Oxygen Dynamics in a Chemostat with Substrate Inhibition
This Demonstration simulates cell growth in a chemostat limited by the oxygen mass transfer rate, which depends on the dissolved oxygen concentration. Cell growth is also inhibited by substrate concentration in the reactor; therefore a proportional control is used to maintain the substrate concentration below a critical value.
: substrate concentration (mg/L)
: inhibition constant (mg/L)
: maximum specific growth rate )
: saturation constant (mg/L)
: oxygen saturation constant (mg/L)
: biomass concentration (mg/L)
: dissolved oxygen concentration (mg/L)
: critical dissolved oxygen concentration (mg/L)
: dissolved oxygen saturation concentration or solubility of oxygen in the broth (mg/L)
: gassing rate (L/min)
: stirrer speed )
: feed substrate rate (L/h)
: proportional control constant
: inhibitory substrate concentration (mg/L)
: dilution rate )
Inhibitory substrates at high concentrations reduce , the specific growth rate, below that predicted by the Monod equation. The empirical inhibition function can be written:
If substrate concentrations are low, the term is smaller than and , and the inhibition function is represented by coupled Monod equations . The plots show inhibition of the oxygen uptake and specific growth rates.
The oxygen mass transfer rate , could be represented by :
The transfer coefficient , varies with and according to :
Proportional control of the feed rate is based on the exit concentration using:
where is the error, represented by . If is zero, then takes the value and the process runs out of control .
 P. M. Doran, Bioprocess Engineering Principles, Boston: Elsevier, 1995.
 I. J. Dunn, E. Heinzle, J. Ingham and J. E. Prvenosil, Biological Reaction Engineering, 2nd ed., Weinheim, Germany: VCH Verlagsgesellschaft mbH, 2003.