Model-based design of secondary drying using in-line near-infrared spectroscopy data

This article deals with the design and optimization of the secondary drying stage, via design space calculation, of a freeze-drying process. A simple and well known mathematical model was used to this purpose: the kinetic parameters of the water desorption step were determined, either off-line or in-line, using the measurement of the residual amount of water (C-s) in one of the processed samples through Near-Infrared spectroscopy. In the first approach, three tests, at different values of heating shelf temperature, are employed: the measurement of C-s versus time allows estimating the desorption rate and, finally, the kinetic constant at the given temperature. Arrhenius plot is used to get the parameters expressing the dependence of the kinetic constant on product temperature, thus allowing the calculation of the design space. In the second approach, the kinetic parameters are estimated in-line, focusing on the first part of the secondary drying stage, where the variation of product temperature is more relevant, hence allowing to track the evolution of the desorption rate (via C-s measurement) versus product temperature. A fitting procedure is then used, looking for the kinetic parameters that provide the best fit between calculated and measured values of C-s. By this way only one test is required to get the design space. Drying of sucrose and of sucrose - arginine mixtures were used as case studies, to point out the effectiveness of the proposed method. Examples of the design spaces that can be obtained are presented and discussed, focusing on the effect of operating parameters like the heating rate and the residual water content at the beginning of the secondary drying, as well as on the constraint about the maximum allowed temperature.