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

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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.