Two-Phase Flow in Porous Media: Scaling of Steady-State Effective Permeability

TL;DR

This study investigates the scaling behavior of steady-state effective permeability in two-phase flow through porous media, revealing different power law exponents depending on flow states and viscosity contrasts.

Contribution

It demonstrates that the effective permeability exhibits power law scaling with capillary number, with distinct exponents for different flow regimes and viscosity conditions, supported by experiments and simulations.

Findings

Power law dependence of permeability on capillary number observed.

Different exponents identified for stagnant cluster and non-stagnant states.

Simulation results align with experimental findings across viscosity contrasts.

Abstract

A recent experiment has considered the effective permeability of two-phase flow of air and a water-glycerol solution under steady-state conditions in a two-dimensional model porous medium, and found a power law dependence with respect to capillary number. Running simulations on a two-dimensional network model a similar power law is found, for high viscosity contrast as in the experiment and also for viscosity matched fluids. Two states are found, one with stagnant clusters and one without. For the stagnant cluster state, a power law exponent 0.50 is found for viscosity matched fluids and 0.54 for large viscosity contrast. When there are no stagnant clusters the exponent depends on saturation and varies within the range of 0.67 - 0.80.