Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
MetadataShow full item record
Predictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the single-cell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers.