| 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. |
| Genre: | Article |
| ProdID: | 70020693 |
| Citation Author: | Bekins, B. A.; Warren, E.; Godsy, E. M. |
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| Citation End Page: | 268 |
| Citation Issue: | 2 |
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| Citation Language: | English |
| Citation Larger Work Title: | Ground Water |
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| Citation Number Of Pages: | 8 |
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| Citation Publisher: | Ground Water Publ Co |
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| Citation Search Results Text: | A comparison of zero-order, first-order, and monod biotransformation models; 1998; Article; Journal; Ground Water; Bekins, B. A.; Warren, E.; Godsy, E. M. |
| Citation Start Page: | 261 |
| Citation Volume: | 36 |
| Citation Year: | 1998 |
| Type: | citation/reference |
| Text: | A comparison of zero-order, first-order, and monod biotransformation models; 1998; Article; Journal; Ground Water; Bekins, B. A.; Warren, E.; Godsy, E. M. |
| URL (THUMBNAIL): | http://pubs.er.usgs.gov/thumbnails/outside_thumb.jpg |
| Date Other: | Thu, 1 Jan 1998 00:00 -0600 |
| Publisher: | Ground Water Publ Co |
