(47c) Solution of a Four-Component Population Balance Model for Wet Granulation Via Constant-Number Monte Carlo
In the past, granulation population balance models (PBMs) typically were one-dimensional with granule size as the characteristic of interest. However, various attributes such as particle morphology, size, porosity, wettability, and binder viscosity can play key roles in determining the overall size and composition of the granules that are produced. Our previous research considered the impact of composition on two-component granulation [1,2]. In this work, we present a stochastic model for multicomponent granulation in which binder, moisture and two solid powders (e.g., pharmaceutical drug and excipient) are treated as explicit components that affect granulation. A modified KTGF (kinetic theory of granular flow) kernel that incorporates a critical Stokes number analysis for evaluating collision efficiency  is used in the model. Specifically, we combine the physical description for surface roughness given by Stepanek et al.  with a consideration for the degree of moisture evaporation from binder due to heat effects in order to evaluate granulation growth profiles and granule composition. Because we expect the smoothest powder to be assimilated into a granule faster than the second powder, the compositional distribution across various size classes (“sieve cuts”) and at various times in the granulation is studied. In addition, higher temperatures are expected to decrease the coagulation constant contained within the kernel due to an increased rate of moisture removal and binder solidification. Therefore, heterogeneities within granule structures due to a local binder “age” are examined. All simulations are conducted via constant-number Monte Carlo and results compared with experimental data (obtained from a fluidized bed granulator with continuous addition of binder). Upon solving the PBM, other comparison points include: granule growth profile, loss on drying (LOD), binder distribution, particle size distribution. The status of this research is presented.
 C. L. Marshall Jr., P. Rajniak, T. Matsoukas, Numerical simulations of two-component granulation: Comparison of three methods, Chemical Engineering Research and Design In Press, Corrected Proof (2010) doi:10.1016/j.cherd.2010.06.003.
 C. L. Marshall, Jr., T. Matsoukas, P. Rajniak, Multicomponent Population Balance Modeling of Granulation with Continuous Addition of Binder (2011--in preparation)
 L. Liu, J. Litster, S. Iveson, B. Ennis, Coalescence of deformable granules in wet granulation processes, AIChE Journal 46 (2000) 529-539.
 F. Stepanek, P. Rajniak, C. Mancinelli, R. Chern, R. Ramachandran, Distribution and accessibility of binder in wet granules, Powder Technology 189 (2009) 376-384.