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 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

Use of existing pore models and X-ray computed tomography to predict saturated soil hydraulic conductivity

“…The influence of tortuosity is important in unsaturated soil samples where the water-film on pore walls is the primary flow path, and is also important in fully-saturated soils when considering bifurcations and the resulting flow-path network. An alternative to direct measurement of pore tortuosity is random-walk experiments, as described in Nakashima and Kamiya (2007), who utilize a measure of particle displacement over time throughout discretized pore space on a rigid (digital-voxel) grid. A random-walk experiment in free space will have no obstruction to displacement, and in confined space (i.e.…”

Application of X-ray microtomography to quality assessment of fibre cement boards

“…where A is a constant, which depends on implemented image lattice parameters and in [9,10] is assumed as 1.…”

“…That is useful to recognize the shapes of the complex objects immersed in investigated volume. Another one, called 'random walk' was created to assess the magnitude of pore interconnectivity of tested material [7][8][9][10]. The latter algorithm performs the simulation of the diffusion of virtual particles, called 'walkers' in the interconnected network of pores.…”

Comparing time-resolved infrared thermography and X-ray computed tomography in distinguishing soil surface crusts

“…In order to further segment the void space into individual pore networks, Nakashima and Kamiya (2007) implemented the Hoshen and Kopelman algorithm for cluster labeling to identify connected pores in 3D binarized CT data as well as to quantify the surface of isolated pores and surface-to-volume ratio.…”

“…The segmented reconstructed volume was transformed to a series of 2D binary slices. The cluster label program, written by Nakashima and Kamiya (2007), based on the Hoshen and Kopelman algorithm, was applied to identify and calculate the surface and the volume of isolated pore networks.…”