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Diffusion ellipsoids of anisotropic porous rocks calculated by X‐ray computed tomography‐based random walk simulations

Water molecules and contaminants migrate in water‐saturated porous strata by diffusion in systems with small Péclet numbers. Natural porous rocks possess the anisotropy for diffusive transport along the percolated pore space. An X‐ray computed tomography (CT) based approach is presented to quickly characterize anisotropic diffusion in porous rocks. High‐resolution three‐dimensional (3‐D) pore images were obtained for a pumice and three sandstones by microfocus X‐ray CT and synchrotron microtomography systems. The cluster‐labeling process was applied to each image set to extract the 3‐D image of a single percolated pore cluster through which diffusing species can migrate a long distance. The nonsorbing lattice random walk simulation was performed on the percolated pore cluster to obtain the mean square displacement. The self‐diffusion coefficient along each direction in the 3‐D space was calculated by taking the time derivative of the mean square displacement projected on the corresponding direction. A diffusion ellipsoid (i.e., polar representation of the direction‐dependent normalized self‐diffusivity) with three orthogonal principal axes was obtained for each rock sample. The 3‐D two‐point autocorrelation was also calculated for the percolated pore cluster of each rock sample to estimate the pore diameter anisotropy. The autocorrelation ellipsoids obtained by the ellipsoid fitting to the high correlation zone were prolate or oblate in shape, presumably depending on the eruption‐induced deformation of magma and regional stress during sandstone diagenesis. The pore network anisotropy was estimated by calculating the diffusion ellipsoid for uniaxially elongated or compressed rock images. The degree and direction of the geological deformation of the samples estimated by the pore diameter anisotropy analysis agreed well with those estimated by the pore network anisotropy analysis. We found that the direction of the geological deformation coincided with the direction of the major (or minor) principal axis of the prolate (or oblate) diffusion ellipsoid for each sample. Thus, it can be concluded that the deformation‐induced pore structure anisotropy is responsible for the anisotropy of the diffusive transport properties.