Hertz-Mindlin Theory of Contacting Grains and the Effective-Medium Approximation for the Permeability of Deforming Porous Media

Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or stress is important to a wide variety of processes, ranging from shale formations into which a fracking liquid is injected to CO2 sequestration in geological formations. We propose a novel model for estimating the effective permeability of such porous media. Given the pore-size distribution (PSD) of a porous medium before deformation, as well as the Young's modulus of its grains, the model uses Hertz-Mindlin theory of contact between grains to compute the new PSD that results from applying an external pressure P to the medium and utilizes the updated PSD in the effective-medium approximation to estimate the effective permeability at P. Comparison between the predictions and experimental data for several types of sandstones indicates excellent agreement between the two.