Optimal Control of the Primary and Secondary Drying Stages of Bulk Solution Freeze Drying in Trays

Abstract

The problem of operating a tray freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem with the use of the rigorous unsteady state mathematical model of Sadikoglu and Liaois 191 that has been found to describe satisfactorilv the exoerimental dvnamic . . . behavior of the primary and secondary drying stages of bulk solution freeze drying of pharmaceuticals in trays. The heat input to the material being dried and 400 SADIKOGLU. LIAPIS. AND CROSSER the drying chamber pressure are considered to be control variables. Constraints are placed on the system state variables by the melting and scorch temperatures during primary drying, and by the scorch temperature during secondary drying. Necessary conditions of optimality for both the primary and secondary drying stages are derived and presented, and an approach for constructing the optimal control policies that would minimize the drying times for both the primary and secondary drying stages, is presented. The theoretical approach presented in this work was applied in the freeze drying of skim milk, and significant reductions in the drying times of primary and secondary drying were obtained, when compared with the drying times obtained using the operational policies reported in the literature, by using the optimal control policies constructed from the theory presented in this work. Furthermore, it is shown that the optimal control policy leads to the desired in practice result of having at the end of secondary drying temperature and bound water concentration profiles (in the dried layer) whose gradients are very small. It is also shown that by using the optimal control policy and an excipient capable of increasing the melting temperature without affecting product quality, one can significantly reduce the drying time of the primary drying stage.

The drying rates of spray freeze drying systems increase through the use of stratified packed bed structures

“…1a) of the packed particles in a tray increases and makes the resistances to heat and mass transfer in the packed bed to increase. It would be interesting in the future to investigate whether the use in SFD systems of time optimal control [24] for the total pressure in the drying chamber of the freeze dryer and for the heat input during the primary drying stage, could prevent the formation of a secondary dried layer.…”

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

“…It should be noted that no claim is made that this is the optimal program of process control, such can only be identified by solving the time optimal control problem for freeze drying in vials, as demonstrated for freeze drying of slabs by Sadikoglu et al (1998). For Case I or III, after a period of time of primary drying, it may happen that T lp ‫ס‬ T up ‫ס‬ T max will raise T II (t,z,r) above the melting temperature T m at some point along the bottom of the frozen layer, if no appropriate control of T lp (T lp ‫ס‬ T up ) is undertaken (this corresponds to a masstransfer limited process; for the operational strategies in this work, only mass-transfer limited behavior was observed during primary drying).…”

Optimal Control Policy of the Microwave Primary Freeze Drying of Random Solids

“…[45][46][47] There are few papers strictly concerning optimization of MWFD [3,38] ; however, there are works dealing with optimal control of the freeze-drying process using conventional heating methods. [30,32,[34][35][36] Therefore, the objective of the present work is to determine the optimal control policy of the microwave freeze-drying primary stage of the random solids to improve the drying rate and simultaneously achieve desired product quality. The vacuum chamber pressure and microwave power are considered controllable factors in the microwave freeze-drying system in order to avoid gas breakdown (corona discharge) and melting.…”

“…[5][6][7][8][9] Many mathematical analyses presented in papers concerning freeze drying with conventional heating can be adapted in the modeling of MWFD. [28][29][30][31][32][33][34][35][36] Generation of volumetric heat sources by microwave energy is governed by the same mechanisms regardless of the type of microwave-assisted drying method. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][37][38][39][40][41][42][43][44] When liquid water is present in investigated material, the distribution of electric field strength in a sample is considered.…”