Coalescence model for induction growth behavior in high shear granulation

Abstract

Complex wet granulation behavior is often dependent on process parameters and formulation properties simultaneously. Mathematical models of granulation need to account for the complex physics if they are to be predictive. In this paper, a physically-based coalescence model is evaluated for use in the three-dimensional volume-based framework. The Liu coalescence kernel [20] is calculated for the three-dimensional system as a function of (1) the solid, liquid and gas volumes that form the granule, (2) an empirical correlation for granule mechanical properties as they depend on the granule composition and strain rate, and (3) the process conditions. A complex but well characterized industrial formulation is used as a case study. For this formulation, the granule strength varies over an order of magnitude for a range of conditions that correspond to actual behavior during granulation as granules densify due to consolidation. The kernel predicts that most collisions will result in rebound early in the granulation. As granules densify they become stronger, but also surface wet, resulting in Type I coalescence for many collisions once the average granule porosity drops below a critical value of 0.37. A kernel sub-model that incorporates changes in granule mechanical properties as a function of composition can then describe classic induction time behavior. The model is compared to an experimental study in a 50L horizontal axis high shear granulator. Measurements of the size, porosity and morphology are used to identify rate process mechanisms over the course of the wet granulation process. The proposed coalescence model successfully describes the experimentally observed induction behavior as a function of composition, based on comparison to the kernel regime map for this formulation. The experimental value of critical porosity corresponding to the observed induction time, and continued growth of surface wet granules well past 1mm in size also match the micro-scale behavior predicted by the kernel. This comparison shows that the physically-based kernel can be used to predict complex granulation behavior such as induction growth.