Keywords: Lattice Boltzmann method, multiphase flow simulation, Darcy law, porous media, kinematic viscosity.

Abstract: In this paper, we present a Lattice Boltzmann simulation of multiphase flow in a homogeneous two-dimensional porous media. For this study, we develop a program based on lattice Boltzmann equation. The underlying theoretical model makes it possible to couple the state equation of a non-ideal fluid with the pressure tensor at the interface and uses the excess free-energy density formalism. The fluid properties can be  prescribed in a thermodynamically consistent manner, which remains accurate at states close to the critical point. We have simulated some known two-phase flow configurations, like displacement of vapor by its liquid in homogeneous two-dimensional porous media reconstructed by image treatment under the action of an external flow field. We present also results for the averaged velocity as a function of time iteration and the permeability of two dimensional porous media as a function of kinematic viscosity and mesh resolution. Our results confirm that the LBM scheme reproduces Darcy’s law through the analysis of the dependency of the permeability on the kinematic viscosity.