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Theory of Gas Injection Processes Franklin M. Orr, Jr. Stanford University Stanford, California 2005 Library of Congress Cataloging-in-Publication Data Orr, Franklin M., Jr. Theory of Gas Injection Processes / Franklin M. Orr, Jr. Bibliography: p. Includes index. ISBN xxxxxxxxxxx 1. Enhanced recovery of oil. I. Title. XXXXX XXXXX 2005 Franklin M. Orr, Jr. All rights reserved. No part of this book may be reproduced, in any form or by an means, without permission in writing from the author. To Susan . i Preface This book is intended for graduate students, researchers, and reservoir engineers who want to understand the mathematical description of the chromatographic mechanisms that are the basis for gas injection processes for enhanced oil recovery. Readers familiar with the calculus of partial derivatives and properties of matrices (including eigenvalues and eigenvectors) should have no trouble following the mathematical development of the material presented. The emphasis here is on the understanding of physical mechanisms, and hence the primary audience for this book will be engineers. Nevertheless, the mathematical approach used, the method of characteristics, is an essential part of the understanding of those physical mechanisms, and therefore some effort is expended to illuminate the mathematical structure of the flow problems considered. In addition, I hope some of the material will be of interest to mathematicians who will find that many interesting questions of mathematical rigor remain to be investigated for multicomponent, multiphase flow in porous media. Readers already familiar with the subject of this book will recognize the work of many students and colleagues with whom I have been privileged to work in the last twenty-five years. I am much indebted to Fred Helfferich (now at the Pennsylvania State University) and George Hirasaki (now at Rice University), working then (in the middle 1970’s) at Shell Development Company’s Bellaire Research Center. They originated much of the theory developed here and introduced me to the ideas of multicomponent, multiphase chromatography when I was a brand new research engineer at that laboratory. Gary Pope and Larry Lake were also part of that Shell group of future academics who have made extensive use of the theoretical approach used here in their work with students at the University of Texas. I have benefited greatly from many conversations with them over the years about the material discussed here. Thormod Johansen patiently explained to me his mathematician’s point of view concerning the Riemann problems considered in detail in this book. All of them have contributed substantially to the development of a rigorous description of multiphase, multicomponent flow and to my education about it in particular. Thanks are also due to many Stanford students, who listened to and helped me refine the ex-planations given here in a course taught for graduate students since 1985. Their questions over the years have led to many improvements in the presentation of the important ideas. Much of the ma-terial in this book that describes flow of gas/oil mixtures follows from the work of an exceptionally talented group of graduate students: Wes Monroe, Kiran Pande, Jeff Wingard, Russ Johns, Birol Dindoruk, Yun Wang, Kristian Jessen, Jichun Zhu, and Pavel Ermakov. Wes Monroe obtained the first four-component solutions for dispersion-free flow in one dimension. Kiran Pande solved for the interactions of phase behavior, two-phase flow, and viscous crossflow. Jeff Wingard considered problems with temperature variation and three-phase flow. Russ Johns and Birol Dindoruk greatly extended our understanding of flow of four or more components with and without volume change on mixing. Yun Wang extended the theory to systems with an arbitrary number of components, and Kristian Jessen, who visited for six months with our research group during the course of his PhD work at the Danish Technical University, contributed substantially to the development of efficient algorithms for automatic solution of problems with an arbitrary number of components in the oil or injection gas. Kristian Jessen and Pavel Ermakov independently worked out the first solutions for arbitrary numbers of components with volume change on mixing. Jichun Zhu and Pavel Ermakov contributed substantially to the derivation of compact versions of key proofs. Birol Dindoruk, Russ Johns, Yun Wang, and Kristian Jessen kindly allowed me to use example solutions ... - tailieumienphi.vn
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