An easy-to-implement multi-scale computation of permeability coefficient for porous materials

In this paper, the multi-scale analysis based on the homogenization method is applied to the Stokes flow. This formulation allows computing permeability by solving a special Stokes flow problem in a unit cell. In particular, a simplified unit cell with characteristic radius is proposed to account for the complexity of the pore network. The determination of this unit cell is an inverse homogenization optimization process: to find the characteristic radius that yields a single laboratory permeability test data. Using the determined characteristic radius, the permeability coefficients can be computed for various void radios. Such an approach is applied to sands and clays. An agreement between the computed and measured values of the permeability coefficient is found.