Advanced modelling of atypical heat transfer in vial freeze-drying processes


Product quality is paramount in pharmaceutical industries for guaranteeing the reproducible delivery of the therapeutic benefits explicated in the label. Today, both in pharmaceutical and biological industries, assurance of product quality and safety is based on the Quality-by-Design paradigm. This initiative states that final product quality should be built-in during the process and not merely tested as previously done. To this end, the product and process design should be based on the understanding of the physical phenomena taking place during the process and of the interaction between process and product.

In pharmaceutical industries, freeze drying is widely used as preservation method for heat sensitive products, such as vaccines. This drying process comprises three main steps: freezing, devoted to the formation of ice crystals and the solidification of the product; primary drying, during which ice crystals are removed by sublimation; secondary drying, during which the adsorbed water is removed from the product until the target value of residual moisture content is achieved.

The position of the vial on the shelf of the equipment may affect the effectiveness of the freeze-drying process, as it directly impacts the product temperature value. Temperatures above a critical value compromise the porous structure of the product, resulting in its collapse and rejection. It is possible to classify two groups of vials in function of their position on the shelf: the “edge vials” are those located on the shelf periphery, whereas “central vials” are located in the center of the shelf and not directly exposed to the chamber door and walls. Vials placed at the edges of the shelves may experience higher temperatures as compared to those placed at the center and could have a higher rejection risk.

The “edge vial effect”, as it is typically referred to, represents a significant issue in vial freeze-drying. Most of the experimental studies conducted so far have difficulties in determining the exact mechanisms causing the edge vial effect. Consequently, proposing effective heat transfer predictions for freeze-drying cycle design and scale-up has been a challenge.

A team of researchers from INRA and AgroParisTech at Université Paris-Saclay in France and GlaxoSmithKline Biologicals SA in Belgium tackled this challenge: Bernadette Scutellà and colleagues developed a detailed 3D mathematical model for analyzing heat transfer in the vials. Their main aims were the prediction of the heat flows in vials differently located on the shelf and the understanding of the role played by the different heat transfer mechanisms, thus to provide an efficient prediction of the edge vial effect. This work was published in the journal Applied Thermal Engineering.

The authors used COMSOL Multiphysics to solve numerically the 3D model of the heat transfer during the second step of the freeze-drying process, i.e. primary drying. The simulation represented a part of the freeze-drying chamber with five vials strategically located at the edges of the shelves in contact and not in contact with a metallic rail. Heat transfer mechanisms considered in the numerical experiments included: radiation, evaluated by the hemi-cube method taking into consideration the shadowing effect in the system; gas conduction near solids, evaluated by simulating a fictitious layer built at the interface of the solid and the gas; contact conduction between the solids, simulated as proposed in previous study of Scutellà et al. (2017a).

The numerical predictions were validated against experimental measurements of heat flow rates received by edge and central vials at different chamber pressure and shelf temperature values, which corroborated the overall predictive capacity and accuracy of the mathematical model especially for the cases relevant to pharmaceutical applications. By using the developed mathematical model, the authors successfully predicted the heat flows received by the five vials located at the edge and in the center of the shelves.

Among the three major heat transfer mechanisms investigated in the study, gas conduction proved to be the leading cause of higher heat transfer at the edges than in the center. Furthermore, the rail contributed more to the radiation heat transfer than the walls. These findings were original, as previous literature attributed the edge vial effect mainly to the radiation from the drying chamber door and walls.

The proposed model is versatile and can be used in predicting the edge vial effect for various loading configurations and equipment characteristics. The information obtained in such cases will help in designing efficient freeze-dryer process which will, therefore, enhance the quality of the product.

Advanced modelling of atypical heat transfer in vial freeze-drying processes - Advanced Engineering

Temperature profiles and heat fluxes in the edge vial in contact with the rail and in the central vial at a shelf temperature of 0 °C and a chamber pressure of 4 Pa. Arrow length indicates flux magnitude on a logarithmic scale, to improve the visualization of smaller fluxes from top, wall and rail.

Figure adapted from Scutellà, B., Plana-Fattori, A., Passot, S., Bourlès, E., Fonseca, F., Flick, D., & Tréléa, I. (2017b). 3D mathematical modelling to understand atypical heat transfer observed in vial freeze-drying. Applied Thermal Engineering, 126, 226-236, with permission from Elsevier.

About the author

Dr. Bernadette Scutellà received her M.S. in Food Engineering at the University of Salerno in 2013. She was awarded of a PhD from AgroParisTech for studies on the mathematical modelling of freeze-drying process in 2017. Presently, she is drying scientist at in the Technical Research and Development department at GSK Vaccines, Rixensart, Belgium. She is in charge of freeze-drying cycle development, transfer and scale-up, as well as of the evaluation of novel process monitoring and drying technologies.

Her research interest presently focuses mathematical modelling of transport phenomena, rheology and thermodynamics in pharmaceutical and biological processes.

About the author

Dr. Artemio Plana-Fattori studied Atmospheric Sciences in the Universidade de Sao Paulo and later in the Université of Lille.

After 20 years teaching and conducting research in Brazil, he joined AgroParisTech in 2010, where he has working with numerical modeling applied to food engineering.

About the author

Dr. Stéphanie Passot is an Associate Professor in the graduate institute in science and engineering AgroParisTech (Paris Institute of Technology for Life, Food and Environmental Sciences). She was awarded her Ph.D. for studies in pharmaceutical freeze-drying, focusing on protein formulation, freeze-drying cycle development and relationships between thermal properties and biological activity. Stephanie’s research interests remain in this area and include the understanding of the physico-chemical mechanisms of degradation of biological products (microorganisms, proteins) during freezing and freeze-drying.

About the author

Dr. Erwan Bourlès studied Food Process Engineering and received his PhD from the University of Angers, France in 2009. Following his thesis, he worked for 2 years as research engineer on the scaling up of the freeze-drying process and stabilization of lactic acid bacteria in the dried state. This work was done in partnership with the joint research unit of Microbiology and Food Process Engineering (INRA/AgroParisTech, France). From 2011 to end 2015, he owned the position of Freeze drying scientist in the Technical Research and Development department at GSK Vaccines Rixensart, Belgium. He was in charge of the development, scaling-up of freeze-drying cycles, process evaluation and transfer towards internal and external sites. Since 2016, he is leading the Filling Drying and Device Drug product Platform in the Technical research and Development department, at GSK in Belgium.

About the author

Dr. Fernanda Fonseca, received her PhD in Biotechnology and Process Engineering in 2001, from AgroParisTech, France. She is a Research Director at the French National Institute for Agricultural Research (INRA), in Versailles-Grignon Centre, France. Her research field is biotechnology and process engineering, with particular emphasis in fermentation, formulation and stabilization of biological products by freezing and freeze-drying. The principal models of study have been lactic acid bacteria, but also proteins, mammalian cells and food products.

Her research interests focus in the thermophysical and chemical changes taking place within biomaterials during freezing and freeze-drying. Recent research has focused on membranes and vitrification of the intracellular environment and in relating these events to biological and functional outcomes. The ambition is to find general principles for simplifying and rationalising the development of new formulated products and optimization of the stabilization process.

About the author

Prof. Denis Flick is a professor and researcher at the joint research unit AgroParisTech/INRA Food Process Engineering. His research area focuses on modelling and numerical simulation of coupled phenomena in food processes, e.g. heat/mass transfer, fluid flow/product deformation, product transformation. He was co-author of 115 articles in international peer reviewed journals and of 150 communications in peer reviewed congresses.

About the author

Prof. Ioan Cristian Trelea received his M.S. degree in automatic control from Institut National Polytechnique de Grenoble, France in 1993 and his Ph.D. degree in process engineering from Ecole Nationale Supérieure des Industries Alimentaires (ENSIA) Massy, France in 1997. He has been associate professor at Institut National Agronomique Paris-Grignon, France (1998-2009) and is now professor at AgroParisTech since 2010.

His teaching and research interest are chiefly in dynamic systems, automatic control, modeling, process and bio-process engineering. He is an author of more than 60 peer-reviewed papers in international scientific journals and was in charge of modeling workpackages in several national and European research projects.


Scutellà, B., Passot, S., Bourlès, E., Fonseca, & Tréléa, I. (2017a). How vial geometry variability influences heat transfer and product temperature during freeze-drying. Journal of Pharmaceutical Sciences, 106:3, 770-778..

Go To Journal of Pharmaceutical Sciences


Scutellà, B., Plana-Fattori, A., Passot, S., Bourlès, E., Fonseca, F., Flick, D., & Tréléa, I. (2017b). 3D mathematical modelling to understand atypical heat transfer observed in vial freeze-drying. Applied Thermal Engineering, 126, 226-236. .

Go To Applied Thermal Engineering

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