This investigation is an outgrowth of my doctoral dissertation at
Princeton University. I am particularly grateful to Professors
George F. Pinder and William G. Gray of Princeton for their advice
during both my research and my writing. I believe that
finite-element collocation holds promise as a numer ical scheme for
modeling complicated flows in porous media. However, there seems to
be a "conventional wisdom" maintaining that collocation is
hopelessly beset by oscillations and is, in some way, fundamentally
inappropriate for multiphase flows. I hope to dispel these
objections, realizing that others will remain for further work. The
U. S. National Science Foundation funded much of this study through
grant number NSF-CEE-8111240. TABLE OF CONTENTS ABSTRACT ;;
FOREWORD ;; ; CHAPTER ONE. THE PHYSICAL SYSTEM. 1.1 Introduction. 1
1.2 The reservoir and its contents. 5 1.3 Reservoir mechanics. 9
1.4 Supplementary constraints. 18 1.5 Governing equations. 26
CHAPTER TWO. REPRESENTING FLUID-PHASE BEHAVIOR. 39 2.1
Thermodynamics of the fluid system. 40 2.2 Standard
equation-of-state methods. 45 2.3 Maxwell-set interpolation.
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