A basic population balance model for fluid bed spray granulation

A basic population balance approach is developed for a granulation process in a fluid bed spray granulator. The particle size distribution predicted by the model is confirmed by plant data. Hence this model is considered to be useful to describe and optimize an industrial process. The model depends on a limited number of parameters (most of these factors can be measured or are known): the spray volume flux, the nucleation fraction (the fraction of the spray volume flux which leads to new particles formed), the nucleation particle diameter, the product withdrawal threshold diameter, and the product withdrawal rate. Analysis of the model reveals a steady-state constraint; a steady state does not exist if the nucleation fraction is too large. For cases where the steady state does exist, the steady-state particle size distribution is solved analytically. A numerical implementation of the model is used to illustrate the transient evolution of the process. The steady-state solution appears to be stable for a constant nucleation fraction. However, if the nucleation fraction depends on the bed height the steady state can be unstable. Such a situation may occur if the spray inlet is near the height of the bed surface. Instead of convergence towards a steady state, the transient solution displays ongoing oscillatory behavior with an oscillation period of a number of hours. A linear stability analysis is performed to confirm the findings on the stability of the steady state.