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

Thomas Ramstad·Alex Hansen
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Abstract

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.

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Thomas Ramstad, Alex Hansen. 2006-01-05. Cluster evolution in steady-state two-phase flow in porous media. https://doi.org/10.1103/physreve.73.026306

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