Control-Oriented Dynamic Modeling of Mashing and Fermentation Processes in Beer Production

Beer production involves interconnected physicochemical and biochemical processes whose dynamic behaviour substantially affects product quality, process duration, and resource consumption. This study develops an integrated, control-oriented mathematical model of the mashing and fermentation stages of beer production. The mashing process was represented as a four-stage cascade system operating at temperature levels of 45, 63, 72, and 78 °C. Component mass balances, Arrhenius-type temperature-dependent kinetic expressions, and enzymatic hydrolysis relationships were used to describe malt extraction and the formation of fermentable sugars. The final sugar concentration obtained from the mashing model was subsequently introduced as the substrate input to the fermentation model. The fermentation process was described using substrate, biomass, and ethanol concentrations as the principal state variables. The Balling relationship was combined with microbial growth and product-formation equations to establish a nonlinear dynamic model. Monod, Aiba, and Tessier kinetic formulations were evaluated using laboratory observations obtained from an industrial brewery. The Monod model demonstrated the closest agreement with the measured growth behavior, with an estimated maximum specific growth rate of 0.92 h⁻¹, a half-saturation constant of 2.4 g L⁻¹, and a coefficient of determination of 0.985. The resulting nonlinear equations were linearized around nominal operating points and transformed into state-space form to support subsequent controller synthesis. Simulation in Python reproduced the expected exponential reduction in substrate concentration, biomass development, and gradual saturation of ethanol production. The proposed integrated model provides a computationally efficient representation of the main brewing stages and can serve as a basis for model predictive control, state estimation, digital-twin development, and real-time process optimization.