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LYOPHILIZATION Introduction Freeze-drying, or lyophilization, is used for a wide range of phar- maceutical products including peptides, proteins, and complex syn- thetic organic molecules. It is a standard method for stabilizing labile products with limited shelf lives in dilute solution. The objective of lyophilization process development is to deliver a cycle that achieves the following: • Acceptable product quality, consistent within a batch and from batch to batch • Operation within the capabilities of the equipment with appropriate safety margins to ensure robustness • Efficient plant utilization via the shortest possible cycle time and full loading of the lyophilizer This paper is motivated by the second and third of these objectives: we should design lyophilization cycles so that the drying rate is as high as possible with the freeze-dryer fully loaded with vials, while remaining safely within the capabilities of the equipment. During freeze-drying the water vapor is driven from the product vials into the product chamber, and from there it travels to the con- denser where it condenses upon low-temperature coils. The con- denser and product chambers are connected by a cylindrical connect- ing tube, or duct (see Figure 1). This paper is concerned with the flow of water vapor from the product chamber to the condenser through such a duct. We show data from production runs in which the vapor flow was high enough to “choke” the system, explain the principles behind choked flow, show mathematical modeling results, and detail how freeze dryers can be tested to learn the maximum drying rate they can support. Gas Flow Can Become “Choked” Consider a straight duct carrying gas from left to right (see Figure 2). The upstream and downstream gas pressures are P u and P d respec- tively, and P u > P d . Gas therefore flows from left to right (high to low pressure). At steady state, conservation of mass calls for the mass flow rate to be constant through the length of the duct. Because gas is compressible and the pressure is decreasing from left to right, the velocity of the gas increases in that direction, with it reaching its max- imum value at the duct exit where the pressure is lowest. Thermodynamic theory shows that for ducts of constant cross-sec- tion the maximum possible velocity that can be achieved is Mach 1 – the speed of sound or sonic velocity (covered in many textbooks on fluid mechanics, see for example White, 1986 [1]). One way to explain this is in terms of a downstream pressure change or distur- bance. In sonic flow, a change in the downstream pressure (P d ) can- not be transmitted upstream because the velocity of the pressure dis- turbance (or pressure wave) travels at the speed of sound. If the flow velocity is greater than or equal to the speed of sound (e.g. sonic or supersonic flow), then any downstream pressure changes cannot trav- el upstream or affect the mass flow rate. For a fixed upstream pressure (P u ), as the downstream pressure (P d ) is gradually reduced, the flow rate will increase but can continue to do so only until the flow velocity reaches Mach 1 at the duct exit. At this point, the flow is said to be “choked” and further reduction in the 1 American Pharmaceutical Review Observation and Implications of Sonic Water Vapor Flow During Freeze-Drying Jim Searles, Ph.D. Eli Lilly and Company Global Parenteral Products Commercialization Technology Center Manufacturing Science and Technology Figure 1. Figure 1. Lyophilizer Diagram. Water vapor flows from the vials in the product chamber onto the condenser coils in the condenser chamber. Flow past the mushroom valve head requires two 90º turns.

LYOPHILIZATION downstream pressure will have no effect on the rate of mass flow. An extreme example of this is leakage from a 1 mm diameter hole in an air cylinder, which is at 1,000 psia and is leaking into a room that is at atmospheric pressure. Slight changes in the pressure of the room will not affect the flow rate because the flow is fully choked. For choked flow, the mass flow rate is determined only by the upstream pressure (P u ) and the size of the hole or flow duct. Speed of Sound Independent of Pressure Kinetic theory finds that the speed of sound in an ideal gas is defined by the following expression: (1) where ν S is the speed of sound, γ is the ratio of specific heats (C P /C V ) for the gas (1.3 for water vapor in the vicinity of 0ºC), and R , T , and M are the ideal gas constant, temperature, and molecular weight, respectively. Note that the speed of sound is independent of pressure and weakly dependent upon temperature. The speed of sound in water vapor at 0 ºC is approximately 400 m/s. Critical Pressure Ratio There is a critical upstream to downstream pressure ratio (K c = P u /P d ) at which the flow will become choked for a particular duct or orifice. For an orifice, K c depends only on the thermody- namic properties of the gas, but for ducts of finite length it will also depend on duct length and flow condi- tions. For water vapor flowing through an orifice, K c = 1.83 (for air or nitrogen K c = 1.89) [1]. Therefore if we assume that the hole in our leaky 1,000 psia air cylinder is a perfect orifice (the length of which causes negligible frictional losses), then air will leak from the cylinder at the same rate for all room pressures below 529 psia. Observed Production Run Problems In this section, we describe the results of two commercial-scale lyophilization runs. Run 1 was a full-scale lyophiliza- tion run for this product, and Run 2, carried out in a different lyophilizer (Lyo B), was a partial load of the same product. Tables 1 and 2 show a comparison of the lyophilizers and the cycle parameters, respectively. The product is a 3.5 mL fill in a 10 mL vial. The con- centration of solutes in the final formulated bulk was 5% w/v. All reported pressures are from capacitance manometers. The lyophiliz- ers inject nitrogen gas into the product chamber as required to main- tain the pressure in that chamber at setpoint. If the product chamber pressure is above setpoint, no nitrogen is injected. Run 1: Chamber Pressure Excursion Run 1 was the first lyophilization cycle run in a production-scale freeze-dryer in which the dryer was fully loaded with product vials. Figure 3 shows selected process data for this run. At the beginning of primary drying, the shelf temperature was ramped up to a setpoint of 30°C from -45°C. The product chamber pressure was maintained at the 100 mT setpoint for the first 1.7 hours of this ramp. Approximately 1.7 hours into the ramp, the product chamber pressure began to increase rapidly until it reached 150 mT (at an elapsed time of 2.3 hours). At this point, an interlock shut down the flow of heat transfer fluid (HTF) through the shelves. With flow of HTF interrupted, the heat supply for sublimation was largely elim- inated and product chamber pressure began to fall. Once it decreased to below 110 mT, the interlock was relieved and HTF flow resumed until the interlock was again triggered. The system cycled through this sequence 6 times over 4.5 hours. During this time, the condens- er pressure remained between 18 and 35 mT, and condenser temper- ature was –70 to –75°C (fluctuations in the condenser pressure result from fluctuations in the condenser temperature caused by liquid nitro- gen injections into the condenser coils). As the initial shelf temperature ramp progressed from 0 to 2.5 hours, the condenser pressure dropped continuously from 100 to 25 mT; however, the condenser temperature remained unchanged. This is evidence of decreasing nitro- gen gas injection into the product chamber to maintain the 100 mT setpoint, resulting in a decreasing nitrogen partial pressure in the condenser (the nitrogen will not condense on the condenser coils). This is also confirmation of the increasing rate of water vapor generation from the product during this time. The same sequence operated in reverse order from 5.5 to 9 hours. Once the sublimation rate had decreased to such a level that nitrogen injection was required to maintain the product chamber pressure at set- point, the sublimation rate continued to drop, the nitrogen injection rate continued to increase, and the condenser pressure increased as well due to the increasing mole frac- tion of nitrogen in the condenser. Manufacturing personnel verified that the mushroom valve was fully open during the run. No blockage by ice 2 American Pharmaceutical Review Figure 2. Figure 2. Straight Duct. Upstream and downstream gas pressures are Pu and Pd respectively, and Pu > Pd. Gas therefore flows from left to right (high to low pressure). At steady-state, conservation of mass calls for the mass flow rate to be constant through the length of the duct. Because gas is compressible and the pressure is decreasing from left to right, the velocity of the gas increases from left to right, with it reaching its maximum value at the duct exit. Table 1. Comparison of Lyophilizers Lyophilizer Lyo A Lyo B Connecting duct dimensions 0.57, 0.81 0.80, 1.22 (diameter, length)(m) Connecting duct nominal 0.26 0.50 cross-sectional area (m 2 ) Connecting duct valve Mushroom Butterfly (14 cm stroke) Gas flow obstructions None Connecting duct partially obstructed by thermal radiation shield Usable shelf area for product 20.1 m 2 22.3 m 2 Space capacity (product vials) 34,400 38,280 Maximum Supportable Sublimation Rate 15.8 kg hr -1 19.7 kg hr -1 at 100 mT (from water sublimation tests) 0.79 kg hr -1 • m -2 0.88 kg hr -1 • m -2

LYOPHILIZATION was visible. Since the condenser was maintaining temperature and there was such an extreme pressure difference between the condens- er and the chamber, the most likely cause of the pressure deviation was excessive vapor flow between the condenser and chamber. The subsequent sections address this point further. If the lyophilization cycle were to remain unchanged, runs using Lyo A would have to be limited to a partial load. Run 2: Chamber Pressure Near Failure Run 2 was carried out in Lyophilizer B, which has a larger diame- ter connecting duct. It can hold 38,280 vials of the product, but in this case was loaded with 25,500. Figure 3 shows selected primary dry- ing process data. Similar to Run 1 the condenser pressure decreased continuously during the initial primary drying shelf ramp to 30°C. The condenser pressure bottomed out at 37 mT at the completion of the ramp, and rose to 60 mT over the subsequent 2.5 hours. Once the shelf fluid inlet temperature reached 30°C the product chamber pres- sure exceeded 100 mT, climbing to a peak of 110 mT at an elapsed time of 4.3 hours. Shelf heat transfer fluid flow remained uninter- rupted because the product chamber pressure never reached the alarm point of 150 mT. At an elapsed time of 5.5 hours the product thermocouple data revealed that the first vials had begun to complete primary drying, pressure control was regained, and over the subsequent 2.8 hours the condenser pressure continuously increased as the fraction of water vapor decreased. Although the connecting duct in Lyo B is of a significantly larger diameter than that for Lyo A and we loaded fewer vials into Lyo B, we still experienced a slight pressure control problem. We subse- quently learned that the connecting duct contains a thermal radiation shield to block the vials line of sight to the condenser coils. The shield consisted of angled stainless-steel slats that partially restricted water vapor flow. Summarized Observations from Product Runs • During both runs, we experienced failures to maintain product chamber pressure at setpoint early in primary drying. Because the condenser pressure remained significantly lower than the product chamber pressure, the product chamber overpressure events were due to resistance to water vapor flow from the chamber to the con- denser. • Although the cross-sectional area of the connecting duct in Lyo B is twice that of Lyo A and we loaded fewer vials into Lyo B, we still failed to maintain product chamber at setpoint with Run 2. Investigation Strategy Given the above results, our objective was to determine the maximum number of vials of this product that we could run in these lyophilizers while maintaining the current cycle at its pressure setpoint. To this end, we pursued three parallel activities: I. Water sublimation tests in lyophilizers A and B to determine the maximum sublimation rate (kg hr -1 ) that each could support while maintaining a chamber pressure of 100 mT. II. Gas flow modeling of the lyophilizers to understand the mechanism limiting the achievable sublimation rate, and to confirm the results from the above sub- limation tests. III. Small-scale tests to measure the product sublimation rate at the beginning of pri- mary drying once the shelf has first reached 30°C, when it is expected to be at its maximum. The tests should take into account the significant position- dependent drying heterogeneity for large and small scale to estimate an effective per-vial product sublimation rate (kg hr -1 vial -1 ). The maximum number of vials for a lyophilizer could then be calculated as the maximum sublimation rate supportable (kg hr -1 ) divided by the effective per-vial sublimation rate (kg hr -1 vial -1 ). The per-vial sublimation rate testing will not be dis- cussed in this paper. Rather we will focus 3 American Pharmaceutical Review Table 2. Lyophilization Cycle Parameters Step Operating Parameters Hold Freezing Freeze to –45ºC at 30ºC/hr Hold 3 hours Primary Drying 30ºC shelf fluid inlet T Hold for at least 100 mT chamber pressure 22.5 hours, advance once all product thermocouples are 26°C or above Secondary Drying 50°C shelf fluid inlet T Hold for at least 100 mT chamber pressure 11.0 hours, advance once all product thermocouples are 46°C or above Figure 3. Figure 3. Results from Lots 1 and 2. The pressure and temperature fluctuations during Lot 1 are the result of shelf fluid stoppage in response to the chamber overpressure alarm at 1.3 hours. The chamber pressure during Lot 2 also exceeded the set point.

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LYOPHILIZATION here upon our finding that the capacity of this product in our lyophilizer was limited by water vapor flow from the chamber and condenser, and discuss items I and II: full-scale water sublimation tests and gas flow modeling. Water Sublimation Rate Tests The objective of the water sublimation rate tests was to measure the maximum sublimation rate (kg hr -1 ) that each lyophilizer could sup- port while maintaining a chamber pressure of 100 mT. The procedure is quite simple, and consists of two parts outlined in detail below. For an effective test, both the product and condenser chambers must have well-calibrated capacitance manometers installed. Procedure Shelf Temperature at which Failure Occurs 1. Load each shelf of the lyophilizer with tray ring(s) into which plas- tic film has been affixed (2-mil thick film works well). Do this with the shelves at room temperature because condensate on the shelves will cause the plastic film to adhere to the shelf during tray loading. Tape thermocouples to the upper shelf surface(s) if it will later be desired to calculate shelf heat transfer coefficients (a use- ful exercise). 2. Transfer water into each film-lined tray ring to a depth of approxi- mately 1-inch. Know the mass of water placed into each ring. This does not need to be done under aseptic conditions as particulate content will not affect the drying rate of a water-only system. 3. Freeze the water by cooling the shelves. Cool to below –40°C. 4. Initiate vacuum to the desired setpoint (the pressure for which you seek the maximum supportable sublimation rate). Wait for the pressure to stabilize at the setpoint. 5. Begin a continuous shelf temperature ramp at approximately 20°C hr -1 . 6. Monitor the product chamber pressure. Continue the shelf temper- ature ramp past the shelf temperature at which the product cham- ber pressure first exceeded setpoint, preferably to the maximum shelf temperature for which the unit is capable. 7. Stop the run, empty the lyophilizer, and prepare for the second part of the test (detailed below). It may be that the lyophilizer is able to maintain the pressure setpoint throughout the entire run. We have seen this in some of our units set at 200 mT up to 65°C shelf. If this is the case then you will want to perform the second part of the test below at a shelf T of 65°C. If the pressure started to depart from setpoint at, for example, +40°C, then the second part of the test should be conducted at 1-3°C below that shelf temperature (to account for thermal lag during the ramp). Maximum Supportable Sublimation Rate 1. Repeat steps 1-4 as described above. 2. Ramp the shelf temperature as fast as possible to 1-3°C below the temperature found in step 6 above, coincident with the initial loss of pressure control. 3. Hold for long enough to sublime only 10-20% of the water. We have used 6-10 hours successfully. Excessive drying will result in severe pitting of the ice sheet, and this will lead to erroneous results. 4. End the run and warm the ice sheet to just below freezing. 5. Weigh the contents of each tray ring (it is easier to unload and weigh ice sheets than liquid water- we break up the ice sheets and put the pieces into pre-tared plastic trash cans). Calculate the sub- limation rate for each shelf or tray ring using the elapsed time that the shelf temperature was at setpoint (do not include the time required for ramping to that temperature). The result is the maximum supportable sublimation rate. The sec- tions below will lend insight into the conditions leading to a choked flow diagnosis. Other possible causes are also discussed below. Results Figure 4 shows the sublimation rate tests for Lyo A. In panel A, we see that as the sublimation rate increased due to the increasing shelf temperature, the condenser pressure dropped as the controller for the nitrogen purge valve reduced the nitrogen gas flow rate. At an elapsed time of 7.4 hours, the condenser pressure reached a minimum value of 20 mT (the nitrogen purge valve was then fully closed) and the chamber pressure began to increase above the setpoint. This occurred once the shelf inlet fluid temperature reached +20°C. Note from Figure 4A that the system is fundamentally stable in that, as shelf temperature was increased above that which first induced choked flow, the chamber pressure increased. While we know that higher pressures increase the heat transfer coefficient from the top of the shelf to the product, this does not result in a runaway situation because a 10% higher chamber pressure also means that at choked flow, the connecting duct can accommodate a 10% higher mass flow rate. For the second test, shown in panel B of Figure 4, we chose to run at a shelf temperature of +19°C. We were pleased to find that we were just past failure, with the chamber pressure holding from 103- 104 mT. As expected, the condenser pressure was 20-30 mT through- out the test. In the early part of panels A and B, we see a quick burn- off of water from small spills, a transient event that resolved itself early enough to avoid interfering with the results. Overall results from these tests are shown in Table 1. The maximum supportable sublimation rates at 100 mT product chamber pressure are 15.8 and 19.7 kg hr -1 for lyophilizers 1 and 2, respectively. Gas Flow Modeling As part of our investigation we modeled the flow of water vapor from the product to condenser chambers. The following adiabatic flow equation was used [reference 2]: (2) where γ = ratio of specific heats for the gas/vapor (1.3 for water vapor in the vicinity of 0ºC) M n = Mach number of the flow at the duct entrance M x = Mach number of the flow at the duct exit f D = Darcy friction factor L = length of duct D = diameter of duct If the flow is choked then the equation is solved with Mx = 1. The throughput is related to the inlet Mach number by (3) where we write for convenience (4) where A = cross section area of duct T = initial temperature of gas/vapor M = molecular weight of gas/vapor (0.018 for water vapor) 4 American Pharmaceutical Review

LYOPHILIZATION Computational results were provided by Gordon Livesey of BOC Edwards Vacuum Systems, and are shown in Figures 5-7. As seen in Figure 5, as the modeled condenser pressure is reduced, flow of water vapor increases in a highly non-linear fashion. Note that a significant flow rate can be induced with a very small pressure difference. For many production lyophilization cycles, one may see a negligible pressure difference (often within the calibration limits of the sensors) even though there is gas flow. Examining the “Orifice” series in Figure 5A, one can see that, as the condenser pressure reaches approximately 0.06 Torr (60 mT), the flow becomes fully choked and further condenser pressure reductions do not result in increased flow. The data point named “Ice Test” rep- resents the ice sublimation test discussed above. Panel A shows that the number of bends is an important factor (0°C gas modeled). Modeling two bends gives a good fit to the data and is reasonable due to the presence of the mushroom valve (see two bends in gas flow in Figure 1). Also note that the complexity of the flow path (e.g. increased number of bends) has a profound impact upon the maxi- mum-attainable flow rate. Additional bends not only reduce the max- imum-achievable flow rate under choked conditions, but also reduce the flow rates for any given condenser pressure. Also note that sys- tems with more bends require a larger pressure difference to achieve choked flow. Panel B shows that the gas temperature does not have a large impact (2 bends modeled). Small-scale measurements of water vapor tem- perature in the connecting duct confirmed that 0°C, the value that fits this data the best, is indeed reasonable (data not shown). We modeled 100% water vapor, but under most operating condi- tions we are injecting N 2 gas to maintain chamber pressure at the desired setpoint. Therefore, we expect that at less-than-choked water vapor flows the results shown in Figure 5 will not be quantitatively accurate. Pure nitrogen flow rates (kg hr -1 ) are about 25% higher than those for water vapor under the same pumping conditions. Interesting is the fact that even when the flow has reached sonic conditions as it enters the condenser, the Reynolds number (Re) is only about 1,000. The transition from viscous laminar to turbulent flow begins at ~2,000 [2]. It will not be fully-developed, however, due to the small length to diameter ratio of the duct. Figure 6 shows the predicted maximum water vapor flow rate for Lyo A as a function of chamber pressure. The constraint imposed by choked flow is the velocity of sound, therefore because gas density is a linear function of pressure, the maximum mass flow rate increases linearly with pressure. In Figure 7, we present the predicted choked pressure ratios (cham- ber/condenser) for lyophilizer A for different duct configurations. “Orifice” is for a duct of zero length, and the predictions for different numbers of bends use the actual duct length. One cannot have choked flow if the ratio is less than that for a perfect orifice (1.83). For most lyophilizer duct configurations, a ratio of greater than 3 will confirm choked flow. The ratio for the product and water runs in Lyo A was greater than 4, so we are confident in our choked flow diagnosis. 5 American Pharmaceutical Review Figure 4. Figure 4. Water Sublimation Test Results for Lyophilizer A. Panel A: Inducing choked flow: the chamber pressure first departed from set- point when the shelf temperature reached 20°C. Panel B: Sublimation rate test at the incipient choke point (shelf T 20°C). Figure 5. Figure 5. Predicted Water Vapor Flow Rate (kg/hr) as a Function of Condenser Pressure (mTorr) for Lyophilizer A with the Product Chamber Held at 100 mT. The green square is the result from the water sublimation test. A: The number of bends is an important factor (0°C gas modeled). Two bends results in a good fit to the data and is reasonable due to the presence of the mushroom valve. The complexi- ty of the flow path (e.g. increased number of bends) has a profound impact upon the maximum-attainable flow rate and the condenser pressure required to achieve choked conditions. B: The gas tempera- ture does not have a large impact (2 bends modeled). Small-scale measurements of water vapor temperature in the connecting tube confirmed that 0°C, the value that fits this data the best, is indeed reasonable (data not shown).

LYOPHILIZATION However, a ratio between these values will require more detailed investigation. Note that while duct length has a minor effect (orifice vs. zero bends), the complexity of the flow path will have a profound impact (number of bends). This is important because a given lyophilizer will have its own characteristic pressure ratio for choked flow; however, this ratio will hold over a wide range of operating pressures. The situation for Lyo B was somewhat different because the con- necting duct contained a radiation shield. It was constructed of stain- less-steel slats that are angled to prevent a direct line-of-sight between vials loaded into the product chamber and the condenser coils (to reduce radiative cooling of the product). However, we found that the shield also served to dramatically restrict gas flow. Although the nominal cross-sectional area of the duct is twice that of Lyo A, it only supported 25% greater flow. Maximum Drying Rate Requires Low Pressures Chang and Fischer (1995) demonstrated that the maximum attain- able primary drying rate at a given product temperature is achieved with the lowest possible chamber pressure [3]. The reader is referred to Figure 8 for this discussion. A given product temperature implies a corresponding water vapor pressure of the ice interface. Therefore, the lower the chamber pressure, the greater the driving force for mass transfer of water vapor from the ice interface in the product to the chamber. This benefit is somewhat counteracted by the fact that, within the range of pressures used for lyophilization, lower pressures increase the resistance to heat transfer from the upper surface of the shelf to the vial. This phenomenon was first reported by Steven Nail in 1980 [4]. For this reason, a higher shelf temperature is required to attain a similar product temperature at lower chamber pressures. The lowest chamber pressure to be used at industrial scale will be limited by practical issues such as the maximum shelf temperature that one is willing to use, the effect of these conditions upon uniformity of dry- ing rate, and as discussed in this paper, how the product chamber pressure setpoint impacts equipment capability. During lyophilization cycle development, we should already know and be constrained by the primary drying collapse temperature of the product. In Figure 8, we have superimposed a line representing a notional maximum attainable drying rate due to choked flow. It is proportional to chamber pressure as discussed above. Therefore, while maximum sublimation rate for a given product temperature can be found at the lowest feasible operating pressure, use of lower pres- sure increases the risk of encountering equipment limitations imposed by choked flow. 6 American Pharmaceutical Review Figure 6. Figure 6. Predicted Maximum Water Vapor Flow Rate for Lyophilizer A as a Function of Chamber Pressure. The constraint imposed by choked flow is the velocity of sound, therefore because gas density is a linear function of pressure, the maximum mass flow rate increases linearly with pressure. Imposed upon Figure 2 is a similar relationship, convey- ing the concept that while maximum sublimation rate (for a given product temperature) can be found at the lowest feasible operating pressure, use of lower pressure increases the risk of encountering equipment limitations imposed by choked flow. Figure 7. Figure 7. Predicted Minimum Chamber/Condenser Choked Pressure Ratios for Different Duct Configurations (Water Vapor Flow). “Orifice” is for a duct of zero length, and the predictions for different numbers of bends use the actual duct length. All predictions use the actual duct diameter. Note that while duct length has a minor effect, the complex- ity of the flow path will have a profound impact, with more bends requiring a greater pressure ratio to achieve maximum flow conditions. Figure 8. Figure 8 from Chang and Fischer [3] given product temperature the highest sublimation rate is at the lowest possible chamber pressure. However, the maximum “choked flow” drying rate limit of a given lyophilizer decreases as a linear function of pressure. So while the highest per-vial productiviy can be found at the lowest pressures, we observe decreasing equipment capability at lower pressures as well.

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LYOPHILIZATION Conclusions and Recommendations This finding of sonic flows is new to the lyophilization literature. The phenomenon represents a fundamental limitation in lyophilizer drying rate capacity. The limitation posed by sonic, “choked” flow is a function of the cross-sectional area and aerodynamic properties of the gas flow path between the vials and the condenser coil surfaces. Choked flow can be diagnosed by the ratio of the product chamber to condenser pressures. One will not have choked flow if the ratio is less than that for a perfect orifice (1.83). For most lyophilizer duct configurations, a ratio of greater than 3 will confirm choked flow. However, a ratio between these values will require more detailed investigation. Our diagnosis of choked flow is based upon the fact that the prod- uct chamber to condenser pressure ratio was greater than 4, that our model predicted sonic velocities under our specific conditions, and that we were past the point at which we could maintain chamber pres- sure at the desired setpoint. The options to resolve a choked flow issue are: a) Reduce loading in the lyophilizer to reduce the overall sublimation (and therefore gas flow) rate b) Increase the pressure during primary drying to increase the maxi- mum sublimation rate that the lyophilizer can support (beware that product temperature will be increased unless the shelf temperature is not reduced as well) c) Reduce the sublimation rate by using a lower primary drying shelf temperature. These adjustments are much easier if one knows the relationship between drying rate, product temperature, shelf temperature, and chamber pressure as depicted in Figure 8. Lyophilizers should be specified, designed, and tested with specif- ic capabilities in mind. One of these capabilities should be the mini- mum required drying rate (kg hr -1 ) supportable by the system while maintaining a specific product chamber pressure. Users should con- duct drying rate tests at a range of operating pressures to learn if their lyophilizer meets design specifications and to know their true capac- ity. We should pay close attention to design of the flow path, includ- ing valves and radiation shields. Lyophilizers should have well calibrated capacitance manometers on both the product and condenser chambers. This will allow accu- rate measurement of the chamber to condenser pressure difference. Lyophilizer manufacturers and users should further pursue Process Analytical Technologies (PAT) that measure the current sublimation rate. Such technology will enable us to immediately ascertain the actual drying rate of our product (something nearly impossible to measure at large scale today). One cannot obtain an accurate drying rate by simply dividing the mass sublimed by the total primary dry- ing time because, as many have noted, the sublimation rate is not con- stant throughout primary drying. The maximum drying rate is usual- ly found at the beginning of primary drying once the shelf tempera- ture has reached setpoint. For business purposes, users should understand how much of their available drying rate capacity is being used. For example, if your lyophilizer is capable of drying at 20 kg hr -1 at the pressure setpoint, then you want to target lyophilization cycles that dry close to this maximum (with an appropriate safety factor). Acknowledgements Many thanks to R. Gordon Livesey of BOC Edwards for useful discussions and for carrying out the modeling calculations. His email address is Gordon.Livesey@bocedwards.com. References 1. F. White. Fluid Mechanics, McGraw-Hill, 1986. 2. R. Livesey. Flow of Gases Through Tubes and Orifices. In J. Lafferty (ed), Foundations of Vacuum Science and Technology, Wiley-Interscience, 1998. 3. B. S. Chang and N. L. Fischer. Development of an Efficient Single- Step Freeze-Drying Cycle for Protein Formulations. Pharmaceutical Research, 12:831-837 (1995). 4. S. Nail. The Effect of Chamber Pressure on Heat Transfer in the Freeze-Drying of Parenteral Solutions. J. Parenter. Drug Assoc., 34:358-68 (1980). 7 American Pharmaceutical Review Jim Searles is in the Global Parenteral Products group in Manufacturing Science and Technology at Eli Lilly and Company in Indianapolis, Indiana. He earned his Ph.D. in Chemical Engineering from the University of Colorado in 2000. His areas of expertise include lyophilization and technical trans- fer. Jim worked for Merck & Co., Vaccine Technology and Engineering from 1994-1998 and 2000-2002.