Numerical validation of various mixing rules sed for up-scaled geo-physical properties

Mixing rules are widely used to express effective properties of coefficients appearing in heterogeneous diffusion like processes. Since most of the mixing rules were derived to compute the effective dielectric constant, εeff, in this work, we confine our interest to the electrostatic behavior of mixtures. This paper focuses on the validation of mixing rules by comparing them with the effective properties computed from the numerical solution of div(εgradΦ) =0 including boundary conditions. One of the issues concerns the very large number of grid blocks required to obtain convergence. We choose the checkerboard configuration as the input for the heterogeneous ε field as a realistic example that is amenable to analysis. We compare the convergence rates of a Finite Element Model (FEM) and a Finite Difference Model (FDM).