Nonlinear partial differential equations model related to ethanol production

Abstract

Abstract The study presents a mathematical model of an ethanol production system via fermentation. This model was extended from the established model to examine mass transfer and the inhibition effects on microbial such as yeasts or bacteria, sugar as its substrate and ethanol for the product. In this study, two types of laboratory-scale fermentation are considered, i.e. shaker fermentation and shaker-free fermentation. This led to studying the coupled diffusionreaction and coupled diffusion-reaction-advection models from a previous mathematical model which describes mass transfer. A better understanding of those model able to predict the behaviour of mass transfer effect on fermentation scenarios. The effect of the diffusion coefficient and the advection coefficient are investigated to simulate the dynamical behaviour of the system. Since the model is nonlinear partial differential equations (PDEs), Gear’s algorithm, a numerical method was employed to solve the system while the Nelder–Mead method is utilised to estimate the value of the parameters. The result shows that the diffusion does not have a huge impact on the whole ethanol production system but is contrary to advection. In order to affect the ethanol production system, only tiny advection value is needed, however, a big diffusion value is necessary to achieve the same effect.