# Feedback Control in an Activated Sludge Reactor

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This Demonstration considers a model for the dynamics of a continuous reactor for treating an inhibitory substrate. The degradation rate is influenced by the concentrations of both the substrate and the dissolved oxygen, which are measured by an electrode. The biomass concentration is assumed constant, maintained in a sedimentation tank. Liquid phase balances for both the substrate and the dissolved oxygen are essential aspects of the model. This is important since the reactor is designed to avoid high concentrations of substrate, which would cause inhibitory behavior. This is accomplished by feeding the substrate at controlled flow rates, ensuring that the substrate concentration does not become too high.

Contributed by: R. Ricardo Sánchez (January 2023)
Open content licensed under CC BY-NC-SA

## Details

Notation

: substrate concentration

: inhibition constant

: maximum reaction velocity

: saturation constant

: oxygen saturation constant

: dissolved oxygen concentration

: critical dissolved oxygen concentration

: dissolved oxygen saturation concentration or solubility of oxygen in the broth

: feed substrate rate

: proportional control constant

: integral control constant )

: derivative control constant )

: set value for oxygen uptake rate

: oxygen uptake rate

: transfer coefficient )

: reaction rate for substrate

: reaction rate for oxygen

: Yield coefficient, oxygen to substrate

Kinetic parameters

Inhibitory substrates at high concentrations reduce the maximum reaction velocity, below that predicted by a kinetic equation. The inhibition function may be expressed empirically as:

.

If substrate concentrations are low, the term is lower in magnitude than and , and the inhibition function reduces to the double Monod equation. You can observe the inhibition effect on oxygen uptake rate and the dissolved oxygen concentration.

Oxygen transfer

The oxygen mass transfer rate can be represented by:

.

Oxygen uptake rate

The oxygen uptake rate can be represented by:

and .

Control process

Proportional, integral and derivative control of the feed rate can be set by:

where is the error and is represented by . If , then = and the process runs out of control.

Reference

[1] J. B. Snape, I. J. Dunn, J. Ingham and J. E. Prenosil, Dynamics of Environmental Bioprocesses: Modelling and Simulation, New York: VCH, 1995.

## Permanent Citation

R. Ricardo Sánchez

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