Computer Simulation of Radial Viscous Fingering in Two-Dimension Porous Media

A computer model of capillary and viscous fingering in a porous medium is presented which treats the medium as a square lattice connected with randomly chosen radius. The fractal properties of the model are studied for circular shell-shell aggregation by a Monte Carlo simulation. The simulation results show that the dimension D increases with decrease of the viscous ratio M and increase of the throat radius. It is found that the displacement process is stable when M=1, and viscous fingering pattern of porous media in the limit M → ∞ is similar to the diffusion-limited aggregation pattern in a uniform system. For larger viscous ratio M and smaller positive integer k, the fluid is situated in the co-existence region of viscous and capillary fingering.