On the use of a dual-scale model to improve understanding of a pharmaceutical freeze-drying process.

The evolution of product temperature and of residual ice content in the various vials of a batch during a freeze-drying process can be significantly affected by local conditions around each vial. In fact, vapor fluid dynamics in the drying chamber determines the local pressure that, taking into account the heat flow from the shelf and, eventually, radiation from chamber surfaces, is responsible for the sublimation rate and product temperature. These issues have to be taken into account when using mathematical simulation to predict the evolution of the product as a consequence of the operating conditions (recipe design), as well as during the scale-up of a recipe obtained in a small-scale equipment to a large-scale unit. In this framework, a dual-scale model can significantly improve the understanding for pharmaceuticals freeze-drying processes: it couples a three-dimensional model, describing the fluid dynamics in the chamber, and a second mathematical model, either mono- or bi-dimensional, describing the drying of the product in each vial. Thus, it can be profitably used to gain knowledge about process dynamics, and to improve the design of the equipment, as well as the performance of the control system of the process.