Archie's law from a fractal model for porous rocks

Abstract

Electrical conductivity of porous rocks is related to the porosity through the empirical relation known as Archie's law. The principal motivation behind the present paper is to show that the fractal nature of the pore space is important for the validity of this relation. A random walk, on two variations of a three-dimensional deterministic fractal model, is simulated and the result leads to a realistic exponent for Archie"s law.