Estimating in-situ monod biodegradation parameters using a novel explicit solution of a one-dimensional contaminant transport equation

We present a novel, explicit closed form solution using the Lambert W funct ion to a steady-state one-dimensional contaminant transport equation incorp orating the Monod expression for biodegradation. This new solution overcome s some of the limitations associated with using the existing implicit solut ion and provides a simple method of describing biodegradation at contaminat ed sites using the Monod equation. The field-scale applicability of this ap proach was tested using data on phenol and toluene biodegradation from prev iously published studies. A review of published Monod kinetic parameters fo r hydrocarbon biodegradation indicated that in most cases, the half saturat ion coefficient was lower than 5 mg/L, suggesting that the commonly used fi rst-order approximation is valid only at low substrate concentrations. Whil e the Monod equation does not have this limitation and can usually provide an accurate description of biodegradation at contaminated sites, its nonlin ear nature presents computational and parameter estimation difficulties com pared with the linear and relatively simple first- and zero-order approxima tions. The explicit closed form solution to the Monod equation presented in this study greatly simplifies its use and appears to be an attractive appr oach to describe contaminant biodegradation in the field.