Heating policies during the primary and secondary drying stages of the lyophilization process in vials: Effects of the arrangement of vials in clusters of square and hexagonal arrays on trays

The dynamic behavior of the primary and secondary drying stages of the lyophilization process were studied when (a) single vials located at different positions on the tray were individually being dried, and (b) the vials on the tray are arranged in clusters of square and hexagonal arrays and all the vials on the tray are simultaneously being dried. For both cases (a) and (b), fast drying times and relatively more uniform distributions of temperature and concentration of bound water at the end of the secondary drying stage are obtained by heat input control that runs the lyophilization process close to the melting and scorch temperature constraints. The heating control policies for the systems of case (b) are found to be more conservative and significantly more complex than those for the systems of case (a), because in case (b) there are vials on the tray that are in their secondary drying stage while other vials on the same tray have not yet completed their primary drying stage. Furthermore, the analysis and synthesis of the results presented in this work (i) indicate the minimum number of vials and their relative locations on the tray that have to be monitored by sensors so that the dynamic drying state of all the vials being dried simultaneously on the tray, could be satisfactorily determined in real time and appropriate, if necessary, control action could be applied, and (ii) suggest changes in the design of the freeze drying equipment so that the production rate of the freeze dryer could be improved and the product could also have enhanced properties of stability and quality at the end of the lyophilization process.