Dynamic Simulation and Control of a Continuous Bioreactor Based on Cell Population Balance Model

Document Type : Research Article

Authors

Department of Chemical Engineering, Ferdowsi University, P.O. Box 91775-1111 Mashhad, I.R. IRAN

Abstract

Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured-segregated model is used for dynamic simulation and controller synthesis. The mathematical model consists of a partial integro-differential equation describing the dynamics of the cell mass distribution (PBE) and an ordinary integro-differential equation accounting for substrate consumption. In order to solve the mathematical model, three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used to approximate the PBE model by a coupled set of nonlinear ordinary differential equations (ODEs). Then the resulted ODEs are solved by 4th order Rung-Kutta method. The results indicated that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results showed that although the PI controller has simpler structure, the GLC has better performance.

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References

[1] Munch, T., Sonnleitner, B. and Fiechter, A., New Insights into the Synchronization Mechanism with Forced Synchronous Cultures of Saccharomyces Cerevisiae, J. Biotechnol., 24, 299 (1992).
[2] Parulekar, S. J., Semones, G. B., Rolf, M. J., Lievense, J. C. and Lim, H. C., Induction and Elimination of Oscillations in Continuous Cultures of Saccharomyces Cerevisiae, Biotechn. Bioeng., 28, 700 (1986).
[3] Patnaik, P. R., Oscillatory Metabolism of Saccharo-myces Cerevisiae: An Overview of Mechanisms and Models, Biotechnology Advances, 21, 183 (2003).
[4] Strassle, C., Sonnleitner, B. and Fiechter, A., A Predictive Model for the Spontaneous Synchro-nization of Saccharomyces Cerevisiae Grow in Continuous Culture. II. Experimental Verification,
J. Biotechnol., 9, 191 (1989).
[5] Porro, D. E., Martegani, B., Ranzi, M. and Alberghina, L., Oscillations in Continuous Cultures of Budding Yeasts: A Segregated Parameter Analysis, Biotechnol. Bioeng., 32, 411 (1988).
[6] Munch, T., Sonnleitner, B. and Fiechter, A., The Decisive Role of the Saccharomyces Cerevisiae Cell Cycle Behavior for Dynamic Growth Characterization,  J. Biotechnol., 22, 329 (1992).
[7] Beuse, M., Bartling, R., Kopmann, A., Diekmann, H. and Thoma M., Effect of the Dilution Rate on the Mode of Osillation in Continuous Cultures of Saccharomyces Cerevisiae, J. of Biotechnology, 61, 15 (1998).
[8] Cazzador, L., Mariani, L., Martegani, E. and Alberghina, L., Structured Segregated Models and Analysis of Self-Oscillating Yeast Continuous Cultures, Bioprocess Eng., 5, 175 (1990).
[9] Jones, K. D. and Kompala, D. S., Cybernetic Model of the Growth Dynamics of Saccharomyces Cerevisiae in Batch and Continuous Cultures, J. Biotechnology, 71, 105 (1999).
[10] Martegani, E., Porro, D., Ranzi, B. M. and Alberghina, L., Involvement of a Cell Size Control Mechanism in the Induction and Maintenance of Oscillations in Continuous Cultures of Budding Yeast, Biotechnol. Bioeng., 36, 453 (1990).
[11] Strassle,  C., Sonnleitner,  B., Fiechter,  A., A Predictive Model for the Spontaneous Synchronization of Saccharomyces Cerevisiae Grown in Continuous Culture. I. Concept, J. Biotechnol., 7, 299 (1988).
[12] Mantzaris,  N. V.,  Srienc,  F., Daoutidis, P., Nonlinear Productivity Control Using a Multi-Stage Cell Population Balance Model, Chem. Eng. Sci., 57, 1 (2002).
[13] Fredrickson, A. G. and Mantzaris, N. V., A New Set of Population Balance Equations for Microbial and Cell Cultures, Chem. Eng. Sci., 57, 2265 (2002).
[14] Ramkrishna, D., Kompala, D. S. and Tsao, G. T., Are Microbes Optimal Strategists?, Biotechnol. Prog., 3, 121 (1987).
[15] Sheppard, J. D. and Dawson, P. S., Cell Synchrony and Periodic Behavior in Yeast Populations, Canadian  J. Chem. Eng., 77, 893 (1999).
[16] Zhang, Y., Henson, M. A. and Kevrekidis, Y.G., Nonlinear Model Reduction for Dynamic Analysis of Cell Population Models, Chem. Eng. Sci., 58, 429 (2003).
[17] Henson, M. A., Dynamic Modeling and Control of Yeast Cell Populations in Continuous Biochemical Reactors, Comp. Chem. Eng., 27, 1185 (2003).
[18] Mantzaris, N. V., Daoutidis, P., Cell Population Balance Modeling and Control in Continuous Bioreactors, J. Process Control, 14, 775 (2004).
[19] Zhu, G. Y., Zamamiri, A. M., Henson, M. A. and Hjortso, M. A., Model Predictive Control of Continuous Yeast Bioreactors Using Cell Population Models,Chem. Eng. Sci., 55, 6155 (2000).
[20] Zhang, Y., “Dynamic Modeling and Analysis of Oscillatory Bioreactors”, PhD Theses, LouisianaStateUniversity, Chem. Eng. Department, (2002).
[21] Hjortso, M. A. and Nielsen, J., A Conceptual Model of Autonomous Oscillations in Microbial Cultures, Chem. Eng. Sci., 49, 1083 (1994).
[22] Hjortso, M. A. and Nielsen, J., Population Balance Models of Autonomous Microbial Oscillations,
J. Biotechnol., 42, 255 (1995).
[23] Mantzaris, N. V., Liou, J. J., Daoutidis, P. and Srienc, F., Numerical Solution of a Mass Structured Cell Population Balance Model in an Environment of Changing Substrate Concentration, J. Biotechnol., 71, 157 (1999).
[24] Mantzaris,  N. V.,  Daoutidis,  P. and  Srienc,  F., Numerical Solution of Multi-variable Cell Population Balance Models: I. Finite Difference Methods, Comp. Chem. Eng., 25, 1411 (2001).
[25] Mantzaris, N. V., Daoutidis, P. and Srienc, F., Numerical Solution of Multi-variable Cell Population Balance Models: II. Spectral Methods, Comp. Chem. Eng., 25, 1441 (2001).
[26] Mantzaris,  N. V.,  Daoutidis,  P.  and  Srienc,  F., Numerical Solution of Multi-variable Cell Population Balance Models: III. Finite Element Methods, Comp. Chem. Eng., 25, 1463 (2001).
[27] Finlayson, B. A., “Nonlinear Analysis in Chemical Engineering”, McGraw-Hill, (1980).
[28] Kurtz, M. J., Zhu, G. Y., Zamamiri, A. M., Henson, M. A. and Hjortso, M. A., Control of Oscillating Microbial Cultures Described by Population Balance Models, Ind. Eng. Chem. Research, 37, 4059 (1998).
[29] Zhang, Y., Zamamiri, A. M., Henson, M. A. and Hjortso, M. A., Cell Population Models for Bifurcation Analysis and Nonlinear Control of Continuous Yeast Bioreactors, J. Process Control. , 12, 721 (2002).
[30] Kurtz, M. J., Zhu, G. Y., Zamamiri, A. M., Henson, M. A. and Hjortso, M. A., Control of Oscillating Microbial Cultures Described by Population Balance Models, Ind. Eng. Chem. Research,
37, 4059 (1998).
[31] Shahrokhi, M. and Fanaei, M. A., State Estimation in a Batch Suspension Polymerization Reactor, Iranian Polymer J., 10, 173 (2001).
[32] Soroush, M. and Kravaris, C., Nonlinear Control of a Batch Polymerization Reactor: An Experimental Study, AIChE J., 38, 1429 (1992).

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