An important application of the presented modeling framework in this work is the quantification of properties of the frozen product and their variability among vials and among repetitions of the process, i.e. batch heterogeneity. Such heterogeneity is regarded as one of the main design challenges of freezing and of freeze-drying processes, since it may result in a variability in critical quality attributes. Predicting and quantifying batch heterogeneity is therefore an essential step towards a rational design of the freezing process.