Thesis Summary:

In this thesis, special emphasis is placed on the activated sludge process in reactive settling, in secondary settling tanks (SSTs) and sequencing batch reactors (SBRs). Among the topics covered are the development of a modern one-dimensional mathematical model and the imple- mentation of numerical schemes to simulate reactive settling in the SBRs. The governing model consists of a coupled system of strongly degenerate parabolic convection-difusion-reaction con- servation law equations, with unknowns being the concentrations of solid (bacteria; activated sludge) and liquid (substrates) components as functions of height and time. It is also of in- terest to develop the fitting of experimental data obtained from a pilot SST with variable cross-sectional area to the model of reactive settling. The thesis has the following objectives: First, to formulate a physical-mathematical model based on mass conservation equations to model the reactive settling process of the SBRs where the upper surface is a moving boundary. Second, to develop a reliable numerical scheme (consistent and stable) for the governing equa- tions derived from the first objective, considering a space discretization with a fixed number of cells across which the surface moves, and to demonstrate that the numerical scheme is monotone and satisfies an invariant region property (in particular, it preserves positivity) when executed in a simple splitting formulation. Third, to fit a reactive settling model to experimental data from a pilot plant which has a variable cross-sectional area, where the model equations are extended, including additional terms for hydrodynamic dispersion and heuristic mixing. Fourth, to perform an appropriate spatial transformation of the governing equations from the first objective to a fixed domain and discretize them using a monotone explicit scheme and a semi-implicit variant, formulations which among other advantages are easier to implement compared to the approach of the second objective.

ISI Publications from the Thesis

Raimund BüRGER, Julio CAREAGA, Stefan DIEHL, Romel PINEDA: A model of reactive settling of activated sludge: comparison with experimental data. Chemical Engineering Science, vol. 267, article: 118244 (13pp), (2023).

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).

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).