(11d) Population Balance Modeling of Granulation of Excipient with Continuous Addition of Binder

The simulation of granulation based on population balance (PB) models has increased substantially through a combination of advances in the speed of desktop computing and increased contact between the field of granulation and that of the population balance community. Nonetheless, granulation is treated as involving a single component, the solid powder of interest. In reality, granulation involves at least two components, excipient and binder; simulations that treat the process as one that involves a single pseudo-component account for the effects of the binder indirectly via the granulation kernel. This lumped approach treats the kernel in an empirical fashion and, while this may be both acceptable and practical in many situations, it is also of limited use when results in one system are used to extrapolate behavior in other systems. In this paper, we present simulations of granulation in which the binder is treated explicitly. Specifically, we conduct simulations of an idealized fluidized bed granulator in semi-batch mode with the excipient being loaded at time zero and the binder introduced continuously during granulation. This requires a two-component PB model in which each granule is characterized by the amount of excipient and the amount of binder. The agglomeration kernel is modeled based on the collision rate obtained by the kinetic theory of granular flow (KTGF) combined with a geometric model for the sticking probability of granules based on the fractional coverage of the granule surface by the binder. Three numerical methodologies are used to establish the accuracy of the numerical solution: (i) a discrete system model in which a granule with i units of excipient and j units of binder is represented as an explicit size class whose evolution is followed in time; (ii) PB model based on the quadrature method of moments; and (iii) a Monte Carlo simulation of the bicomponent problem. The goal of the study is two-fold: to compare the results of the simulation to actual granulation experiments with a binder and a single excipient, and to establish the accuracy of the DQMOM method against Monte Carlo and the rigorous discrete method, both of which are more accurate but computationally more demanding that DQMOM.