On the prediction of Darcy permeability in nonisotropic periodic two-dimensional porous media

Numerical computations of Stokes flow through a representative range of arrays of squares and rectangles are carried out. In each case, the unit-cell aspect ratio is the same as the particle aspect ratio. A deterministic analytical pore-scale model, based on a Poiseuille approximation to the actual flow field, provides a simple expression characterizing the trends of the numerical results. This model incorporates dependence on porosity and on a particle shape factor, and discriminates between regular and staggered arrays. The analytic expression. derived is shown to agree remarkably well with the numerical results, especially tit low porosities.