Lattice‐Boltzmann simulation of two‐phase flow in porous media

TLDR

The sphere‑pack model reproduces laboratory experiments on hysteretic capillary pressure–saturation behavior of water–tetrachloroethylene in a glass‑bead porous medium. We employ a parallel Shan‑Chen lattice Boltzmann framework to simulate two‑fluid pore‑scale flow, validating it against ideal systems before applying it to the synthetic sphere‑pack medium. The simulations match measured hysteretic capillary pressure–saturation curves, including entry pressure, displacement slopes, irreducible saturation, and residual entrapment, and reveal that systems with 1200 versus 150 spheres differ significantly, indicating a lower bound on the representative elementary volume.

Abstract

We simulate two‐fluid‐phase flow at the pore scale using a lattice Boltzmann (LB) approach. Using a parallel processing version of the Shan‐Chen model that we developed, we simulate a set of ideal two‐fluid systems and a model two‐fluid‐phase porous medium system comprised of a synthetic packing with a relatively uniform distribution of spheres. We use the set of ideal two‐phase systems to validate the approach and provide parameter information, which we then use to simulate a sphere‐pack system. The sphere‐pack system is designed to mimic laboratory experiments conducted to evaluate the hysteretic capillary pressure saturation relation for a system consisting of water, tetrachloroethylene, and a glass bead porous medium. Good agreement is achieved between the measured hysteretic capillary pressure saturation relations and the LB simulations when comparing entry pressure, displacement slopes, irreducible saturation, and residual entrapment. Our results further show that while qualitatively similar results are obtained when comparing systems consisting of 1200 spheres and 150 spheres, there is a significant difference between these two levels, suggesting a lower bound on the size of a representative elementary volume.