Effect of solute dilution on non-linear reaction kinetics

Abstract:

Subsurface environments are biogeochemical reactors, in which many biogeochemical processes occur as pulses where reactant release is localized in space and time, such as: pulse of nitrates released by rain event on a field, pulse of metals or pharmaceutical compounds due to bank filtration, daily pulse of gas (O2, CO2) released by roots in soils. Such pulse reactors are characterized by spatially and temporally variable concentration gradients that often occur at scales that are not resolved by biogeochemical and reactive transport models. Yet, biogeochemical reaction kinetics are generally studied in the lab from batch reactors where concentrations are uniform. Here we investigate the effective kinetics of pulse reactors resulting from coupled diffusion and fluid-mineral reactions such as dissolution/precipitation. We focus on nonlinear reactions where the reaction rate is a power-law function of local concentrations. In this common situation, the effect of chemical gradients on reaction kinetics is expected to be particularly important. We derive analytical results for the effective kinetics and the evolution of total mass through a weak-coupling approximation for transport and reaction. These results are validated by comparison to direct numerical simulations of the diffusion-reaction equation (DRE) for a wide range of Damk\"ohler numbers and exponents characterizing the reaction nonlinearity.

We first consider the case of a diffusing pulse of reactant in a homogeneous velocity field evolving under the action of diffusion and reaction with the mineral phase. The resulting spatially and temporally variable chemical gradients lead to power law kinetics for the average reaction rates, with exponents that differ from those of batch reactors. Solute mixing is found to either accelerate or slow down the average reaction kinetics, depending on the local kinetic laws. We derive approximate analytical solutions for the evolution of concentration distribution in time and space allowing us to predict the effective reaction kinetics resulting from the non-uniformity of the concentration field. In a second step, we investigate the effect of mixing in heterogeneous permeability fields on reaction kinetics, using CrunchFlow simulations. The enhancement of mixing resulting from plume stretching is shown to affect the scaling of the mean reaction rate with the mean concentration. We discuss the link between the flow heterogeneity and the average reaction kinetics. These results open new perspectives to understand and model coupled mixing and fluid-mineral reactions in heterogeneous media.