Use of Laboratory Data in Freeze Drying Process Design: Heat and Mass Transfer Coefficients and the Computer Simulation of Freeze Drying

Abstract

Freeze drying process development normally proceeds via an empirical “trial and error” experimental approach which is both time consuming and uncertain in reliable extrapolation to production equipment. This research describes the use of phenomenological theory, with key parameters determined by laboratory experiments, to guide the experimental program to optimize the primary drying stage of the process for a given product/container combination. The theoretical description of primary drying is a problem in coupled heat and mass transfer which can be satisfactorily described using a steady-state model where the heat flow is given by the product of the mass flow and the heat of sublimation. Generally, mass transfer is impeded by three barriers or resistances: resistance of the dried product layer, resistance of the semi-stoppered vial, and resistance of the chamber. Resistance, defined as a ratio of pressure difference to mass flow, is experimentally determined for each barrier. The resistance of the dried product normally increases with time as the thickness of dried product increases and typically accounts for over 90% of the total resistance to mass transfer. Heat flow from the shelf surface to the subliming ice is impeded by three barriers: the interface between the shelf surface and the bottom of the tray used to contain the vials, the interface between the tray and the vial bottom, and the ice between the bottom of the vial and the sublimation surface. Heat flow is described in terms of heat transfer coefficients, defined as the ratio of the heat flux to temperature difference, where the heat transfer coefficients are experimentally determined for each vial and tray of interest. Vial and tray heat transfer coefficients increase with increasing pressure and are quite sensitive to variations in degree of flatness of the vial or tray bottom. Steady-state transport theory is used to define six equations with eight variables where the equations contain mass transfer resistances and heat transfer coefficients which are determined from laboratory experiments. The variables are the sublimation rate and the pressures and temperatures throughout the system. Our procedure is to fix two of the variables (i.e., chamber pressure and shelf temperature) and solve, via a computer program, for the other six variables. Solutions are obtained for 0, 20, 40, 60, 80. and 100% completion of primary drying, thereby providing sublimation rate and the relevant temperatures and pressures as a function of time during the freeze-drying cycle defined by the input parameters chosen (i.e., the chamber pressure and shelf temperature profile with time). Thus, computer-generated freeze-drying cycles may be generated for any combination of product, container, and process parameters desired. Agreement between theoretical and experimental cycles is satisfactory. Use of this approach is demonstrated with the following applications: (1) a study of the effect of changes in chamber pressure and shelf temperature on drying time and product temperature: (2) the effect of shelf temperature variability and vial heat transfer coefficient variability on uniformity of drying: and (3) cycle optimization.