3D mathematical modelling to understand atypical heat transfer observed in vial freeze-drying

Abstract

In pharmaceutical freeze-drying, the position of the product container (vial) on the shelf of the equipment constitutes a major issue for the final product quality. Vials located at the shelf edges exhibit higher product temperature than vials located at the centre, which in turn often results in collapsed product. A physics-based model was developed to represent heat transfer phenomena and to study their variation with the distance from the periphery of the shelf. Radiation, conduction between solids, and conduction through low-pressure water vapour were considered. The modelling software package COMSOL Multiphysics was employed in representing these phenomena for a set of five vials located at the border of the shelf, close to the metallic guardrail. Model predictions of heat fluxes were validated against experimental measurements conducted over a broad range of shelf temperatures and chamber pressures representative for pharmaceutical freeze-drying. Conduction through low-pressure water vapour appeared as the dominant mechanism explaining the additional heat transfer to border vials compared to central ones. The developed model constitutes a powerful tool for studying heterogeneity in freeze-drying while reducing experimental costs. Highlights:• A 3D mathematical model of heat transfer in freeze-drying is proposed.• The role of several heat transfer mechanisms is explored.• Knudsen effect is considered for conduction inside low-pressure water vapour.• Radiation heat transfer is evaluated using the surface-to-surface model.• Atypical heat transfer is explained mainly by gas conduction rather than radiation.

Effect of Freeze Dryer Design on Heat Transfer Variability Investigated Using a 3D Mathematical Model

“…Table 1 summarizes the characteristics of the three main mathematical models published in literature investigating the mechanisms responsible for heat transfer variability between edge and central vials during freeze-drying. 8,11,12 Two different approaches were used to describe the freeze-drying process: the dynamic state and the steady state. Gan et al 11 used the dynamic 2D model previously developed by Sheehan and Liapis 13 to describe the heat transfer during freeze-drying in edge and central vials.…”

“…Recently, two mathematical models describing the heat transfer in edge vials assuming steady state were published. 8,12 Pikal et al 8 used the theory described in Pikal 14 to evaluate the edge vial effect in terms of increment of vial heat transfer coefficient in edge vials compared to central vials Δ .…”

“…Furthermore, the use of a 1D model can be a limitation for the computation of complex heat fluxes (as, for example, radiation and gas conduction in the drying chamber). A step further in the understanding of the heat transfer mechanisms responsible of the edge vial effect was performed in Scutellà et al, 12 who developed a 3D mechanistic mathematical model of heat transfer during sublimation. This model allows a detailed computation of the radiation heat fluxes between all the components of the considered system and of the conduction through the gas surrounding the vial in the drying chamber using a moderate number of model parameters (i.e., 5, Table 1).…”

“…In the present work, the model presented by Scutella et al 12 was further investigated to simulate three different vial loading configurations: vials partially shielded by the rail, vials totally shielded by the rail and vials totally exposed to the chamber walls. The performance of the models of Pikal et al 8 and Scutellà et al 12 was compared with experimental data published in literature. 7 Then, the importance of the vial loading configuration on the heat transfer was assessed.…”

The application of dual-electrode through vial impedance spectroscopy for the determination of ice interface temperatures, primary drying rate and vial heat transfer coefficient in lyophilization process development

“…Clearly there is a need to extend this work to encompass; (i) the determination of heat transfer coefficient as a function of chamber pressure and (ii) the investigation of the impact of vial size and shape [34]. Further work is also required in terms of the basic models used to understand the physical origin of the dielectric loss process that has been exploited in this work.…”