Using mathematical modeling to optimize secondary drying stage of lyophilization technology

During lyophilization frozen water and moisture associated with dissolved substances are removed, desorption occurs in the process of secondary drying. This stage is one of the main stages of the technological process in terms of duration comparable with primary freeze drying and is of paramount importance for the further storage of lyophilisates. Mathematical modeling of secondary drying and the use of these methods in calculating design space of the process are described in the presented article. The equations for calculating the rate of secondary drying, residual moisture, and other conditions on the basis of values of the temperature of the heat-transfer fluid and pressure in the freezedrying chamber are shown. Possibilities for determining design space boundaries on the basis of the composition of lyophilisate, required values of residual moisture and drying kinetics are demonstrated. The proposed mathematical model makes it possible to estimate the duration of the secondary drying process for various values of temperature and pressure in the chamber within the design space.