The technique of investigating 3-dimensional interconnections and the shapes of crystals in a rock by X-ray computerized tomography (CT) and image analysis was developed using a graphic granite specimen as an example. Fifty 2-dimensional tomographic images (slices) of the graphic granite were obtained ‘non-destructively’ using a medical X-ray CT scanner. Since a CT value of the specimen was decreased with increasing cross-sectional sample area by the effect of beam-hardening, the CT value was corrected using the area of each slice. Binary images of the slices were made comparing one of them with a thin-section of the slice. Using the binary images, connection analysis of quartz rods in the graphic granite specimen was performed on the basis of percolation theory (cluster labelling). This analysis showed that at least 89.9% of the quartz rods were connected in three dimensions. Furthermore, the 3-dimensional shape of the quartz rods was analysed using the 2-point correlation function calculated from the binary images. The average shape of the quartz rods was obtained by fitting an ellipsoid to the high-value region of the 2-point correlation function. The elongation axis of the ellipsoid agreed well with the crystallographicc-axes of the quartz rods.

[1] The transport properties (porosity, surface-to-volume ratio of the pore space, diffusion coefficient, and permeability) of a porous medium were calculated by image analysis and random walk simulation using the digital image data on the pore structure of a bead pack (diameter 2.11 mm). A theory developed for laboratory experiments of nuclear magnetic resonance was applied to the random walk simulation. The threedimensional data set (256 3 voxels) of the bead pack was obtained by microfocus X-ray computed tomography at a spatial resolution of 0.053 mm. An original cluster labeling program, Kai3D.m, was used to estimate the porosity and surface-to-volume ratio. The surface-to-volume ratio and diffusion coefficient were calculated by an original random walk program, RW3D.m. The calculations were completed on a personal computer in reasonable time ( 13 hours). The permeability was estimated by substituting the results of Kai3D.m and RW3D.m into the Kozeny-Carman equation. The results for the porosity, surface-to-volume ratio, and diffusion coefficient were within 5-8% of measured values, whereas the calculated permeability involved an error of 35%. The promising results of the present study indicate that it is possible to estimate the permeability of porous media with reasonable accuracy by the diffusometry and random walk simulation. Because, in principle, the diffusometry could be performed by proton nuclear magnetic resonance logging, the method of estimating the transport properties presented here is applicable to the in situ measurement of strata. We open the original Mathematica 1 programs (Kai3D.m and RW3D.m) used to calculate the porosity, surface-to-volume ratio, and diffusion coefficient at the authors' home page to facilitate the personal-computer-based study of porous media using X-ray computed tomography.

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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 Ò 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 Xray CT images of a rhyolitic lava sample having an anisotropic pore structure. The programs are available at

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