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Effect of X-ray \(\mu\)CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils

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Abstract

X-ray micro-computed tomography (\(\mu\)CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of effective properties of the material—such as the permeability (k) and the hydrodynamic dispersion coefficient (\(D_h\))—, through the solutions of the Stokes equation (SE) and Advection-Diffusion equation (ADE), respectively. In this study, the effect of the image resolution on these properties is discussed. For such purpose, four different resolutions are evaluated for both a real sample of Fontainebleau sand and a numerically generated sample created by degrading the Fontainebleau image with highest resolution. The SE was computed using the commercial software GeoDict. To solve the ADE, a Finite Volume software was developed which includes a high order total variation diminishing scheme for advection. The analysis of dispersion was based on numerical breakthrough curves. Our model was tested in a large range of Peclet numbers (Pe) and travel distances, accurately describing the transition between diffusion and advection dominated regimes of dispersion. The \(D_h\) exhibits a linear increase with travel distance for Pe \(> 10\). This classical effect increases with increasing Pe. The percentage change on k and \(D_h\) increases with decreasing resolution in agreement with the corresponding behavior of porosity, specific surface and pore size distributions. The images directly scaled with the \(\mu\)CT showed more discrepancy than the numerically scaled images. The criteria to estimate the quality of permeability from the pore size distribution proposed on our previous study remains valid. The \(D_h\) is less sensitive to resolution than k.

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Notes

  1. Rescaling or resizing is the process of increasing or decreasing the number of pixels in an image or voxels in a volume. This process is not lossless. Rescaling a volume to a smaller number of voxels, and then rescaling it back to the original resolution, results in an image sightly different from the original one (Danahy et al. 2007).

  2. PV is the time required for the concentration to completely fill the porous volume under study.

  3. The CXTFIT software has the option to compute the BTC given the effective coefficients of a column experiment (direct problem).

Abbreviations

BTC:

Break thought curve

\(D_x\) :

x percentage of pores that have a diameter \(D_x\)

\(d_x\) :

x percentage of grains that have a diameter \(d_x\)

FDM:

Finite difference method

FEM:

Finite elements method

FVM:

Finite volume method

LBM:

Lattice Boltzmann method

macro ADE:

Advection dispersion equation at macro scale

micro ADE:

Advection diffusion equation at micro scale

\(\mu\)CT:

Micro computed tomography

MUMPS:

MUltifrontal massively parallel solver

PEEK:

PolyEtherEtherKetone

PSD:

Pore size distribution

RF:

Rescaling factor

SPH:

Smooth particle hydrodynamics

TVD:

Total variation diminishing

VOI:

Volume of interest

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Acknowledgements

We are grateful to Dr. D.A. Amor-Quiroz for helping us with proofreading the present manuscript and making the content clearer. Permeability computations were performed using the FlowDict module of the GeoDict software package.

Funding

This study was supported by the PROTINUS project funded in the framework of the European Union’s Horizon 2020 research. It benefited from a PhD Grant from the CONACYT Reference no.240912/383935, and a grand concerning the access to the X-ray Thomograph from Labex OSUG@2020 (Investissements d’Avenir-ANR-10-LABX-0056).

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  1. Univ. Grenoble Alpes, CNRS, IRD, Grenoble INP, IGE, 38000, Grenoble, France

    Miriam Patricia Ortega-Ramírez & Laurent Oxarango

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  1. Miriam Patricia Ortega-Ramírez
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Correspondence to Laurent Oxarango.

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Ortega-Ramírez, M.P., Oxarango, L. Effect of X-ray \(\mu\)CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils. Transp Porous Med 137, 307–326 (2021). https://doi.org/10.1007/s11242-021-01557-7

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