Granulation is a process of particle size enlargement where a mixture of powders and a binder is agitated to form a granular product. This unit operation can be found in pharmaceutical, mineral processing, foodstuffs, and fertilizer industries. Granulation circuits often operate well below design capacity and typically even suffer from process instabilities due to a lack of understanding of the dynamics of the process. These shortcomings may be alleviated through the development of high-fidelity models for use in advanced process system engineering techniques. However, modeling particulate processes present many problems due to the wide range of length and time scales present. While there has been a strong focus in literature to understand granulation fundamentals and to model rate processes using Population Balance Equations (PBEs), there has been little qualitative analysis focusing on bridging these modeling concepts. This work describes an integration framework where simple representations of complex models at the microscale are used to derive a multidimensional PBE model based on fundamental granulation principles for use in macroscopic applications.

A multiscale approach to granulation modeling is presented where three scales are analyzed: the microscale, mesoscale, and macroscale. At the microscale, individual particle interactions and the motion of the powder bed are a focus. A soft-sphere Discrete Element Method (DEM) model is used to analyze particulate trajectories, predict collision rates, and simulate particle flow patterns in a high-shear granulator. A coalescence model for deformable, surface wet particles is used in parallel with the DEM simulation to predict coalescence efficiency of colliding particles.

Mesoscale modeling involves predicting rate processes found in granulation processes such as agglomeration, consolidation, growth and breakage. PBEs are commonly used to model process dynamics at the mesoscale. A serial integration scheme is used to derive a coalescence kernel which provides relationship between the complex microscale DEM/Coalescence model and the mesoscale PBE model. The coalescence kernel used predicts agglomeration is the product of the particle collision rate of and coalescence efficiency of the colliding particles. The DEM simulation shows that particle collision rates for high-shear mixers follow that of a simple ortho-kinetic kernel which assumes particles collide as a consequence of a laminar shearing motion. A multidimensional coalescence efficiency model was derived from microscale analysis which provided a relationship between efficiency and particle size, pore saturation, porosity, and impeller speed. Together, these high-fidelity multidimensional population balance equations can be used at the macroscale to optimize process performance and control particle size in granulation circuits.