Ideal Con tin uous Stirred-tank Fermen ter

For the steady-state operation of a CSTF, the change of cell concentration with time is equal to zero (dCx/dt = 0) since the microorganisms in the vessel grow just fast enough to replace those lost through the outlet stream, and Eq. (6.27) becomes 

28) shows that the required residence time is equal to Cx -Cx, times l/rx, which is equal to the area of the rectangle of width Cx- Cx. and height l/rx on the l/rx versus Cx curve. 

From Eq. (6.30), Cs can be calculated with a known residence time and the Monod kinetic parameters as  

It should be noted, however, that the preceding expression is only valid when rm /imax 1. If rm max 1, the growth rate of the cells is less than the rate of cells leaving with the outlet stream. 

Consequently, all of the cells in the fermenter will be washed out and Eq. (6.31) is invalid. 

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