Abstract
We present a phase-field model for single-phase flow and reactive transport where ions take part in mineral precipitation/dissolution reactions. The evolving interface between fluid and mineral is approximated by a diffuse interface, which is modeled using an Allen–Cahn equation. As the original Allen–Cahn equation is not conservative, we apply a reformulation ensuring conservation of the phase-field variable and address the sharp-interface limit of the reformulated model. This model is implemented using a finite volume scheme and the discrete conservation of the reformulated Allen–Cahn equation is shown. Numerical examples show how the discrete phase-field variable is conserved up to the chemical reaction.
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Acknowledgements
The author would like to thank Florian Frank (FAU Erlangen-Nürnberg) for useful discussions on the phase-field formulation. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation—Flanders (FWO) and the Flemish Government—department EWI. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 327154368—SFB 1313.
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Bringedal, C. (2020). A Conservative Phase-Field Model for Reactive Transport. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_50
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DOI: https://doi.org/10.1007/978-3-030-43651-3_50
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