Mathematical models and computer simulations are essential to describe, predict and control the complicated interactions of the processes. The number of reactions and organism species that are involved in the system may be very large. An accurate description of such systems can therefore result in highly complex models, which may not be very useful from a practical, operational point of view. The thesis contains a thorough discussion on aspects concerning the mathematical modelling of the activated sludge, sedimentation and biofilm processes

A reduced order dynamic model, describing an activated sludge process performing carbonaceous removal, nitrification and denitrification with reasonable accuracy, is presented. The main objective is to combine knowledge of the process dynamics with mathematical methods for estimation and identification. The identifiability of the model is investigated using both off-line and on-line methods, and its dynamic behaviour is validated by simulations of a recognized model. The information required by the identification algorithms are based on directly measurable real-time data

The simplified model may serve as a tool for predicting the dynamic behaviour of an activated sludge process, since the parameters can be tracked on-line during varying operating conditions. The model is aimed for operation and control purposes as an integral part of a hierarchical control structure

The main objective of the work on settler modelling is to support and enlighten recent theoretical results. A new settler model is compared to a traditional layer model by means of numerical simulations. Emphasis is put on the numerical solution’s ability to approximate the analytical solution of the conservation law written as a non-linear partial differential equation

The new settler model is consistent in this respect. Several problems that occur when integrating a model of the biological reactor with a model of the settler are also discussed. In particular, the concentrations of the biological components of the particulate material are of importance for an accurate description of the sludge that is recycled to the biological reactor

Two one-dimensional algorithms have been evaluated. The first algorithm is commonly used and some of its inherent problems are discussed. The second algorithm, which is preferred, is a new analytically derived method. Few attempts have been made to take into account the influence of higher order organisms in biofilm systems when developing or applying mathematical models. This work describes a simplified modelling approach to include some possible effects of higher order organisms on nitrification, based on a proposed hypothesis of their oxygen consumption in the biofilm. Three different models are developed and investigated. Model simulations are validated using data from a laboratory experiment using continuous-flow suspended-carrier biofilm reactors, where the predators were selectively inhibited