Multidimensional modeling of granulation processes: A multiscale approach

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. Day-to-day operation of granulation processes can suffer from process instabilities and typically operate well below design capacity. 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 in this work 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 3-D soft-sphere Discrete Element Method (DEM) model is used analyze particle 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.; 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. This multiscale PBE model can be used at the macroscale optimize process performance and control particle size in granulation circuits. A case study is presented where a multidimensional model is used in a Nonlinear Model Predictive Control (NMPC) framework to control the mean particle size for batch high-shear granulation. A stochastic approach is used to solve the nonconvex problem in a more global fashion than a simple gradient-based approach.