Oxygen is necessary for all aerobic fermentation (by definition) [cf. Equation (798)]. Maintaining the appropriate concentration of dissolved oxygen in fermentation is important for the efficient operation of a fermentor. For oxygenlimited systems, it is necessary to design a fermentor to maximize the oxygen transfer between the injected air bubble and the cell. Typically, a fermentor contains a gas sparger, heat transfer surfaces, and an impeller, such as the one shown in Text Figure 718 for a batch reactor. A chemostat has a similar configuration, with the addition of inlet and outlet streams. 

(R7.21) 



Analogous to slurry reactor steps 
Figure R7.21 


(R7.23) 

where: 



Combining Equations (R7.22) through (R7.24) and rearranging, we obtain 

Yeast 

(R7.25) 

For many yeast cells, diffusion across the cell membrane can be neglected. 



The rate law for oxygen consumption (uptake) generally follows either MichealisMenten or firstorder kinetics. In many systems it depends on the particular growth phase of the bacteria cell. Typical respiration rates for singlecell yeast and bacteria are on the order of 100 to 600 mg O_{2}/g cellh. For firstorder kinetics we have 

(R7.26) 

where k_{r} is the specific reaction rate for oxygen uptake, s^{1}, and h is the effectiveness factor for diffusion and reaction of oxygen inside the cell. Combining equations (R7.26), (R7.22), and (R7.23) gives 

Bacteria 

(R7.27) 

We can observe from Equations (R7.25) and (R7.27) that at low cell
concentrations, transport steps C, D, and E (mass transfer of oxygen to and within
the cell) become rate limiting. 



where the Reynolds number for this system is defined as 


(R7.28) 

When gas is present, the power input, Pg is reduced for a given propeller speed ^{8} and is a function of gas flow rate, impeller speed and diameter, and the Reynolds number. The ration of the power input with gas present, Pg, to that without gas present () is 


(R7.29) 

Table R7.21. Mass Transfer Coefficients In Fermentor 1. Lowviscosity broths Van't Reit (1): 

 
2. NonNewtonian correlations 

Perez and Sandall (2): 
(R7.210) 



Yagi and Yoshida (3): 
(R7.211) 



Ranade and Ulbrecht (4):  
(R7.212) 




[Comment: These correlations were obtained in tanks having a volume of 12 dm^{3} or less (5).]  

Other parameters in the correlations are:



3. Effect of solids (6):
(1) K. Van't Reit, Fund. Eng. Chem. Proc. Des. Dev., 18, 357 (1979) 
The functions F_{1} and F_{2} are generally given graphically
for different types of fluids and different geometric configurations. ^{9,10}