Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs

Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs Synopsis

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.