Batch or Plug-Flow Fermenter

An ideal stirred fermenter is assumed to be well mixed so that the contents are uniform in composition at all times. Another ideal fermenter is the plug-flow fermenter, the analysis of which is analogous to the ideal batch fermenter. 

If liquid medium is inoculated with a seed culture, the cell will start to grow exponentially after the lag phase. The change of the cell concentration in a batch fermenter is equal to the growth rate of cells in it  

To derive the performance equation of a batch fermentation, we need to integrate Eq. (6.20) to obtain  

It should be noted that Eq. (6.21) only applies when rx is larger than zero. Therefore, t1 in Eq. (6.21) is not the time that the culture was inoculated, but the time that the cells start to grow, which is the beginning of the accelerated growth phase. 

The rate for an autocatalytic reaction is slow at the start because the concentration of X is low. It increases as cells multiply and reaches a maximum rate. As the substrate is depleted and the toxic products accumulate, the rate decreases to a low value. 

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