Upscaling Mixed-Limited Reactions for Equilibrium and Fast Complete Kinetic Reactions in Radial and 1-D Flow.

The new upscaling approach that implements the lamella concept utilizing the Lagrangian frame of reference gives a promising result when applied to the calcite precipitation equilibrium mixing-limited reaction. Here it is applied to the radial injection case representing aquifer remediation. To approximate aerobic biodegradation, the irreversible bimolecular kinetic reaction case is studied here also using the lamella approach for the one dimensional case. The theoretical rate for the mixing-limited kinetic reaction is derived from Gramling et al. (2002) for the special case where the total concentration of the injected component equals the total concentration of the ambient component, and then this special case is generalized for arbitrary concentrations. The results for both the equilibrium and the kinetic reaction cases are tested numerically versus COMSOL which matched the theoretical cases very well.