Simulation of freezing step in vial lyophilization using finite element method

Determination of heat transfer and temperature profile during freezing step is fundamental to predict the final structure of a lyophilized product. The aim of this study was to develop and optimize a dynamic model based on finite element method for simulation of freezing step in order to study final product morphology in both vertical and radial directions. Different factors have been taken into account: chamber pressure, shelf temperature, vial shape, initial solution temperature, nucleation temperature and phase changes. The dynamic axisymmetric model proposed could simulate temperature of each point in the vial and position of liquid-solid interface, without necessity of fitting parameters or questionable assumptions. In addition, the model was extended to predict the average crystal size in each element and the influence of different factors was examined.