Abstract A mathematical model of the activated-sludge process has been derived which considers the fate of bacteria which flocculate, bacteria which do not flocculate, and two forms of ciliated protozoa. Computer simulation techniques have been used to study the population dynamics of these organisms in a single completely-mixed and a series of completely-mixed activated-sludge reactor systems; in both cases steady-state solutions were obtained. At steady state, the concentration of soluble substrate in the effluent is determined by the growth rate (fixed by the sludge-wastage rate) of the sludge bacteria. The concentration of dispersed bacteria in the effluent is similarly determined by the growth rate of the ciliated protozoa. The model predicts that the habit of ciliated protozoa would have a considerable effect on effluent quality. A plant containing only free-swimming ciliates would produce a fairly turbid effluent whereas a plant containing attached ciliates would produce a highly clarified effluent. Activated-sludge plants which contain no protozoa would be expected to deliver very turbid effluents although the concentration of soluble substrates would be precisely the same in all three cases. It was possible to simulate successions of organisms which are qualitatively similar to those observed in practice when an activated-sludge plant is set into operation. The results of the model predictions are discussed in the light of full-scale and experimental-scale observations.
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