A lattice Boltzmann model for two-phase flow in porous media

In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for velocity are accurate and also have a second-order convergence rate in space. Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems.