  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 packs. 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.
