Using Mathematical Modeling and Prior Knowledge for QbD in Freeze-Drying Processes

Abstract

This chapter deals with the use of mathematical modeling to get quality-by-design in a freeze-drying process. The target is to identify the design space of the process, i.e., the values of the operating conditions that allow maintaining product temperature below the limit value during primary and secondary drying stages, with a sublimation rate compatible with the capacity of the condenser, avoiding choking flow in the duct connecting the chamber to the condenser, minimizing drying duration, and getting the target value of residual moisture in the final product. Mathematical models of product evolution in the vials during the whole process, and of the freeze-drying equipment, are presented, and the experimental investigation required to get the values of model parameters is discussed, pointing out that model accuracy and level of parameters uncertainty influence the quality of the results. Then, the use of mathematical models to calculate the design space for primary and secondary drying stages is presented, pointing out how the design space can be used to optimize the cycle and to analyze the effect of any deviation of process variables from their set-point values.