Two-Phase Reservoir Flow Calculations

Abstract

A mathematical model of flow in two space dimensions has been developed for two partially miscible phases and incorporated in an IBM 360/65 computer program. This program can be used to predict production capabilities, to evaluate hydro-carbon reserves and to compare alternate proposals for reservoir exploitation. The reservoir behavior is described by a set of differential equations that result from combining Darcy's law and the law of conservation of mass for each phase in the system. These equations include the effects of viscous, capillary and gravitational forces, and permit one phase to be soluble in the other. The differential equations are approximated by difference equations that are implicit in pressure and saturation and explicit in relative permeability. A simultaneous solution of the difference equations is obtained using ei ther alternating-direction or strongly implicit iteration procedures. A Newtonian iteration procedure has been implemented to improve convergence when using the dissolved gas drive fluid model. The program has been used successfully to model areal and cross-sectional problems on both laboratory and field scale. To illustrate the program use, two examples are included' a two-dimensional simulation of a Buckley-Leverett displacement, and a calculation of a laboratory natural depletion experiment. INTRODUCTION Predictions of reservoir performance provide the basic data for long-range planning, design and operation of the reservoir. Information such as estimates of recoverable reserves, forecasts of producing trends and evaluations of proposed addi tional recovery proj ects are derived from the se predictions. They are also useful in hearings before regulatory bodies, in preparing unitization agree-ments, and in analysis of joint ventures. The goal of the research program reported here has been to develop the methods and an associated reservoir simulation computer program to analyze