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A comparison of zero-order, first-order, and monod biotransformation models

Ground Water

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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/K(S) and in the zero-order approximation the error is K(s)/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 K(s), it may 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.A formal error analysis is presented showing that the relative error in the first-order approximation is S/KS and in the zero-order approximation the error is KS/S where S is the substrate concentration and KS is the half-saturation constant. The problems that arise when the first-order approximation is used outside the range for which it is valid are examined. 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.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
A comparison of zero-order, first-order, and monod biotransformation models
Series title:
Ground Water
Volume
36
Issue:
2
Year Published:
1998
Language:
English
Publisher:
Ground Water Publ Co
Publisher location:
Westerville, OH, United States
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
261
Last page:
268
Number of Pages:
8