Grain consolidation and electrical conductivity in porous media

Abstract

A simple geometrical model is proposed for diagenesis. Diagenesis is the process by which granular systems evolve geologically from unconsolidated, high-porosity packings toward more consolidated, less porous, materials. We find that the relation between the electrical conductivity σ and the porosity φ can be approximated by a nontrivial power law over a wide range of porosity for both ordered and disordered lattice configurations. The most realistic model is generated from a dense disordered packing. This leads to a problem involving both short-range structural disorder and correlated percolation. In comparison with experiment, our calculations (on both ordered and disordered systems) are shown to reproduce the qualitative trends found in recent data on the conductivity of systems comprised of fused glass beads.