Effects of Heterogeneity, Connectivity, and Density Variations on Mixing and Chemical Reactions Under Temporally Fluctuating Flow Conditions and the Formation of Reaction Patterns

Solute mixing, spreading, and fast chemical reactions in aquifers are strongly influenced by spatial variability of the hydraulic properties, temporal flow fluctuations, and fluid density differences. We study the coupling of heterogeneity, transient forcing, and density-driven flow on mixing and chemical reactions between two fluids of different density under a stable stratification. We consider the reaction of the fast dissolution of calcite. We find that temporal fluctuations and heterogeneity cause strong local enhancement of the mixing and reaction rates and this impact increases with the degree of connectivity of hydraulic conductivity. The global mixing and reactivity, however, are on the order of or smaller than their homogeneous counterparts due to heterogeneity-induced fluid segregation. The local maxima of the mixing and reaction rates are found to be located around strongly stretched regions corresponding to high velocity zones where dispersive mass transfer mechanisms are increased by dispersion. We also find that density variations compress the interface, which in turn emphasizes local maxima in mixing and reaction rates. Numerical results provide evidence that the stretching of the interface induced by spatial heterogeneity and transient effects coupled with density variations lead to the formation of complex patterns of reactive hotspots, zones of enhanced reaction efficiency, and that its distribution is directly linked to the deformation properties and topology of the flow field. These results provide new insights into the role of spatial and temporal variability on the mixing and reaction efficiency as well as the formation of reactive geochemical patterns in actual environmental systems.