## Preprint 2021-15

## Raimund Bürger, Julio Careaga, Stefan Diehl, Romel Pineda:

### A moving-boundary model of reactive settling in wastewater treatment

### Abstract:

Reactive settling is the process of sedimentation of small solid particles in a fluid with simultaneous reactions between the components of the solid and liquid phases. This process is important in sequencing batch reactors (SBRs) in wastewater treatment plants. In that application the particles are biomass (bacteria; activated sludge) and the liquid contains substrates (nitrogen, phosphorus) to be removed through reactions with the biomass. The operation of an SBR in cycles of consecutive fill, react, settle, draw, and idle stages is modeled by a system of spatially one-dimensional, nonlinear, strongly degenerate parabolic convection-diffusion-reaction equations. This system is coupled via conditions of mass conservation to transport equations on a half line, whose origin is located at a moving boundary and that model the effluent pipe. A monotone and invariant-region-preserving finite difference scheme is proposed and applied to simulate operating cycles and the denitrification process within an SBR.

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

**Raimund BüRGER, Julio CAREAGA, Stefan DIEHL, Romel PINEDA: ***A moving-boundary model of reactive settling in wastewater treatment. Part 1: Governing equations*. Applied Mathematical Modelling, vol. 106, pp. 390-401, (2022).

**Raimund BüRGER, Julio CAREAGA, Stefan DIEHL, Romel PINEDA: ***A moving-boundary model of reactive settling in wastewater treatment. Part 2: Numerical scheme*. Applied Mathematical Modelling, vol. 111, pp. 247-269, (2022).