Critical Path Analysis of the Hydraulic and Electrical Properties of Pore Network Models.

The transport properties of strongly heterogeneous porous media are dominated by the connectivity of the most permeable parts.   Critical path analysis (CPA) is a method that uses elements of percolation theory to estimate macroscopic transport properties of heterogeneous media that is highly disordered at the microscale.  Several earlier numerical investigations of CPA on pore network models raised questions about the applicability of CPA to porous media.  Among other things, these studies found that (i.) in well-connected 3D networks, CPA predictions were inaccurate and became worse when heterogeneity was increased; and (ii.) CPA could not fully explain the transport properties of 2D networks.  To clarify the performance of CPA, we made numerical computations of hydraulic and electrical conductivities on 2D and 3D networks with differing pore geometries and radius distributions.  A new CPA derivation for the relationship between electrical and hydraulic properties includes an additional term that improves the agreement with 3D numerical results, particularly when the pore radius distribution is highly heterogeneous. Agreement of CPA predictions with 2D network calculations is similar, although 2D networks are not well-suited for evaluating the general applicability of CPA to porous media.