ON THE DYNAMIC BEHAVIOUR OF A CLASS OF BIOREACTOR WITH NON-CONVENTIONAL YIELD COEFFICIENT FORM
Keywords:
bifurcation analysis, continuous flow, limit cycle, local stability analysis, steady-state multiplicity, unstructured kinetic models
Abstract
The goal of this work is to analyze by numerical bifurcation the dynamical behavior of a class of continuous bioreactor used to hydrolyze cellulose using Cellulomonas cellulans, taking into account the effect of modeling the growth rate of this microorganism by six different kinetics models (monotonic and non-monotonic). Furthermore, it is considered that the biomass yield can be modeled as a constant or a variable case, for the variable case, a substrate dependent Gaussian-type function was proposed. The proposed non-conventional yield function is a realistic approach that describes the behavior of the cellular yield, unlike other models, this one is bounded to the maximum cellular yield and can be extrapolated to several operation conditions. Numerical results show changes in the equilibrium branches due to the kinetic growth model used. The non-conventional model of biomass yield produces a shift in the steady state multiplicity intervals, and new limit cycles were found with certain specific values of dilution rate and substrate feed
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Agrawal, P., Lee, C., Lim, H.C. y Ramkrishna, D. (1982). Theorical investigations of dynamic behavior of isothermal continuous stirred tank biological reactors. Chemical Engineering Science 37, 453.
Ajbar, A. (2001). On the existence of oscillatory behavior in unstructered models of bioreactors. Chemical Engineering Science 56, 1991.
Ajbar, A. y Alhumaizi, K. (2012). Dynamics of the chemostat : A bifurcation theory approach. CRC Press Taylor & Francis Group, USA.
Álvarez-Ramírez, J., Álvarez, J. y Velasco, A. (2009). On the existence of sustained oscillations in a class of bioreactors. Computers & Chemical Engineering 33, 4.
Allen, L.J.S. (2007). An Introduction to Mathematical Biology. Pearson/Prentice Hall, NJ.
Crooke, P.S., Wei, C.-J. y Tanner, R.D. (1980). The effect of the specific growth rate and yield expressions on the existence of oscillatory behavior of a continuous fermentation model. Chemical Engineering Communications 6, 333.
Dong, Q.L. y Ma, W.B. (2013). Qualitative analysis of the chemostat model with variable yield and a time delay. Journal of Mathematical Chemistry 51, 1274.
Fu, G. y Ma, W. (2006). Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake. Chaos, Solitons & Fractals 30, 845.
Fu, G., Ma, W. y Shigui, R. (2005). Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake. Chaos, Solitons & Fractals 23, 873.
Garhyan, P., Elnashaie, S.S.E.H., Al-Haddad, S.M., Ibrahim, G. y Elshishini, S.S. (2003). Exploration and exploitation of bifurcation/chaotic behavior of a continuous fermentor for the production of ethanol. Chemical Engineering Science 58, 1479.
Gray, P. y Scoot, S.K. (1990). Chemical oscillations and instabilities. Non-linear chemical kinetic. Clarendon Press. Oxford,
Huang, X., Zhu, L. y Chang, E.H.C. (2007). Limit cycles in a chemostat with general variable yields and growth rates. Nonlinear Analysis: Real World Applications 8, 165.
Ibrahim, G., Habib, H. y Saleh, O. (2008). Periodic and chaotic solutions for a model of a bioreactor with cell recycle. Biochemical Engineering Journal 38, 124.
Karaaslanl, C.C¸ . (2012) Bifurcation analysis and its applications. En: Numerical simulation - from theory to industry, (M. Andriychuk,ed.), Pp. 3. Intech.
Lara-Cisneros, G., Femat, R. y Perez, E. (2012). On dynamical behaviour of two-dimensional biological reactors. International Journal of Systems Science 43, 526.
Lenbury, Y. y Chiaranai, C. (1987). Bifurcation analysis of a product inhibition model of a continuous fermentation process. Applied Microbiology and Biotechnology 25, 532.
Lenbury, Y.W. y Punpocha, M. (1989). The effect of the yield expression on the existence of oscillatory behavior in a three-variable model of a continuous fermentation system subject to product inhibition. Biosystems 22, 273.
Namjoshi, A., Kienle, A. y Ramkrishna, D. (2003). Steady-state multiplicity in bioreactors: Bifurcation analysis of cybernetic models. Chemical Engineering Science 58, 793.
Nelson, M.I. y Sidhu, H.S. (2005). Analysis of a chemostat model with variable yield coefficient. Journal of Mathematical Chemistry 38, 605.
Nelson, M.I. y Sidhu, H.S. (2008). Analysis of a chemostat model with variable yield coefficient: Tessier kinetics. Journal of Mathematical Chemistry 46, 303.
Nelson, M.I., Sidhu, H.S. (2009). Analysis of a chemostat model with variable yield coefficient: Tessier kinetics. Journal of Mathematical Chemistry 46, 303.
Nielsen, J.H., Villadsen, J. y Lide?n, G. (2003). Bioreaction Engineering Principles (3rd. ed.). Springer. New York.
Pilyugin, S.S.W., Paul. (2003). Multiple limit cycles in the chemostat with variable yield. Mathematical Biosciences 182, 151.
Gupta, P., Samant, K., and Sahu, A. (2012). Isolation of cellulose-degrading bacteria and determination of their cellulolytic potential. International Journal of Microbiology 2012, 1. Sterner, R.W., Small, G. E. & Hood, J. M. (2012). The conservation of mass. Nature Education Knowledge 3, 20.
Strogatz, S.H. (1994). Nonlinear dynamics and chaos : With applications to physics, biology, chemistry, and engineering. Perseus Books Publishing, L.L.C. Massachusetss, U.S.
Sun, J.-Q. y Luo, A.C.J. (2012). Global Analysis of Nonlinear Dynamics. Springer, New York.
Sun, K., Tian , Y., Chen, L. y Kasperski, A. (2010). Nonlinear modelling of a synchronized chemostat with impulsive state. Mathematical and Computer Modelling 52, 227.
Wu, W., & Chang, H.-Y. (2007). Output regulation of self-oscillating biosystems: Model-based pi/pid control approches. Industrial & Engineering Chemistry Research.
Zhang, Y. & Henson, M.A. (2001). Bifurcation analysis of continuous biochemical reactor models. Biotechnology Progress 17, 647.
Published
2020-01-24
How to Cite
Gómez-Acata, R., Lara-Cisneros, G., Femat, R., & Aguilar-López, R. (2020). ON THE DYNAMIC BEHAVIOUR OF A CLASS OF BIOREACTOR WITH NON-CONVENTIONAL YIELD COEFFICIENT FORM. Revista Mexicana De Ingeniería Química, 14(1), 149-165. Retrieved from http://rmiq.org/ojs311/index.php/rmiq/article/view/1230
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Section
Simulation and control
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