A consistent modelling methodology for secondary settling tanks in wastewater treatment

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid–liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models.

Research highlights► A consistent modelling methodology (CMM), which can be used to construct models for all processes in WWT systems, was presented. ► Following the CMM, a 1D model for the SST was presented. It takes into account most of the previously published physical phenomena considered for 1D models, such as hindered settling, compression and dispersion. Most importantly, simulations can be made with a proven consistent and reliable numerical method (PDE solver). ► The impacts of the three constitutive assumptions (on settling, compression and dispersion) were demonstrated by means of simulations. ► Our robust (simulation) model for the SST can handle all types of physically possible initial conditions and feed inputs. We have in an example illustrated that the Takács model generates an unphysical solution, which is a consequence of the fact that Takács’ minimum-flux update does not always take an important physical principle (the entropy condition) into account. ► As a consequence of the CMM, together with the fact that there are proven reliable PDE solvers available now, it is highly recommended that the traditional layer models should be replaced by reliable ones.