Model for heat and mass transfer in freeze-drying of pellets

Lyophilizing frozen pellets, and especially spray freeze-drying, have been receiving growing interest. To design efficient and safe freeze-drying cycles, local temperature and moisture content in the product bed have to be known, but both are difficult to measure in the industry. Mathematical modeling of heat and mass transfer helps to determine local freeze-drying conditions and predict effects of operation policy, and equipment and recipe changes on drying time and product quality. Representative pellets situated at different positions in the product slab were considered. One-dimensional transfer in the slab and radial transfer in the pellets were assumed. Coupled heat and vapor transfer equations between the temperature-controlled shelf, the product bulk, the sublimation front inside the pellets, and the chamber were established and solved numerically. The model was validated based on bulk temperature measurement performed at two different locations in the product slab and on partial vapor pressure measurement in the freeze-drying chamber. Fair agreement between measured and calculated values was found. In contrast, a previously developed model for compact product layer was found inadequate in describing freeze-drying of pellets. The developed model represents a good starting basis for studying freeze-drying of pellets. It has to be further improved and validated for a variety of product types and freeze-drying conditions (shelf temperature, total chamber pressure, pellet size, slab thickness, etc.). It could be used to develop freeze-drying cycles based on product quality criteria such as local moisture content and glass transition temperature.