Effective Kinetics of Chemical Gradient Reactors

International audienceSubsurface environments are biogeochemical reactors characterized by a range of chemical gradients, such as: gradients of dissolved oxygen in the unsaturated zone, gradients of electron donors and acceptors in the hyporheic zone, gradients of chemical compounds in contaminated sites, gradients of groundwater age and dissolved species in catchments. Yet, effective reaction kinetics are generally estimated from batch reactors, i.e. zero gradient conditions. Here we investigate the effect of chemical gradients on the effective kinetics of fluid-mineral reactions (dissolution/precipitation). We focus on non-linear reactions, where the reaction rate is a non-linear function of local concentrations and the exponent is related to the reaction stoichiometry. In this common situation, the effect of chemical gradients on reaction kinetics is expected to be particularly important. We combine reactive transport models with solute mixing theories to establish effective fluid-mineral kinetics, and relate them to mixing rates. We compare the resulting kinetics of chemical gradients to homogeneous systems for a range of Damköhler numbers in order to investigate the respective roles of reaction and mixing processes.We perform Crunchflow simulations of a diffusing pulse of reactant, which create spatially and temporally variable chemical gradients. Numerical results show that effective kinetics of chemical gradient reactors significantly differ from those of batch reactors. For kinetic power law exponents larger than one, chemical gradients in a diffusive pulse are found to increase the overall reaction rate in comparison to batch kinetics. On the opposite, for kinetic power law exponents lower than one, the effective kinetics of chemical gradient reactors are slower than those of batch reactors. We identify two different regimes where local concentration evolution is primarily diffusion-controlled and reaction-controlled. This allows deriving approximate analytical solutions for the evolution of concentration distribution in time and space due to diffusion and reaction. We thus link the effective reaction kinetics to the Damköhler number and the non-linear reaction exponent. These results open new perspectives to understand and model coupled mixing and fluid-mineral reactions in heterogeneous media