# Petroleum Reservoir Simulations

In this highly anticipated volume, the world-renowned authors take a basic approach to present the principles of petroleum reservoir simulation in an easy-to-use and accessible format. Applicable to any oil and gas recovery method, this book uses a block-centered grid and a point-distributed grid. It treats various boundary conditions as fictitious wells, gives algebraic equations for their flowrates and presents an elaborate treatment of radial grid for single-well simulation to analyze well test results and to create well pseudo-functions necessary in conducting a practical reservoir simulation study. This book is accompanied by companion site that includes a single-phase simulator, a userâs manual, data and output files for four solved problems. The easy-to-use simulator allows students, readers and educators to input new problems and get their solutions.

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Published: November 2013

Imprint: Gulf Publishing Company

ISBN: 978-0-12-799974-6

## Contents

• 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 Userâ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

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