Over the past decade, the use of numerical reservoir simulation with high- speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who may possess little or no background in the numerical mathematics upon which they are based. Yet in spite of our best efforts to improve numerical methods so as to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is constantly faced with a myriad of decisions that have nothing to do with the problem he really wants to solve. He must decide on various numerical questions not directly germane to the problem at hand. For example, he may have a choice among several simulators that use different numerical methods. He may have to pick an iteration method. He definitely will have to choose the grid spacing as part of the reservoir description, and probably will also have to select the time step size. And perhaps the biggestbugaboo of all is the choice of iteration parameters.
It is this engineer-user that I have had in mind while writing this book, one who wants to learn how to deal more effectively with the numerical decisions mentioned above. I hope he also has some curiosity about the inner workings of the “black box” that is a reservoir simulator, and I have tried to satisfy that curiosity, as well
as to prepare him to read the literature, should he wish to study recent developments and future research in greater depth than I have been able to provide here.
as to prepare him to read the literature, should he wish to study recent developments and future research in greater depth than I have been able to provide here.
The first chapter combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve. The next four chapters provide basic theory on the numerical solution of simple partial differential equations. The final chapter brings together this basic theory as it applies to the numerical solution ofmultidimensional, multiphase flow problems
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