Nonlinear Dynamics of a Controlled Stirred Tank Bioreactor With Predator-Prey Relationship

• Authors: Bolesław Tabiś , Szymon Skoneczny , Wojciech S. Stryjewski
• Languages of publication: EN

Abstracts

EN

The paper presents the dynamic characteristics of a continuous tank bioreactor for microbiological process, with a developed predator-prey food chain. The presence of the predator microorganism considerably influences the position and stability character of steady-states. There appears to exist a wide range of unstable steady-states and high-amplitude oscillations of state variables. Without automatic control, the system can operate only in unsteady conditions. From technological point of view, this circumstance is unfavorable. It was shown that oscillations can be removed by employing automatic control with continuous P or PI controllers. Moreover, the use of a controller with integrating element causes removal of the predator from the bioreactor. The paper discusses an application of this phenomenon for practical purposes.

Keywords

EN

predator-prey; dynamics; automatic control; steady states; bioreactor

• Publisher: De Gruyter Open
• Journal: Chemical and Process Engineering
• Year: 2014
• Volume: 35
• Issue: 3
• Pages: 349-360

Dates

published

1 - 9 - 2014

accepted

1 - 1 - 2014

online

17 - 10 - 2014

received

20 - 3 - 2013

revised

27 - 12 - 2013

Contributors

author

Bolesław Tabiś

• Cracow University of Technology, Department of Chemical and Process Engineering, ul. Warszawska 24, 31-155 Kraków, Poland

author

Szymon Skoneczny

• Cracow University of Technology, Department of Chemical and Process Engineering, ul. Warszawska 24, 31-155 Kraków, Poland

author

Wojciech S. Stryjewski

• Cracow University of Technology, Department of Chemical and Process Engineering, ul. Warszawska 24, 31-155 Kraków, Poland

References

• Ajbar A., 2001b. On the existence of oscillatory behavior in unstructured models of bioreactors. Chem. Eng. Sci., 56, 1991-1997. DOI: 10.1016/S0009-2509(00)00423-1.[Crossref]
• Ajbar A., Alhumazi K., 2012. Dynamics of the chemostat. A bifurcation theory approach. CRC Press, London - New York.
• Alhumazi K., Ajbar.A., 2005. Dynamics of predator-prey interactions in continuous cultures. Eng. Life Sci., 5, 139-147. DOI: 10.1002/elsc.200420062.[Crossref]
• Butler G.J., Hsu S.B., Waltman P., 1983. Coexistence of competing predators in chemostat. J. Math. Biol., 17, 133-151. DOI: 10.1007/BF00305755.[Crossref]
• Chi C.T., Howell J.A., Pawlowsky U., 1974. The regions of multiple stable steady states of a biological reactor with wall growth, utilising inhibitory substrates. Chem. Eng. Sci., 29, 207-211. DOI: 10.1016/0009-2509(74)85046-3.[Crossref]
• Dunn I.J., Heinzle E., Ingham J., Prenosil J.E., 2003. Biological reaction engineering. Dynamic modelling fundamentals with simulation examples. Wiley-VCH Verlag, Weinhem.
• El-Owaidy H.M., Moniem A.A., 2003. On food chain in a chemostat with distinct removal rates. Appl. Math. ENotes, 3, 183-191.
• Li B., Kuang Y., 2000. Simple food chain in a chemostat with disting removal rates. J. Math. Anal. Appl., 242, 75-92. DOI: 10.1006/jmaa.1999.6655.[Crossref]
• Lotka J.A., 1925. Elements of physical biology, Williams & Wilkins, Baltimore.
• Luyben W.L., 1999. Process modeling, simulation and control for chemical engineers. McGraw-Hill, Inc., New York-Toronto.
• Moghadas S.M., Gumel A.B., 2003. Dynamical and numerical analyses of a food-chain model. Appl. Math. Comp., 142, 35-49. DOI: 10.1016/S0096-3003(02)00282-5.[Crossref]
• Moussa M.S., Hooijmans C.M., Lubberding H.J., Gijzen H.J., Loosdrecht M.C.M., 2005. Modelling nitrification, heterotrophic growth and predation in activated sludge. Water Res., 39, 5080-5098. DOI: 10.1016/j.watres.2005.09.038.[Crossref]
• Onysko K.A., Robinson C.W., Budman H.M., 2002. Improved modelling of the unsteady-state behavior of an immobilized-cell, fluidized-bed bioreactor for phenol biodegradation. Can. J. Chem. Eng., 80, 239-252. DOI: 10.1002/cjce.5450800209.[Crossref]
• Olivieri G., Russo M. E., Marzocchella A., Salatino P., 2011. Modeling of an aerobic biofilm reactor with doublelimiting substrate kinetics: Bifurcational and dynamical analysis. Biotechnol. Progress, 27, 1599-1613. DOI: 10.1002/btpr.690.[WoS][Crossref]
• Pavlou S., 1999. Computing operating diagrams of bioreactors. J. Biotechnol., 71, 7-16. DOI: 10.1016/S0168-1656(99)00011-5.[Crossref]
• Ratsak C.H., Maarsden K.A., Kooijman S.A.L.M., 1996. Effects of protozoa on carbon mineralization in activated sludge. Water Res., 30, 1-12. DOI: 10.1016/0043-1354(95)00096-4.[Crossref]
• Russo M.E., Maffettone P.I., Marzocchella A., Salatino P., 2008. Bifurcation and dynamical analysis of a continuous biofilm reactor. J. Biotechnol., 135, 295-303. DOI: 10.1016/j.jbiotec.2008.04.003.[WoS][Crossref]
• Scudo F.M., Ziegler J.R., 1978. The golden age of theoretical ecology: 1923-1940. Springer-Verlag, Berlin, Heidenberg, New York.
• Tabiś B., 1996. Investigation of parametric dependency and linear stability of a cascade of stirred tank bioreactors. Inż. Chem. Proc., 17, 279-294 (in Polish).
• Tabiś B., Malik J., 1996. Steady states multiplicity in a cascade of stirred tank bioreactors for phenol degradation.
• Inż. Chem. Proc., 17, 645-651 (in Polish).
• Tabiś B., Malik J., 1998. Stability characteristics of a biochemical reactor with predator-prey relationship. A substrate inhibition case. Chem. Eng. J., 70, 179-188. DOI: 10.1016/S1385-8947(98)00094-1.[Crossref]
• Tsuchiya M.M., Drake J.F., Jost J.L., Fredrickson A.G., 1972. Predator-prey interactions of Distyostelium discoideum and Eschierichia coli in continuous culture. J. Bacteriol., 110, 1147-1153.
• Volterra V., 1926. Variazione e fluttuazioni del numero d’individui in specie animali conviventi. Mem. Accad. Nazion. Lincei, 2, 31-113.
• Yang R.D., Humphrey A.E., 1975. Dynamics and steady state studies of phenol biodegradation in pure and mixed cultures. Biotechnol. Bioeng., 17, 1211-1235. DOI: 10.1002/bit.260170809.[Crossref]
• Zhu H., Campell S.A., Wolkowicz G.S.K., 2002. Bifurcation analysis of a predator-prey system with nonmonotonic functional response. SIAM J. Appl., 63, 636-682. DOI: 10.1137/S0036139901397285.[Crossref]

Identifiers

DOI

10.2478/cpe-2014-0026