The growth of baker's yeast (S. cerevisiae) on glucose may...

The growth of baker's yeast $(S$. cerevisiae) on glucose may be simply described by the following equation: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+3 \mathrm{O}_{2}+0.48 \mathrm{NH}_{3} \underset{\text { yeast }}{\longrightarrow} \underset{10}{\longrightarrow} \mathrm{NO}_{3}+4.32 \mathrm{H}_{2} \mathrm{O}+3.12 \mathrm{CO}_{2} $$ In a batch reactor of volume $10^{5} 1$, the final desired yeast concentration is $50 \mathrm{gdw} / 1 .$ Using the above reaction stoichiometry: a. Determine the concentration and total amount of glucose and $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}$ in the nutrient medium. b. Determine the yield coefficients $Y_{X / S}$ (biomass/glucose) and $Y_{X / O_{2}}$ (biomass/oxygen). c. Determine the total amount of oxygen required. d. If the rate of growth at exponential phase is $r_{x}=0.7 \mathrm{gdw} / 1-\mathrm{h}$, determine the rate of oxygen consumption (g $\left.\mathrm{O}_{2} / \mathrm{l}-\mathrm{h}\right)$. e. Calculate the heat-removal requirements for the reactor (recall eq. $6.26$ ).

The growth of baker's yeast $(S$. cerevisiae) on glucose may be simply described by the following equation:
$$
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+3 \mathrm{O}_{2}+0.48 \mathrm{NH}_{3} \underset{\text { yeast }}{\longrightarrow} \underset{10}{\longrightarrow} \mathrm{NO}_{3}+4.32 \mathrm{H}_{2} \mathrm{O}+3.12 \mathrm{CO}_{2}
$$
In a batch reactor of volume $10^{5} 1$, the final desired yeast concentration is $50 \mathrm{gdw} / 1 .$
Using the above reaction stoichiometry:
a. Determine the concentration and total amount of glucose and $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}$ in the nutrient medium.
b. Determine the yield coefficients $Y_{X / S}$ (biomass/glucose) and $Y_{X / O_{2}}$ (biomass/oxygen).
c. Determine the total amount of oxygen required.
d. If the rate of growth at exponential phase is $r_{x}=0.7 \mathrm{gdw} / 1-\mathrm{h}$, determine the rate of oxygen consumption (g $\left.\mathrm{O}_{2} / \mathrm{l}-\mathrm{h}\right)$.
e. Calculate the heat-removal requirements for the reactor (recall eq. $6.26$ ).

Key Concepts

Oxygen Transfer and Consumption

In aerobic fermentations, oxygen plays a critical role as a terminal electron acceptor. Understanding the oxygen consumption rate in relation to biomass production, as well as quantifying the total oxygen demand, is crucial for designing the aeration system and maintaining optimal growth conditions in the reactor.

Heat Removal in Fermentation

Fermentation processes are often exothermic, generating heat as a byproduct of microbial metabolism. Properly calculating and designing the heat removal systems—that is, the cooling requirements—is vital to maintain the reactor at optimal operating temperatures, ensure microbial activity is not hindered, and prevent thermal runaway.

Batch Reactor Operation

A batch reactor is a closed system where the reaction occurs without any additional input or removal of material during the process. This operating mode requires precise initial calculations of nutrient and oxygen amounts, as all reactants are loaded at the start and must support the desired level of microbial growth throughout the batch cycle.

Reaction Stoichiometry

This concept involves using a balanced chemical equation to determine the proportions in which reactants combine and products are formed. It is critical for calculating how much of each substrate (such as carbon sources and nitrogen sources) is required and how much product (biomass, byproducts) will be generated in the fermentation process.

Mass and Mole Balances

Mass and mole balances are employed to account for the input, output, and accumulation of each component in the reactor. This principle ensures that the conservation of mass is maintained and is used to relate the quantities of substrates consumed and products formed during the batch fermentation.

Yield Coefficients

Yield coefficients, often expressed as mass of product per mass of substrate (or per mass of oxygen, etc.), are key parameters in fermentation processes. They provide a measure of the efficiency with which substrates are converted into biomass or other desired products and are essential for scaling up the process and optimizing reactor operation.

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