Modeling the competition between floc-forming and filamentous bacteria in activated sludge waste water treatment systems I. Evaluation of mathematical models based on kinetic selection theory

One of the main reasons for failing of the sedimentation process in activat ed sludge waste water treatment systems is the phenomenon of filamentous bu lking. This occurs when filamentous bacteria overgrow Roc-forming bacteria, in this paper mathematical models are discussed which describe the competi tion of Aocs and filaments based on the kinetic selection theory. It is pro ven with a stability analysis for a continuous reactor, that, in order to c ontrol filamentous bulking, the dilution rate plays a crucial role. Moreove r, it is shown that coexistence of both organisms is generically not possib le. Afterwards the continuous reactor model is extended in order to describ e a standard waste water treatment system. Due to the complexity of the ext ended model it is difficult to perform the stability analysis analytically. It is proven that the model can be reduced without loss of stability prope rties. For the reduced model it is proven with a stability analysis that th e transport terms play a crucial role in the survival of one or the other o rganism. As for the continuous reactor model it is shown that coexistence o f both organisms is generically not possible. (C) 2000 Elsevier Science Ltd . All rights reserved.