Importance of Kv Distribution in Freeze Drying Part I: A Holistic Model to Predict Changes in Kv Bimodal Distribution as a Function of Pressure

Measurement of heat transfer coefficients (Kv) is an important part of freeze-dryers characterization and as well a necessary step for executing any modelling. In most cases only an average value of Kv is calculated, or an average value of center and edge vials is provided. Our aim is to go a step further and to describe the overall Kv distribution various vial/ freeze drier combinations, whatever the pressure. From an experimental point of view, in this article we propose three methods to calculate the Kv value for individual vials based on the ice sublimation gravimetric method. The first method we use is the most usual one, where the Kv value is calculated based on the mass of sublimated ice and the product temperature measured in selected vias. In the second method, the average product temperature is estimated for each vial, based on the mass difference before and after sublimation and the Kv value is calculated accordingly. In the third method, the Kv is estimated by comparison to sublimation results from a simulation. Results from methods 2 and 3 are very similar results and are slightly different from those of method 1. Method 1 was shown to exhibit a systematic bias due to the fact that it is based on the temperature of recording of selected vials only, which are not representative for all positions. Once the individual values of Kv have been calculated, it is possible to establish a distribution for each method. It was observed that an overlay of two normal distributions describing the center and the edge vials provides a good representation of the empirical distribution. Furthermore, we propose a holistic model aiming to calculate the Kv distribution for any specified pressure.