The behavior of effective rate constants for bimolecular reactions in an asymptotic transport regime

Previous research has shown that rate constants measured in batch tests (κ) may over-predict the amount of product formation when used in continuum models, and that these rate constants are often much greater than effective ones (κ(eff)) determined from upscaling studies. However, there is evidence that mixing is more important than the rate constants when using upscaled models. We use a numerical two-dimensional pore-scale porous medium with an approach similar to an experimental column test, and focus on the scenario of the displacement and mixing of two solutions with irreversible bimolecular reactions. Break-through curves of multiple cross-sectional averaged concentrations are analyzed for conservative and reactive transport, as well as the segregation of reactant species along the cross-sections. We compute effective parameters for the continuum scale in order to better understand the impact of using intrinsic rate constants in upscaled models. For a range of Damköhler numbers (Da), we compute effective reaction rate parameters and a reaction effectiveness factor; the latter is described by an empirical formula that depends on the Damköhler number and captures the upscaled system behavior. Our pore-scale results also confirm the segregation concept advanced by Kapoor et al. (1997). We find that for Da>1, κ(eff)<<κ, and yet the relative difference in total mass transformation between the pore-scale simulation and what is predicted by the upscaled continuum model using κ is about 10%. The explanation for this paradox is that the early transition of the regime from rate-limited to mixing-limited results in a model that is relatively insensitive to the rate constant because mixing controls the availability of reactants. Thus, the reaction-rate parameter used in the model has limited influence on the rate of product computed.