A Multiphase Gray-scale Lattice Boltzmann Model

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 LB method to model multiphase flow (e.g., gas and liquid or water and oil) in a semi-porous medium. We compare the solution to test cases as well as applying it to real porous media.