Abstract
We investigate reactive flow and transport in evolving porous media. Solute species that are transported within the fluid phase are taking part in mineral precipitation and dissolution reactions for two competing mineral phases. The evolution of the three phases is not known a-priori but depends on the concentration of the dissolved solute species. To model the coupled behavior, phase-field and level-set models are formulated. These formulations are compared in three increasingly challenging setups including significant mineral overgrowth. Simulation outcomes are examined with respect to mineral volumes and surface areas as well as derived effective quantities such as diffusion and permeability tensors. In doing so, we extend the results of current benchmarks for mineral dissolution/precipitation at the pore-scale to the multiphasic solid case. Both approaches are found to be able to simulate the evolution of the three-phase system, but the phase-field model is influenced by curvature-driven motion.
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Acknowledgments
Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 – 390740016. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). This research was supported by the DFG Research Training Group 2339 Interfaces, Complex Structures, and Singular Limits and Research Unit 2179 MadSoil. The authors thank Sergi Molins, Berkeley Lab, for bringing [9] to our attention. We further acknowledge the insightful discussions with Florian Frank and Helmut Abels.
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Appendix
Appendix
In order to justify the resolutions chosen in our simulations, we provide a grid convergence analysis for the cases where no analytical results are available for comparison. Note that in both level-set and phase-field approach parameters 𝜖 and ξ are used respectively to adjust the spatial extent of the stripe in which the interfaces are treated. As already mentioned, a smaller choice of parameters increases precision of the geometry evolution. Yet, a lower bound is given by some multiple of the discretization length. As such, we investigate both the impact of mesh refinement as well as parameter reduction 𝜖,ξ on constant meshes. The results of our convergence studies are presented in Fig. 8 for the level-set model and in Fig. 9 for the phase-field approach. For clarity, the data at final simulation time T are additionally listed in Tables 4 and 5.
Level-Set: Simulation results for different spatial resolution and choice of the level-set parameter 𝜖 in case of the diffusive case (top), equilibrium flow case (bottom). Volume and surface area of mineral P as well as mass conservation with respect to solute B are presented
Phase-field: Simulation results for different spatial resolution and choice of the phase-field parameter ξ in case of the diffusive case (top), equilibrium flow case (bottom). Volume and surface area of mineral P as well as mass conservation with respect to solute B are presented
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Kelm, M., Gärttner, S., Bringedal, C. et al. Comparison study of phase-field and level-set method for three-phase systems including two minerals. Comput Geosci 26, 545–570 (2022). https://doi.org/10.1007/s10596-022-10142-w
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DOI: https://doi.org/10.1007/s10596-022-10142-w
Keywords
- Pore-scale
- Moving boundary
- Reactive transport
- Phase-field method
- Level-set method
- Multiphase solid