This book addresses three important aspects of modeling petroleum reservoirs. The first aspect is the development of governing equations from physical principles. The second is the analysis of the mathematical structure of the governing equations and the development of numerical methods for their solution. This part of the book examines incompressible flow problems to motivate an analysis of the standard black-oil model. The discussion compares numerical methods from other fields to the most common methods used in petroleum engineering. The third aspect is the construction of algorithms for the solution of the resulting large linear systems on digital computers. The purpose of the monograph is to introduce new and emerging viewpoints on several difficult problems in petroleum reservoir modeling, with special relevance to enhanced oil recovery technologies. The book is aimed at engineers and applied mathematicians having some familiarity with the basics of petroleum engineering, advanced engineering mathematics, and numerical methods.
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