Computer simulations of two-fluid immiscible displacement flow in porous media.

Abstract

Two general-purpose computer programs have been developed for modelling the displacement of a wetting fluid by a non-wetting one in porous media. A microscopic approach is applied for the solution of the governing equations at the pore level. The porous medium is represented by a two-dimensional network of interconnected capillaries. One program makes use of a stochastic approach based on the aspects of random walks, invasion percolation and on the notion of the phase diagram for immiscible displacement. The other program makes use of a deterministic approach based on a relaxation technique in order to solve for the pressure field, and on certain rules for the advancement of the interface. The series of simulations undertaken successfully predicts certain important phenomena such as: (a) monophasic flow in porous media, (b) the effects of capillary and viscous forces on the dynamic behaviour of the displacing fluid and on the oil recovery, (c) the island formation and the island size distribution as a result of the interplay of viscous and capillary forces, (d) the fractal behaviour of the displacing fluid, (e) the transition from one distinct behaviour of the displacing fluid to another, and (f) the effects of local anisotropy and heterogeneity of the porous medium on the dynamic behaviour of the displacing fluid. The validity of the algorithms is tested by comparing the numerical results with physical experiments available in the literature. Comparisons between the two approaches reveal that (a) the stochastic approach is more efficient in terms of execution time in the computer, (b) the deterministic approach better describes the physics of the problem, and (c) the deterministic approach has more potential to be extended to other problems. It is proposed that the present programs can be used to successfully predict two-fluid immiscible displacement flow in porous media for other relevant situations.