Cluster evolution in steady-state two-phase flow in porous media

We report numerical studies of the cluster development of two-phase flow in a steady-state environment of porous media. This is done by including biperiodic boundary conditions in a two-dimensional flow simulator. Initial transients of wetting and nonwetting phases that evolve before steady state has occurred, undergo a crossover where every initial pattern is broken up. For flow dominated by capillary effects with capillary numbers in order of 10⁻⁵, we find that around a critical saturation of nonwetting fluid the nonwetting clusters of size s have a power-law distribution n_s∼s^−τ with the exponent τ=1.92±0.04 for large clusters. This is a lower value than the result for ordinary percolation. We also present scaling relation and time evolution of the structure and global pressure.