On the effective transport properties of heterogeneous materials

This paper provides a new homogenization scheme, which is a combination of the theoretical and experimental approaches, for modeling effective transport properties of heterogeneous materials. Differ from the classical methods, this method considers a free conductivity of the reference matrix that is not a pre-defined parameter and can be calibrated based on an inverse analysis using available microscopic and macroscopic data. This technique is illustrated using experimental data of electrical conductivity of rocks published in literature. We show that the conductivity of the reference matrix can be approximated by linear or quadratic functions of the porosity. The proposed approach can be used to model materials containing highly contrast phases.