Simulating biodegradation under mixing-limited conditions using Michaelis-Menten (Monod) kinetic expressions in a particle tracking model

摘要

Recent studies have demonstrated that effective field-scale bioremediation reactions rates are significantly lower than batch- or lab-scale rates, when the same law of mass action is used to represent the reaction at both scales. The mismatch is usually attributed to poor mixing of reactants brought about by heterogeneity. A recent method, based on a purely Lagrangian particle tracking (FT) theoretical development, successfully reproduces the effects of mixing-limited bimolecular reaction (A + B → C) from two benchmark experiments. In this numerical method, the reactants are represented by particles, and the small-scale physics are directly translated into a combination of two probabilities that govern whether: (1) reactant particles are collocated during a short time interval, and (2) two collocated particles favorably transform into a reaction. The latter is due to thermodynamics and is independent of scale of mixing. The former directly accounts for the degree of mixing in any system. We extend the application of the FT method to biodegradation, which is commonly characterized by more complex Michaelis-Menten (Monod) chemical kinetics. The advantage of the PT method is that it explains the variation of reaction rate based on mixing-controlled particle collisions instead of using empirical parameters. The FT method not only matches the Michaelis-Menten (Monod) equation under ideal conditions, but also captures the characteristics of non-ideal conditions such as imperfect mixing, disequilibrium, and limited availability of the active sites. We show these using hypothetical systems and also successfully apply the method to a column study of carbon tetrachloride biodegradation.