Simulating the early stage of high-shear granulation using a two-dimensional Monte-Carlo approach

Abstract

A two-dimensional (2-D) model of a granulation process is presented in this paper. It aims to simulate an entire granulation batch without the use of an initial experimental or fictitious 2-D density function, by taking the experimental operating conditions into account. The mass of liquid and solid in the granules are the two predicted internal variables. The 2-D population balance equation is solved by a Constant Number Monte-Carlo method. This is a stochastic technique tracking the evolution of a population, whilst performing the calculations with a fixed number of particles. This is achieved by reducing or increasing the sample volume when an event results in a net production or a net decrease in the number of particles, respectively. An original multi-population approach is developed to describe the early stage of the process, where small numbers of granules are formed amongst a large number of primary particles. It consists of separating the primary particles from the granule population. A specific intensive variable is introduced to keep track of the repartition of masses. The overall density function is reconstructed a posteriori from the combination of the two populations. This approach allows the simulation to commence from the initial addition of liquid at the start of the process, rather than to start from an early granule size distribution. The early stage of the granulation process, frequently referred as nucleation, can therefore be studied numerically. Four different mechanisms are implemented. Nucleation and re-wetting describe the addition of liquid to the system. The interactions between liquid and solid phases are modelled by a layering process. An aggregation model is also included to simulate the growth of particles undergoing frequent collisions. Finally, the relevance of this new model is demonstrated by confronting the simulations to real experimental data.