  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.
