Freeze-Drying of Pharmaceutical Proteins in Vials: Modeling of Freezing and Sublimation Steps

The commercial finite element code FEMLAB was used to perform two-dimensional axisymmetric simulations of the temperature profiles and the moving front velocities of standard BSA (bovine serum albumin)-based formulations used to stabilize pharmaceutical proteins during the freeze-drying process. The simulations were validated with both experimental and numerical approaches. In an initial step, the heat transfer phenomena taking place during the cooling of liquid solutions was studied in commercial size glass vials without freezing or sublimation. Then, this model was extended and validated for the freezing process of aqueous BSA-based solutions encountered in the industrial freeze-drying processes with the same vials in order to confirm the identified values of the different thermal conductances between the product and the shelf and between the product and the surroundings. Finally, the conductances between the product and the shelf and between the vial and the surroundings thus determined were used in a dynamic sublimation model with two zones and a moving sublimation front similar to the ones previously proposed in the literature. The simulations showed a satisfactory agreement between experimental and simulated data. The results of this study demonstrated that the freeze-drying process of pharmaceutical proteins in glass vials for standard industrial operating conditions was mainly controlled by the heat transfer from the shelf and the surroundings to the product sublimation front.