Dynamic and chaotic behavior of periodically forced fermentors for bioethanol production

In this preliminary paper, the dynamic responses of bioethanol fermentors to sinusoidal periodic perturbations of the feed concentration have been investigated. It is shown that the steady state autonomous model of the unforced fermentor can be reduced analytically to a cubic polynomial. This analytical form enables to implement the global bifurcation analysis to divide the parameter space into regions with different number of steady state solutions; moreover, the discriminant of the cubic polynomial is used for the analysis of the nature of the number of the steady state solutions. The bifurcation analysis shows that the locus of the fold points is equivalent to the locus of the discriminant of the cubic polynomial in the (D, C-so) plane. It has been shown that the periodic operation of the autonomous fermentor gives higher average ethanol concentration than the corresponding unstable steady state. The investigation reveals that the centre of forcing has significant effect on the dynamic response of the periodically forced fermentors. Chaotic behavior is developed when the centre of forcing is relatively close to a homoclinic infinite period orbit, while quasi-periodicity is developed when the centre of forcing is in the neighborhood of a Hopf bifurcation point. The system shows interesting phase planes at certain forcing amplitudes. It has been shown that within the parameters range studied the best policy for production of bioethanol is to operate the forced fermentors in the frequency locking regions at small forcing amplitudes. (C) 2010 Elsevier Ltd. All rights reserved.