Solution technique for a multi-dimensional population balance model describing granulation processes

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

“…Population balance models have been used in case of other particulate handling processes such as crystallization [40,41] and granulation [42][43][44][45] but not for mixing till date.…”

Parallel Simulation of Population Balance Model-Based Particulate Processes Using Multicore CPUs and GPUs

“…(i) aggregation as the only source term, eliminating breakage and nucleation terms ( nuc = 0); (ii) "growth terms": drying/rewetting, layering, and consolidation are neglected; (iii) an empirical aggregation kernel proposed by Madec et al [54] is used, yielding the following PBE (7). Please see Appendix A for details of the aggregation kernel used and Appendix D for the numerical solution of the PBM based on a hierarchical twotiered algorithm proposed by Immanuel and Doyle III [55]:…”

“…Although the underlying mechanisms of such processes are yet to be thoroughly grasped, granulation, a particle design process, is one such area where substantial progress has been made over the years [5]. The approaches for modeling such systems are as numerous as they are varied: Discrete Element Modeling (DEM) [6], Population Balance Modeling (PBM) [3,[7][8][9][10][11][12][13], hybrid models by combining PBM with DEM [14], PBM with Volume of Fluid (VoF) methods [15], and PBM with Computational Fluid Dynamics (CFD) [16], to name a few. Of the aforementioned, the most widely used are the DEM and PBM methods.…”

“…Population Balance (PB) models are more suited to simulate a very large number of particles over lengthy time periods due to the semimechanistic approach (compared to more mechanistic approaches such as DEM and VoF) it utilizes to describe the dynamics of granulation processes [17]. Because of these advantages, PBM offers a very efficient manner of developing a comprehensive model of a granulation process, which can be simulated within a realistic time frame to be further used in control and optimization [18], since it provides a convenient mathematical framework whereby the detail of the model is user specific and depends on the kernel formulations specified by the user [7].…”

“…From now on, the term "grid size" will be used to refer to the total number of bins in a grid. This approach has two important benefits: (a) it enables decoupling of individual mesoscopic processes like aggregation, consolidation, and layering; (b) it improves the numerical solution of the aggregation model due to the mutually exclusive nature of the internal coordinates [7]. This 3-dimensional model can now describe changes in the volume distribution of particle volume with respect to time [3], as follows:…”