Effective reaction parameters for mixing controlled reactions in heterogeneous media

Sound understanding of mixing-controlled reactions in heterogeneous media is needed for the realistic modeling of contaminant transport in aquifers and is a precondition for the evaluation of natural attenuation processes, the design of nuclear waste disposal, and the engineered remediation of contaminated sites. In this work, we study the bimolecular dissolution-precipitation equilibrium reaction, adapted after De Simoni et al. (2005). Because of advective and dispersive transport of the reacting species, the system is globally in nonequilibrium because the effective reaction rate is limited by the finite rate of transport and thus is affected by the heterogeneity of the formation. We study the macroscopic formulation of such a reactive transport system in terms of mixing-controlled reaction parameters which integrate the impact of spatial heterogeneity. The apparent chemical saturation is found to be a function of the concentration variance and is generally greater than its local-scale equivalent. This explains why water samples taken from pumping wells are normally nonequilibrium with respect to minerals existing in the aquifer, even when local equilibrium is to be expected. The reaction rate is given by the product of a reaction factor, associated with the local equilibrium constant and concentration variance, and a mixing factor, which is the product of the microdispersion coefficient and the square gradient of the mean and perturbation concentration fields. The mixing factor dominates the description of the reaction rate in the upscaled macroscopic models. The reaction rate predicted by macroscopic models is controlled by two competing effects: The large heterogeneity-induced macrodispersion coefficient leads to an increase of reaction rate, while a more smoothed concentration gradient may lead to a decrease of the reaction rate. Macroscopic models may only give a good approximation at large time and away from the plume center of mass because of the balanced variance budget but significantly underestimate reaction rate near the plume center because of the smoothed concentration gradient field. In fact, in an application example, reaction rate is maximum around the plume center, where a homogeneous equivalent medium would predict zero rates.