Population Balance Modeling of Particle Size and Porosity in Fluidized Bed Spray Agglomeration

Fluidized bed spray agglomeration is a unit operation applied for the size enlargement of solid granules by aggregation. End-use agglomerate properties crucially depend on agglomerate size and porosity, which, in turn, depend on the operating conditions of the fluidized bed process. In the context of plant automation in an inherently uncertain process environment, the application of process control algorithms is crucial. To facilitate the application of advanced control algorithms relying on accurate yet computationally efficient models, we present a novel population balance model for the evolution of the agglomerate size and porosity. In contrast to other models presented in the literature, the porosity is incorporated by means of a power law relationship with the agglomerate size, which is parametrized by the agglomerate fractal dimension. In order to test the new model, the fractal dimension of agglomerates, produced in a series of batch and continuous experiments, is investigated and correlated to the fluidized bed process conditions. Additionally, based on the experiments, an empirical model for the aggregation kinetics is proposed and kinetic parameters are estimated and also correlated to the process conditions. The proposed model is validated by comparing measured particle size distributions from experiments with model predictions. The results show good agreement; i.e., the relative error of the particle size distributions is below 7% for all validation experiments.