Excluded-volume explanation of Archie’s law

Abstract

The empirical relation between the electrical conductivity and the porosity of rocks is called Archie’s law. Although it has been known for many years, attempts to explain this law are quite recent. These explanations have used effective-medium theories, special percolation models, and fractal pore structures. In this paper it is shown, contrary to previous suggestions, that ordinary percolation theory can account for the zero pore-space threshold and may account for the power-law behavior which was derived from the available experimental data. In this respect simple percolation is more general than the previous explanations.