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Explicit oxygen concentration expression for estimating extant biodegradation kinetics from respirometric

C T Goudar¹, T G Ellis

¹School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019, USA. chetan.goudar.b@bayer.com

Biotechnology and Bioengineering

|September 6, 2001

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This study introduces a straightforward method using the Lambert W function to accurately estimate biodegradation kinetic parameters from respirometric oxygen uptake data. The new explicit solution simplifies calculations for dissolved oxygen, improving biodegradation modeling.

Area of Science:

Environmental Microbiology
Biochemical Engineering
Mathematical Modeling

Background:

Respirometric experiments are crucial for determining biodegradation kinetics.
Estimating kinetic parameters like maximum growth rate (μm) and Monod constant (Ks) is vital for environmental and industrial applications.
Existing methods often rely on complex numerical solutions for biodegradation models.

Purpose of the Study:

To develop a simple, explicit, and accurate method for estimating biodegradation kinetic parameters.
To utilize the Lambert W function for solving biodegradation equations derived from the Monod model.
To validate the new method using both synthetic and experimental respirometric data.

Main Methods:

A novel closed-form solution based on the Lambert W function was derived for the Monod biodegradation equation.

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The solution was coupled with oxygen uptake equations to provide an algebraic expression for dissolved oxygen concentration.

The method was tested using synthetic data with added noise and experimental data from ethylene-glycol biodegradation.

Main Results:

The Lambert W function-based solution accurately predicted dissolved oxygen concentrations (accuracy ~10^-15).
Nonlinear optimization using the W function approach yielded accurate estimates for Monod kinetic parameters (μm and Ks).
The method demonstrated suitability for estimating kinetic parameters from real-world respirometric data.

Conclusions:

The Lambert W function offers a computationally simple and highly accurate approach for estimating biodegradation kinetic parameters.
This explicit solution simplifies the analysis of respirometric data compared to traditional numerical methods.
The method is well-suited for practical application in biodegradation studies and environmental modeling.