Monte Carlo simulations of radial displacement of oil from a wetted porous medium: fractals, viscous fingering and invasion percolation

A numerical random-walk method for simulating pore-size radial displacement of oil from wetting porous media under varying conditions of pore-size distribution, wettability, mobility ratio and capillary numbers is described. The algorithm involves Monte Carlo decision making, random walks and percolation theory. The likelihood of having a walker start from a peripheral site, or from the origin, is determined by the viscosity ratio, M. Sticking probabilities, however, depend on the interfacial tension, gamma , and the solid-liquid contact angle, theta . Three limiting behaviours are identified in terms of viscosity ratio and capillary number: viscous fingering, plug flow and invasion percolation. Numerical experiments are performed for M=13 ( gamma =18 mN m -1 , theta =50 degrees ), and for M=7.6*10 -5 ( gamma =66 mN m -1 , theta =70 degrees ) at flow rates spanning four decades on a porous network of pores and sites having a log-normal size distribution. Typical runs last about 5-10 min. Preliminary evidence of partially dendritic growth at high capillary number is discussed. Agreement with previously reported experiments is excellent.