Oxygen Dynamics in a Chemostat with Substrate Inhibition

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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.

Contributed by: R. Ricardo Sánchez (August 2022)
Open content licensed under CC BY-NC-SA




: 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 [2]. The plots show inhibition of the oxygen uptake and specific growth rates.

Oxygen Transfer

The oxygen mass transfer rate , could be represented by [1]:


The transfer coefficient , varies with and according to [2]:

with .

Control Process

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 [2].


[1] P. M. Doran, Bioprocess Engineering Principles, Boston: Elsevier, 1995.

[2] I. J. Dunn, E. Heinzle, J. Ingham and J. E. Prvenosil, Biological Reaction Engineering, 2nd ed., Weinheim, Germany: VCH Verlagsgesellschaft mbH, 2003.

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