A combined experimental and modeling approach to study the effects of high-shear wet granulation process parameters on granule characteristics

Abstract

The purpose of the current work is to study the effects of high-shear wet granulation process parameters on granule characteristics using both experimental and modeling techniques. A full factorial design of experiments was conducted on three process parameters: water amount, impeller speed and wet massing time. Statistical analysis showed that the water amount has the largest impact on the granule characteristics, and that the effect of other process variables was more pronounced at higher water amount. At high water amounts, an increase in impeller speed and/or wet massing time showed a decrease in granule porosity and compactability. A strong correlation between granule porosity and compactability was observed. A three-dimensional population balance model which considers agglomeration and consolidation was employed to model the granulation process. The model was calibrated using the particle size distribution from an experimental batch to ensure a good match between the simulated and experimental particle size distribution. The particle size distribution of three other batches were predicted, each of which was manufactured under different process parameters (water amount, impeller speed and wet massing time). The model was able to capture and predict successfully the shifts in granule particle size distribution with changes in these process parameters.

Keywords::

• Wet granulation
• granule size
• porosity
• compaction
• population balance model

Acknowledgments

The authors would like to thank James Bergum, Ajit Narang, Munir Hussain, and David Trinkle for their contributions and help to this work.

Declaration of interest

Anwesha Chaudhury and Rohit Ramachandran would like to acknowledge funding by the NSF-ERC on Structured Organic Particulate Systems, through grant NSF-ECC 0540855.

Appendix

(i) Aggregation kernel: A mechanistic kernel proposed by Immanuel and Doyle^[34] that was based on the physical theory suggested by Liu et al.^[30] was used for the purpose of representing the aggregation phenomenon efficiently. A detailed derivation of the kernel can be found in the respective references. The aggregation phenomenon has been categorized under two cases- type I and type II coalescence. Type I is said is occur under the conditions

whereas Type II coalescence occurs under the condition

Here St_v is the viscous Stoke’s number, h₀ is the depth of liquid on the surface of the granule, h_a represents the height of the surface asperities, St_def is the Stokes deformation number, is the harmonic mean of the diameter of the two aggregating particles, Y_d is the yield stress and E* is expressed as a function of the Poisson ratios, v and Young’s modulus, E of the two particles as

Based on this, the attractive potential between the particles is quantified as

For type I coalescence. For type II coalescence, two processes are involved, forward path and reverse path. The net attractive potential under this case is given as:

Where, ψ is the net attractive potential, h is the separation distance between the particles and u is the varying relative velocity of the particles as they approach each other. Based on the formulation by Smoluchowski, the aggregation kernel can be obtained as a function of the Fuch’s stability ratio, W as:

Where c₁ is an adjustable constant. The Fuch stability ratio can be represented as a function of the radius (r_i) of the particle (p_i), the Boltzmann constant, k and the temperature, T for type I coalescence as

And for type II coalescence as

(ii) Consolidation: Consolidation is a negative growth term representing the compaction of granules due to the escape of air from the pores. It has been modeled using the empirical equation proposed by Verkoejin et al.^[38] as:

Where ϵ is the porosity of the particle, s, l and g are the solid, liquid and gas volumes of the particle respectively, ϵ_min is the minimum porosity and c is the compaction rate. The porosity of particles is given by:

(iii) Drying/rewetting: Powder aggregation is significantly affected by the addition of liquid binder to the system. Binder catalyses the process of the formation of aggregates. The rate of liquid can be obtained from a mass balance as:

where,

In the above equations, is the binder spray rate, c_binder is the concentration of solid binder in the slurry added, is the rate of liquid being evaporation (here = 0), m_{solidfraction} is the volume of solid for the particles in each bin and L is the liquid content.