A Comparison of Zero‐Order, First‐Order, and Monod Biotransformation Models

Abstract

Under some conditions, a first‐order kinetic model is a poor representation of biodegradation in contaminated aquifers. Although it is well known that the assumption of first‐order kinetics is valid only when substrate concentration, S, is much less than the half‐saturation constant, K s, this assumption is often made without verification of this condition. We present a formal error analysis showing that the relative error in the first‐order approximation is S/Ks and in the zero‐order approximation the error is Ks/S. We then examine the problems that arise when the first‐order approximation is used outside the range for which it is valid. A series of numerical simulations comparing results of first‐ and zero‐order rate approximations to Monod kinetics for a real data set illustrates that if concentrations observed in the field are higher than Ks, it may be better to model degradation using a zero‐order rate expression. Compared with Monod kinetics, extrapolation of a first‐order rate to lower concentrations under‐predicts the biotransformation potential, while extrapolation to higher concentrations may grossly over‐predict the transformation rate. A summary of solubilities and Monod parameters for aerobic benzene, toluene, and xylene (BTX) degradation shows that the a priori assumption of first‐order degradation kinetics at sites contaminated with these compounds is not valid. In particular, out of six published values of Ks for toluene, only one is greater than 2 mg/L, indicating that when toluene is present in concentrations greater than about a part per million, the assumption of first‐order kinetics may be invalid. Finally, we apply an existing analytical solution for steady‐state one‐dimensional advective transport with Monod degradation kinetics to a field data set.

Comparison of Four Nitrate Removal Kinetic Models in Two Distinct Wetland Restoration Mesocosm Systems

“…These systems can be characterized by a linear NO 3 -N concentration profile, which is often unrealistic in systems with longer residence times that allow NO 3 -N to become limited. The model assumes the system is closed, anoxic, completely or partially mixed, independent of hydraulic loading rates, and insignificantly influenced by other kinetic reactions occurring within the system [43]. The model can be expressed as [44]:…”

“…Therefore, removal rates (J FO ) increase linearly with NO 3 -N concentration assuming removal efficiency does to not change in relation to NO 3 -N load [46]. The model also assumes that the substrate concentration is significantly smaller than the half-saturation constant (K s , the concentration supporting an uptake rate of 50% of the maximum rate), the system is well mixed, has no significant influences from water losses or gains, and is dependent on only one reactant [14,43,47,48]. The ρ FO , the mass transfer coefficient (cm d −1 ), accounts for the intrinsic ability for the soil to retain NO 3 -N by including depth, which is often ignored by using other removal rate constants (i.e., k (d −1 )) in first order decay model evaluations.…”

Diffuse hydrological mass transport through catchments: scenario analysis of coupled physical and biogeochemical uncertainty effects

“…(1) Sinkkonen and Paasivirta (2000), (2) Aronson and Howard (1997), (3) Suarez and Rifai (1999), 4) Rogers et al (2002), (5) Baresel et al (2006), (6) Baresel and Destouni (2007), (7) Destouni et al (2010), (8) Mulligan and Yong (2004), ( errors (Bekins et al, 1998;Suarez and Rifai, 1999;Washington and Cameron, 2001;Mulligan and Yong, 2004). Nevertheless, Table 2 demonstrates that the investigated λτ g range in this paper is relevant for a wide range of different environmental pollutants and characteristic catchment conditions; the latter because the investigated travel time pdfs bound a wide range of different possible catchment situations regarding advective transport and its associated uncertainties (see comparisons between different scenarios and catchment examples in Darracq et al, 2010a, b).…”

A Monte Carlo simulation method for assessing biotransformation effects on groundwater fuel hydrocarbon plume lengths

“…In general, hydrocarbon biotransformation rates are compound-specific and reflect local biogeochemical conditions within a plume (Vroblesky, Chapelle, 1994;Chapelle et al, 1996) and the characteristics of the local microbiological consortia (Borden, Bedient, 1986;Bekins et al, 1998). Nevertheless, from a practical, field-oriented engineering perspective, a simple global first-order kinetic model is often used in site investigations (e.g., Wilson et al, 1995;Buscheck et al, 1996).…”