Fractional model applied to fermentation process kinetics

Abstract

Biofuels are promising alternatives to partially or fully replace oil and natural gas-based fuels in combustion engines due to less environmental impact than fossil fuels. The production of biofuels through alcoholic fermentation in chemical reactors has been an increasing interest to the industry. Several kinetic models have been examined to determine the kinetics of fermentation of microorganisms. The study and determination of this kinetic model are considered the most important step of a fermentative process since it will define the rate of production and consumption of the main constituents. The mathematical method used to model the chemical reactor equation is based on fractional calculations, more specifically the Caputo fractional derivative is applied in the Monod equation, which is responsible for modeling the reactors. It is noteworthy that fractional derivatives are an excellent tool for describing processes involving the so-called memory effect and heredity properties since in many cases they refine the solution.