Calculation of Oxygen Transport in the Fermenter Solution

Oxygen is supplied to a fermentation almost exclusively in the form of air which is sparged into the fermenter from the bottom in gaseous form. Thus, the oxygen supply problem translates into a gas-liquid oxygen transfer problem. The corresponding oxygen transfer equation is Eq. (8.28). 

The left-hand side of Eq. (8.29b) contains only quantities which are dependent on the physical quantities of the system kL depends on the surface properties between the liquid and gaseous phases, such as surface tension a depends on the degree of partitioning of gas bubbles [02]equ is constant at constant temperature and constant pressure. 

The right-hand side only contains quantities which are dependent on the biological parameters of the system the growth rate pt primarily depends on cell type, Yx 0 depends on cell type (molecular composition) and C-source, and cell density X is determined by the status of the fermentation. The amount of air required in a fermentation is given by the quantity wm [Eq. (8.30)] and is usually of the order of 0.1—2. 

According to Henry s law (p02 = H [02]), an increase in pressure favors an increased oxygen concentration in the liquid phase however, the increased partial pressure of C02 has to be taken into account 

Empirically, it has been found that the mass transfer coefficient kL is proportional to the square root of the impeller speed N [Eq. (8.31)] (Richards, 1961). 

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