Development of simplified models for the freeze-drying process and investigation of the optimal operating conditions

This paper is focused on the modelling of the primary drying of a lyophilization process in vials. A detailed mono-dimensional model taking into account mass and energy balances in the dried layer and at the sublimating interface, energy balance in the frozen layer and along the vial wall is set up; the mathematical model is validated using experimental data obtained in a pilot scale freeze-dryer, pointing out that the role of the glass wall can be relevant on the dynamics of the process. This model is suitable and has been used for off-line optimization; for on-line monitoring purposes, i.e. observer design, and for model-based control design such a detailed model is not useful, due to the high number of equations and of processes taken into consideration. Thus, two simplified models, that allow for analytical solution, have been developed: both models assume pseudo-stationary conditions because of the slow dynamics of the process, but while the first does not take into consideration the heat balance at the vial wall, this is explicitly considered in the second model. The results obtained with both models have been compared with the predictions of the detailed model for validation purposes.