(343d) Parameter Estimation and Sensitivity Analysis in Beer Fermentation Modelling and Dynamic Optimisation

Growing economic pressure experienced by the UK alcohol industry as a result of a global surge in beer product supply has created an extremely competitive environment for breweries, many of whom are seeking to reap the benefits of model-based process intensification and optimisation (Rodman and Gerogiorgis, 2016). While beer production is a multistage process, improving fermentation efficiency has the strongest potential for return on both capital and time investment on the entire process, as the batch time often exceeds 120 hours and is the throughput bottleneck. Improvements to beer production have been historically obtained by incrementally altering proven recipes via trial and error, in an effort to achieve a more desirable product, as a result of the limited understanding this complex chemical system. Nowadays it is essential to employ accurate models of the fermentation process in order to achieve reliable dynamic simulations and subsequent process optimisation: trial and error is no longer a competitive strategy, as empirical investigative campaigns would imply a prohibitively high cost, not only in terms of equipment use and personnel time for sampling and analysis, but also due to lost beer production as result of the necessary process downtime and off-spec production of undesirable (hence non-marketable) output.

The complexity of the fermentation biochemical system (Vanderhaegen et al., 2006) renders comprehensive dynamic model formulation cumbersome and the required parameter estimation prohibitive. Numerous previous publications (Engasser, 1981; Gee and Ramirez, 1988; de Andrés-Toro 1998; Trelea et al., 2001) have postulated reduced order models, which are concise enough to allow for parameter estimation on the basis of experimental campaign data, but also suitably descriptive by considering the most essential subset of important biochemical reactions via selective aggregation. Subsequent process optimisation studies have been successfully performed on the basis of these foregoing models, primarily addressing batch time minimisation or ethanol yield maximisation (de Andrés-Toro, 1998; Carrillo-Ureta, 2001), or both (Rodman and Gerogiorgis, 2016). A necessary assumption of process optimisation studies is that all parameter datasets published in the original fermentation modelling papers are accurate and consistent.

The present paper has relied on a comprehensive compilation of original time-dependent concentration data for beer fermentation campaigns (Gee, 1990; de Andrés-Toro, 1996) in order to perform an parameter estimation study (Dochain, 2003) for the respective reduced-order dynamic models. The Simulink environment has been used within MATLAB^®, enabling the implementation of a nonlinear least squares method on the basis of the trust-region reflective algorithm for systematic parameter vector estimation. Remarkable discrepancies have been identified between the originally published parameter vectors and the corresponding ones determined herein, with the latter (our own results) universally improving dynamic model fidelity - and remarkably so, for certain critical parameters. Furthermore, we have performed systematic sensitivity analyses in order to assess and elucidate the relative significance of parametric discrepancy on the validity of dynamic simulation and optimisation results; the evolution of certain concentration observables is of particular interest, inasmuch as the latter govern process performance (: ethanol) and flavour (: diacetyls, ethyl acetate).

This comprehensive sensitivity analysis illustrates how state trajectory model predictions are affected by individual model parameters (DiStefano, 2013). Our new parameter set is subsequently used for further dynamic simulations towards attainable fermentation envelope visualisation. Multi-objective dynamic optimisation (time minimisation and ethanol maximisation) has also been performed with the new parameter vector we have determined, to investigate how and to what extent optimal operation is affected by parametric uncertainty, and thereby assess the validity of prior optimisation studies. 

LITERATURE REFERENCES

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