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Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

Davit, Yohan and Wood, Brian D. and Debenest, Gérald and Quintard, Michel Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media. (2012) Transport in Porous Media, vol. 95 (n° 1). pp. 213-238. ISSN 0169-3913

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Official URL: http://dx.doi.org/10.1007/s11242-012-0040-y

Abstract

In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t)is smaller than the characteristic time (τ1) for the relaxation of the effective macroscale param-eters (i.e., whent ≤τ1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ1) (i.e., whent τ1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the timescale (τ2) associated with exchange processes between the two regions(i.e., when t τ2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq∞)in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects.

Item Type:Article
Additional Information:Thanks to Springer Verlag. The original publication is available at http://www.springerlink.com
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Oregon State University (USA)
Other partners > University of Oxford (UNITED KINGDOM)
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Deposited By: Michel QUINTARD
Deposited On:09 Apr 2013 08:58

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