Monte Carlo simulation of two-phase flow in porous media: Invasion with two invaders and two defenders

We report the results of extensive Monte Carlo simulations of a novel model of two-phase flow in porous media, recently proposed by us (Phys. Rev. Lett. 80 (1998) 3248), in which the two fluids act both as the invading as well as the defending fluids. The phenomenon is relevant to several multiphase flow problems in porous systems and, in particular, in fractured porous media. Our simulations show that the structure of the fluids’ clusters is volatile and changes with the time t and length scale. Moreover, ns, the number of clusters of size s, 〈s〉, the mean cluster size, and the fluids’ saturations all oscillate aperiodically with t, indicating the continuing breakup and recoalescence of the clusters. The effect of flow of thin films of the wetting fluid on the dynamics of the displacement is shown to be strong. Novel dynamical scaling laws for the cluster-size distribution are obtained. The results are in qualitative agreement with experimental observations.