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Significance of shape factor on permeability anisotropy of sand: representative elementary volume study for pore-scale analysis

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Abstract

This paper is a study of determination of representative elementary volume (REV) size suitable for pore-scale flow simulation (PFS) and evaluation of permeability anisotropy for sand based on Kozeny–Carman (KC) equation. We extracted small digitized samples for PFS from the 3D structures of Toyoura sand and glass beads obtained by X-ray computed tomography. Using the digitized samples with various sizes, we performed a series of flow simulations. We characterized the sample size using the ratio of the porous length L to the median grain diameter \(D_{50}\). The \(L/D_{50}\) of REV was determined on the basis of statistical evaluation on coefficients of variations of the simulated values of void ratio, specific surface, hydraulic conductivity and hydraulic tortuosity. We confirmed that the hydraulic properties obtained from the PFS using the REV size determined agreed well with the past experimental studies. We also conducted PFSs in the horizontal direction to evaluate the permeability anisotropy. We clarified that the shape factor in the KC equation has a strong influence on permeability anisotropy even though previous studies treated hydraulic tortuosity as the only factor that affects the permeability anisotropy.

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Abbreviations

k :

Hydraulic conductivity

\(D_{50}\) :

Mean grain diameter

e :

Void ratio

\(e_{\mathrm {m}}\) :

Measured void ratio

U :

Inlet constant seepage velocity

i :

Hydraulic gradient

\({\varDelta }_{\mathrm {p}}\) :

Pressure drop

\(\rho \) :

Water density

g :

Gravitational acceleration (9.81 m/s)

L :

Sample size

CV:

Coefficient of variation

\(A_{\mathrm {STL}}\) :

Surface area of STL file

\(A_{\mathrm {eff}}\) :

Effective surface area

\(\mu \) :

Water dynamic viscosity

\(\phi \) :

Shape factor

\(\tau _{\mathrm {h}}\) :

Hydraulic tortuosity

\(S_{\mathrm {S}}\) :

Specific surface

\(\psi \) :

Particle sphericity

\(\psi _{\mathrm {k}}\) :

Krumbein’s particle sphericity

〈u〉:

Volume average of the magnitude of flow velocity

〈ud〉:

Volume average of the velocity component along the flow direction

\(\tau _{\mathrm {e}}\) :

Electric-tortuosity

\(\lambda \) :

Confidence factor

E :

Allowable error

\(N_{\mathrm {run}}\) :

Required number of PFSs

\(r_{k}\) :

Hydraulic anisotropy

\(\phi _{\mathrm {V}}\) :

Shape factor for flow along vertical direction

\(\phi _{\mathrm {H}}\) :

Shape factor for flow along horizontal direction

\(\tau _{\mathrm {hV}}\) :

Hydraulic tortuosity for flow along vertical direction

\(\tau _{\mathrm {hH}}\) :

Hydraulic tortuosity for flow along horizontal direction

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Authors and Affiliations

  1. Environmental Management Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan

    Jun Katagiri

  2. Faculty of Agriculture, University of the Ryukyus, Nakagami-gun, Okinawa, Japan

    Sho Kimura

  3. Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan

    Shohei Noda

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  1. Jun Katagiri
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Correspondence to Jun Katagiri.

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Katagiri, J., Kimura, S. & Noda, S. Significance of shape factor on permeability anisotropy of sand: representative elementary volume study for pore-scale analysis. Acta Geotech. 15, 2195–2203 (2020). https://doi.org/10.1007/s11440-020-00912-0

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