## An Industrial Bakers Yeast Fermentation Model

A mathematical model of an industry fed-batch fermentation process, which was given in [19], is used to describe the system. The kinetics of yeast metabolism that is considered in the model is based on the bottleneck hypothesis [18]. The model is governed by a set of differential equations derived from mass balances in the system. It comprises the following equations: Balance equations:

dJVtC1 = F • S0 " (yOx + OT + m) • V •* (B.1)

x/s e/ s d(V ■ C0) dt d(V ■ Cc) dt d(V ■ Ce) dt d(V ■ X)

where, Cs, Co, Cc, Ce, X, and V are state variables which denote concentrations of glucose, dissolved oxygen, carbon dioxide, ethanol, and biomass, respectively; V is the liquid volume of the fermentation; F is the feed rate which is the input of the system; m is the glucose consumption rate for the maintenance energy; Ye/s and Y°Ja are yield coefficients; kLao and kLac are volumetric mass transfer coefficients; S0 is the concentration of feed. Glucose uptake rate:

Oxidation capacity:

L. Z. Chen et al.: Modelling and Optimization of Biotechnological Processes, Studies in Computational Intelligence (SCI) 15, 113-114 (2006)

Specific growth rate limit:

Qs,lim = yCx (B.9) Oxidative glucose metabolism:

Ys/o Qo

Reductive glucose metabolism:

Ethanol uptake rate:

Oxidative ethanol metabolism:

Ethanol production rate:

Total specific growth rate:

Carbon dioxide production rate:

Oxygen consumption rate:

Respiratory Quotient:

The model parameters and initial conditions that are used for dynamic simulations are listed in Table B.1 and Table B.2.

Table B.1. The parameter values of the industrial model.

Parameters

Values m

KLao

Yc/e

Yo/e Ks

Yc/s

Ye/s

Yo/s ftcr co

Yx/e

Yox x/s

KLac red Yx/s

0.00321 600 0.0008 0.68 0.0001 1028 0.002 2.35 0.70805 1.89 0.06 1.9 0.2 2.17 0.15753 2.41 x 10 2.0 0.00001 4.57063 470.4 0.1

 State variables Values Cs 5 x 10~4 V 50000 Ce 0 Co 2.4 x 10~4 Cc 0 X 0.54