Mixing Limited Reaction Rates in Radial Groundwater Flow Upscaled by the Lamella Approach at Continuum-Scales.

Abstract:

Upscaling mixing-limited reactive transport of injectates involved in in-situ groundwater treatment schemes remains challenging due to the non-commutation between averaging approaches and nonlinearities in the reaction rate expressions and due to the difficulty in quantifying mixing. The Eulerian effective plume model (macrodispersion model) generally overestimates the reaction rate due to the overestimated mixing of the plume, whereas Lagrangian particle or streamtube approaches do not provide an explicit means for keeping track of mixing extent. The lamella approach is a new modeling tool that overcomes the abovementioned shortcomings by combining mixing measures such as the scalar dissipation rate with a Lagrangian modeling focus on front-tracking. This approach involves dividing the moving interface between the displacing-displaced solutions into approximately linear segments (set of lamellae) on which the mixing-limited reactions take place and studying the transport mechanisms and the chemical reactions on them. This approach is summarized in application to idealized radial injection, where mixing between the injected and displaced solutions leads to calcite precipitation..The theoretical reaction rate found via the simplified lamella approach is compared with explicit simulation using a finite elements (COMSOL) framework fitted with the representative multicomponent equilibrium reaction network.