On the dynamic behaviour of a class of bioreactor with non-conventional yield coefficient form

Sobre el comportamiento dinámico de un tipo de biorreactor con un coeficiente de rendimiento no convencional

R.V. Gómez-Acata¹, G. Lara-Cisneros², R. Femat², R. Aguilar-López¹*

¹ Departamento de Biotecnología y Bioingeniería, CINVESTAV-IPN, Av. Instituto Politécnico Nacional 2508, San Pedro Zacatenco, DF. *Corresponding author. E-mail: raguilar@cinvestav.mx

² División de Matemáticas Aplicadas, IPICYT, Camino a la Presa San José 2055, San Luis Potosí, S.L.P., México.

Recibido 27 de Febrero de 2014
Aceptado 19 de Febrero de 2015

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, talcing into account the effect of mo deling 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 appro ach that describes the behavior of the cellular yield, unlike other model_t, 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.

Key words: bifurcation analysis, continuous flow, limit cycle, local stability analysis, steady-state multiplicity, unstructured kinetic models.

Resumen

El objetivo de este trabajo es analizar mediante bifurcation numerica el comportamiento dinámico de una clase de biorreactor continuo, utilizado para la hidrolisis de carboximetilcelulosa por Cellulomonas cellulans, tomando en cuenta el efecto de modelar la velocidad de crecimiento de este microorganismo por seis diferentes modelos cineticos no estructurados (monotonicos y no-monotónicos). En el analisis se considera que el rendimiento celular puede ser modelado como un valor constante o variable, para este ultimo caso, fue propuesta una funcion tipo Gaussiana dependiente de la concentration de sustrato. El modelo para el rendimiento celular variable utilizadorepresenta un enfoque mas realista para describir el rendimiento celular, a diferencia de otros modelos reportados, la funcion es acotada al maximo rendimiento celular y puede ser extrapolado a diferentes condiciones de operation. Los resultados numericos revelan cambios en las ramas de equilibrio debido al modelo de crecimiento utilizado. El modelo no convencional del coeficiente de rendimiento ocasiona un desplazamiento en los intervalos de multiplicidad de estados estacionarios, cambios en la estabilidad de los puntos de equilibrio y el surgimiento de ciclos límite a ciertos valores específicos de la tasa de dilution y de la concentration del sustrato de alimentation.

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Acknowledgements

R.V.G.A wishes to acknowledge to the CINVESTAV and the CONACyT for the doctoral scholarship number 290564; Gerardo Lara-Cisneros thanks CONACyT for the postdoctoral fellowship grant.

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