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 the present LB model. Then in the framework of the LB method, we adopted a local scheme developed in some previous works for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also performed 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 large-scale problems.