In this work, we extend the model to batches comprising vials packed in three spatial dimensions, as is the case in pallet freezing. We simulated the process and compared the model predictions with engineering run data of the Janssen COVID-19 vaccine. The model qualitatively reproduced all experimentally observed trends; we thus apply it to characterize several freezing phenomena, such as the occurrence of thermal spikes and a stationary phase in the thermal evolution profiles. We further study how nucleation kinetics, storage temperature and batch size affect process duration. To promote the use and further development of the model, we provide open source access to it in the form of a python package.