期刊
IMA JOURNAL OF APPLIED MATHEMATICS
卷 81, 期 5, 页码 877-897出版社
OXFORD UNIV PRESS
DOI: 10.1093/imamat/hxw039
关键词
homogenization; reactive flow; periodic unfolding; two scale convergence; porous media; non-Lipschitz reaction rates
资金
- Technology Foundation STW [07796]
- Statoil through the Akademia grant
- German Research Foundation DFG [GRK 1398]
- Netherlands Organisation for Scientific Research NWO [DN 81-754]
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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