at Yx/o Yp/0 V dt with yield coefficients Yx/S, Yv/S, Yx/0, and Yp/0 and maintenance coefficients mx and m0 being constants characteristic of a particular penicillin producing strain. Whereas Bajpai and Reuss  have considered the overall mass transfer coefficient K;a to be constant, we have assumed K;a to be a function of agitation power input Pw and flow rate of oxygen fg (as fg = Qg = Qgf suggested by .
The values of a and /3 are assigned so that the dependence of penicillin concentration on K;a showed behavior very similar to the predictions of
The change in the bioreactor volume during fed-batch process operation is provided by a modified form of Eq. 2.8, which is
The effect of acid/base addition on the bioreactor volume is accounted for by Fa/b (volumetric feed rate of acid/base addition) The term F]oss accounts for evaporative loss during fermentation. The loss in volume due to evaporation is in fact more significant than the acid/base addition term in industrial cultivations. Normally the air entering the bioreactor is fairly dry and after bubbling through the broth it is at about 90 - 100 % relative dV dt
= F + Fa/b - Fio humidity. Typically, 10 to 20 % of the total broth can be lost due to evaporation during one week of fermentation, the actual amount depending on the temperature of the fermentation. Fioss is a function of temperature and culture volume V of the cultivation broth. An accurate relationship can be developed by carrying out a set of experiments at different temperatures and measuring the humidity of the inlet and exit gas and the volume of the culture broth at different times during each experiment.
Neglecting all other sources of heat generation except that caused by microbial reactions, the volumetric heat production rate is given as:
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