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

TL;DR

This paper uses numerical simulations to study how clusters of two-phase flow develop and evolve in steady-state porous media, revealing a power-law distribution of cluster sizes near a critical saturation point.

Contribution

It introduces a new simulation approach with biperiodic boundary conditions to analyze cluster development and identifies a specific power-law distribution with a critical exponent.

Findings

Cluster size distribution follows a power-law with exponent ~1.92.

Non-wetting clusters exhibit critical behavior near a specific saturation.

Scaling relations and pressure evolution are characterized.

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 $n_s \sim s^{-\tau}$ with the exponent $\tau = 1.92 \pm 0.04$ 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.