This batch operation obeys the following equations:

with if ,

,

,

,

where , and )

and is the volume of reacting media in the fermentor, is the biomass concentration, is the substrate concentration, is the inlet flow rate, is the feed concentration of sterile nutrient, is the product concentration, is the saturation constant, is the maximum specific growth rate, is the yield coefficient, and and are the rate constants in the product kinetics.

The biomass concentration becomes constant and the product concentration and volume increase linearly because they depend linearly on the biomass and the inlet flow rate, respectively. The total biomass increases linearly versus time. This behavior corresponds to a situation where the growth rate of biomass is limited by the feeding rate.