  A new homogenization approach for the simulation of multi-phase flows in
heterogeneous porous media is presented. It is based on the lattice Boltzmann
method and combines the grayscale with the multi-component Shan-Chen method.
Thus, it mimics fluid-fluid and solid-fluid interactions also within pores that
are smaller than the numerical discretization. The model is successfully tested
for a broad variety of single- and two-phase flow problems. Additionally, its
application to multi-scale and multi-phase flow problems in porous media is
demonstrated using the electrolyte filling process of realistic 3D lithium-ion
battery electrode microstructures as an example. The new method shows
advantages over comparable methods from literature. The interfacial tension and
wetting conditions are independent and not affected by the homogenization.
Moreover, all physical properties studied here are continuous even across
interfaces of porous media. The method is consistent with the original
multi-component Shan-Chen method. It is accurate, efficient, easy to implement,
and can be applied to many research fields, especially where multi-phase fluid
flow occurs in heterogeneous and multi-scale porous media.
