numerical Methods
7.6 Miscible Displacement
7.7 Bibliographical Remarks
Exercises
8. The Black Oil Model
8.1 Basic Differential Equations
8.1.1 The Basic Equations
8.1.2 Rock Properties
8.1.3 Fluid Properties
8.1.4 Phase States
8.2 Solution Techniques
8.2.1 The Newton-Raphson Method
8.2.2 The SS Technique
8.2.3 The Sequential Technique
8.2.4 Iterative IMPES
8.2.5 Well Coupling
8.2.6 The Adaptive Implicit and Other Techniques
8.3 Comparisons between Solution Techniques
8.3.1 An Undersaturated Reservoir
8.3.2 A Saturated Reservoir
8.3.3 The Ninth SPE Project: Black Oil Simulation
8.3.4 Remarks on Numerical Experiments
8.4 The Second SPE Project: Coning Problems
8.5 Bibliographical Remarks
Exercises
9. The Compositional Model
9.1 Basic Differential Equations
9.1.1 The Basic Equations
9.1.2 Equations of State
9.2 Solution Techniques
9.2.1 Choice of Primary Variables
9.2.2 Iterative IMPES
9.3 Solution of Equilibrium Relations
9.3.1 Successive Substitution Method
9.3.2 Newton-Raphson’s Flash Calculation
9.3.3 Derivatives of Fugacity Coefficients
9.3.4 Solution of Peng-Robinson’s Cubic Equation
9.3.5 Practical Considerations
9.4 The Third SPE Project: Compositional Flow
9.4.1 PVT Phase Behavior Study
9.4.2 Reservoir Simulation Study
9.4.3 Computational Remarks
9.5 Bibliographical Remarks
Exercises
10. Nonisothermal Flow
10.1 Basic Differential Equations
10.1.1 The Basic Equations
10.1.2 Rock Properties
10.1.3 Fluid Properties
10.2 Solution Techniques
10.2.1 Choice of Primary Variables
10.2.2 The SS Technique
10.3 The Fourth SPE Project: Steam Injection
10.3.1 The First Problem
10.3.2 The Second Problem
10.4 Bibliographical Remarks
Exercises
11. Chemical Flooding
11.1 Basic Differential Equations
11.2 Surfactant Flooding
11.2.1 Effective Salinity
11.2.2 Binodal Curves
11.2.3 Tie Lines for Two Phases
11.2.4 Tie Lines for Three Phases
11.2.5 Phase Saturations
11.2.6 Interfacial Tension
11.2.7 Interfacial Tension without Mass Transfer
11.2.8 Trapping Numbers
11.2.9 Relative Permeabilities
11.3 Alkaline Flooding
11.3.1 Basic Assumptions
11.3.2 Mathematical Formulations of Reaction
Equilibria
11.4 Polymer Flooding
11.4.1 Viscosity
11.4.2 Permeability Reduction
11.4.3 Inaccessible Pore Volume
11.5 Foam Flooding
11.5.1 Critical Oil Saturation
11.5.2 Critical Surfactant Concentration
11.5.3 Critical Capillary Force
11.5.4 Oil Relative Permeability Effects
11.5.5 Gas-liquid Ratio Effects
11.5.6 Gas Velocity Effects
11.6 Rock and Fluid Properties
11.6.1 Adsorption
11.6.2 Phase-specific Weights
11.6.3 Phase Viscosities
11.6.4 Cation Exchange
11.7 Numerical Methods
11.8 Numerical Results
11.8.1 Example 1
11.8.2 Example 2
11.8.3 Example 3
11.9 Application to a Real Oilfield
11.9.1 Background
11.9.2 The Numerical Model
11.9.3 Numerical History Matching
11.9.4 Predictions
11.9.5 Assessment of Different Development Methods
11.10 Bibliographical Remarks
Exercises
12. Flows in Fractured Porous Media
12.1 Flow Equations
12.1.1 Dual Porosity/Permeability Models
12.1.2 Dual Porosity Models
12.2 The Sixth SPE Project: Dual Porosity Simulation
12.3 Bibliographical Remarks
Exercises
13. Welling Modeling
13.1 Analytical Formulas
13.2 Finite Difference Methods
13.2.1 Square Grids
13.2.2 Extensions
13.3 Standard Finite Element Methods
13.3.1 Triangular Finite Elements
13.3.2 Rectangular Finite Elements
13.4 Control Volume Finite Element Methods
13.4.1 Well Model Equations
13.4.2 Horizontal Wells
13.4.3 Treatment of Faults
13.4.4 Corner Point Techniques
13.5 Mixed Finite Element Methods
13.5.1 Rectangular Mixed Spaces
13.5.2 Triangular Mixed Spaces
13.6 Well Constraints
13.7 The Seventh SPE Project: Horizontal Well Modeling
13.8 Bibliographical Remarks
Exercises
14. Special Topics
14.1 Upscaling
14.1.1 Single Phase Flow
14.1.2 Two-phase Flow
14.1.3 Limitations in Upscaling
14.2 History Matching
14.3 Parallel Computing
14.3.1 Domain Decomposition
14.3.2 Load Balancing
14.3.3 Data Communication
14.3.4 Time Step Size and Communication Time Control
14.4 Oil Recovery Optimization
14.5 Surface Network Systems
14.5.1 Hydraulic Models of Flow Devices
14.5.2 Models of Links and Nodes
14.6 Bibliographical Remarks
15. Nomenclature
15.1 English Abbreviations
15.2 Subscripts
15.3 Base Quantities
15.4 English Symbols
15.5 Greek Symbols
15.6 Generic Symbols Used in Chapters 4 and 5
16. Units
16.1 Unit Abbreviations
16.2 Unit Conversions
16.3 SI and Other Metric Systems
Bibliography
Index