Typical Material Balance Problems in Bioprocesses

Warm-up example 6. A continuous stirred-tank reactor (CSTR) of volume V is fed with a stream of F L/h and with a substrate concentration of So [kg/L], The transformation speed of the substrate within the reactor is directly proportional to its concentratitMi (—kS), where k has units of l/h. If we can assume that the concentration of the substrate at the output stream is equal to the concentration within the reactor, and the reactor is operated under steady state (Fig. 8.4), then express the substrate concentration at the output stream (S) as a function of known variables (F, V, k, and 5o). 

the focus is to analyze what is happening in the reactor, in this case a bioreactor. In addition, the data related to the reactions (substrate transformation) are given in mass units. Thus  

Therefore, the substrate concentration at the output stream as a function of F, So, V, and k is 

Warm-up example 7. A clever young chemical engineering student is proposing that you analyze the previous problem, but this time instead of using one reactor of volume V, he is suggesting using two reactors of volume VH each. He is clever, but not as well prepared as you, and so he asks you to investigate two alternatives, to maximize the disappearance of the substrate, as follows (a) Use both reactors in parallel, (b) Use both reactors in series, (c) What would your recommendation be and 

Then in both bioreactors we get the same output concentration as follows  

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