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