Applications of critical path analysis to uniform grain packings with narrow conductance distributions: I. Single-phase permeability

Abstract

Accurate estimation of single-phase permeability (k) has broad application in numerous areas, particularly modeling flow and transport in porous materials. Various techniques have been proposed in the literature to estimate k from other medium's properties, such as porosity, grain and/or pore size distribution, and pore connectivity. Among them critical path analysis (CPA) from statistical physics − first developed to model fluid flow in media with broad conductance distributions − has been successfully applied to heterogeneous soils and rocks. However, its application to uniform sphere and/or glass bead packs that represent homogeneous porous media with narrow conductance distributions needs to be investigated. In this study, we invoke concepts from CPA and estimate k from average grain diameter and formation factor in uniform sand and glass bead packings. By comparing theory with eight datasets including 105 packs from the literature, we demonstrate that CPA estimates permeability in homogeneous media accurately. We also compare our CPA-based model estimations with those from the Kozeny–Carman, Revil and Cathles, and RGPZ models. Results indicate that the CPA approach estimates k more precisely than other three models studied here.