The heat-transfer system supplying the heat of sublimation of ice is limited in the amount of heat that can be transferred
in a given period of time. This situation may arise because of limitations in the electrical power that can be provided to
heat the silicone oil or other heat-transfer fluid, or perhaps because of limitations in the internal shelf heat-transfer
coefficient due to the design of internal flow channels in the shelves and the heat-transfer fluid type and flow rate.
Equipment limitations of the type described above take the form of a maximum sublimation rate that can be supported by the
equipment irrespective of the pressure in the system, and they therefore appear as a horizontal line forming an upper boundary
on the design space.
There is another, more complicated limitation on the performance of freeze-dryers; this limitation has to do with the dynamics
of vapor flow in the duct that connects the chamber to the condenser.5 Vapor flows through this duct because of the difference in water vapor pressure between the chamber and the condenser. Normally,
the higher the pressure difference, the higher the flow rate of water vapor through the duct. The pressure drops continuously
across the length of the duct. Because the mass flow rate of water vapor is constant along the duct, the velocity increases.
Thermodynamic theory shows, however, that there is a limit to this velocity corresponding to the speed of sound in water vapor—about
400 meters per second—or Mach 1. The speed of sound does not change with pressure. As the velocity of water vapor approaches
Mach 1, the flow of water vapor is choked, and further reduction in the downstream pressure has no influence on the mass flow
rate through the duct. In freeze-drying, choked flow is characterized by loss of control of pressure in the chamber.
Unlike the equipment limitations described above, the limitation imposed by choked flow depends upon the pressure in the system,
where the mass flow rate choke point is directly proportional to pressure. The boundary on the design space imposed by choked
flow would have the general shape shown by the solid blue line in Figure 4. Thus, for the sake of this example, the design
space is bounded by the upper product temperature isotherm on the right, and by the line representing the choke point on the
left. Any process conditions in the design space would be acceptable. Of course, it is most desirable to operate near the
apex of this space, because the apex represents the most efficient process conditions.
Ice Slab Testing for Equipment Qualification
A useful way to identify equipment limitations is to carry out a series of ice slab tests on a freeze-dryer. This is generally
done by lining a tray ring with plastic sheeting and adding approximately one-half inch of water to each tray. The water is
frozen, the system is evacuated to the desired pressure, and the shelf temperature is increased using a linear ramp rate.
At some point, control of chamber pressure will be lost—this corresponds to the choke point. To measure the sublimation rate
supported by the equipment at this pressure, it is necessary to repeat the experiment at the appropriate pressure and shelf
temperature, carrying out sublimation until a significant fraction of the initial mass of ice has sublimed. This set of experiments
is then repeated at a new pressure until enough data points have been determined to define the choke point line illustrated
in Figure 4. The choke point data in this graph is based on gravimetric ice slab testing of a production scale freeze-dryer.
Of course, TDLAS capability significantly reduces the labor involved in this type of equipment qualification; it does so by
eliminating the need to repeat each experiment after the choke point has been identified. In principle, the entire curve could
be generated in one ice slab experiment.
It is also necessary to monitor other aspects of equipment performance during ice slab testing. This monitoring would include
checking the condenser to make sure that the temperature remains below, for example, –50 °C. This type of limitation on equipment
capability would appear as a horizontal line on the design space.