Abstract
This paper proposes and analyzes a mathematical model for the production of bioethanol in a continuous bioreactor with recycling. The kinetics correspond to the use of Saccharomyces bayanus for the fermentation of sugars found in wastewater from soft drinks. The proposed model considers product growth latency, which was experimentally found in batch studies of ethanol production. Furthermore, the inhibition effect of ethanol is expressed by a modified version of the classical Andrew's model for substrate inhibition. The proposed model consists of only three ordinary differential equations containing a minimal number of operating parameters, which include the bioreactor residence time, glucose feed concentration, recycle ratio and the fraction of biomass removed from the reactor by the flow. The positivity and the boundedness of solutions of the model were confirmed under reasonable restrictions of parameters. The stability analysis showed that there is a value of residence time at which an exchange of stability occurs between the trivial washout and non-washout solutions. This critical value depends only on the substrate feed concentration, biomass death rate, recycle ratio and purge fraction. Dynamic simulations of the model were carried out for substrate concentration in the range of 100-250 g/L, commonly used for the production of ethanol. An inverse response due to the inhibition effects of ethanol was observed in the time evolution of substrate and biomass concentrations. Parametric studies showed that ethanol concentration increases with the recycle ratio, with the inverse of residence time and with the inverse of purge fraction. The effect of ethanol latency has, on the other hand, a substantial effect on ethanol concentration. Despite its unstructured nature and the fact that some parameters such as temperature and acidity were not taken into consideration, the proposed model managed to provide useful results on the bioreactor-settler stability and the effect of key parameters on its dynamic behavior, which could pave the way for future optimization studies.