General anisotropic effective medium theory for the effective permeability of heterogeneous reservoirs

One of the techniques to calculate the effective property of a heterogeneous medium is the effective medium theory. The present paper presents a general mathematical formulation for the effective medium approximation using a self-consistent choice of the effective permeability, to apply it to the case of a general anisotropic 2D medium and to the case of a 3D isotropic medium with randomly oriented ellipsoidal inclusions. The 2D results are compared with analytical results and with a homogenization technique with good result. The 3D correlations are used to derive percolation thresholds in two-phase systems with a large permeability contrast, which are compared to numerical results from the literature, also with good results.