Gas-Liquid Mass Transfer in Fermentors

As the thermal conductivity of stainless steel is 13 kcal h °(A, the heat 

A fouling factor of 2000 kcal h m °C is assumed. The overall heat transfer resistance 1/1/ based on the outer tube surface is 

The log mean of the temperature differences 15 and 5 °C at both ends of the cooling coil is 

The required heat transfer area (outer tube surface) A is 

Gas-liquid mass transfer plays a very important role in aerobic fermentation. The rate of oxygen transfer from the sparged air to the microbial cells suspended in the broth or the rate of transfer of carbon dioxide (produced by respiration) from the cells to the air often controls the rate of aerobic fermentation. Thus, a correct knowledge of such gas-liquid mass transfer is required when designing and/or operating an aerobic fermentor. 

Resistances to the mass transfer of oxygen and carbon dioxide (and also of substrates and products) at the cell surface can be neglected because of the minute size of the cells, which may be only a few microns. The existence of liquid films or the renewal of a liquid surface around these fine particles is inconceivable. The compositions of the broths in well-mixed fermentors can, in practical terms, be assumed uniform. In other words, mass transfer resistance through the main body of broth may be considered negligible. 

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Gas-liquid mass transfer in fermentors is discussed in detail in Section 12.4. In dealing with in gas-sparged stirred tanks, it is more rational to separate and a, because both are affected by different factors. It is possible to measure a by using either a light scattering technique [9] or a chemical method [4]. Ihe average bubble size can be estimated by Equation 7.26 from measured values of a and the gas holdup e. Correlations for have been obtained in this way [10, 11], but in order to use them it is necessary that a and d are known. 

As most biochemical reactions occur in the liquid phase, bioreactors usually handle liquids. Processes in bioreactors often also involve a gas phase, as in cases of aerobic fermentors. Some bioreactors must handle particles, such as immobilized enzymes or cells, either suspended or fixed in a liquid phase. With regard to mass transfer, microbial or biological cells may be regarded as minute particles. 

Steady-State Mass Balance Method In theory, the Ki a in an apparatus that is operating continuously under steady-state conditions could be evaluated from the flow rates and the concentrations of the gas and liquid streams entering and leaving, and the known rate of mass transfer (e.g., the oxygen consumption rate of microbes in the case of a fermentor). However, such a method is not practical, except when the apparatus is fairly large and highly accurate instruments such as flow meters and oxygen sensors (or gas analyzers) are available. 

Thus, when deahng with gas transfer in aerobic fermentors, it is important to consider only the resistance at the gas-liquid interface, usually at the surface of gas bubbles. As the solubihty of oxygen in water is relatively low (cf. Section 6.2 and Table 6.1), we can neglect the gas-phase resistance when dealing with oxygen absorption into the aqueous media, and consider only the liquid film mass transfer coefficient Aj and the volumetric coefficient k a, which are practically equal to and K a, respectively. Although carbon dioxide is considerably more soluble in water than oxygen, we can also consider that the liquid film resistance will control the rate of carbon dioxide desorption from the aqueous media. 

The most traditional application of the fermentor is in batch mode. In anaerobic fermentations the reactor looks like a normal batch reactor, since gas-liquid contact is not an important design consideration. Depending on the reaction, the microbes may or may not be considered as a separate phase. For aerobic fermentations, oxygen is bubbled through the media, and mass transfer between phases becomes one of the major design factors. 

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