Batch growth of micro-organisms

After inoculation, assuming no lag phase, the resultant growth can be analysed by considering the unsteady-state material balances for the substrate and biomass. The general form of this balance for a fermenter is  

Since a batch process is being considered, the flow in and out of the fermenter are both zero and the expression reduces to  

The yield coefficient may also be expressed in its integral form as  

If the growth follows the Monod kinetic model, then equation 5.62 may be substituted into equation 5.115 to give  

The condition of the fermentation after any time t would then be given by  

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