The degradation of toxic compounds in Sequencing Batch Reactors (SBRs) poses inhibition problems. Time Optimal Control (TOC) methods may be used to avoid such inhibition thus exploiting the maximum capabilities of this class of reactors. Biomass and substrate online measurements, however, are usually unavailable for wastewater applications, so TOC must use only related variables as dissolved oxygen and volume. Although the standard mathematical model to describe the reaction phase of SBRs is good enough for explaining its general behavior in uncontrolled batch mode, better details are needed to model its dynamics when the reactor operates near the maximum degradation rate zone, as when TOC is used. In this paper two improvements to the model are suggested: to include the sensor delay effects and to modify the classical Haldane curve in a piecewise manner. These modifications offer a good solution for a reasonable complexification tradeoff. Additionally, a new way to look at the Haldane K-parameters (μo,KI,KS) is described, the S-parameters (μ*,S*,Sm). These parameters do have a clear physical meaning and, unlike the K-parameters, allow for the statistical treatment to find a single model to fit data from multiple experiments.
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Acknowledgments The financial support from CONACYT through projects 46093Y and 51244 is acknowledged. This paper includes results of the EOLI project that is supported by the INCO program of the European Community, Contract number ICA4-CT-2002-10012. Manuel J. Betancur thanks UPB, CESAME and the CE INCO-DEV bursary contract ICB1-CT-2002-80006. The scientific responsibility rests with the authors.
- Haldane model
- Mathematical model
- Time optimal control