Coupling activated sludge models and population balance models to predict size distribution dynamics of nitrifier microcolonies in sludge flocs

Activated sludge microcolonies are receiving growing scientific interest due to their crucial role as building blocks in macroscopic activated sludge flocs. This work introduces a hybrid population balance model that describes the dynamic effects of growth and erosion processes on the microcolony size distribution (MSD) of autotrophic bacteria. The model combines ordinary differential equations with a population balance equation (PBE) and represents the different phases of the system's operation cycle. A sample from a wastewater treatment system was collected to estimate its (steady-state) MSD, which was then used to parametrize the model. The identified model provides a precise quantification of the primary statistics of the data inferred MSD and effectively captures its shape. The results show that the observed distribution is reachable from an hypothetical initial condition of dispersed autotrophic bacteria. The proposed modeling framework not only explains the observed MSD but also predicts the effects of operational parameter changes. As an example of this, the model predicts that reducing the sludge retention time unexpectedly increases microcolony sizes, suggesting directions for further experimental research. The framework's flexible structure facilitates the integration of additional bioflocculation mechanisms, enabling its adaptation to a wider range of scenarios.