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

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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 non-wetting phases that evolve before steady-state has occurred, undergo a cross-over where every initial patterns are broken up. For flow dominated by capillary effects with capillary numbers in order of 10⁻⁵, we find that around a critical saturation of non-wetting fluid the non-wetting clusters of size s have a power-law distribution nₛ 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.