Homogenization of a pore scale model for precipitation and dissolution in porous media

Neuss-Radu M, Pop IS, Kumar K (2016)


Publication Status: Published

Publication Type: Journal article

Publication year: 2016

Journal

Publisher: OXFORD UNIV PRESS

Book Volume: 81

Pages Range: 877-897

Journal Issue: 5

DOI: 10.1093/imamat/hxw039

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).

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APA:

Neuss-Radu, M., Pop, I.S., & Kumar, K. (2016). Homogenization of a pore scale model for precipitation and dissolution in porous media. IMA Journal of Applied Mathematics, 81(5), 877-897. https://dx.doi.org/10.1093/imamat/hxw039

MLA:

Neuss-Radu, Maria, Iuliu Sorin Pop, and Kundan Kumar. "Homogenization of a pore scale model for precipitation and dissolution in porous media." IMA Journal of Applied Mathematics 81.5 (2016): 877-897.

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