What is a leak and how to measure the leak rate in vacuum systems?

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Apart from the vacuum systems themselves and the individual components used in their construction (vacuum chambers, piping, valves, detachable [flange] connections, measurement instruments, etc.), there are large numbers of other systems and products found in industry and research which must meet stringent requirements in regard to leaks or creating a so-called “hermetic” seal. Among these are many assemblies and processes in the automotive and refrigeration industries in particular, but also in many other branches of industry. Working pressure in this case is often above ambient pressure. Here “hermetically sealed” is defined only as a relative “absence of leaks”. Generalized statements often made, such as “no detectable leaks” or “leak rate zero”, do not represent an adequate basis for acceptance testing. Every experienced engineer knows that properly formulated acceptance specifications will indicate a certain leak rate (see below) under defined conditions. Which leak rate is acceptable is also determined by the application itself.

Types of leaks

Differentiation is made among the following leaks, depending on the nature of the material or joining fault:

Leaks in detachable connections: Flanges, ground mating surfaces, covers
Leaks in permanent connections: Solder and welding seams, glued joints
Leaks due to porosity: particularly following mechanical deformation (bending!) or thermal processing of polycrystalline materials and cast components
Thermal leaks (reversible): opening up at extreme temperature loading (heat/cold), above all at solder joints
Apparent (virtual) leaks: quantities of gas will be liberated from hollows and cavities inside cast parts, blind holes and joints (also due to the evaporation of liquids)
Indirect leaks: leaking supply lines in vacuum systems or furnaces (water, compressed air, brine)
“Serial leaks”: this is the leak at the end of several “spaces connected in series”, e.g. a leak in the oil-filled section of the oil pan in a rotary vane pump
“One-way leaks”: these will allow gas to pass in one direction but are tight in the other direction (very seldom) An area which is not gas-tight but which is not leaky in the sense that a defect is present would be the
Permeation (naturally permeability) of gas through materials such as rubber hoses, elastomer seals, etc. (unless these parts have become brittle and thus “leaky”).

Calculating leak rate, leak size and mass flow

No vacuum device or system can ever be absolutely vacuum-tight and it does not actually need to be. The simple essential is that the leak rate be low enough that the required operating pressure, gas balance and ultimate pressure in the vacuum container are not influenced. It follows that the requirements in regard to the gas-tightness of an apparatus are the more stringent the lower the required pressure level is. In order to be able to register leaks quantitatively, the concept of the “leak rate” with the symbol Q_L was introduced; it is measured with mbar · l/s or cm³/s (STP) as the unit of measure. A leak rate of Q_L = 1 mbar · l/s is present when in an enclosed, evacuated vessel with a volume of 1 l the pressure rises by 1 mbar per second or, where there is positive pressure in the container, pressure drops by 1 mbar. The leak rate Q_L defined as a measure of leakiness is normally specified in the unit of measure mbar · l/s. With the assistance of the status equation (1.7) one can calculate Q_L when giving the temperature T and the type of gas M, registering this quantitatively as mass flow, e.g. in the g/s unit of measure. The appropriate relationship is then:

(1.7)

(5.1)

where R = 83.14 mbar · l/mol · K, T = temperature in K; M = molar mass in g/mole; Δm for the mass in g; Δt is the time period in seconds. Equation 5.1 is then used
a) to determine the mass flow Δm / Δt at a known pV gas flow of Δp · V/Δt (see in this context the page on the pressure rise test) or
b) to determine the pV leak gas flow where the mass flow is known (see the following example).
Example for case b) above:
A refrigeration system using Freon (R 12) exhibits refrigerant loss of 1 g of Freon per year (at 77°F or 25°C). How large is the leak gas flow Q_L? According to equation 5.1 for M(R12) = 121 g/mole:

Thus, the Freon loss comes to Q_L = 6.5 · 10^–6 mbar · l/s. According to the “rule of thumb” for high vacuum systems given below, the refrigeration system mentioned in this example may be deemed to be very tight. Additional conversions for Q_L are shown in Tables VIIa and VIIb in Chapter 9.

Table VIIa Conversion of throughput (Q_pv) units; (leak rate) units

Table VIIb Conversion of throughout (Q_pV) units: (leak rate) units

Total leak rate < 10^-6 mbar · l/s:  Equipment is very tight
Total leak rate 10^-5 mbar · l/s:  Equipment is sufficiently tight
Total leak rate > 10^-4 mbar · l/s:  Equipment is leaky

A leak can in fact be “overcome” by a pump of sufficient capacity because it is true that (for example at ultimate pressure p_end and disregarding the gas liberated from the interior surfaces):

(5.2)

(Q_L Leak rate, Seff the effective pumping speed at the pressure vessel)

Where Seff is sufficiently great it is possible – regardless of the value for the leak rate Q_L – always to achieve a pre-determined ultimate pressure of pend. In practice, however, an infinite increase of Seff will run up against economic and engineering limitations (such as the space required by the system).

Whenever it is not possible to achieve the desired ultimate pressure in an apparatus there are usually two causes which can be cited: The presence of leaks and/or gas being liberated from the container walls and sealants.
Partial pressure analysis using a mass spectrometer or the pressure rise method may be used to differentiate between these two causes. Since the pressure rise method will only prove the presence of a leak without indicating its location in the apparatus, it is advisable to use a helium leak detector with which leaks can, in general, also be located much more quickly.

In order to achieve an overview of the correlation between the geometric size of the hole and the associated leak rate it is possible to operate on the basis of the following, rough estimate: A circular hole 1 cm in diameter in the wall of a vacuum vessel is closed with a gate valve. Atmospheric pressure prevails outside, a vacuum inside. When the valve is suddenly opened all the air molecules in a cylinder 0.39 inches (1cm) in diameter and 1082ft (330m) high would within a 1-second period of time “fall into” the hole at the speed of sound (330 m/s). The quantity flowing into the vessel each second will be 10¹³ mbar times the cylinder volume (see Fig. 5.1). The result is that for a hole 1 cm in diameter Q_L (air) will be 2.6 · 10⁴ mbar · l/s. If all other conditions are kept identical and helium is allowed to flow into the hole at its speed of sound of 970 m/s, then in analogous fashion the Q_L (helium) will come to 7.7 · 10⁺⁴ mbar · l/s, or a pV leaking gas current which is larger by a factor of 970 / 330 = 2.94. This greater “sensitivity” for helium is used in leak detection practice and has resulted in the development and mass production of highly sensitive helium-based leak detectors (see page on leak detectors with mass spectrometers).

Fig 5.1 Correlation between leak rate and hole size

Shown in Figure 5.1 is the correlation between the leak rate and hole size for air, with the approximation value of Q_L(air) of 10_⁺⁴ mbar · l/s for the “1 cm hole”. The table shows that when the hole diameter is reduced to 1 μm (= 0.001 mm) the leak rate will come to 10^-4 mbar · l/s, a value which in vacuum technology already represents a major leak (see the rule of thumb above). A leak rate of 10^-12 mbar · l/s corresponds to hole diameter of 1 Å; this is the lower detection limit for modern helium leak detectors. Since the grid constants for many solids amount to several Å and the diameter of smaller molecules and atoms (H₂, He) are about 1 Å, inherent permeation by solids can be registered metrologically using helium leak detectors. This has led to the development of calibrated reference leaks with very small leak rates (see page on calibrating leak detectors). This is a measurable “lack of tightness” but not a “leak” in the sense of being a defect in the material or joint. Estimates or measurements of the sizes of atoms, molecules, viruses, bacteria, etc. have often given rise to everyday terms such as “watertight” or “bacteria-tight”; see Table 5.1.

Compiled in Figure 5.2 are the nature and detection limits of frequently used leak detection methods.

Table 5.1 Estimating borderline leak rates. As opposed to vapor, it is necessary to differentiate between hydrophilic and hydrophobic solids. This also applies to bacteria and viruses since they are transported primarily in solutions.

Fig 5.2 Leak rate ranges for various leak detection processes and devices

The standard helium leak rate

Required for unequivocal definition of a leak are, first, specifications for the pressures prevailing on either side of the partition and, secondly, the nature of the medium passing through that partition (viscosity) or its molar mass. The designation “helium standard leak” (He Std) has become customary to designate a situation frequently found in practice, where testing is carried out using helium at 1 bar differential between (external) atmospheric pressure and the vacuum inside a system (internal, p < 1 mbar), the designation “helium standard leak rate” has become customary. In order to indicate the rejection rate for a test using helium under standard helium conditions it is necessary first to convert the real conditions of use to helium standard conditions (see the section on conversion equations below). Some examples of such conversions are shown in Figure 5.3.

Fig 5.3 Examples for conversion into helium standard leak rates

Conversion equations

When calculating pressure relationships and types of gas (viscosity) it is necessary to keep in mind that different equations are applicable to laminar and molecular flow; the boundary between these areas is very difficult to ascertain. As a guideline one may assume that laminar flow is present at leak rates where Q_L > 10^-5 mbar · l/s and molecular flow at leak rates where Q_L < 10_^-7 mbar · l/s. In the intermediate range the manufacturer (who is liable under the guarantee terms) must assume values on the safe side. The equations are listed in Table 5.2.
Here indices “I” and “II” refer to the one or the other pressure ratio and indices “1” and “2” reference the inside and outside of the leak point, respectively.

Table 5.2 Conversion formulae for changes of pressure and gas type

Terms and definitions

When searching for leaks one will generally have to distinguish between two tasks:

Locating leaks and
Measuring the leak rate.
In addition, we distinguish, based on the direction of flow for the fluid, between the

a. vacuum method (sometimes known as an “outside-in leak”), where the direction of flow is into the test specimen (pressure inside the specimen being less than ambient pressure), and the
b. positive pressure method (often referred to as the “inside-out leak”), where the fluid passes from inside the test specimen outward (pressure inside the specimen being greater than ambient pressure).

The specimens should wherever possible be examined in a configuration corresponding to their later application – components for vacuum applications using the vacuum method and using the positive pressure method for parts which will be pressurized on the inside. When measuring leak rates we differentiate between registering
a. individual leaks (local measurement) – sketches b and d in Figure 5.4, and registering
b. the total of all leaks in the test specimen (integral measurement) – sketches a and c in Figure 5.4.

Fig 5.4Leak test techniques and terminology.

a: Integral leak detection; vacuum inside specimen
b: Local leak detection; vacuum inside specimen
c: Integral leak detection (test gas enrichment inside the enclosure); pressurized test gas inside specimen
d: Local leak detection; pressurized test gas inside the specimen

The leak rate which is no longer tolerable in accordance with the acceptance specifications is known as the rejection rate. Its calculation is based on the condition that the test specimen may not fail during its planned utilization period due to faults caused by leaks, and this to a certain degree of certainty. Often it is not the leak rate for the test specimen under normal operating conditions which is determined, but rather the throughput rate of a test gas – primarily helium – under test conditions. The values thus found will have to be converted to correspond to the actual application situation in regard to the pressures inside and outside the test specimen and the type of gas (or liquid) being handled.

Where a vacuum is present inside the test specimen (p < 1 mbar), atmospheric pressure outside, and helium is used at the test gas, one refers to standard helium conditions. Standard helium conditions are always present during helium leak detection for a high vacuum system when the system is connected to a leak detector and is sprayed with helium (spray technique). If the specimen is evacuated solely by the leak detector, then one would say that the leak detector is operating in the direct-flow mode. If the specimen is itself a complete vacuum system with its own vacuum pump and if the leak detector is operated in parallel to the system’s pumps, then one refers to partial-flow mode. One also refers to partial stream mode when a separate auxiliary pump is used parallel to the leak detector.

When using the positive pressure method, it is sometimes either impractical or in fact impossible to measure the leakage rate directly while it could certainly be sensed in an envelope which encloses the test specimen. The measurement can be made by connecting that envelope to the leak detector or by accumulation (increasing the concentration) of the test gas inside the envelope. The “bombing test” is a special version of the accumulation test (see the page on Integral and Industrial testing). In the so-called sniffer technique, another variation of the of the positive pressure technique, the (test) gas issuing from leaks is collected (extracted) by a special apparatus and fed to the leak detector. This procedure can be carried out using either helium or refrigerants or SF₆ as the test gas.

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