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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 

References

Abdurahman, N. H., Rosli, Y. M. and Azhari, N. H., “Development of a membrane anaerobic system (MAS) for palm oil mill effluent (POME) treatment”, Desalination 266 (2011) 208–212 ; doi:10.1016/j.desal.2010.08.028.CrossRefGoogle Scholar
Abdurahman, N. H., Rosli, Y. M., Azhari, N. H. and Tam, S. F., “Biomethanation of palm oil mill effluent (POME) by membrane anaerobic system (MAS) using POME as a substrate”, World Acad. Sci. Eng. Technol. 5 (2011) 276–281 ; http://waset.org/publications/2297/biomethanation- of-palm-oil-mill-effluent-pome-by-membrane-anaerobic-system-mas-using-pome-as-a-substrate.Google Scholar
Ardestani, F., “Survey of the nutrient utilization and cell growth kinetic with Verhulst, Contois and exponential models for Penicillium brevicompactum ATCC 16024 in batch bioreactor”, World Appl. Sci. J. 16 (2012) 135–140 ;http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.390.1023&rep=rep1&type=pdf.Google Scholar
Contois, D. E., “Kinetics of bacterial growth: relationship between population density and specific growth rate of continuous cultures”, J. Gen. Microbiol. 21 (1959) 40–50 ; doi:10.1099/00221287-21-1-40.CrossRefGoogle ScholarPubMed
Dulac, H., Points singulieres des equations differentielles, Fascicule 61 of Mém. Sci. Math. (Gauthier-Villars, Paris, 1934).Google Scholar
Emerald, F. M. E., Prasad, D. S. A., Ravindra, M. R. and Pushpadass, H. A., “Performance and biomass kinetics of activated sludge system treating dairy wastewater”, Int. J. Dairy Technol. 24 (2012) 609–615; doi:10.1111/j.1471-0307.2012.00850.x.CrossRefGoogle Scholar
Gawande, N. A., Reinhart, D. R. and Yeh, G.-T., “Modeling microbiological and chemical processes in municipal solid waste bioreactor, Part I: Development of a three-phase numerical model BIOKEMOD-3P”, Waste Manag. 30 (2010) 202–210; doi:10.1016/j.wasman.2009.09.009.CrossRefGoogle ScholarPubMed
Guerrero, L., Montalvo, S., Coronado, E., Chamy, R., Poirrier, P., Crutchik, D., Snchez, E., De La Rubia, M. A. and Borja, R., “Performance evaluation of a two-phase anaerobic digestion process of synthetic domestic wastewater at ambient temperature”, J. Environ. Sci. Health A 44 (2009) 673–681; doi:10.1080/10934520902847794.CrossRefGoogle ScholarPubMed
Hemsi, P., Shackelford, C. and Figueroa, L., “Calibration of reactive transport models for remediation of mine drainage in solid-substrate biocolumns”, J. Environ. Eng. 136 (2010) 914–925; doi:10.1061/(asce)ee.1943-7870.0000234.CrossRefGoogle Scholar
Hidaka, T., Horie, T., Akao, S. and Tsuno, H., “Kinetic model of thermophilic l-lactate fermentation by Bacillus coagulans combined with real-time PCR quantification”, Water Res. 44 (2010) 2554–2562; doi:10.1016/j.watres.2010.01.007.CrossRefGoogle ScholarPubMed
Hu, W. C., Thayanithy, K. and Forster, C. F., “A kinetic study of the anaerobic digestion of ice-cream wastewater”, Process Biochem. 37 (2002) 965–971; doi:10.1016/S0032-9592(01)00310-7.CrossRefGoogle Scholar
Isik, M. and Sponza, D. T., “Substrate removal kinetics in an upflow anaerobic sludge blanket reactor decolorising simulated textile wastewater”, Process Biochem. 40 (2005) 1189–1198 ; doi:10.1016/j.procbio.2004.04.014.CrossRefGoogle Scholar
Jordan, D. W. and Smith, P., Nonlinear ordinary differential equations, 2nd edn.Oxford Applied Mathematics and Computing Series (Clarendon Press, NewYork, USA, 1989).Google Scholar
Mazutti, M. A., Corazza, M. L., Filho, F. M., Rodrigues, M. I., Corazza, F. C. and Treichel, H., “Inulinase production in a batch bioreactor using agroindustrial residues as the substrate: experimental data and modeling”, Bioprocess Biosyst. Eng. 32 (2009) 85–95 ; doi:10.1007/s00449-008-0225-5.CrossRefGoogle Scholar
Nelson, M. I., Balakrishnan, E. and Sidhu, H. S., “A fundamental analysis of continuous flow bioreactor and membrane reactor models with Tessier kinetics”, Chem. Eng. Commun. 199 (2012) 417–433; doi:10.1080/00986445.2010.525155.CrossRefGoogle Scholar
Nelson, M. I., Balakrishnan, E., Sidhu, H. S. and Chen, X. D., “A fundamental analysis of continuous flow bioreactor models and membrane reactor models to process industrial wastewaters”, Chem. Eng. J. 140 (2008) 521–528; doi:10.1016/j.cej.2007.11.035.CrossRefGoogle Scholar
Nelson, M. I., Kerr, T. and Chen, X. D., “A fundamental analysis of continuous flow bioreactor and membrane reactor models with death and maintenance included”, Asia Pac. J. Chem. Eng. 3 (2008) 70–80; doi:10.1002/apj.106.CrossRefGoogle Scholar
Pavlostathis, S. G. and Giraldo-Gomez, E., “Kinetics of anaerobic treatment”, Water Sci. Technol. 24 (1991) 35–59 ; http://www.iwaponline.com/wst/02408/wst024080035.htm.CrossRefGoogle Scholar
Pinna, A., Lallai, A., Mura, G. and Grosso, M., “Comparison across different models for the description of batch biodegradation processes”, Chem. Eng. Trans. 149 (2009) 1227–1232 ; doi:10.3303/CET0917205.Google Scholar
Poh, P. E. and Chong, M. F., “Biomethanation of palm oil mill effluent (POME) with a thermophilic mixed culture cultivated using POME as a substrate”, Chem. Eng. J. 164 (2010) 146–154 ; doi:10.1016/j.cej.2010.08.044.CrossRefGoogle Scholar
Ramirez, I., Mottet, A., Carrère, H., Dèlèris, S., Vedrenne, F. and Steyer, J., “Modified ADM1 disintegration/hydrolysis structures for modeling batch thermophilic anaerobic digestion of thermally pretreated waste activated sludge”, Water Res. 43 (2009) 3479–3492 ; doi:10.1016/j.watres.2009.05.023.CrossRefGoogle ScholarPubMed
Sun, S. L., Wu, B., Zhao, D. Y., Zhang, X. X., Zhang, Y., Li, W. X. and Cheng, S. P., “Optimization of Xhhh strain biodegradation with metal ions for pharmaceutical wastewater treatment”, J. Environ. Biol. 30 (2009) 877–882; http://www.jeb.co.in/journal\_issues/200909\_sep09\_supp/paper\_18.pdf.Google Scholar
Zhang, J., Shao, X., Townsend, O. V. and Lynd, L. R., “Simultaneous saccharification and co-fermentation of paper sludge to ethanol by Saccharomyces cerevisiae RWB222 Part I: Kinetic modeling and parameters”, Biotechnol. Bioeng. 104 (2009) 920–931; doi:10.1002/bit.22464.CrossRefGoogle ScholarPubMed