Reactors for Freely Suspended Cells

Fermentation vessels tend to be large because reaction rates are low. Typical batch reaction times are measured in days. Freely suspended mammalian cells are cultivated in conventionally agitated reactors up to 20,000 L in volume. Ethanol production with freely suspended yeast uses vessels 100 times larger, and wastewater treatment by the activated sludge process or in lagoons can be larger by another factor of 100. 

The reaction rates presented in Section 12.2.1 can be combined to give a fairly comprehensive model for cell growth, substrate consumption, and product generation in 

Develop a model for the anaerobic batch fermentation of glucose to ethanol and coproduct CO2 using S. cerevisiae. The starting mixture contains 10% glucose. The inoculum is 0.0005 w/w. Product inhibition stops cell growth at 14% ethanol. Assume kj = 0 but allow cannibalization of cellular material when the substrate is completely consumed. 

SOLUTION The initial conditions for a batch reactor are i = io and X = Xo at t Equation 12.13 gives the cell growth when there is inhibition by the product  

Equation 12.15 governs substrate consumption. For a batch reactor with all the substrate charged initially, 

The typical bioreactor is a two-phase stirred tank. It is a three-phase stirred tank if the cells are counted as a separate phase, but they are usually lumped with the aqueous phase that contains the microbes, dissolved nutrients, and soluble products. The gas phase supplies oxygen and removes by-product CO2. The most common operating mode is batch with respect to biomass, batch or fed-batch with respect to nutrients, and fed-batch with respect to oxygen. Reactor aeration is discussed in Chapter 11. This present section concentrates on reaction models for the liquid phase. 

As with most modeling efforts, the mathematical formulation is the easy part. Picking the right values from the literature or experiments is more work. An immediate task is to decide how to characterize the substrate and product concentrations. The balance equations for substrate and product apply to the carbon content. The glucose molecule contains 40% carbon by weight so S will be 0.4 times the glucose concentration, and 5q = 0.04. Similarly, 

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