A systematic approach for reducing complex biological wastewater treatment models

Biological wastewater treatment systems comprise a variety of processes which occur at vastly different rates. Biological growth, mass transfer, hydraulics and chemical reactions all occur simultaneously and are all inter-dependent. In this paper we address the question 'to what extent can we de-couple these processes, and what are the associated issues? We aim to introduce people who work with biological wastewater treatment models to analytical tools which may be used for model reduction. We present a quantitative technique to compartmentalise states into fast, medium and slow. From this we have provided an algorithm for eliminating state variables from a model based on whether they affect the process in the selected 'time scale of interest'. Through the technique presented we provide a means of quantifying the interaction between state variables, the 'speed' of a state and whether it is a candidate for reduction. A simple case study of a biological wastewater treatment process is presented. We were able to reduce four biological and 19 settler differential equations into algebraic equations. This resulted in significant savings in integration time. Application of the technique also highlighted the strong coupling between the slower biomass states and the rest of the model