A Method for Calculating Multi-Dimensional Immiscible Displacement

Abstract

Published in Petroleum Transactions, AIME, Vol 216, 1959, pages 297–308. Paper presented at 34th Annual Fall Meeting of Society of Petroleum Engineers at Dallas, Tex. Oct. 4–7, 1959. ABSTRACT A numerical solution of equations describing two-phase flow in porous media shows promise in providing a technique for predicting the displacement from sands of oil by water or gas. The description includes the influence of relative permeability, fluid viscosities and densities, gravity, and capillary pressure, and, though tested only for two-dimensional cases, should be equally applicable in three-dimensional geometry. Two numerical methods are presented: the first method is quite general in its applicability; the second method can be used only with certain types of boundary conditions but requires less computing. Comparisons of computed results with data from laboratory models are presented. These data were taken on a water flood of a stratified model and on water floods of a five-spot model for favorable and unfavorable mobility ratios. On the stratified model, excellent agreement with recovery at breakthrough was obtained; agreement with recovery after breakthrough was poor. In the five-spot model, good agreement was obtained with recovery at and after breakthrough. INTRODUCTION The purpose of this paper is twofold; first, to present a reservoir engineering method requiring knowledge only of rock geometry and the normally measured rock and fluid properties for calculating the multi-dimensional flow of water displacing oil from porous, water-wet rock containing connate water; and, second, to investigate the validity of the method by comparing results of calculations with previously observed displacements in laboratory models. The availability of such a verified technique of reservoir analysis would afford major advantages. First, it would demonstrate that the fundamental macroscopic concepts of two-phase fluid mechanics, i.e., relative permeability and capillary pressure, yield an adequate description of the physical process.