Application of critical path analysis for permeability prediction in natural porous media

Abstract

Critical path analysis (CPA), originally developed to describe electrical conductance in semiconductors, has been shown recently to hold some promise in describing transport properties of porous media. I applied some previously developed concepts in CPA and percolation theory to predict permeability in a suite of sandstone, carbonate, and clay-rich samples. I assumed that the pore sizes in my samples exhibited fractal scaling and expressed the electrical formation factor as a function of porosity using universal scaling from percolation theory. The resulting CPA permeability predictions match the measured values very well. In addition, I show how considering the scale-dependence of the percolation threshold yields two characteristic length scales for transport properties: the critical pore size, and the sample size. This work suggests that the CPA framework is appropriate for describing transport properties of natural porous media, and provides a theoretical basis for understanding the permeability of tight rocks like shale in which laboratory permeability measurements are difficult.