Mathematical modeling of vacuum freeze-drying for technology transfer from laboratory to industrial scale

The paper focuses on mathematical description of vacuum freeze-drying applied to dispersed and biologically active materials used in the production of finished dosage forms and composite polymer systems. The aim of the study was to develop a modeling approach supporting technology transfer of freeze-drying from laboratory to industrial scale while maintaining product uniformity and quality. The proposed method combines a one-dimensional drying kinetics model with computational fluid dynamics for simulation of water vapor distribution inside the lyophilizer chamber. The model describes the first and second drying periods, layer-by-layer movement of the sublimation front, coupled heat and mass transfer in frozen and dried regions, and diffusion-controlled moisture removal during secondary drying. Experimental investigations were carried out on a Labconco pilot freeze-dryer operated at 5–10 Pa with a condenser temperature of 188 K using a model peptide solution. Calculated temperature profiles showed good agreement with experimental data: the difference factor equaled 1.76 and the similarity factor reached 54.77, confirming model adequacy. Computational fluid dynamics simulations demonstrated nonuniform water vapor distribution within the chamber and increasing vapor concentration near the condenser during sublimation. The results indicate that integration of drying kinetics modeling with gas-dynamic simulations enables rational selection of operating regimes, reduction of drying time, and decrease in batch rejection risk. The developed approach is recommended for efficient scale-up and industrial implementation of vacuum freeze-drying technologies.