A Systems Description of Flow Through Porous Media

PREFACE

1. POROUS-MEDIA FLOW

1.1 Introduction

1.2 Notation

1.3 Single-phase flow

1.3.1 Governing equations

1.3.2 Finite-difference discretization

1.3.3 Example 1 - Single-phase flow in a simple reservoir

1.3.4 Incompressible flow

1.3.5 Mass-conservative formulation

1.3.6 Well models

1.4 Two-phase flow

1.4.1 Governing equations

1.4.2 Nature of the equations

1.4.3 Relative permeabilities

1.4.4 Example 2 - Two-phase flow in a simple reservoir

1.4.5 Buckley-Leverett equation

1.4.6 Linear approximation

1.4.7 Formation volume factors

1.4.8 Finite-difference discretization

1.4.9 Example 3 - Inverted five-spot

1.4.10 Sources of nonlinearity

1.4.11 Incompressible flow

1.4.12 Fluid velocities

2. SYSTEM MODELS

2.1 System equations

2.1.1 Partial-differential equations

2.1.2 Ordinary-differential equations

2.1.3 State-space representation

2.1.4 Linearized equations

2.2 Single-phase flow

2.2.1 System equations

2.2.2 Example 1 continued - Location matrix

2.2.3 Prescribed pressures and flow rates

2.2.4 Well models

2.2.5 Example 1 continued - Well model

2.2.6 Elimination of prescribed pressures

2.2.7 System energy

2.3 Two-phase flow

2.3.1 System equations

2.3.2 Well operating constraints

2.3.3 Computational aspects

2.3.4 Lift tables

2.3.5 Control valves

2.3.6 Streamlines

2.3.7 System energy

3 SYSTEM RESPONSE

3.1 Free response

3.1.1 Homogeneous equation

3.1.2 Diagonalization

3.1.3 Stability

3.1.4 Singular system matrix

3.1.5 Example 1 continued - Free response

3.2 Forced response

3.2.1 Nonhomogeneous equation

3.2.2 Diagonalization and modal analysis

3.2.3 Singular system matrix

3.3 Numerical simulation

3.3.1 Explicit Euler discretization

3.3.2 Implicit Euler discretization

3.3.3 Picard and Newton-Raphson iteration

3.3.4 Numerical stability

3.3.5 IMPES

3.3.6 Computational aspects

3.3.7 Control aspects

3.3.8 Stream line simulation

3.4 Examples

3.4.1 Example 1 continued - Stability

3.4.2 Example 2 continued - Mobility effects

3.4.3 Example 3 continued - Well constraints

3.4.4 Example 3 continued - Time-stepping statistics

3.4.5 Example 3 continued - System energy

NOMENCLATURE
INDEX