Compartment based population balance modeling of a high shear wet granulation process using data analytics

A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process

In this study, a hybrid modeling framework was developed for predicting size distribution and content uniformity of granules in a bi-component wet granulation system with components of differing hydrophobicities. Two bi-component formulations, (1) ibuprofen-USP and micro-crystalline cellulose and (2) micronized acetaminophen and micro-crystalline cellulose, were used in this study. First, a random forest method was used for predicting the probability of nucleation mechanism (immersion and solid spread), depending upon the formulation hydrophobicity. The predicted nucleation mechanism probability is used to determine the aggregation rate as well as the initial particle distribution in the population balance model. The aggregation process was modeled as Type-I: Sticking aggregation and Type-II: Deformation driven aggregation. In Type-I, the capillary force dominant aggregation mechanism is represented by the particles sticking together without deformation. In the case of Type-II, the particle deformation causes an increase in the contact area, representing a viscous force dominant aggregation mechanism. The choice between Type-I and II aggregation is determined based on the difference in nucleation mechanism that is predicted using the random forest method. The model was optimized and validated using the granule content uniformity data and size distribution data obtained from the experimental studies. The proposed framework predicted content non-uniform behavior for formulations that favored immersion nucleation and uniform behavior for formulations that favored solid-spreading nucleation.

Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.