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We 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.

Plain Language Summary When fluids propagate through subsurface porous media, flow instabilities can be either detrimental or advantageous depending on the application. The interplay between viscous instabilities and fluid mixing has been studied extensively for single-phase two-component mixtures, but not for applications that involve two phases (e.g., oil and gas) that exchange multiple species. In this first study of mixing in partially miscible two-phase flow, we find that the dynamics are profoundly different. In single-phase flow, viscous fingering increases the interface between two fluids (of the same phase) and diffusion across that interface drives the mixing. In two-phase flow, mass exchange between the phases creates a two-phase mixing zone. In this zone, two phases coexist that have different velocities, which lead to an expansion of the mixing zone. Diffusion occurs both within each phase and between the phases, and the interphase mass exchange significantly enhances mixing. Because this thermodynamic mixing is extremely efficient, viscosity contrasts are quickly homogenized, and hydrodynamic instabilities (fingering) are less pronounced. In fluid mechanical terms, dissipation drives mixing in single phase, while production may dominate in two-phase flow. These findings have broad implications for the prediction of instabilities and mixing behavior in subsurface applications that involve multiple partially miscible fluid phases.