Quantifying Impacts of Microcosm Mass Loss on Kinetic Constant Estimation

Abstract

Microcosm experiments to assess microbial reductive dechlorination of chlorinated aliphatic hydrocarbons typically experience 5–50% mass loss due to frequent sampling events and diffusion through septa. A literature review, however, reveals that models fit to such experiments for kinetic constant estimation have generally failed to account for experimental mass loss. To investigate possible resultant bias in best-fit parameters, a series of numerical experiments was conducted in which Monod kinetic models with and without mass loss were fit to more than 1300 synthetic data sets, generated using published microcosm data. Models that failed to account for mass loss resulted in significant fitted parameter bias. Bias ranged from 5 to 45% of the parameter magnitude for Monte Carlo simulations with low (approximately 10%) mass loss to 20–120% for simulations with high (approximately 40%) mass loss. In addition, for high mass loss simulations, best-fit values consistently fell along the bounds of the optimization range. These results suggest that failure to properly account for mass loss in microcosms may lead to inaccurate estimation of kinetic constants and may explain some of the literature-reported variability in these parameters. A model is presented that provides a method for including sampling and diffusional mass losses to improve kinetic constant estimation accuracy.

Microbial Reductive Dechlorination by a Commercially Available Dechlorinating Consortium Is Not Inhibited by Perfluoroalkyl Acids (PFAAs) at Field-Relevant Concentrations

“…Abiotic batch reactor model fitting revealed that a simple first-order diffusive mass loss term, R i s in eq , underestimated the chlorinated ethene mass in reactors over time (see Figure S5). To avoid potential Monod kinetic parameter estimation bias, an improved method for estimating chlorinated ethene mass loss into the rubber stopper was implemented . This approach used time superposition of an analytical solution for planar diffusion of a chemical compound i from an aqueous phase at concentration C i a into a semi-infinite solid rubber phase…”

“…A numerical model, implemented in SciPy, was formulated to simulate MRD in batch reactors using the following mass balance equation: , normald normald t ( V a C i a ) + normald normald t ( V g C i g ) = V normala R i normalb + R i normals where i corresponds to PCE, TCE, cis -DCE, VC, or ethene, t is time [T], V a and V g are the aqueous and gaseous phase volumes [L 3 ], respectively, C i a and C i g are the aqueous and gaseous phase concentrations [M/L 3 ], respectively, R i b is the overall MRD reaction rate [M/L 3 /T], and R i s is the mass transfer rate [M/T] between the reactor aqueous phase and the stopper. Typical of other MRD models, it was assumed that partitioning between aqueous and gaseous phases conformed to Henry’s law and MRD was governed by Monod kinetics.…”

“…A numerical model, implemented in SciPy, 61 was formulated to simulate MRD in batch reactors using the following mass balance equation: 62,63…”

“…To avoid potential Monod kinetic parameter estimation bias, an improved method for estimating chlorinated ethene mass loss into the rubber stopper was implemented. 63 This approach used time superposition of an analytical solution for planar diffusion of a chemical compound i from an aqueous phase at concentration C i a into a semiinfinite solid rubber phase. 67 = i k j j j j j y…”