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Predictive modeling is the key factor for saving time and resources withrespect to manufacturing processes such as fermentation processes arising e.g.\in food and chemical manufacturing processes. According to Zhang et al. (2002),the open-loop dynamics of yeast are highly dependent on the initial cell massdistribution. This can be modeled via population balance models describing thesingle-cell behavior of the yeast cell. There have already been severalpopulation balance models for wine fermentation in the literature. However, thenew model introduced in this paper is much more detailed than the ones studiedpreviously. This new model for the white wine fermentation process is based ona combination of components previously introduced in literature. It turns itinto a system of highly nonlinear weakly hyperbolic partial/ordinaryintegro-differential equations. This model becomes very challenging from atheoretical and numerical point of view. Existence and uniqueness of solutionsto a simplified version of the introduced problem is studied based on semigrouptheory. For its numerical solution a numerical methodology based on a finitevolume scheme combined with a time implicit scheme is derived. The impact ofthe initial cell mass distribution on the solution is studied and underlinedwith numerical results. The detailed model is compared to a simpler model basedon ordinary differential equations. The observed differences for differentinitial distributions and the different models turn out to be smaller thanexpected. The outcomes of this paper are very interesting and useful forapplied mathematicians, winemakers and process engineers.

Existence, Uniqueness and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations