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Dispersion in Porous Media with Heterogeneous Nonlinear Reactions

Guo, Jianwei and Quintard, Michel and Laouafa, Farid Dispersion in Porous Media with Heterogeneous Nonlinear Reactions. (2015) Transport in Porous Media, 109 (3). 541-570. ISSN 0169-3913

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Official URL: http://dx.doi.org/10.1007/s11242-015-0535-4

Abstract

The upscaling of mass transport in porous media with a heterogeneous reaction at the fluid–solid interface, typical of dissolution problems, is carried out with the method of volume averaging, starting from a pore-scale transport problem involving thermodynamic equilibrium or nonlinear reactive boundary conditions. A general expression to describe the macro-scalemass transport is obtained involving several effective parameterswhich are given by specific closure problems. For representative unit cell with a simple stratified geometry, the effective parameters are obtained analytically and numerically, while for those with complicated geometries, the effective parameters are only obtained numerically by solving the corresponding closure problems. The impact on the effective parameters of the fluid properties, in terms of pore-scale Péclet number Pe, and the process chemical properties, in terms of pore-scale Damköhler number Da and reaction order (n), is studied for periodic stratified and 3D unit cells. It is found that the tortuosity effects play an important role on the longitudinal dispersion coefficient in the 3D case, while it is negligible for the stratified geometry. When Da is very small, the effective reaction rate coefficient is nearly identical to the pore-scale one, while when Da is very large, the reactive condition turns out to be equivalent to pore-scale thermodynamic equilibrium, and the macro-scale mass exchange term is consequently given in a different form from the reactive case. An example of the application of the macro-scale model is presented with the emphasis on the potential impact of additional, non-traditional effective parameters appearing in the theoretical development on the improvement of the accuracy of the macro-scale model.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://link.springer.com The original PDF of the article can be found at Transport in Porous Media website : http://link.springer.com/article/10.1007%2Fs11242-015-0535-4
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
French research institutions > Institut National de l'Environnement Industriel et des Risques - INERIS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:28 Aug 2015 13:26

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