Numerical experiments with the Lamellae Upscaling Concept with Approximate Handling of Coalescence of the Reaction Front
Résumé
The challenge in characterizing mixing-limited reaction rates between displacing and displaced groundwater solutions (Figure 1, left panel) is the in quantifying mixing extent that is controlled by small scale heterogeneity. We describe limited numerical 2D testing of the lamella approach that focuses on the deformation of the moving front, treated as a set of linearized patches termed lamellae. We simulate flow and reactive transport in a recently characterized sample of Massillon sandstone to provide Eulerian test data for comparison with the new Lagrangian lamella-based solution. In our numerical experiments particle tracking is used to approximate the lamellar positions and deformations at any given time, and reactions are calculated on each lamella in proportion to the local scalar dissipation rate. The simulated data show the effect of small scale heterogeneity including strong shearing and local collapse or coalescence (Figure 1, right panel) of the reaction front on the global reaction rate. We propose a simple approximation to handle coalescence in the lamella-based upscaling and we test it against the simulated data.