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Petroleum Reservoir Simulations
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Preface Introduction Nomenclature 1 Introduction 1.1 Background 1.2 Milestones for the Engineering Approach 1.3 Importance of the Engineering and Mathematical Approaches 1.4 Summary 1.5 Exercises 2 Single-Phase Fluid Flow Equations in Multidimensional Domain 2.1 Introduction 2.2 Properties of Single-Phase Fluid 2.3 Properties of Porous Media 2.4 Reservoir Discretization 2.5 Basic Engineering Concepts 2.6 Multidimensional Flow in Cartesian Coordinates 2.7 Multidimensional Flow in Radial-Cylindrical Coordinates 2.8 Summary 2.9 Exercises 3 Flow Equations Using CVFD Terminology 3.1 Introduction 3.2 Flow Equations Using CVFD Terminology 3.3 Flow Equations in Radial-Cylindrical Coordinates Using CVFD Terminology 3.4 Flow Equations Using CVFD Terminology in any Block Ordering Scheme 3.5 Summary 3.6 Exercises 4 Simulation with a Block-Centered Grid 4.1 Introduction 4.2 Reservoir Discretization 4.3 Flow Equation for Boundary Gridblocks 4.4 Treatment of Boundary Conditions 4.5 Calculation of Transmissibilities 4.6 Symmetry and Its Use in Solving Practical Problems 4.7 Summary 4.8 Exercises 5 Simulation with a Point-Distributed Grid 5.1 Introduction 5.2 Reservoir Discretization 5.3 Flow Equation for Boundary Gridpoints 5.4 Treatment of Boundary Conditions 5.5 Calculation of Transmissibilities 5.6 Symmetry and Its Use in Solving Practical Problems 5.7 Summary 5.8 Exercises 6 Well Representation in Simulators 6.1 Introduction 6.2 Single-Block Wells 6.3 Multiblock Wells 6.4 Practical Considerations Dealing with Modeling Well Operating Conditions 6.5 Summary 6.6 Exercises 7 Single-Phase Flow Equation for Various Fluids 7.1 Introduction 7.2 Pressure Dependence of Fluid and Rock Properties 7.3 General Single-Phase Flow Equation in Multi Dimensions 7.4 Summary 7.5 Exercises 8 Linearization of Flow Equations 8.1 Introduction 8.2 Nonlinear Terms in Flow Equations 8.3 Nonlinearity of Flow Equations For Various Fluids 8.4 Linearization of Nonlinear Terms 8.5 Linearized Flow Equations in Time 8.6 Summary 8.7 Exercises 9 Methods of Solution of Linear Equations 9.1 Introduction 9.2 Direct Solution Methods 9.3 Iterative Solution Methods 9.4 Summary 9.5 Exercises 10 Introduction to Modeling Multiphase Flow in Petroleum Reservoirs 10.1 Introduction 10.2 Reservoir Engineering Concepts in Multiphase Flow 10.3 Multiphase Flow Models 10.4 Solution of Multiphase Flow Equations 10.5 Material Balance Checks 10.6 Advancing Solution in Time 10.7 Summary 10.8 Exercises A User's Manual for Single-Phase Simulator A.1 Introduction A.2 Data File Preparation A.3 Description of Variables Used in Preparing a Data File A.4 Instructions to Run Simulator A.5 Limitations Imposed on the Compiled Version A.6 Example of a Prepared Data File References Author Index Subject Index