A comparison of various methods for the numerical evaluation of porous media permeability tensor from pore-scale geometry

In this work, several boundary value problems used to numerically evaluate the absolute permeability tensors of porous media using core-scale images are compared and discussed. The various configurations differ by the type of boundary conditions used to compute the flow at the micro-scale. The issue is the ability of the method to capture anisotropy correctly and to avoid possible percolation artifacts. This study is carried on two-dimensional synthetic, isotropic or anisotropic, porous media, that are chosen to illustrate the various difficulties mentioned above. A new method is proposed which consists in embedding the porous medium in question in a homogenized one. Using an iterative optimization procedure on the surrounding permeability, the method determines the absolute permeability tensor of the original medium. The equivalent permeability tensor that minimizes the effect on the surrounding porous medium is, unlike that of classical methods, de facto symmetrical due to the use of periodic boundary conditions and exhibits significantly lower permeabilities. The way in which non-diagonal terms of the permeability tensor are obtainedwith the various methods are thoroughly discussed