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Equivalence between volume averaging and moments matching techniques for mass transport models in porous media

Davit, Yohan and Quintard, Michel and Debenest, Gérald Equivalence between volume averaging and moments matching techniques for mass transport models in porous media. (2010) International Journal of Heat and Mass Transfer, 53 (21-22). 4985-4993. ISSN 0017-9310

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Official URL: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.05.032

Abstract

This paper deals with local non-equilibrium models for mass transport in dual-phase and dual-region porous media. The first contribution of this study is to formally prove that the time-asymptotic moments matching method applied to two-equation models is equivalent to a fundamental deterministic perturbation decomposition proposed in Quintard et al. (2001) [1] for mass transport and in Moyne et al. (2000) [2] for heat transfer. Both theories lead to the same one-equation local non-equilibrium model. It has very broad practical and theoretical implications because (1) these models are widely employed in hydrology and chemical engineering and (2) it indicates that the concepts of volume averaging with closure and of matching spatial moments are equivalent in the one-equation non-equilibrium case. This work also aims to clarify the approximations that are made during the upscaling process by establishing the domains of validity of each model, for the mobile–immobile situation, using both a fundamental analysis and numerical simulations. In particular, it is demonstrated, once again, that the local mass equilibrium assumptions must be used very carefully.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com/science/article/pii/S0017931010002747
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)
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Deposited By: Yohan DAVIT
Deposited On:21 Nov 2013 11:16

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