Estimation of Apparent Rates in Biological Systems

In biochemical engineering we are often faced with the problem of estimating average apparent growth or uptake/secretion rates. Such estimates are particularly useful when we compare the productivity of a culture under different operating conditions or modes of operation. Such computations are routinely done by analysts well before any attempt is made to estimate true kinetics parameters like those appearing in the Monod growth model for example. 

In this section we shall use the standard notation employed by biochemical engineers and industrial microbiologists in presenting the material. Thus if we denote by Xv the viable cell (cells/L) or biomass (mg/L) concentration, S the limiting substrate concentration (mmol/L) and P the product concentration (immol/L) in the bioreactor, the dynamic component mass balances yield the following ODEs for each mode of operation  

In this case there is a continuous addition of nutrients to the culture by the feed stream. There is no effluent stream. The governing equations are  

In this case, there is a continuous supply of nutrients and a continuous withdrawal of the culture broth including the submerged free cells. The governing equations for continuous cultures are the same as the ones for fed-batch cultures (Equations 7.20-7.22). The only difference is that feed flowrate is normally equal to the effluent flowrate (Fm=Fout=F) and hence the volume. V, stays constant throughout the culture. 

Perfusion cultures of submerged free cells are essentially continuous cultures with a cell retention device so that no cells exit in the effluent stream. The governing ODEs are 

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