The Gibbsian permeability model of porous media

A first-principles equation quantifying the permeability of fluid flow through a porous medium is developed. Existing treatments, like the popular Kozeny–Carman permeability equation, are phenomenological models, which are based on scaling arguments of one-dimensional flow. This paper shows that basic multi-dimensional flow effects make the Kozeny–Carman permeability inaccurate. The current model is based on second law considerations following Gibbs' thermodynamic equation and is generally valid for multi-dimensional porous media geometries and flows. Examples are used to illustrate the accuracy and relative simplicity of the new Gibbs permeability model against the Kozeny–Carman approach. In practice, the new model allows the permeability to be calculated with a single experimental trial compared to the multiple trials needed with D'Arcy's original method and that are required to calibrate the Kozeny–Carman model.