Mathematica Programs for the Analysis of Three-Dimensional Pore Connectivity and Anisotropic Tortuosity of Porous Rocks using X-ray Computed Tomography Image Data

Abstract

Understanding of the transport properties of porous rocks is important for safe nuclear waste disposal because harmful contaminated groundwater can migrate along pore spaces over long distances. We developed three original Mathematica® version 5.2 programs to calculate the transport properties (porosity, pore connectivity, surface-to-volume ratio of the pore space, and anisotropic tortuosity of the pore structure) of porous rocks using three-dimensional (3-D) 8-bit TIFF or BMP X-ray computed tomography (CT) images. The pre-processing program Itrimming.nb extracts a 3-D rectangular region of interest (ROI) from the raw CT images. The program Clabel.nb performs cluster-labeling processing of the pore voxels in the ROI to export volume, surface area, and the center of gravity of each pore cluster, which are essential for the analysis of pore connectivity. The random walk program Rwalk.nb simulates diffusion of non-sorbing species by performing discrete lattice walks on the largest (i.e., percolated) pore cluster in the ROI and exports the mean-square displacement of the non-sorbing walkers, which is needed to estimate the geometrical tortuosity and surface-to-volume ratio of the pore. We applied the programs to microfocus X-ray CT images of a rhyolitic lava sample having an anisotropic pore structure. The programs are available at http://www.jstage.jst.go.jp/browse/jnst/44/9/ and http://staff.aist.go.jp/nakashima.yoshito/progeng.htm to facilitate the X-ray CT approach to groundwater hydrology.

KEYWORDS:

• anisotropy
• diffusometry
• diffusion tensor
• MRI
• NMR
• permeability
• percolation cluster
• pore size
• porous media
• self-diffusion coefficient
• X-ray CT