Details

Notation:

: 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 )

Kinetics

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].

References

[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.