Determination of mass and heat transfer parameters during freeze-drying cycles of pharmaceutical products

The principal aim of this study was to evaluate the water vapour mass transfer resistance of the dried layer and the vial heat transfer coefficient values of a pharmaceutical product during the primary drying period. First, overall vial heat transfer coefficient values, Kv, were determined by a gravimetric method based on pure ice sublimation experiments. Thus, it was possible to set up a map of the total heat flux received by each vial throughout the plate surface of our pilot scale freeze-dryer. Important heterogeneities were observed for the vials placed at the plate edges and for the vials placed at the center of the plate. As well, the same gravimetric method was also used to precisely determine the influence of main lyophilization operating parameters (shelf temperature and gas total pressure) or the vial types and sizes on these overall heat transfer coefficient values. A semi-empirical relationship as a function of total gas pressure was proposed. The transient method by pressure rise analysis (PRA method) after interrupting the water vapour flow between the sublimation chamber and the condenser, previously set up and validated in our laboratory, was then extensively used with an amorphous BSA-based formulation to identify the dried layer mass transfer resistance values, Rp, the ice front temperature, and the total heat transfer coefficient values, Kv, with or without annealing treatment. It was proved that this method gave accurate and coherent data only during the first half of the sublimation period when the totality of the vials of the set was still sublimating. Thus, this rapid method allowed estimation of, on line and in situ, the sublimation front temperature and the characterization of the morphology and structure of the freeze-dried layer, all along the first part of the sublimation period. The estimated sublimation temperatures shown by the PRA model were about 2 degrees C lower than the experimental values obtained using thermocouples inserted inside the vial, in accordance with previous data given by this method for similar freeze-drying conditions. As well, by using this method we could confirm the homogenization of the dried layer porous structure by annealing treatment after the freezing step. Furthermore, frozen matrix structure analysis (mean pore diameter) using optical microscopy and mass transfer modelling of water vapour by molecular diffusion (Knudsen regime) allowed, in some cases, to predict the experimental values of this overall mass transfer resistance directly related to the freeze-dried cake permeability.