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About this book

The past decade has seen remarkable growth in research related to petroleum reseIVoir simulation. This growth reflects several developments, not the least of which is the increased interest in oil recovery technologies requiring sophisticated engineer­ ing. Augmenting this interest has been the broader availability of supercomputers capable of handling the tremendous computational demands of a typical reseIVoir simulator. The field of reseIVoir simulation incorporates several major facets of applied mathematics. First, in view of the varieyt and complexity of the processes encoun­ tered, it is imperative that the modeler adopt a systematic approach to establishing the equations governing reseIVoir flows. Second, the mathematical structure of these flow equations needs to be carefully analyzed in order to develop appropriate and efficient numerical methods for their solution. Third, since some aspects of the discretized flow equations are typically stiff, one must develop efficient schemes for solving large sparse systems of linear equations. This monograph has three parts, each devoted to one of these three aspects of reseIVoir modeling. The text grew out of a set of lectures presented by the authors in the autumn of 1986 at the IBM Scientific Center in Bergen, Norway. We feel that it is only appropriate to caution the reader that many of the ideas that we present in this monograph do not reflect standard approaches in petroleum reseIVoir simulation. In fact, our aim is to outline promising new ways of attacking reseIVoir simulation prob­ lems, rather than to compile another textbook for the mainstream.

Table of Contents


I. Basic Mechanics of Oil Reservoir Flows

A petroleum reservoir is a complicated mixture of porous rock, brine, and hydrocarbon fluids, usually residing underground at depths that prohibit extensive measurement and characterization. Petroleum reservoir engineers face the difficult task of using their understanding of reservoir mechanics to design schemes for recovering hydrocarbons efficiently. In the past decade or so the reservoir engineer’s reliance on mathematical models has grown at a remarkable rate, and, in view of the evolution of many other successful branches of engineering, it seems fair to expect this reliance to continue increasing. This monograph examines several aspects of the development of mathematical reservoir models. Before embarking on technical discussions, though, we shall give a brief, relatively nontechnical survey of how an oil reservoir works.
Myron B. Allen

II. Numerical Analysis of Reservoir Fluid Flow

In this chapter we shall consider several model problems of varying complexity in petroleum reservoir fluid flow. Although the physical assumptions behind these models are very restrictive, these models contain many qualitative aspects in common with more realistic fluid models. As a result, an understanding of the simple models will be essential to our work in the following chapters.
John A. Trangenstein

III. Numerical Linear Algebra for Reservoir Simulation

The focus in Chapter 3 will be on the solution of large, sparse sets of linear equations. This will be discussed in the context of the black oil model, but this is not the only application. The solution methods discussed here apply equally well to other models, such as compositional and thermal models, that are commonly used in reservoir simulation.
Alda Behie


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