Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media. Issue 14 (29th July 2019) - Richesson, Samuel; Sahimi, Muhammad
Abstract: 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. Key Point: This demonstrates the first application of the effective‐media approximation to estimating the permeability of deforming porous media