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Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium

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Abstract

Diffusion is an important transport process in low permeability media, which play an important role in contamination and remediation of natural environments. The calculation of equivalent diffusion parameters has however not been extensively explored. In this paper, expressions of the equivalent diffusion coefficient and the equivalent diffusion accessible porosity normal to the layering in a layered porous medium are derived based on analytical solutions of the diffusion equation. The expressions show that the equivalent diffusion coefficient changes with time. It is equal to the power average with p = −0.5 for small times and converges to the harmonic average for large times. The equivalent diffusion accessible porosity is the harmonic average of the porosities of the individual layers for all times. The expressions are verified numerically for several test cases.

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Abbreviations

C (kg/m3):

solute concentration in the liquid phase.

D(m 2/s):

effective diffusion coefficient (as defined by Gillham et al. 1984).

D eq (m2/s):

equivalent diffusion coefficient.

L (m):

layer thickness.

n (-):

diffusion accessible porosity.

n eq (-):

equivalent diffusion accessible porosity.

R (-):

retardation factor.

t (s):

time.

x (m):

distance from the top of the first layer.

X̅ p :

power average with power = p.

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Authors and Affiliations

  1. Hydrogeology and Engineering Geology Group, Department of Geology-Geography, Katholieke Universiteit Leuven, Redingenstraat 16, 3000, Leuven, Belgium

    Marijke Huysmans & Alain Dassargues

  2. Hydrogeology and Environmental Geology, Department of Georesources, Geotechnologies and Building Materials (GEOMAC), Université de Liège, B 52/3, 4000, Liège, Belgium

    Alain Dassargues

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  1. Marijke Huysmans
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  2. Alain Dassargues
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Correspondence to Marijke Huysmans.

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Huysmans, M., Dassargues, A. Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium. Transp Porous Med 66, 421–438 (2007). https://doi.org/10.1007/s11242-006-0028-6

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