Quality by Design in the Secondary Drying Step of a Freeze-Drying Process

This paper is focused on the secondary drying step of a freeze-drying process, where the bound water is desorbed from the (partially) dried product, with the goal to achieve the target value of residual moisture in the final product. Mathematical modeling is used to get a deep understanding of the process, i.e., to study the effect of the operating variables (mainly the temperature of the heating shelf and the duration of the operation) on the state of the product (temperature and residual moisture). An innovative tool is used to provide an effective support to get quality by design: it is based on the measurement of the desorption rate, through the test of pressure rise, and on a mathematical model of the process. It allows us to monitor in-line the process, as well as to determine the kinetic parameters of water desorption and their dependence on the operating conditions. The mathematical model of the process is used to calculate the design space of the secondary drying process, i.e., to identify those operating conditions that allow the fulfillment of product quality requirements, and then to minimize the duration of the secondary drying. The case study used to test the proposed methodology is the drying of 5% w/w aqueous solutions of sucrose: a linear dependence of the desorption rate on the residual moisture is evidenced by the experimental investigation, and the Arrhenius equation appears to adequately describe the dependence of the kinetic constant on the temperature, with a frequency factor equal to 277 s(-1), and an activation energy equal to 37,714 J mol(-1). The model is then used to calculate the design space, as well as to optimize the operating conditions; in case the target value of residual moisture is 2%, the duration of secondary drying can be decreased from 16 h in case of constant shelf temperature to 7.35 h in case the recipe is optimized.