(28e) Dynamic Optimisation of Beer Fermentation: Sensitivity Analysis of Attainable Process Performance Vs. Product Flavour Constraint Levels

To achieve maximum plant throughput and the highest profitability attainable, there is a strong incentive to optimise the fermentation stage in beer production, given the time-consuming and energy-intensive nature of the process (Rodman and Gerogiorgis, 2016). Process complexity prevents the use of comprehensive deterministic models in dynamic optimisation studies: with over 600 chemical species reported (Vanderhaegen et al., 2006), such computational implementations would require prohibitively laborious parameterisations and equally expensive execution. Nevertheless, it is desirable to use a reduced-order kinetic model (considering only the most important species and their interactions within the chemical system) toward dynamic simulation and optimisation of beer fermentation, in order to systematically investigate process performance under varying operating conditions.

The yeast culture suspended within cylindro-conical fermentation vessels is an integral part of the process: the cell enzymatic effect on the sugar content produced in wort pre-processing induces its conversion to ethanol and ensures the desired alcohol concentration level in the beverage. Cell activity is highly sensitive to system temperature (Landaud et al., 2001), influencing the fermentation effective rate and ultimately the process performance. The selection and implementation of an appropriate dynamic temperature profile is thus the most important factor influencing the required processing time, so it is a focus of the present dynamic optimisation study. The system temperature also influences the progression of a multitude of side reactions, many of which lead to the production of undesirable by-product species which are known to have detrimental effects on product flavour beyond certain concentration levels; novel temperature manipulation profiles must thus explicitly incorporate such considerations.

A published and validated kinetic model of beer fermentation considers the dynamic behaviour of a yeast culture (active, latent and dead cells) and its effect on sugar and ethanol concentrations, in addition to two undesirable by product species: ethyl acetate and diacetyl compounds (de Andrés-Toro, 1998). This model has formed the basis of several prior 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). The novelty of our published optimisation study, however, is the comprehensive visualisation of the four-dimensional attainable envelope of beer fermentation, and the multi-objective optimisation of ethanol production and batch duration under explicit product flavour constraints (Rodman & Gerogiorgis, 2016).

Expert beer tasters and connoisseurs confirm that for a given beer product, the harmful concentrations of both ethyl acetate and diacetyl compounds are actually indistinguishable below certain levels, rendering further reduction towards concentration minimisation redundant or at least less important. Marketing and commercial operations of beer brewing corporations pay particular importance to such thresholds, not only because they may well be subjective and/or local market-dependent, but also because regional, national and/or cultural taste patterns affect desirable flavour perceptions enormously. This experiential reality has motivated the present study, which presents an alternative approach to the formulation of the dynamic multi-objective optimisation problem, in an effort to understand how the arbitrary selection of flavour constraints may impact optimal manufacturing policies.

The sensitivity analysis of attainable process performance (how can we maximise ethanol production while also minimising fermentation duration?) with respect to product flavour constraint levels (how can we ensure that the harmful by-product concentration constraints will be respected?) addresses the importance of technoeconomic optimisation without unnecessary effort and expenditure. Moreover, the novel objective function employed achieves an explicit visualisation of the optimal temperature manipulation profile as a function of the two-dimensional space of by-product constraint levels. A deterministic approach with explicit temperature control vector parameterisation is used to solve the formal optimisation problem; a comparative evaluation of suitable nonlinear programming (NLP) algorithms (Schlegel et al., 2005) will be illustrated. Solving this dynamic optimisation problem over a wide range of realistic threshold values on both by-products allows us to map the attainable concentration of product ethanol and production batch times, thus enabling beer production plant operators to rapidly visualise if and how process performance can be significantly improved as a function of tolerable by-product levels.

LITERATURE REFERENCES

1. Carrillo-Ureta, G., Roberts, P., Becerra, V., 2001. Genetic algorithms for optimal control of beer fermentation. Proceedings of the IEEE International Symposium on Intelligent Control, 391-396.

2. de Andrés-Toro, B., et al. 1998. A kinetic model for beer production under industrial operational conditions. Math. Comput. Simulat. 48(1): 65-74.

3. Vanderhaegen, B., et al., 2006. The chemistry of beer aging â?? a critical review. Food Chem. 95(3): 357-381.

4. Xiao, J., Zhou, Z., Zhang, G., 2003. Ant colony system algorithm for the optimization of beer fermentation control. J. Zhejiang Univ.5(12): 1597-1603.

5. Schlegel, M., Stockmann, K., Binder, T. and Marquardt, W., 2005. Dynamic optimization using adaptive control vector parameterization. Comput. Chem. Eng. 29(8): 1731-1751.

6. Rodman, A.D., Gerogiorgis, D.I., 2016. Multi-objective process optimisation of beer fermentation via dynamic simulation, Food Bioprod. Process. (in press, available online).

7. Landaud, S., Latrille, E., Corrieu, G., 2001. Top pressure and temperature control the fusel alcohol/ester ratio through yeast growth in beer fermentation. J. Inst. Brewing, 107(2): 107-117.