An investigation on the robustness and accuracy of permeability estimation from 3D μ-CT images of rock samples based on the solution of Laplace's equation for pressure

摘要

This study aims to present a simple method to calculate the permeability of porous materials using mu-CT images and an approximation based on the solution of Laplace's equation for pressure. For this purpose, an in-house computer program was developed based on finite difference method to determine the distribution of pressure in voxelated pore space. Afterwards, approximate permeability was obtained using Euclidean distance map of the pore space and a simple upscaling scheme for a range of porous media including idealized channels of elementary cross sections, Boolean models of spherical grains, bundles of capillary tubes and digital rocks obtained from mu-CT imaging. Next, a comparison was made between the Laplace permeability approximation and the analytical solutions of idealized microstructure and digitally-computed permeability of a number of rock samples using the Stokes solver and the lattice-Boltzmann method. It has been revealed that the estimated permeability values are in good agreement over the investigated range of porosity. The developed Laplace permeability solver was also well matched with the results of experimental measurement on a real rock sample. As an illustration of the applicability of the proposed method, the anisotropy of permeability at pore scale and the cross-correlation between permeability and connected macro-porosity was analyzed for the experimentally investigated rock sample. In conclusion, the results of this paper suggest that the proposed permeability solver is suitable for rough estimation of permeability and hence rough evaluation of heterogeneity/anisotropy from mu-CT images of rocks, particularly for large datasets with high number of pore voxels.