A comparison of model order reduction techniques for a four-dimensional population balance model describing multi-component wet granulation processes

Abstract Three-dimensional (3-D) population balance equations are often used to model wet granulation processes, simulating distributions in particle size, liquid binder content, and porosity. In multi-component granulation, two or more solid components are present, and granule composition becomes a fourth distributed parameter. In this study, a four-dimensional (4-D) population balance model for multi-component wet granulation is presented and solved. Population balance models of high order are computationally expensive, limiting their applicability in analysis and design. The 4-D model was reduced to a combination of lower-dimensional models using the lumped parameter technique, in which one or more particle characteristics is assumed to be fixed within the remaining distributions. The reduced order models were compared with the full 4-D model for accuracy and computation time. Significant time savings were observed for all reduced order models. The 3-D model with gas volume as the lumped parameter showed the most promising results as an alternative to the 4-D model, which can be attributed to the limited influence of gas volume on aggregation and breakage rates.