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Cite Details

I. Battiato, D. M. Tartakovsky, A. M. Tartakovsky and T. Scheibe, "On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media", Adv. Water Resour., vol. 32, doi:10.1016/j.advwatres.2009.08.008, pp. 1664-1673, 2009

Abstract

Reactive transport in porous media is a complex nonlinear phenomenon that involves both homogeneous (bio-)chemical reactions between species dissolved in a fluid and heterogeneous reactions that occur on liquid-solid interfaces. We establish sufficient conditions under which macroscopic reaction-diffusion equations (RDEs) provide an adequate averaged description of pore-scale processes. These conditions are represented by a phase diagram in a two-dimensional space, which is spanned by Damkohler number and a scale-separation parameter. This phase diagram shows that highly localized phenomena in porous media, including precipitation on (and/or dissolution of) a porous matrix, do not lend themselves to macroscopic (upscaled) descriptions. To compute the predictive errors resulting from the use of macroscopic RDEs, we upscaled the pore-scale RDEs to the continuum (macroscopic) scale and used pore-scale numerical simulations to verify various upscaling assumptions.

BibTeX Entry

@article{battiato-2009-breakdown,
author = {I. Battiato and D. M. Tartakovsky and A. M. Tartakovsky and T. Scheibe},
title = {On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media},
year = {2009},
urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/battiato-2009-breakdown.pdf},
journal = {Adv. Water Resour.},
volume = {32},
doi = {10.1016/j.advwatres.2009.08.008},
pages = {1664-1673}
}