Calculation of the effective permeability of saturated random porous media

Estimation of the effective permeability tensor is an essential part of Darcy-scale representations of flow in porous media. The permeability tensor itself is a property of the medium, and depends only on the microscale geometry of the system. Determining the functional relationships between effective permeability (or conductivity in the general sense) and the structure of the medium is an old problem, with the earliest results for ordered porous media dating the 1920's. In this presentation, we report on the results of (1) detailed theory development, and (2) computations for the effective permeability tensor in fully-saturated random sphere packs, with a focus on the computational results. The theory is developed by volume averaging the Stokes equations, and using developing appropriate closures via potential theory, and has been reported on previously. For the computations, we have adopted an immersed boundary method to fully resolve the pore-scale velocity field. From our results, we compute the hydraulic permeability for both ordered and random media, and we compare these results with existing analytical solutions for the hydraulic conductivity in periodic arrays.