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.

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In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.

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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