A COMPARISON OF ZERO-ORDER, FIRST-ORDER, AND MONOD BIOTRANSFORMATION MODELS

Under some conditions, a first-order kinetic model is a poor represent ation of biodegradation in contaminated aquifers, Although it is well known that the assumption of first-order kinetics is valid only when s ubstrate concentration, S, is much less than the half-saturation const ant, K-S, this assumption is often made without verification of this c ondition. We present a formal error analysis showing that the relative error in the first-order approximation is S/K-S and in the zero-order approximation the error is K-S/S. We then examine the problems that a rise 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 r eal data set illustrates that if concentrations observed in the field are higher than K-S, it may be better to model degradation using a zer o-order rate expression. Compared with Monod kinetics, extrapolation o f a first-order rate to lower concentrations under-predicts the biotra nsformation potential, while extrapolation to higher concentrations ma y grossly over-predict the transformation rate. A summary of solubilit ies and Monod parameters for aerobic benzene, toluene, and xylene (BTX ) degradation shows that the a priori assumption of first-order degrad ation kinetics at sites contaminated with these compounds is not valid . In particular, out of six published values of K-S 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 transpo rt with Monod degradation kinetics to afield data set.