Fractal Nature of Capillary and Viscous Fingering in Two-Dimensional Porous Media

A computer model of capillary and viscous fingering in a porous media is presented, which treats the media as a square lattice connected with randomly chosen radius. The fractal properties of the model are studied for shell-shell aggregation method by Monte Carlo simulation. The simulation results show that the dimension D increases along with increasing of M and decreasing of μ, where M and μ are the ratios of the viscosity of the two fluids and the most probable radius of the throat in porous media respectively. It is found that there exist four regions for fluid.