Turgay Ertekin, Qian Sun, Jian Zhang
608; Softcover
SPE Textbook Series Vol. 28
ISBN: 978-1-61399-693-5
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Reservoir simulation has been in practice for more than 50 years, but it has recently gained significant momentum because of its wider application to the increasingly complex reservoir systems of today. Reservoir Simulation: Problems and Solutions provides petroleum engineers with extensive practice in the art of problem solving, strengthening their critical-thinking solution strategies and preparing them for the unique problems they will encounter in this dynamic field. Built on the fundamental concepts and solutions of the original exercises found in Basic Applied Reservoir Simulation (Turgay Ertekin, Jamal H. Abou-Kassem, and Gregory R. King), this new book provides an additional 180 exercises and solutions that fully illustrate the intricacies of reservoir-simulation methodology.

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Basic Applied Reservoir Simulation
Turgay Ertekin, J.H. Abou-Kassem and G.R. King

Turgay Ertekin is Professor Emeritus of Petroleum and Natural Gas Engineering at the Pennsylvania State University (Penn State), where he has been a member of the faculty for more than 40 years. Throughout his career, Ertekin has gained extensive experience in the development and application of fluid-flow models in porous media and mathematical modeling of flow problems. He is an accomplished presenter, having delivered or participated in more than 300 invited lectures, paper presentations, and seminars. Ertekin has also published more than 300 works, including five books and five book chapters. He holds a PhD degree in petroleum and natural gas engineering from Penn State and MS and BS degrees in petroleum engineering from Middle East Technical University. Ertekin is an active SPE Distinguished Member, having held various positions on the SPE Editorial Board, including 2 years as the executive editor of SPE Formation Evaluation. He is the recipient of the 1988 SPE Distinguished Achievement Award for Petroleum Engineering Faculty, the 2001 SPE Lester C. Uren Award, the 2007 SPE A Peer Apart Award, the 2008 SPE Outstanding Associate Editor Award, and the 2013 SPE Honorary Membership Award. Ertekin is currently the editor-in-chief of the Journal of Petroleum Exploration and Production Technology.


Qian Sun is a research engineer at New Mexico Institute of Mining and Technology.  His research focuses mainly on numerical reservoir simulation and artificial-intelligence applications in reservoir engineering. Sun has authored or coauthored numerous papers for conferences and refereed journals, one book, and one book chapter. He holds PhD and master’s degrees in petroleum and natural gas engineering from Penn State and a bachelor’s degree in petroleum engineering from University of Tulsa.


Jian Zhang is a PhD graduate at Penn State.  His research focuses on rate- and pressure-transient analysis, numerical reservoir simulation, artificial neural networks, and neuro-simulation. He holds a PhD degree in petroleum and natural gas engineering, with a minor in computational science, from Penn State; an MS degree in chemical engineering from Miami University; and MS and BS degrees in optical engineering and optical science and information, respectively, from Beijing Jiaotong University.

Preface vii
Acknowledgments ix

Chapter 1 – Introduction 1
1.1 Analysis of Reservoir Dynamics and Plausible Methodologies 2
1.2 Problems and Solutions 3

Chapter 2 – Reservoir Rock and Fluid Properties and Basic Reservoir Engineering Concepts 7
2.1 Reservoir Rock Properties 7
2.2 Reservoir Fluid Properties 7
2.3 Reservoir Rock and Fluid Interactions 8
2.4 Basic Reservoir Engineering Concepts 9
2.5 Problems and Solutions 12

Chapter 3 – Basic Mathematics of Reservoir Modeling 39
3.1 Basic Differential Calculus 39
3.2 Finite-Difference Analogs of Derivatives: A Short Review of Finite-Difference Calculus 40
3.3 Matrix Representation of Algebraic Equations 44
3.4 Problems and Solutions 45

Chapter 4 – Flow Equations Describing Single-Phase Flow In Porous Media 61
4.1 Flow Geometries and Flow Dimensions 61
4.2 Single-Phase Flow Equations in Porous Media 63
4.3 Problems and Solutions 65

Chapter 5 – Gridding Methods and Finite-Difference Representation of Single-Phase Flow Equations 93
5.1 Grid Types and Grid Design 93
5.2 Finite-Difference Representation of Single-Phase Flow Equations 95
5.3 Truncation Error, Stability, and Consistency Analysis of Finite-Difference Schemes 101
5.4 Problems and Solutions 103

Chapter 6 – Coupling of the Well Equation with the Reservoir Flow Equations 143
6.1 Boundary-Condition Specification at the Well 143
6.2 Wellbore Models 143
6.3 Abou-Kassem and Aziz Model for Off-Centered Wells 147
6.4 Babu and Odeh’s Model for Horizontal Wells 149
6.5 Vertical Multilayer Well Models 150
6.6 Problems and Solutions 155

Chapter 7 – Solution Methods for Systems of Linear Algebraic Equations 193
7.1 Solution Methods 193
7.2 Ordering of Gridblocks 205
7.3 Problems and Solutions 208

Chapter 8 – Numerical Solution of Single-Phase Flow Equations 281
8.1 Single-Phase Incompressible Flow 281
8.2 Single-Phase Slightly Compressible Flow 284
8.3 Single-Phase Compressible Flow Equation 287
8.4 Problems and Solutions 290

Chapter 9 – Numerical Solution of Multiphase-Flow Equations in Porous Media 451
9.1 Multiphase-Flow Equations 451
9.2 Solution Techniques for Solving Multiphase-Flow Equations of Porous Media 452
9.3 Problems and Solutions 463

Chapter 10 – Reservoir Simulation in Practice 507
10.1 Mathematical Models of A Reservoir 507
10.2 Uncertainty in Reservoir Simulation 508
10.3 Incentives for Carrying Out a Reservoir-Simulation Study 509
10.4 Objectives of a Simulation Study and Prioritization of Objectives 509
10.5 Problems and Solutions 509

Chapter 11 – Classical Reservoir Engineering Protocols as Subsets of Reservoir Simulation 591
11.1 Reservoir Engineering Analysis Tools: Numerical vs. Analytical 591
11.2 Problems and Solutions 591
Index 601

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