A volume-based multi-dimensional population balance approach for modelling high shear granulation

A volume-based multi-dimensional population balance model based on the approach used by Verkoeijen et al. 2002. Population balances for particulate processes—a volume approach. Chemical Engineering Science 57, 2287-2303], is further developed and applied to a wet granulation process of pharmaceutically relevant material, performed in a high shear mixer. The model is improved by a generalization that accounts for initial non-uniformly distributed liquid and air among the different particle size classes. Only the wet massing period of the granulation process has been modelled and it is experimentally found that the pores in the granules are fully saturated by liquid, i.e., no air is present in the granules during this period. Hence, an alternative model formulation is used as no model for the air in the granules is needed. Particle volume distribution, liquid saturation, liquid-to-solid ratio and porosity of the granules can all be modelled, as these properties can all be expressed as combinations of three model parameters, i.e., the volume fraction of solid material, total liquid fraction and the liquid fraction inside the granules. The model is also improved by introducing a new coalescence kernel and by increasing the number of size classes used. The simulated results are compared to measurements from a series of five designed experiments where impeller speed and water content are varied. It is found that the evolution of the volume, liquid saturation and porosity distributions could all be explained by fitting the compaction and coalescence rate constants.