Multiple CS TFs in Series

If the final cell concentration is larger than CXopt, the best combination of two fermenters for a minimum total residence time is a CSTF operated at CXopt followed by a PFF, as explained already. However, the cultivation of microorganisms in the PFF is limited to several experimental cases, such as the tubular loop batch fermenter (Russell et al., 1974) and scraped tubular fermenter (Moo-Young et al., 1979). Furthermore, the growth kinetics in a PFF can be significantly different from that in a CSTF. 

Another more practical approach is to use multiple CSTFs in series, since a CSTF operated at CXopl followed another CSTF connected in series is also better than one CSTF. 

Hill and Robinson (1989) derived an equation to predict the minimum possible total residence time to achieve any desired substrate conversion. They found that three optimally designed CSTFs connected in series provided close to the minimum possible residence time for any desired substrate conversion. 

By solving Eqs. (6.50), (6.51), and (6.52) simultaneously, we can calculate either dilution rate with the known cell concentration, or vice versa. 

Therefore, by knowing the dilution rate of each fermenter, you can estimate the cell concentration of each fermenter, or vice versa. 

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