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Despite improvements in fermentation method, recent studies still discover numerous weaknesses throughout the entire fermentation process. Accordingly, this calls for a new improvised study. This study presents a mathematical model of an ethanol production system via fermentation; 1) shaker fermentation, and 2) shaker-free fermentation. This model was extended from an 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. For critical view on the description of mass transfer, the study of the coupled diffusion-reaction and coupled diffusionreaction-advection models from a previous mathematical model was also carried out. The understanding of the models enabled accurate prediction on the behaviour of mass transfer effect on fermentation scenarios. The effect of the diffusion coefficient and the advection coefficient were 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 was utilised to estimate the value of the parameters. The result shows that the diffusion was insignificant on the whole ethanol production system but is on the 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.

Nonlinear partial differential equations model related to ethanol production