(233f) Towards a General Model for Twin-Screw Wet Granulation: Development and Calibration of a Novel Three Compartmental PBM Model
For this development, a unique collection of experimental datasets at different locations inside the granulator was created (after the wetting zone, after the first and second kneading zone). This gives significant insight into what mechanisms take place at what location. When granulating the preblend, the main differences are observed in the granule size distribution (GSD) when the liquid to solid (L/S) ratio changes. At low L/S ratio, the GSD exhibits bimodality, whereas at high L/S ratio the GSD shows unimodal behaviour.
Based on these observations, a novel Population Balance Model (PBM) was developed for predicting the GSD at the end of the outlet of the granulator starting from the pre-blend. In PBM, physical mechanisms, such as aggregation and breakage of granules, are represented by kernels which are often semi-empirical in nature. This work pointed out that none of the traditional kernels from literature could reproduce our experimental observations (i.e. calibration failed), mainly because their shape was contradicting the observed trends and no single set of kernels could predict both unimodal and bimodal behaviour. Therefore, novel kernels had to be developed.
In the model we propose, prediction of both the unimodal and the bimodal behaviour with one single aggregation kernel structure is possible. The developed kernel consists of a convolution of a continuously monotonic increasing function (to drive the GSD to higher granule sizes) and a smooth stepping function to drive the GSD to bimodal behaviour when needed. This stepping function can be reduced in weight or completely switched off in case of unimodal behaviour. The breakage kernel (only used in the kneading zones) is a combination of attrition and uniform breakage.
The hypothesis for this aggregation kernel is that aggregation is the source of bimodality, whereas in literature it is often suggested to be caused by breakage. However, from the performed measurements of the GSD in the wetting zone, it is evident that bimodality is induced in this zone, where breakage is highly unlikely. With changing L/S ratio, the amount of available liquid is quite different. When low amounts are available in the system (low L/S ratio), particles cannot grow larger than a certain size because there simply is not sufficient liquid available to promote further granulation to larger sizes. In this way, hypothesised mechanistic knowledge is built into the mathematical model. If breakage would be the source of bimodality, there is no reason why there are differences at different L/S ratios, as the observed friability is expected to be similar in both cases.
The full model is in fact a combination of three PBM models in series: a PBM compartmental model. For each zone for which data is gathered, a compartment is made: the wetting zone (preblend to after the addition of the liquid binder), kneading zone 1 (from after the wetting zone to after the first kneading elements), kneading zone 2 (just before the second kneading elements up until the end of the granulator barrel).
The model structure proposed for the aggregation kernel yields good results for a range of L/S ratios. The use of one single kernel to achieve this is a major step forward as it points out that similar mechanisms are occurring but at a different rate for different L/S ratios.