  Predictive modeling is the key factor for saving time and resources with
respect 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 mass
distribution. This can be modeled via population balance models describing the
single-cell behavior of the yeast cell. There have already been several
population balance models for wine fermentation in the literature. However, the
new model introduced in this paper is much more detailed than the ones studied
previously. This new model for the white wine fermentation process is based on
a combination of components previously introduced in literature. It turns it
into a system of highly nonlinear weakly hyperbolic partial/ordinary
integro-differential equations. This model becomes very challenging from a
theoretical and numerical point of view. Existence and uniqueness of solutions
to a simplified version of the introduced problem is studied based on semigroup
theory. For its numerical solution a numerical methodology based on a finite
volume scheme combined with a time implicit scheme is derived. The impact of
the initial cell mass distribution on the solution is studied and underlined
with numerical results. The detailed model is compared to a simpler model based
on ordinary differential equations. The observed differences for different
initial distributions and the different models turn out to be smaller than
expected. The outcomes of this paper are very interesting and useful for
applied mathematicians, winemakers and process engineers.
