Singh Mehakpreet, Kumar Ashish, Shirazian Saeed, Ranade Vivek, Walker Gavin
Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland.
Pharmaceutical Engineering, Faculty of Pharmaceutical Sciences, Ghent University, 9000 Gent, Belgium.
Pharmaceutics. 2020 Nov 27;12(12):1152. doi: 10.3390/pharmaceutics12121152.
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.
由于多组分系统，推荐应用多维群体平衡方程（PBEs）来模拟制粒过程。无论应用领域如何，求解多维PBEs的数值格式选择仅由（尺寸）数密度预测的准确性驱动。然而，混合各组分，即颗粒（辅料和活性成分）和黏合剂液体，在预测药物制粒过程中的颗粒组成分布方面起着关键作用。因此，一种数值格式应该能够准确地预测这一点。在此，我们在预测混合状态的准确性和适用性方面比较了单元平均技术（CAT）和有限体积格式（FVS）。为了量化系统中的混合程度，研究了平方和χ2参数以观察黏合剂用量与其平均值的偏差。结果表明，对于双组分群体平衡方程，由FVS计算的积分矩的准确预测会导致χ2参数的不准确预测。此外，单元平均技术（CAT）以中等精度预测矩；然而，它计算组分混合χ2参数的精度高于有限体积格式。针对一些基准核进行了数值测试，文献中已有其解析解。还将表明，两种数值方法同样能很好地预测系统中形成的颗粒的平均尺寸；然而，有限体积格式计算这些结果所需的时间更少。
