Activated Sludge Process in a Batch Reactor

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The total suspended solids concentration is given by:
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The rate of the attachment step is taken as:
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The uptake substrate into the biomass follows Monod kinetics:
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Cell death is assumed to follow first-order kinetics:
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Notation:
: mass transfer coefficient
: storable substrate fraction (dimensionless)
: saturation constant
: specific death rate
The model is described in detail in [1, Example 3.3.1. Model of a Batch Activated Sludge Process].
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.
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