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A BIOLOGICAL TREATMENT OF INDUSTRIAL WASTEWATERS: CONTOIS KINETICS

Part of: Numerical problems in dynamical systems Mathematical biology in general

Published online by Cambridge University Press:  30 April 2015

RUBAYYI T. ALQAHTANI ,
MARK I. NELSON  and
ANNETTE L. WORTHY
RUBAYYI T. ALQAHTANI*
Affiliation:
Department of Mathematics, Faculty of Science, Al-Imam Muhammad Ibn Saud Islamic University, Riyadh, Kingdom of Saudi Arabia email rtaa648@uowmail.edu.au, rtalqahtani@imamu.edu.sa
MARK I. NELSON
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email mnelson@uow.edu.au, annette\_worthy@uow.edu.au
ANNETTE L. WORTHY
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email mnelson@uow.edu.au, annette\_worthy@uow.edu.au
*
✉rtaa648@uowmail.edu.au
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Abstract

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This paper analyses the steady-state operation of a generalized bioreactor model that encompasses a continuous-flow bioreactor and an idealized continuous-flow membrane bioreactor as limiting cases. A biodegradation of organic materials is modelled using Contois growth kinetics. The bioreactor performance is analysed by finding the steady-state solutions of the model and determining their stability as a function of the dimensionless residence time. We show that an effective recycle parameter improves the performance of the bioreactor at moderate values of the dimensionless residence time. However, at sufficiently large values of the dimensionless residence time, the performance of the bioreactor is independent of the recycle ratio.

Keywords

bioreactorchemostatContois growth kineticsstirred tankwater treatment

MSC classification

Primary: 65P40: Nonlinear stabilities
Secondary: 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 4 , April 2015 , pp. 397 - 415
Copyright
© 2015 Australian Mathematical Society 

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