Computational methods in subsurface flow.

*(English)*Zbl 0577.76001
New York - London etc.: Academic Press (Harcourt Brace Jovanovich, Publishers). XIII, 473 p. $ 69.00 (1983).

The present book of the authors, who have a long experience with numerical simulation of various subsurface phenomena, should be of considerable interest to professional groundwater hydrologist, engineers, and research scientists who want to solve or model subsurface problems using numerical techniques. The book should also serve as an excellent text book for orienting those interested in the field, at a graduate or senior undergraduate level in geoscience and engineering.

The book represents the first major effort to organise the vast material dealing with the numerical simulation of various problems associated with subsurface flow, ranging from oil reservoirs to groundwater reservoirs. Among the problems covered in this book are groundwater flow and contaminant transport, moisture movement in variably saturated soils, land subsidence and similar flow and deformation processes in soil and rock mechanics, and oil and geothermal reservoir engineering.

The material of the book is divided into four basic parts. The first part is devoted to fundamental concepts in numerical methods. Chapter 1 of the book presents introductory material on partial differential equations and outlines various solution approaches that have been applied to subsurface flows. Chapters 2 and 3 present the fundamental theory of the finite element method.

Chapters 4-6, constituting the second part, provide details on how the finite element approach can be used to solve a wide range of subsurface problems. In chapter 4, attention is focussed on isothermal fluid flow in porous medium reservoirs. The subjects treated range from simple problems of saturated groundwater flow to more complex ones of moisture movement and multiphase flow in petroleum reservoirs. In chapter 5, more difficult problems of solute transport and energy transport are analysed. Various types of practical situations are discussed. These include contaminant transport in single-phase flow and energy transport in single- and two- phase flow. Chapter 6 deals with the fluid flow and mechanical deformation of conventional and fractured porous media. Included in this chapter is the treatment of material nonlinearities and discrete-fracture as well as double porosity conceptual idealization of fractured systems. Alternative techniques related to finite elements, viz., point and subdomain collocation techniques and the increasingly popular boundary element technique, that have been used to solve subsurface flow problems, are given in chapter 7.

The third and fourth parts deal with the finite difference theory and application of this and other associated techniques to some of the problems for which the finite element method may not be optimal. In chapter 8, a simple and concise way to derive finite difference formulas is presented. In chapter 9, several types of difference approximations and solution schemes are described for single - and multiphase flow problems in reservoir engineering. The last chapter of the book is devoted to other alternative numerical methods that are based on combinations of the standard finite difference approach and classical mathematics. Included in the discussions are semianalytical finite difference techniques and their applications to unsaturated flow and free surface flow problems, and the method of characteristics and its application to single- and two-phase flow and solute transport problems.

Most of the original references are cited at the end of each chapter and should prove to be a valuable source of references. The book is well arranged, logically presented, easy to read and is reasonably complete and self-contained. The work is a significant contribution to the physical - mathematical aspect of subsurface flow simulation and belongs in the library of every serious groundwater hydrologists, as well as the civil engineers, chemical engineers, petroleum engineers and others interested in the subject.

The book represents the first major effort to organise the vast material dealing with the numerical simulation of various problems associated with subsurface flow, ranging from oil reservoirs to groundwater reservoirs. Among the problems covered in this book are groundwater flow and contaminant transport, moisture movement in variably saturated soils, land subsidence and similar flow and deformation processes in soil and rock mechanics, and oil and geothermal reservoir engineering.

The material of the book is divided into four basic parts. The first part is devoted to fundamental concepts in numerical methods. Chapter 1 of the book presents introductory material on partial differential equations and outlines various solution approaches that have been applied to subsurface flows. Chapters 2 and 3 present the fundamental theory of the finite element method.

Chapters 4-6, constituting the second part, provide details on how the finite element approach can be used to solve a wide range of subsurface problems. In chapter 4, attention is focussed on isothermal fluid flow in porous medium reservoirs. The subjects treated range from simple problems of saturated groundwater flow to more complex ones of moisture movement and multiphase flow in petroleum reservoirs. In chapter 5, more difficult problems of solute transport and energy transport are analysed. Various types of practical situations are discussed. These include contaminant transport in single-phase flow and energy transport in single- and two- phase flow. Chapter 6 deals with the fluid flow and mechanical deformation of conventional and fractured porous media. Included in this chapter is the treatment of material nonlinearities and discrete-fracture as well as double porosity conceptual idealization of fractured systems. Alternative techniques related to finite elements, viz., point and subdomain collocation techniques and the increasingly popular boundary element technique, that have been used to solve subsurface flow problems, are given in chapter 7.

The third and fourth parts deal with the finite difference theory and application of this and other associated techniques to some of the problems for which the finite element method may not be optimal. In chapter 8, a simple and concise way to derive finite difference formulas is presented. In chapter 9, several types of difference approximations and solution schemes are described for single - and multiphase flow problems in reservoir engineering. The last chapter of the book is devoted to other alternative numerical methods that are based on combinations of the standard finite difference approach and classical mathematics. Included in the discussions are semianalytical finite difference techniques and their applications to unsaturated flow and free surface flow problems, and the method of characteristics and its application to single- and two-phase flow and solute transport problems.

Most of the original references are cited at the end of each chapter and should prove to be a valuable source of references. The book is well arranged, logically presented, easy to read and is reasonably complete and self-contained. The work is a significant contribution to the physical - mathematical aspect of subsurface flow simulation and belongs in the library of every serious groundwater hydrologists, as well as the civil engineers, chemical engineers, petroleum engineers and others interested in the subject.

Reviewer: V.P.Tyagi

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

76M99 | Basic methods in fluid mechanics |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

74L10 | Soil and rock mechanics |

65N06 | Finite difference methods for boundary value problems involving PDEs |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |