(742d) A Combined Mechanistic Model for Nucleation, Aggregation and Breakage In a Population Balance Model of Granulation

Granulation is the generic term for particle agglomeration processes, whereby fine powdery solids are agglomerated together with a liquid/melt binder to form larger aggregates. It finds application in many industries such as pharmaceuticals, fertilisers, detergents and food processing. Despite its widespread use, granulation processes are highly inefficient and current industrial plants operate with high recycle ratios [1]. Thus, there is a clear need for better process design, operation and control of these processes. However, the complexity of the process, the limited number of potential manipulated variables and the large time delay associated with the downstream units make control and operation of granulation processes a challenge. Therefore, the development of a first-principle mathematical model for granulation is vital for the application of model-based strategies for better design, optimisation and control of granulation processes.

The application of population balances, which accounts for the individual sub-processes (e.g. nucleation, aggregation, breakage and consolidation), provides a convenient framework from which the granulation process is modelled and these sub-processes will be the emphasis of this study [2-5]. One major challenge in developing these population balance models is the identification of appropriate kernels for the sub-processes. Due to the limited knowledge of the mechanisms that underlie the granulation process, many of the proposed kernels are empirical or semi-empirical, which may not be valid over a wider operating range. In order to further improve the predictive capabilities of the kernels and to extend their region of validity, one has to directly incorporate the mechanistic features of the process and develop kernels strongly based on first-principles.

In this study a three-dimensional volume-based population balance model for the granulation process is presented, incorporating combined mechanistic formulations for the nucleation, aggregation and breakage phenomena, in combination with an empirical relation for consolidation. Immanuel and Doyle III have presented a methodology for developing the aggregation mechanistic kernel reported in this work [6]. Similarly, the mechanistic formulation of the nucleation kernel has been developed by Poon et al. [7] and both these mechanistic kernels have been quantitatively validated against experimental data for different operating conditions [8]. Therefore, the major focus of this work is the development and validation of the mechanistic breakage kernel.

The breakage kernel is modelled as a quotient of applied external stress on a granule over intrinsic strength of a granule. The external stress in turn is calculated from the derivation of external forces over their contact area. These external forces are a result of (i) fluid forces in the granulator, (ii) particle-particle collisions and (iii) particle-wall collisions. The intrinsic strength of the granule is derived from the capillary, viscous and frictional forces that are responsible for the liquid bridge strength of the granule. Subsequently the individual breakage kernels for the three types (i-iii) of breakage are transformed into an effective breakage kernel that is based on the probability of an ith size particle colliding with another particle of jth size, or a wall. Fluid forces act in addition to forces (ii) and (iii). Qualitative validation of breakage kernel/model was performed and trends of lumped properties (i.e., total particles, average size, binder content and porosity) and distributed properties (i.e., granule size, fractional binder content and porosity distributions) show good agreement with the expected phenomenological behaviour. Successful high-shear granulation experiments were then carried out to mimic breakage only behaviour whereby the rate of breakage is significantly greater than that of nucleation and aggregation. Quantitative validation of the breakage kernel/model against experimental data is currently underway. For the solution of the population balance model, a robust and efficient numerical solution technique was employed [6, 9].

References

1. S.M. Iveson, J.D. Litster, K. Hapgood, and B.J. Ennis. Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review. Powder Technology, 117: 3-39, 2001.

2. L.X. Liu and J.D. Litster., Population balance modelling of granulation with a physically based coalescence kernel. Chemical Engineering Science, 57: 2183-2191, 2002.

3. H.S. Tan, A.D. Salman, and M.J. Hounslow., Kinetics of fluidized bed melt granulation ? II: Modelling the net rate of growth. Chemical Engineering Science, 61: 3930-3941, 2006.

4. Biggs, C.A., Sanders, C., Scott, A.C., Willemse, A.W., Hoffman, A.C., Instone, T., Salman, A.D. and Hounslow, M.J., Coupling granule properties and granule rates in high shear granulation. Powder Technology, 130: 162-168, 2003.

5. I.T. Cameron, F.Y. Wang, C.D. Immanuel, and F. Stepanek., Process systems modelling an applications in granulation: A review. Chemical Engineering Science, 60: 3723-3750, 2005.

6. C.D. Immanuel and F.J. Doyle III. Solution technique for a multi dimensional population balance model describing granulation processes. Powder Technology, 156: 213-225: 2005.

7. J. Poon, C. D. Immanuel, F.J. Doyle III and J.D. Litster. A three-dimensional population balance model of granulation with a mechanistic representation of the nucleation and aggregation phenomena. Chemical Engineering Science, 63: 1315-1329: 2008.

8. J. Poon, R. Ramachandran, C.F.W. Sanders, T. Glaser, C.D. Immanuel and F.J. Doyle III and J.D. Litster, F. Stepanek, F.Y. Wang and I.T. Cameron. Experimental Validation Studies on a Multi-Dimensional and Multi-Scale Population Balance Model of Batch Granulation. Submitted to Chemical Engineering Science.

9. M. A. Pinto and C. D. Immanuel and F. J. Doyle III. A feasible solution technique for higher-dimensional population balance models. Computers and Chemical Engineering, 31: 1242-1256: 2007.