Two-Phase Reservoir Flow Calculations
Authors: Snyder L.J. 
Published: December 2007

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 predict production capabilities, to evaluate hydrocarbon 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 either alternating-direction or strongly implicit iteration procedures. A Newtonian iteration procedure bas 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 producing trends and evaluations of proposed additional recovery projects are derived from these predictions. They are also useful in hearings before predictions. They are also useful in hearings before regulatory bodies, in preparing unitization agreements, 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 the flow of two partially miscible fluids in a two-dimensional reservoir system. This constitutes an extension of previously published analysis to include a representation of dissolved-gas drive as well as gas- or water-drive processes. When possible, improvements in the calculation methods and in the computer programs used to perform the calculations have been made to insure that the analysis is efficient and easy to apply.
The method reported is limited to two-dimensional systems. In many cases, however, sequential analysis of both cross-sectional and areal models of the same reservoir when enable one to account approximately for the effects of three-dimensional How. The analysis considers only two fluid phases, but this is sufficient to model many of the important mechanisms of reservoir drive such as water drive, dissolved-gas drive, gas-cap drive, or secondary recovery methods such as waterflooding and pressure maintenance by gas injection. When three fluid phases are flowing, a more complete analysis phases are flowing, a more complete analysis developed concurrently should be used.
The purpose of this report is to describe the reservoir model considered in this analysis and to present several of the tests made to verify its present several of the tests made to verify its validly. A description the general purpose reservoir simulation program and its use also is included.

THE RESERVOIR MODEL
The flow of two partially miscible fluids in a porous medium is governed by the differential porous medium is governed by the differential equations
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