Mathematical Development and Comparison of a Hybrid PBM-DEM Description of a Continuous Powder Mixing Process

This paper describes the development of a multidimensional population balance model (PBM) which can account for the dynamics of a continuous powder mixing/blending process. The PBM can incorporate the important design and process conditions and determine their effects on the various critical quality attributes (CQAs) accordingly. The important parameters considered in this study are blender dimensions and presence of noise in the inlet streams. The blender dynamics have been captured in terms of composition of the ingredients, (relative standard deviation) RSD, and (residence time distribution) RTD. PBM interacts with discrete element modeling (DEM) via one-way coupling which forms a basic framework for hybrid modeling. The results thus obtained have been compared against a full DEM simulation which is a more fundamental particle-level model that elucidates the dynamics of the mixing process. Results show good qualitative agreement which lends credence to the use of coupled PBM as an effective tool in control and optimization of mixing process due to its relatively fewer computational requirements compared to DEM.