Numerical Simulation Of Miscible And Immiscible Fluid Flows In Porous Media

Abstract

1. Introduction. A variety of ecological problems require the study of porous flows which involve two different fluids. Typical examples are the extraction of oil from a porous reservoir by means of pressure from an injected liquid or gas, and contamination of fresh water wells near a salt water body (see, e.g., refs. 1, 7-9, 15-17, 19, 21, 23, 24, 26-28, 32 and the references contained therein). Such time dependent, two-fluid porous flow problems often fall into one of the following two categories:the miscible case, in which the fluids are allowed to mix, andthe immiscible case, in which the fluids are not allowed to mix. In both cases, the determination of such quantities as velocity, pressure, concentration, and, in the immiscible case, the fluid pressure, concentration, and, in the immiscible case, the fluid interface are of physical interest and must be determined numerically. Computer oriented techniques developed for these and for related purposes include finite elements, finite differences, general variational methods, Galerkin methods, particle methods, and the method of characteristics (see, e.g., 7, 8, 10, 12-14, 16, 18, 20, 22, 23, 28-30). In this paper we will develop two related finite difference techniques, one for the miscible problems and the second for the immiscible ones. The power of the methods is derived from their hybrid structure, which incorporates some of the best aspects of the (Marker-and-cell) method, the Courant, Isaacson and Rees method, and several special techniques developed by Bulgarelli and the present writers 2, 4, 5, 11, 25, 31.