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Title of Journal: Stoch Environ Res Risk Assess

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Abbravation: Stochastic Environmental Research and Risk Assessment

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Springer-Verlag

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DOI

10.1016/0032-5910(82)89003-7

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1436-3259

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Equivalent diffusion coefficient of clayrich geol

Authors: Marco Bianchi HuiHai Liu Jens T Birkholzer
Publish Date: 2012/09/11
Volume: 27, Issue: 5, Pages: 1081-1091
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Abstract

Laboratory experiments in rock samples collected from clayrich formations indicate that the effective molecular diffusion coefficient D is a heterogeneous and anisotropic property Since laboratory measurements of D are representative of a very small volume upscaling is necessary in order to incorporate these data in largescale numerical models of diffusive transport In this work we address the problem of the estimating the equivalent diffusion coefficient D eq in terms of total diffusive flux in a threedimensional domain characterized by a heterogeneous and anisotropic spatial distribution of D D eq was estimated from the results of steadystate diffusive transport simulations through several realizations of the D field The ensemble averages of D eq from fields with different degrees of heterogeneity and anisotropy were then compared with estimates from analytical upscaling expressions based on stochastic as well as poweraveraging approaches These expressions are largely based on similar expressions developed for calculating the effective hydraulic conductivity in heterogeneous and anisotropic domains Comparisons showed that stochastic expressions provide accurate estimates of D eq only for fields characterized by low heterogeneity Within the range of heterogeneity and anisotropy considered our results showed that a poweraveraging expression is very accurate in predicting D eq especially when the parameter p i is estimated through fitting of the numerical results Nonetheless the relationship between this parameter and the anisotropy ratio is linearFunding for this work was provided by the Used Fuel Disposition Campaign Office of Nuclear Energy of the US Department of Energy under Contract Number DEAC0205CH11231 with the Lawrence Berkeley National Lab We thank the Associate Editor and two anonymous referees for their careful review of this manuscript

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