A Computer Method to Calculate Two-Phase Flow in Any Irregularly Bounded Porous Medium

Abstract
A fast method is needed for calculating thoroughly the performance of two-phase flow in reservoir rock with complex geometry. The authors present such a method and show its accuracy by comparison with laboratory performance of a five-spot pattern. In making the performance calculations, the quadrant of the five-spot pattern was divided into four channels. The computer time required for the calculation was one minute. This is roughly about 1/4 minute per channel.

Introduction
By using an electronic computer it is now possible to make reservoir performance calculations in which fewer assumptions and more significant variables are included than was possible with a desk calculator. These performance calculations include such variables as the properties of the reservoir rock and its contained fluids, properties of the rock-fluid system and even different well-spacing patterns. Usually, the more variables that are included the higher the computer cost-and time on the computer is expensive. As a result, a short procedure is needed so the many variables will be included and accurate performance calculations will result. If a reservoir is composed of alternate layers of permeable and impervious rock, and if each conducting layer has a different relative permeability, the combined computer cost for calculating each layer by the present long computer programs (which includes different well-spacing patterns and other variables) would be expensive. The performances of complex spacing patterns in a field often are studied by a potentiometric model, but in these model studies the analogy is to the flow of only a single phase. This paper presents a procedure to calculate the performance of a five-spot pattern with two phases flowing using a potentiometric model as a guide for the dimensions of channels and other related data. The time required to calculate the complete performance is about one minute on the IBM 7090 or four minutes on the IBM 704. The procedure can be extended to calculate the performance of more complex well spacings or an entire field with little modification. The procedure has been tested on the performance of the laboratory water floods of a five-spot pattern reported by Douglas, et al. The range of viscosity ratios in the laboratory experiments is from 0.083 to 754, which is extensive. The accuracy of the performance calculations is excellent as shown by the plotted points in Fig. 1.The recovery as influenced by the geometry of the five-spot, taking into account the deviation from true radial character, has been predicted by Aronofsky and Ramey. The authors used a potentiometric model to determine the sweep efficiency to breakthrough of the flooding agent. Dyes, Caudle and Erickson, by means of a laboratory model, show the influence of mobility ratio on recovery after breakthrough of the injected material. Dyes, et al, used the X-ray shadowgraph technique and miscible phases in their studies. Craig, Geffen and Morse from the analysis of the performance of their laboratory model correlate many variables, including average saturation of a flooding agent determined by permeability relationship. Craig, et al, used X-ray shadowgraphs to determine the sweep efficiencies in sandstone models.
JPT
P. 679^