On Identifiability and Model Validation of a Population Balance Model for Liquid-Liquid-Mixing

In this paper, liquid-liquid-mixer systems modelled by population balance equations are considered. As the control input / manipulated variable, the stirrer speed (and hence the energy dissipation rate) is used to control the distribution of the particle size. Three different measurement signals are considered. We investigate the observability and identifiability of the system for each measurement option and show that only in one scenario the model is observable and structurally identifiable. Further, it is shown that in this scenario, practical identifiability is generally challenging and particular care must be taken to ensure the model with identified parameter values is able to describe the dynamic behaviour of the system.