Simulating Biodegradation Under Mixing-limited Conditions Using Michaelis-Menten (Monod) Kinetic Expressions in a Particle Tracking Model

Abstract:

Recent studies have demonstrated that the typical method of adding mass-action reaction terms to the advection-dispersion equation overestimates the field-scale reaction rates. The mismatch is usually attributed to poor mixing. A recent method, based on a purely Langragian particle tracking (PT) theoretical development, successfully reproduces the results of mixing-limited bimolecular reaction (A+B → C) from two benchmark experiments. In this numerical method, the reactants are represented by particles. The reactions are determined by 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. We extend the application of the PT 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 PT method is not only able to match the Michaelis-Menten (Monod) equation under ideal conditions, but also is able to capture the characteristics of non-ideal conditions such as imperfect mixing, disequilibrium, and limited availability of the active sites. Furthermore, for the ultimate goal of applying the Langragian PT method directly to the field scale problems, this method is implemented to the simulation of carbon tetrachloride (CT) biodegradation at the Schoolcraft, Michigan, site, where the hydraulic properties and reaction kinetics are well understood.