Effective medium analysis of random lattices

Calculations of effective conductivities of generalized random bond lattices representing porous media are compared to approximations using effective medium theory (EMT). We use numerical simulations of flow through 2D and 3D random lattice models, which allow for variable lattice densities and a lognormal distribution of local conductivities, to compare effective conductivities to effective medium approximations. We find that the analytical expressions provide good agreement to the simulations in 2D systems, but are in significant error in 3D systems when the standard deviation of the local conductivities is large.