An Analytical Pore-Scale Model for Predicting Permeability from Electrical Conductivity

Predicting permeability from electrical measurements enables non-invasive subsurface hydrogeophysical characterisation. However, the widely adopted Archie–Kozeny–Carman framework relies on empirical assumptions that oversimplify pore geometry and may fail to adequately represent heterogeneous porous media, potentially leading to biased permeability estimates that are inconsistent with the underlying transport physics. In this paper, we derive, from the Navier–Stokes equations and Ohm’s law, a closed-form model that describes permeability as a function of electrical conductivity and pore geometry. The new model uncovers four distinct electrical transport paths in porous media, of which only one aligns mechanistically with fluid-flow trajectories. This distinction provides a physical explanation for the non-unique relationship between electrical conductivity and permeability. The new model is benchmarked against ten widely used permeability models on a global dataset of 6288 laboratory samples, where it achieves superior predictive accuracy (R2 = 0.70; RMSE = 0.47, MAE = 0.34, bias < 0.01, all in log10 m2), remains stable across soil textures, and stays skilful (R2 > 0.60) under data uncertainties of up to 47%, as performed by Monte Carlo simulations. By contrast, predicting permeability from pore-area alone can produce errors spanning several orders of magnitude. This work offers a physically consistent alternative to empirical approximations for predicting permeability.