A fermentor is fed at
hr with a sterile substrate. In the absence of outlet flow, the volume in the batch-fed fermentor will increase linearly. This Demonstration shows the time-dependent behavior of four functions: the biomass concentration, the substrate concentration, the product concentration, and the volume in the reactor.
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
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.