Explicit oxygen concentration expression for estimating biodegradation kinetics from respirometric experiments

We present a simple method for estimating extant biodegradation kinetic parameters from oxygen uptake data obtained during respirometric experiments. Specifically, a novel closed-form solution based on the Lambert W function is presented for the differential equation describing substrate biodegradation based on the Monod equation. Unlike the existing implicit solution, this novel solution is explicit with respect to the substrate concentration and, when coupled with the oxygen uptake equation, results in a simple algebraic expression for dissolved oxygen concentration in respirometric experiments. This new solution provided highly accurate estimates of dissolved oxygen concentrations with accuracy on the order of 10(-15) for calculations performed using double precision arithmetic. The applicability of this approach for estimating extant biodegradation kinetic; parameters was verified using synthetic dissolved oxygen concentration data that incorporated normally distributed noise to mimic experimental data. A combination of the W function description of oxygen concentration and a nonlinear optimization routine resulted in estimates of the Monod kinetic parameters, mu (m) and K-s, that were close to the actual values, indicating the suitability of this approach for extant kinetic parameter estimation. This approach was subsequently tested on experimental oxygen concentration data obtained during ethylene-glycol biodegradation in respirometric experiments. The availability of simple algorithms for evaluating the W function makes the new solution easier to compute than current methods that rely on numerical solution of differential or nonlinear equations. The simplicity and accuracy associated with use of the W function to describe oxygen concentration data should make it an attractive approach for estimating extant Monod biodegradation kinetic parameters from respirometric experiments. (C) 2001 John Wiley & Sons, Inc.