A Three-Dimensional Population Balance Model of Granulation Employing Mechanistic Kernels
Advancing the chemical engineering fundamentals
Particulate Systems (T2-3)
Keywords: population balances, granulation, multi-dimensional distributions, aggregation, nucleation
Granulation is a particle production process of converting fine powdery solids into larger free-flowing agglomerates. It finds application in a wide range of industries (e.g. pharmaceuticals, fertilisers and minerals). Industrial granulation processes are operated in a highly inefficient manner with large recycle ratios within the process (3-4:1, recycle/product), and hence, an integrated systems model will be crucial aid to alleviate this situation1. A modern view of granulation is a process that is governed by three predominant sub-processes: wetting and nucleation; consolidation and growth; and attrition and breakage2,3. An integrated model that accounts for these major sub-processes as well as the effects of the process inputs (binder addition, agitation rate, number of spray nozzles used for the binder spray, etc.) will enable an in-depth analysis, understanding, and efficient and effective control.
A suitable framework for the mathematical modelling of the granulation process is through population balances. A major challenge in developing these population balances is the identification of appropriate kernels for the sub-processes (e.g., nucleation and aggregation). These issues have been addressed by several authors. The aim of this work is to develop a three-dimensional population balance model for granulation, accounting for the distribution of granules with respect to their size, binder content and porosity. The model incorporates the phenomena of wetting/nucleation, consolidation and aggregation. The nucleation and aggregation phenomena are represented by mechanistic kernels based on detailed particle-level information on these phenomena.
The kernel for the aggregation phenomenon is modelled using theory proposed for the case of porous and elastic granules with or without a binder layer4. The Smoluchowski formulation is employed to derive the dynamic kernel, drawing a parallel with the DVLO theory (a transition state theory that is well established in the emulsion polymerisation literature).
The nucleation stage is regarded as a crucial period during the initial stages of granulation because the nuclei size distribution obtained will impart a large influence on the resultant final granule size distribution. In the model presented here for the nucleation kernel, the initial focus is on the droplet controlled regime, where each droplet gives a single nucleus5. The proposed dynamic kernel is generic, and in addition to ideal situations, it also includes for situations wherein (1) the droplets do not wet the powder rapidly, and (2) once wetted, the penetration rate is not fast enough relative to the bed turnover rate, resulting in partial penetration of the droplet into the powder bed. The model adopts simplifying assumptions on certain other phenomena: (1) The droplets are well spread and do not overlap. (2) If primary particles (fines) are present, then the existent particles receive binder only if the droplets do not wet and penetrate the primary particles fast enough. Most of these assumptions are independent of the core wetting and nucleation phenomena, and could be more easily relaxed in a refined model in the future.
References
1. Bardin, Kinght and Seville, Powder Tech., 140, 169-175, 2004.
2. Iveson, Litster, Hapgood, and Ennis. Powder Tech., 117: 3-39, 2001.
3. Biggs, Sanders, Scott, Willemse, Hoffman, Instone, Salman and Hounslow, Powder Tech., 130, 162-168, 2003.
4. Liu, Litster, Iveson and Ennis, AIChE J., 46, 529-539, 2000.
5. Hapgood, Litster, Biggs and Howes, J. Colloids Inter. Sci., 253, 353-366, 2002.
Presented Monday 17, 15:00 to 15:20, in session Particulate Systems (T2-3).
