Efficiency of Micro-Macro Models for Reactive Two-Mineral Systems

Abstract

In this paper, we introduce a pore-scale model for reactive flow and transport in evolving porous media exhibiting two competing mineral phases. By formal two-scale asymptotic expansion in a level-set framework an effective micro-macro model is derived. As such, our approach comprises flow and transport equations on the macroscopic scale including effective hydrodynamic parameters calculated from representative unit cells. Conversely, the macroscopic solutes' concentrations alter the unit cells' geometrical structure by triggering dissolution or precipitation processes. The numerical implementation of such micro-macro models poses several challenges, especially in terms of geometry representation and computational complexity. In this research, the Voronoi implicit interface method is applied to characterize and evolve the two-mineral structure and first-order convergence is obtained in a test case where analytical solutions are available. Furthermore, we present a sophisticated overall solution strategy for the introduced fully coupled nonlinear micro-macro problem and conduct numerical simulations. In doing so, the significant performance enhancements arising from machine learning techniques are evaluated. To this end, a convolutional neural network is trained on (realistic) unit cell geometries for permeability prediction and deployed in a micro-macro simulation. The outcome is compared to the respective results obtained by classical methods in terms of predictive power and computational effort.