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

Nakashima, Yoshio; Kamiya, Susumu

doi:10.1080/18811248.2007.9711367

Cited by 110 publications

(49 citation statements)

References 33 publications

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“…The random walk approach was first formulated in the 1990s 4,132,133 and found its way into electrochemistry via Kishimoto et al, 128 after having been used to extract the tortuosity of porous rocks. 134 However, the obtained tortuosity is affected by the number of walkers and by the number of time steps chosen for the calculation. This is why, in 99 , 100,000 walkers and 10,000,000 time steps are chosen to ensure high accuracy of the results (cf.…”

Section: Voxel Based Calculation Methodsmentioning

confidence: 99%

Tortuosity in electrochemical devices: a review of calculation approaches

Tjaden

Brett

Shearing

2016

International Materials Reviews

202

188

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The tortuosity of a structure plays a vital role in the transport of mass and charge in electrochemical devices. Concentration polarisation losses at high current densities are caused by mass transport limitations and are thus a function of microstructural characteristics. As tortuosity is notoriously difficult to ascertain, a wide and diverse range of methods has been developed to extract the tortuosity of a structure. These methods differ significantly in terms of calculation approach and data preparation techniques. Here, we review tortuosity calculation procedures applied in the field of electrochemical devices to better understand the resulting values presented in the literature. Visible differences between calculation methods are observed, especially when using porosity-tortuosity relationships and when comparing geometric and flux based tortuosity calculation approaches.

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Section: Voxel Based Calculation Methodsmentioning

confidence: 99%

Tortuosity in electrochemical devices: a review of calculation approaches

Tjaden

Brett

Shearing

2016

International Materials Reviews

202

188

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“…For example, the tortuosity in geologic materials has been estimated based on random walk simulation in the 3D pore space [13,14].…”

Section: Background On Definition Of Tortuositymentioning

confidence: 99%

“…In contrast, Figure 2 describes the output of random walk simulations in confined pore spaces as represented by three simple capillary tube models that percolate in x-direction only. Note that the self-diffusion coefficient (D ∞ ) can be calculated from the limiting slope of the mean square displacement (<r 2 >) averaged over n walkers against time (t) such that [11,14,29]:…”

Section: Quantification Of Tortuosity From Random Walk Simulation In mentioning

confidence: 99%

“…A 3D random walk technique [14] implemented in Mathematica was employed to compute the mean-square displacement of random walkers in the percolating pore space of a simple cubic lattice. Mirror image boundary conditions were applied on the original 3D image of cubic lattice (L 3 ), resulting to an expanded (3L) 3 system where simulations are performed.…”

Section: Quantification Of Tortuosity From Random Walk Simulation In mentioning

confidence: 99%

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Quantification of tortuosity in hardened cement pastes using synchrotron-based X-ray computed microtomography

Promentilla

Sugiyama

Hitomi

et al. 2009

Cement and Concrete Research

242

108

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Tortuosity, as being influenced by the 3D pore micro-geometry, is an important physical quantity to understand better the effect of pore structure on transport properties of cement-based materials. This study attempts to evaluate directly this pore structure-transport parameter from the microtomographic images at spatial resolution of 0.5 µm. This resolution, is by far, to our knowledge, the highest resolution reported for 3D non-invasive imaging of hardened cement pastes. The results show the feasibility of using synchrotron microtomography coupled with 3D image analysis and random walk simulation to measure the diffusion tortuosity that has a direct bearing on transport properties. The tortuosity associated with the percolating pore space seems to reflect the pore morphology that mainly controls the transport properties in young cement pastes; thus, explaining the rough agreement of the results with the computer model or experimental evidence.

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“…(A4). The details of the random walk simulation are described elsewhere (Nakashima and Kamiya 2007;Nakashima et al 2008).…”

Section: Description Of Diffusion Simulationsmentioning

confidence: 99%

Steady-State Local Diffusive Fluxes in Porous Geo-Materials Obtained by Pore-Scale Simulations

Nakashima

Nakano

2012

Transp Porous Med

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Computer simulations of non-sorbing tracers diffusing in fluid-saturated porous sediment/rock were performed using pore-scale X-ray microtomographic images to reveal the following. (i) The histogram of the magnitude of the local diffusive flux vector obeys a unimodal log-normal distribution having a long positive tail. Simulations using model images were also performed to show that the flux broadening in large pores and the flux mixing at the pore network junctions are responsible for the log-normal shape. (ii) The simulation enabled us to directly visualize pore voxels with large and small fluxes, confirming the existence of transport pores and stagnant pores. Because of the unimodal nature, however, it was difficult to distinguish transport pores from stagnant pores using an objective threshold in the histogram. (iii) Another histogram of the flux vector component along the direction of the macroscopic concentration gradient was analyzed. A negative tail was found in the histogram, indicating that local counter diffusion exists in the porous geo-materials. However, the population and intensity of the counter diffusion fluxes are too small and weak to contribute to the overall diffusive transport across the porous media system. A long positive tail representing a large-flux diffusive pathway was also observed in the histogram. However, again, the population of the large-flux transport pores is small. As a result, the main conveyer of the tracer is the stagnant pores (not the transport pores), which have small positive flux values but a large population.

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

Cited by 110 publications

References 33 publications

Tortuosity in electrochemical devices: a review of calculation approaches

Tortuosity in electrochemical devices: a review of calculation approaches

Quantification of tortuosity in hardened cement pastes using synchrotron-based X-ray computed microtomography

Steady-State Local Diffusive Fluxes in Porous Geo-Materials Obtained by Pore-Scale Simulations

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