Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Transverse dispersion across adjacent streamlines can control the amount of mixing and reaction between one or more contaminants and a limiting substrate along the fringes of groundwater plumes. Streamlines in groundwater converge and diverge in heterogeneous porous media, depending on the permeability distribution. When flow is focused in a high-permeability zone, the distance required for a solute to cross a given number of streamlines decreases, and the time allowed for mixing and reaction is reduced. Because the first effect outweighs the latter, the overall result is an enhancement of transverse mixing and reaction. Here we develop a conceptual model of heterogeneous two-dimensional structures facilitating flow focusing. We use the conceptual model to develop simple analytical expressions quantifying the extent to which mixing and reaction are enhanced when flow focusing occurs and compare these to results of numerical simulations. Significant enhancement of transverse mixing and reaction by flow focusing is observed; for the cases considered, flow focusing enhances the amount of reaction by a factor ranging from 1.8 to 11.9. The relatively simple analytical expressions demonstrate that the fraction of the domain height made up by high-permeability inclusions, the fraction of flow that passes through the inclusions, and the fringe bypassing of inclusions determine the amount of mixing and reaction enhancement for the permeability distributions considered. These results partially explain why field-scale dispersivities are larger than laboratory derived dispersivities, where homogeneous and isotropic sediments are typically used. Further work is needed to verify the theoretical results presented here with laboratory and field experiments and to expand the relatively simple analytical expressions to consider more heterogeneous three-dimensional permeability fields.