Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/22554
Title: Homogenization of a pore scale model for precipitation and dissolution in porous media
Authors: Kumar, Kundan
Neuss-Radu, Maria
Pop, Sorin 
Issue Date: 2016
Source: IMA JOURNAL OF APPLIED MATHEMATICS, 81(5), p. 877-897
Abstract: In this article, we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media. The starting point is the pore scale model in van Duijn & Pop (2004), which is a coupled system of evolution equations, involving a parabolic equation which models ion transport in the fluid phase of a periodic porous medium, coupled to an ordinary differential equations modelling dissolution and precipitation at the grains boundary. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but possibly discontinuous function. In order to pass to the limit in these rate functions at the boundary of the grains, we prove strong two-scale convergence for the concentrations at the microscopic boundary and use refined arguments in order to identify the form of the macroscopic dissolution rate, which is again a discontinuous function. The resulting upscaled model is consistent with the Darcy scale model proposed in Knabner et al. (1995).
Keywords: homogenization; reactive flow; periodic unfolding; two scale convergence; porous media; non-Lipschitz reaction rates
Document URI: http://hdl.handle.net/1942/22554
ISSN: 0272-4960
e-ISSN: 1464-3634
DOI: 10.1093/imamat/hxw039
ISI #: 000386131200008
Rights: © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Category: A1
Type: Journal Contribution
Validations: ecoom 2017
Appears in Collections:Research publications

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