Tech Brief: An Explanation of Leak Rate
By: Charles D. Dern, P.E.
Introduction
Personnel involved with freeze-drying technology must deal with evacuated vesls and the testing and criteria that assure that a vesl is free of significant leaks. Traditionally, industries that are involved with vesls subjected to evacuation have measured the relative “tightness” of the vesls by one of two criteria: “rate of ri” or “leak rate.” At first glance, it may appear that the are simply two different terms for the same thing. However, a clor look reveals that this is not the ca.
Basic Definitions
Rate of ri is the amount of pressure change in an evacuated vesl over a given period. (i.e. millitorr per minute, mbar per cond, etc.) For example, if one evacuates a vesl to 100 mTorr, clos the vacuum valve, and then obrves that after one minute, the pressure is 105 mTorr, then the rate of ri is quite simply 5 mTorr per minute. Mathematically the formula is:
Rate of Ri = Finish Pressure - Start Pressure
Elapd Time
Rates of ri can be performed at any pressure below the local ambient pressure and can be done for any length of time. The best pressure at which to test is at the expected working pressure of the vesl. Also, in most cas, the longer the elapd time, the more assurance one will have of obtaining an accurate result.
However, rates of ri, no matter how carefully done, are not an accurate basis for comparing tightness among vesls of various sizes. This is becau rate of ri does not account for the volumes of the vesls in question. If a 10 ft3 vesl and a 100 ft3 vesl have the same rate of ri,
a greater amount of gas must leak into the 100 ft3 vesl to rai the pressure the same amount. (In fact, ten times as much.) To do an accurate comparison therefore, one must account for the respective volumes of the vesls. This is accomplished by a “leak rate.” Obtaining a leak rate involves multiplying “rate of ri” by the system volume. Thus, if a rate of ri is expresd in millitorr per minute (mTorr/min.), then a leak rate is expresd as millitorr x cubic feet per minute (mTorr-ft3/min.) The general formula is:
Leak Rate = (Finish Pressure-Start Pressure) x Volume
Elapd Time
OR
Leak Rate = Rate of Ri x Volume
Example: Assume that vesls of 10 ft3 and 100 ft3 are both evacuated to 100 millitorrs and are maintained at a constant temperature. At this pressure, the 10 ft3 vesl will contain .00132 standard cubic feet (SCF) of gas and the 100 ft3 vesl will contain .0132 SCF of gas. Assume further that each vesl has an identical leak that allows .001 SCF of gas in one minute into each vesl. At the end of one minute, the 10 ft3 vesl would contain .00232 SCF of gas and be a pressure of 176 mTorr for a rate of ri of 76
mTorr/min. The 100 ft3 vesl will contain .0142 SCF of gas and be at a pressure of 107.6 mTorr for a rate of ri of 7.6 mTorr/min. Both chambers have the same leak yet the smaller chamber has the greater rate of ri.
However if the rates of ri are multiplied by the respective chamber volumes one obtains:
10 ft3 x 76 mTorr/min. = 760 mTorr-ft3/min.
and
100 ft3 x 7.6 mTorr/min. =760 mTorr-ft3/min.
The vesls have identical leak rates!
It is important to visualize that even though the 100 ft3 vesl has ten times the evacuated volume of the 10 ft3 vesl, as long as the vesls are at the same pressure and have identical leaks, virtually the same amount of gas will enter into each vesl. This is becau the orifice of each leak “es” approximately the same suction. Furthermore at very low pressures, flow velocity through any small leak path likely will be “choked,” that is, limited by the speed of sound at the conditions in the leak path.
Industry Standards
The Parenteral Society Technical Monograph No.7, Leak Testing of Freeze Dryers notes that a frequently specified Leak Rate for new, clean, dry and empty freeze dryers is 2 x 10-2 mbar-liters/cond (31.8 mTorr-ft3/min).i However, practices in industry for freeze dryers in u vary widely even to the point of accepting equivalent leak rates 50 times less stringent than the Parenteral Society Monograph suggests.
Influencing Factors
The above considerations also lead to the important obrvation that the starting pressure of either rates of ri or of leak rates must be specified. At high vacuum, there is a greater suction through a leak than at low vacuum. Therefore, one should expect lower leak rates and rates of ri at lesr vacuums (higher pressures) and higher leak rates and rates of ri at higher vacuums (lower pressures). In fact, one can obtain a rate of ri or leak rate of "0" with any chamber at atmospheric pressure!
A major concern for tho measuring rates of ri or leak rates is the prence of what are called "virtual leaks.” As the name implies, virtual leaks are not real or actual leaks caud by a breach in the vesl's walls or als. Materials or pockets contained within the vesl can cau a greater rate of ri or leak rate than
through outgassing would otherwi be obtained. Thus, one may be led to believe that there is a defect in the vesl's physical structure when in fact there is not.
One cau of virtual leaks is humidity and/or fluids within the vesl. If the vesl to be tested is not clean, dry and empty, pressure increas caud by the vaporizing of water and/or solvents contained within the vesl can occur. As the fluids vaporize, the pressure within the vesl increas at least in part due to the vaporization and not due to any real problem with the containment components. The out-gassing of volatiles from polymers and/or other substances can also have a similar effect.
A third type of virtual leak occurs when air (or other gas) is trapped in an annular space that has no opening to the outside of the vesl and a pinhole (i.e. very small) opening to the inside (e.g. a cavity within a weld). While the main vesl evacuates rather quickly, the gas trapped in the annular space evacuates much more slowly. Thus, while the vesl will appear to have been evacuated to the desired pressure, there will remain gas that is trapped in the annular space. When a leak rate or rate of ri measurement is attempted, a fal reading will occur due to the gradual leakage of the gas from the annular space into the main vesl.
One indication of virtual leak is a decrea in the rate of ri. As shown on the graph below, when a virtual leak is prent, the rate of ri will taper off as time progress. In the ca of outgassing, the rate at which vapor is emitted from the out-gassing substance slows and eventually stops as the pressure within the vesl becomes greater than vapor pressure of the substance. In the ca where there is gas trapped in an annular space, the rate of ri will slow as the pressure of the gas equalizes with the pressure of the main vesl.
Elasped Time
One possible remedy to the problems is to evacuate the vesl for an extended length of time. This will allow some vapors to be driven off outgassing substances and/or time for gas to evacuate from annular spaces. However, only trial and error experimentation can determine if virtual leaks are prent.
Pressure increas due to virtual leaks can be reduced by ensuring that substances with vapor pressures lower than that of the operating conditions are ud and/or by ensuring that the vesl is constructed without voids.
Vesls that contain refrigeration coils and/or other components which can become very cold can compensate for the above problems. If a surface within the evacuated vesl can be made cold eno
ugh such that out-gassing volatiles or gas from a void will conden onto the surface, then the effect of the virtual leak can be reduced if not completely abrogated. Most important, one must be consistent by always using refrigeration at the same temperature (becau different temperatures will conden different amounts of gas) or by never using refrigeration. Furthermore, it is inaccurate to compare the leak rate of a vesl performed without refrigeration to the leak rate of similar vesl performed with refrigeration.
The Parenteral Society Monograph recommends that freeze-dryer condenrs be kept at -40°C or colder to protect the vacuum pumps. Common practice in the United States is to keep the shelves at or below ambient (=<20°C) while allowing condensing plates to attain their minimum temperature (about -70°C for two-stage systems using refrigerant R507). Again, as long as conditions are maintained consistently from test to test, the conditions will yield validatable results.
Finally, specifying leak rates or rates of ri at pressures well below that of the system's normal operational parameters is unnecessary and potentially costly for veral reasons. Components that satisfactorily contain vacuum at the operating condition can fail at the test condition. In addition, volatiles in substances that do not outgas at the operating condition may do so under the test conditions. As such, a large amount of time, money and effort can be wasted attempting to solve a “
problem” which does not exist at actual operating conditions.
Conclusion
In summary, rates of ri cannot be ud to compare performance of vesls of differing sizes; a leak rate must be specified. Second, when comparing leak rates (or rates of ri between vesls of equal volume), the starting pressures must be approximately equal. Third, whether using leak rates or rates of ri, consideration must be given as to how long the vesl is evacuated and the possible prence of virtual leaks. Last, refrigeration can be ud, but must be ud consistently to yield realistic comparisons and cannot be ud to compare results against data obtained without the u of refrigeration. Of cour, any leak rate done with refrigeration should have the cold trap temperature specified.
If you have further questions regarding leak rate testing, vacuum technology or freeze drying, plea contact the SP Industries sales department at 1-800-523-2327.
Charles D. Dern is a Project Engineer for SP Industries.
Common Units of Leak Rate
International:
millibar-liter per cond (mbar-l/c)
United States:
milliTorr-cubic foot per minute (mTorr-ft3/min.)
Some Uful Conversion Factors
1 mbar-l/c = 1592.97 mTorr-ft3/min.
1 standard atmosphere = 760 torr
= 760 mm Hg
= 29.92 in Hg
mbar
=1010
= 14.7 psia
1 torr = 1 mm Hg
= 1000 millitorrs
= 1.33 millibars
= 133.3 Pascals (N/m2)
1 cubic foot = 28.3
2 liters
i The Parenteral Society, Technical Monograph No.7: Leak Testing of Freeze Dryers, (Wilshire, England: The Parenteral Society, 1995), 9.
