Modeling of the primary and secondary drying stages of the freeze drying of pharmaceutical products in vials: Numerical results obtained from the solution of a dynamic and spatially multi-dimensional lyophilization model for different operational policies

Abstract

A rigorous unsteady state and spatially multidimensional model is presented and solved to describe the dynamic behavior of the primary and secondary drying stages of the lyophilization of a pharmaceutical product in vials for different operational policies. The results in this work strongly motivate the aggressive control of freeze drying and it is found that heat input control that runs the process close to the melting and scorch temperature constraints yields (i) faster drying times, and (ii) more uniform distributions of temperature and concentration of bound water at the end of the secondary drying stage.

Heat Transfer in Freeze-Drying Apparatus

“…It has to be highlighted that in eq. (2) it has been assumed that product temperature is uniform i n t h e r a d i a l d i r e c t i o n , a s i t h a s b e e n demonstrated by means of mathematical simulation and experimental investigations (Pikal, 1985;Sheehan & Liapis, 1998). Various equations can be found in the literature to calculate the heat exchange coefficient K v in case the vial is placed directly over the shelf, i.e.…”

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

“…In most of the studies [19,20,22,25], the heat transfer by radiation from the door and walls of the drying chamber was considered completely responsible of the higher product temperature observed in edge vials. However, Gan et al [18] and Rambhatla et al [7] showed that the presence of the metallic rail surrounding vials also contributes to the heat transfer by means of contact conduction and radiation.…”

“…Several mono-and multi-dimensional mathematical models of freeze-drying were developed in the past years [16][17][18][19][20][21][22][23][24][25], but only few of them explore the sources of the atypical heat flow rate in edge vials. In most of the studies [19,20,22,25], the heat transfer by radiation from the door and walls of the drying chamber was considered completely responsible of the higher product temperature observed in edge vials.…”

Emerging Freeze-Drying Process Development and Scale-up Issues

“…VirTis freeze-drying system for PCR plates (vertical stripes), PCR plates with custom designed Al block (horizontal stripes), and 2R tubing vials (diagonal stripes). Graph plotted using data from (29) literature that describes the freeze-drying process (12,(31)(32)(33)(34)(35)(36)(37). There are differences between these models such as assumptions regarding the geometry of the ice sublimation interface, initial conditions, boundary conditions, and several other basic assumptions.…”