A porous-media model for reactive fluid-rock interaction in a dehydrating rock

We discuss a model for temperature-induced rock dehydration that features fluid liberation through mineral reactions, diffusion of chemically released species, and flow through porous media. This model can be derived either by considering standard conservation laws and flux definitions (Pl¨umper et al.[2017], Beinlich et al. [2020]) or, alternatively, using the variational framework of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling)(Zafferi et al. [2021]) introduced by M. Grmela and H.C. ¨ Ottinger. The latter approach is based on the abstract definition of thermodynamical driving potential and operators characterizing the reversible and dissipative contributions of the processes. By doing so we can show that local equilibrium assumptions are recovered as fast limit of irreversible processes. Ultimately, we rigorously prove that the PDE model so derived admits solutions using a discretization strategy that imitates the numerical implementations.

References

Andreas Beinlich, Timm John, Johannes C Vrijmoed, Masako Tominaga, Tomas Magna, and Yuri Y Podladchikov. Instantaneous rock transformations in the deep crust driven by reactive fluid flow. Nature Geoscience, 13(4):307–311, 2020.

Oliver Plümper, Timm John, Yuri Y Podladchikov, Johannes C Vrijmoed, and Marco Scambelluri. Fluid escape from subduction zones controlled by channel-forming reactive porosity. Nature Geoscience, 10(2):150–156, 2017.

Andrea Zafferi, Dirk Peschka, and Marita Thomas. Generic framework for reactive fluid flows. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, page e202100254, 2021.