A multiphase single relaxation time lattice Boltzmann model for heterogeneous porous media

The lattice Boltzmann (LB) method has been shown to be a highly efficient numerical method for solving fluid flow in confined domains such as pipes, irregularly shaped channels or porous media. Traditionally the LB method has been applied to flow in void regions (pores) and no flow in solid regions. However, in a number of scenarios, this may not suffice. That is partial flow may occur in semi-porous regions. Recently gray-scale LB methods have been applied to model single phase flow in such semi-porous materials. Voxels are no longer completely void or completely solid but somewhere in between. We extend the single relaxation time LB method to model multiphase, immiscible flow (e.g., gas and liquid or water and oil) in a semi-porous medium. We compare the solution to test cases and find good agreement of the model as compared to analytical solutions. We then apply the model to real porous media and recover both capillary and viscous flow regimes. However, some deficiencies in the single relaxation time LB method applied to multiphase flow are uncovered and we describe methods to overcome these limitations.