Cluster evolution in steady-state two-phase flow in porous media
Abstract
Description
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 $n_s \sim s^{-τ}$ with the exponent $τ= 1.92 \pm 0.04$ 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.
12 pages, 11 figures. Minor corrections. Accepted for publication in Phys. Rev. E
12 pages, 11 figures. Minor corrections. Accepted for publication in Phys. Rev. E