## Preprint 2010-15

## Raimund Bürger, Stefan Diehl, Ingmar Nopens:

### A consistent modeling methodology for secondary settling tanks in wastewater treatment

### Abstract:

The aim of this contribution is to build consensus on a consistent modeling methodology (CMM) of complex real processes in wastewater treatment by utilizing both classical concepts and new results from applied mathematics. 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. Although this has been done before, often it has 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 the 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 modeling. 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.

This preprint gave rise to the following definitive publication(s):

**Raimund BüRGER, Stefan DIEHL, Ingmar NOPENS: ***A consistent modelling methodology for secondary settling tanks in wastewater treatment*. Water Research, vol. 45, 6, pp. 2247-2260, (2011).