(369c) Mathematical Modeling of Wet Granulation:

Purpose: To develop basic mathematical models which can be used
in future for simulation and scale-up of the wet granulation process in high
shear or fluidized bed granulators.

Methods: A fundamental model of the wet granulation
process should capture and combine the following three key features:
1.Population balancing of growth and breakage of different granules; 2.
Hydrodynamic modeling of the gas -- solid mixture flow; 3. Modeling of contact
mechanics and granule formation. For pharmaceutical application, the models
should predict also the granule composition. In attempt to solve the above
problem, we first generalized the volume approach of the rigorous population
balances [1,2] and employed it for modeling of 2-component solid + binder or
solid + solid granulation under ideal mixing conditions. For calculation of the
coalescence kernel we employed the Kinetic Theory of Granular Flow (KTGF) for
calculation of number of collisions N_i,j between different classes of granules [ 3
]. For the calculation of the number of successful collisions N_i,j^suc we have proposed the relation

                                                 N_i,j^suc = b^geom b^physN_i,j                                                                                                                                    

where b^geom is the geometrical success factor giving the
probability that colliding particles hit each other on the wet spot and b^phys is the physical success factor which
accounts for the dissipation of kinetic energy by viscous forces and can be
computed from relations proposed in [ 4 ]. For calculation of b^geom we used the results of mesoscale
simulations of the granule formation [ 5 ]. For the evaluation of the average
value of the time dependent N_i,j we interactively employed the FLUENT multiphase model
of granular flow in a pilot plant fluidized bed granulator. Granule breakage
was neglected in the calculations but can be added without much complication.

Results: The developed models can predict both the size and
composition of different granules. Preliminary theoretical results show that
non-uniform granule composition can be caused by the granule -- formation
mechanism (i.e. kernel) and also by the non-ideal mixing in the granulator. The
model also successfully predicts some interesting phenomena observed
experimentally, for example the induction (wetting) period without granule
growth for binder solutions with low concentration of the active component, or
granule segregation under non-ideal flow conditions in laboratory-scale
granulators.

Conclusions: Combination of the population balances with
hydrodynamic modeling of granular flow and with calculation of physically based
coalescence kernels based on the KTGF and mesoscale modeling of granule formation
is a promising tool for the analysis and design of pharmaceutical wet
granulators.

References:

[ 1 ] Rajniak, P.,
& Chern, R.: Mathematical modeling of wet granulation: Combination of
population balances and FLUENT granular model. Poster No.: T3160, AAPS Annual
Meeting, Baltimore, 2004.

[ 2 ] Verkoeijen,
D., Pouw, G.A., Meesters, G.M.H., & Scarlett, B.: Population balances for
particulate processesÑa volume approach. Chem. Eng. Sci.57 (2002) 2287-2303.

[ 3 ] Goldschmidt,
M.J.V. Hydrodynamic modelling of fluidized bed granulation, PhD thesis, Twente
University, 2001.

[ 4 ] Liu, L.X.,
Litster, J.D., Iveson, S.M., & Ennis, B.J.: Coalescence of deformable
granules in wet granulation processes. AIChE J. 46 (2000) 529-539.

[ 5 ] Stepanek,
F., & Ansari, M.A.: Computer simulation of granule microstructure
formation. Chem.Eng.Sci. 60 (2005) 4019-4029.