Fermentation is an essential step in beer brewing: when yeast is added to hoppened wort, sugars released from the grain during germination are fermented into ethanol and higher alcohols. In order to study, simulate and optimise the beer fermentation process, it is necessary to formulate an accurate kinetic model of the chemical system for dynamic simulation of key component concentrations. Since the entire beer production process is a highly complex series of chemical reactions with the presence of over 600 species (Vanderhaegen et al., 2006), many of the specific interactions are not quantitatively understood, rendering the construction of a complete deterministic dynamic model extremely cumbersome. In the fermentation process. A reduced-order dynamic beer fermentation model considering only the key chemical reaction pathways can be used for numerical optimisation of suitable manipulated variable profiles, providing accurate results which can be directly used for industrial implementation to an existing process. A typical optimisation goal in a beer fermentation process is achieving minimum brewing time, while also ensuring several by-product concentrations are monitored in order to maintain high product quality.
Two of the published differential algebraic equation (DAE) models have been successfully validated and indeed provide a detailed representation of the beer fermentation process (Gee and Ramirez, 1988, 1994; de Andrés-Toro, 1998). While they differ in terms of mathematical structure, chemical species considered and parameter values used, both have been demonstrated to predict the primary species profiles in good agreement with real plant data. The latter model has formed the basis of several subsequent optimisation studies which considered various systematic protocols to obtain dynamic temperature manipulation profiles capable of achieving higher production efficiency and improving industrial practice (Carrillo-Ureta et al., 2001; Xiao et al., 2003).
This paper presents a computational implementation of a beer fermentation model which enables the prediction of the dynamic profiles of all species considered: the de Andrés-Toro (1998) model consists of seven ODEs, considering a single sugar, ethanol, three distinct biomass forms and two undesirable by-products (ethyl acetate and diacetyl molecules). Our code has been validated using temperature profile inputs published by several authors (Carrillo-Ureta et al., 1999; Xiao et al., 2003) and indeed predicts species concentration profiles in excellent agreement with published results.
Dynamic optimisation of the beer fermentation process on the basis of our validated model implementation is based on an optimisation algorithm which uses an appropriate objective function (minimisation of fermentation time) and determines a temperature manipulation protocol which improves process operation by minimising fermentation time while also adhering to the prescribed composition quality constraints. The simultaneous consideration of four explicit parameters (fermentation time and concentrations of three key flavour attributes: ethanol, ethyl acetate, diacetyl compounds) enables the exploration of a vast solution space, rendering a truly multi-objective optimisation problem. A focal point of our research (in contrast to certain prior studies on beer fermentation process optimisation) is the use of real industrial plant data in order to validate our model implementation and evaluate the projected process operation improvement against the established temperature manipulation profile of current industrial practice.
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