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Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenised flow and transport equations are solved on the macroscopic scale, while effective parameters are obtained from auxiliary cell problems on possibly evolving reference geometries (micro-scale). Despite their perspective success in rendering lab/field-scale simulations computationally feasible, analytic results regarding the arising two-scale bilaterally coupled system often restrict to simplified models. In this paper, we first derive smooth dependence results concerning the partial coupling from the underlying geometry to macroscopic quantities. Therefore, alterations of the representative fluid domain are described by smooth paths of diffeomorphisms. Exploiting the gained regularity of the effective space- and time-dependent macroscopic coefficients, we present local-in-time existence results for strong solutions to the partially coupled micro-macro system using fixed-point arguments. What is more, we extend our results to the bilaterally coupled diffusive transport model including a level-set description of the evolving geometry. [ABSTRACT FROM AUTHOR]

Reactive flow and transport in porous media is topic of intense research since decades. Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we investigate novel effective dispersion models for reactive transport of electrically charged chemical species in a thin, potentially evolving strip taking into account Taylor–Aris and electroosmotic‐induced dispersion as well as their cross‐coupling effects. We prove positivity of the dispersion coefficient and the existence and uniqueness of strong solutions in the fixed geometry setting. Moreover, we numerically investigate scenarios for both the fixed and evolving geometry situation. The simulation results illustrate the possibility of separating charged species, such that the findings of this study can lead to a better understanding of mixing and separation processes of charged solutes and an improved prediction of breakthrough curves. Finally, we study the limits of vanishing channel width, precipitation layer thickness, and molecular diffusion. We show convergence of the solutions to the corresponding limit cases such as a hyperbolic model or the fixed geometry case. From these results, we can rate the impact of distinct dispersion mechanisms and evaluate the necessity of a detailed modeling for different parameter regimes. [ABSTRACT FROM AUTHOR]

Micro‐macro models for dissolution processes are derived from detailed pore‐scale models applying upscaling techniques. They consist of flow and transport equations at the scale of the porous medium (macroscale). Both include averaged time‐ and space‐dependent coefficient functions (permeability, porosity, reactive surface, and effective diffusion). These are in turn explicitly computed from the time‐ and space‐dependent geometry of unit cells and by means of auxiliary cell problems defined therein (microscale). The explicit geometric structure is characterized by a level set. For its evolution, information from the transport equations solutions is taken into account (micro‐macro scales). A numerical scheme is introduced, which is capable of evaluating such complex settings. For the level‐set equation a second‐order scheme is applied, which enables us to accurately determine the dynamic reactive surface. Local mesh refinement methods are applied to evaluate Stokes type cell problems using P2/P1 elements and a Uzawa type linear solver. Applications of our permeability solver to scenarios involving static and evolving geometries are presented. Furthermore, macroscopic flow and transport equations are solved applying mixed finite elements. Finally, adaptive strategies to overcome the computational burden are discussed. We apply our approach to the dissolution of an array of dolomite grains in the micro‐macro context and validate our numerical scheme. Key Points: We investigate reactive flow and transport problems for mineral dissolutionA fully coupled nonlinear micro‐macro model is considered including evolving microstructures by means of level‐set methodsTaking advantage of parallel computing and a tailored adaptivity scheme, computation times are comparable to purely macroscopic simulations [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]