Hydrothermodynamic mixing of fluids across phases in porous media

Abstract

AbstractWe investigate the coupled dynamics of fluid mixing and viscously unstable flow under both miscible (single‐phase) and partially miscible (two‐phase) conditions, and in both homogeneous and heterogeneous porous media. Higher‐order finite element methods and fine grids are used to resolve the small‐scale onset of fingering and tip splitting. An equation of state determines the thermodynamic phase behavior and Fickian diffusion. We compute global quantitative measures of the spreading and mixing of a diluting slug to elucidate key differences between miscible and partially miscible systems. Hydrodynamic instabilities are the main driver for mixing in miscible flow. In partially miscible flow, however, we find that relative permeabilities spread the two‐phase zone. Within this mixing zone dissolution and evaporation drive mixing thermodynamically while reducing mobility contrasts and thus fingering instabilities. The different mixing dynamics in systems involving multiple phases with mutual solubilities have important implications in hydrogeology and energy applications, such as geological carbon sequestration and gas transport in hydrocarbon reservoirs.