constituents within a volume is called A leak testing tracer gas with low
diffusion. Under fixed conditions, it is diffusivity provides an advantage in
found that lighter gases diffuse more detector probe leak detection techniques
rapidly than the heavier gases. Graham’s because the concentration of the tracer
law of diffusion states, The rates of gas builds up at the leak exit. This allows
diffusion of different gases are inversely detection by a probe to locate the site of a
proportional to their individual molecular leak. With low diffusivity, the tracer gas
masses. Graham’s law can be written does not leave the leak location rapidly.
mathematically in the form of Eq. 12:
A tracer gas of high diffusivity is
(12) D1 = M1 needed for internal pressurization where it
D2 M2 is necessary to fill cul-de-sacs or blind
passageways within a reasonable soak
where D1 and D2 are the rates of diffusion time before testing. A low diffusion rate
of gases 1 and 2 and where M1 and M2 are would not allow a tracer gas to traverse a
the respective molecular masses of these tortuous leak passage, thus making leak
two different gases. detection by tracer gas an unreliable
procedure. Table 2 lists the diffusivities of
typical tracer gases in air at standard
TABLE 2. Diffusivities of tracer gases in air at standard temperature of 0 °C (32 °F) and
standard pressure of 100 kPa (760 torr). (Diffusion coefficient values are calculated from
an empirical equation, after Slattery.2)
Molecular Difffusion
Mass Coefficient
Gas Formula (g·mol–1) mm2·s–1 (ft2·h–1)
Acetylene C2H2 26.0 14.2 (0.55)
Ammonia NH3 17.0 17.0 (0.66)
Argon Ar 39.9 14.7 (0.61)
Benzene 78.1 (0.30)
Butane C6H6 58.1 7.7 (0.33)
Carbon dioxide C4H10 44.0 8.5 (0.52)
Carbon disulfide CO2 76.1 13.4 (0.36)
Carbon monoxide CS2 28.0 9.3 (0.67)
Carbon tetrachloride CO 154.0 17.3 (0.28)
Dichloromethane 84.93 7.2 (0.29)
Ethane CCl4 30.1 7.4 (0.49)
Ethyl alcohol CH2Cl2 46.1 12.6 (0.38)
Ethylene C2H6 28.0 9.8 (0.52)
Refrigerant–11 C2H5OH 137.0 13.4 (0.30)
Refrigerant–12 C2H4 121.0 7.7 (0.32)
Refrigerant–21 CCl3F 103.0 8.3 (0.33)
Refrigerant–22 CCl2F2 86.5 8.5 (0.37)
Refrigerant–112 CHCl2F 204.0 9.5 (0.25)
Refrigerant–114 CHClF2 171.0 6.5 (0.28)
Refrigerant-134a CCl2F–CCl2F 102.0 7.2 (0.28)
Helium CClF2–CClF2 7.2 (2.70)
Hydrogen C2H2F4 4.0 69.7 (2.60)
Hydrogen sulfide He 2.0 67.1 (0.53)
Krypton 24.1 13.7 (0.51)
Methane H2 83.8 13.2 (0.72)
Neon H2S 16.0 18.6 (1.10)
Nitric oxide Kr 20.2 28.4 (0.70)
Nitrogen 30.0 18.1 (0.68)
Nitrous oxide CH4 28.0 17.5 (0.52)
Oxygen Ne 44.0 13.4 (0.68)
Propane 32.0 17.5 (0.39)
Sulfur dioxide NO 44.1 10.0 (0.42)
Sulfur hexafluoride 64.1 10.8 (0.28)
Water N2 146.0 7.3 (0.85)
Xenon N2O 18.0 21.9 (0.42)
O2 131.0 10.8
C3H8
SO2
SF6
H2O
Xe
38 Leak Testing
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conditions of 100 kPa (1 atm) pressure collide elastically with each other and
and a temperature of 0 °C (32 °F). The with the walls of their container.
diffusion coefficient values in Table 2 are 4. In any collection of gas molecules,
calculated and converted from an individual molecules have different
empirical equation.2 speeds. However, their average speed
(including many molecules over a
Brownian Motion of Gases significant period of time) is
dependent on the absolute
One aspect of gaseous behavior that gives temperature (kelvin or rankine
the strongest clue to the nature of gases is degrees). The higher the gas
the phenomenon known as Brownian temperature, the higher the average
motion. This motion, first observed by the molecular speed.
Scottish botanist Robert Brown in 1827, is
the irregular motion of extremely minute Kinetic Theory Explanations of
particles suspended in a fluid. Brownian Gaseous Pressure, Volume and
motion can be observed by focusing a Temperature
microscope on a particle of illuminated
cigarette smoke in a glass tube. The The kinetic theory of gases postulates that
particle does not settle to the bottom of a gas consists mostly of empty space in
the container but continues to move which billions of tiny points representing
randomly in all directions. The smaller molecules are moving randomly. The
the suspended particle under observation, molecular particles collide with each other
the higher the temperature of the fluid, and with the walls of the container. The
the more vigorous is the particle’s volume of a gas sample is the volume of
movement. The existence of Brownian its container. Pressure is exerted by gases
motion suggests that the molecules of because the molecules collide with the
gaseous matter are constantly moving. A walls of the container. Each collision
visible small particle seems to be jostled produces a tiny push or impulse as the
by its neighboring invisible particles. The molecule rebounds from the wall. The
motion of the visible smoke particle thus sum of all of these molecular pushes or
indirectly reflects the motions of the force impulses of impact constitute the
smaller invisible particles of matter. This pressure of the gas on its containment
provides powerful support for the idea walls. The temperature of a gas is a
that gaseous or fluid matter consists of measure of the average speed or kinetic
extremely small particles or molecules in energy of the particles.
constant motion. The theory of moving
molecules of gases is the kinetic molecular Kinetic Theory Explanations of the
theory of matter. Its basic postulates are Gas Laws
these.
The kinetic molecular theory of gases can
1. The molecules of gaseous matter are in be used to explain the observed behavior
motion. of gases as described by the gas laws.
2. Heat causes this molecular motion. Boyle’s Law. The pressure exerted by a gas
at a given temperature depends only on
The kinetic theory of gases can be used to the number of impacts of gas molecules
explain many of the properties and with the walls of the container. If the
characteristics of tracer gases used in leak volume is reduced as sketched in Fig. 4,
testing.
FIGURE 4. Example of Boyle’s law. Doubling of gas pressure
Assumptions Underlying concentrates gas molecules and doubles number of
the Kinetic Theory of Ideal molecular impacts per unit area on chamber walls and piston
Gases in given time period.
The kinetic theory of gases applies only to Force = F Force = 2F
ideal or perfect gases that behave in
accordance with the following Volume = 1 m3 Volume = 0.5 m3
assumptions.
1. Gases consist of tiny molecules so
small and so far apart that the actual
volume of the gas molecules is
negligible compared to the empty
space between them.
2. There are no attractive forces between
gaseous molecules.
3. The molecules of gases travel in
random straight-line motion and
Tracer Gases in Leak Testing 39
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the molecules are more confined. This constituents present (see Fig. 6.)
increases the frequency of molecular Therefore, the partial pressure of a gaseous
collisions with the walls. These more constituent in a gas mixture is not
numerous impacts are observed as a changed by the presence of other gases in
greater pressure. the container. The total pressure exerted
on the walls of the container (or on the
Charles’ Law. If the temperature of a gas diaphragm of a pressure measuring gage)
rises, the average molecular energy and so is equal to the sum of the partial pressures
the average speed of the gas molecules exerted by the individual constituents of
rises. As the molecules move more the gaseous mixture.
energetically, they collide with the walls
of the container more frequently and with Determining
greater momenta, thus producing greater Concentration of Tracer
pressure. (Force is equal to the time rate of Gas in Gas Mixtures from
change of momentum and pressure is the Partial Pressures
force per unit area.) As shown in Fig. 5, if
the temperature is raised, the balloon In many leakage measurements, it is
responds to the increased pressure by desirable or necessary to dilute the tracer
stretching and expanding its diameter. gas being used for leak testing. Use of
diluted tracer gas might be dictated by
Dalton’s Law. According to the kinetic practical considerations such as:
theory of ideal gases, there are no
attractive forces between the molecules of 1. high expense of pure tracer gas filling
gases. On the average, the molecules of large volumes or attaining high
each constituent of a gaseous mixture will pressures;
strike the walls of their container the
same number of times per second and 2. attainment of a more nearly linear or
strike with the same impact forces as they more stable instrument response at a
would if there were no other gases lower concentration of tracer gas;
FIGURE 5. Example of Charles’ law. Raising 3. pure tracer gas providing a much
gas temperature increases molecular higher leakage sensitivity than needed;
velocities and increases gas pressure on
container wall. Under constant atmospheric 4. danger of fire or explosion with a
pressure, impacts by higher velocity flammable tracer gas (in some cases, a
molecules cause increase in gas volume dilute gas mixture lowers the danger
within elastic balloon. of explosions); and
Heated 5. inability to completely evacuate the
balloon test object or test system before filling
with tracer gas. As a result, residual gas
Cooled dilutes the tracer gas added during
balloon pressurizing.
Concentration of the tracer gas in a
test system containing mixed gases
depends on the partial pressure of the
tracer gas. Dalton’s law (Eq. 4) shows the
contributions of each gaseous constituent
to the total gas pressure. The fractional
concentration of the tracer gas T is given
by the term NT in Eq. 13:
FIGURE 6. Example of Dalton’s law: (a) oxygen; (b) nitrogen; (c) nitrogen and oxygen
combined. Partial pressure of each gaseous constituent is not changed by presence of other
gases in the same container. Pressure is exerted on container walls by impacts of individual
molecules of all gas species.
(a) (b) N2 (c)
O2 P=5 N2 and O2
P=7 P = 12
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(13) NT = PT that in the atmosphere at sea level.
P total
Helium is present in the earth’s
= PT atmosphere in the proportion of 5 µL·L–1.
P1 + P2 + P3 + … + Pn With mass spectrometer types of helium
leak detectors, even this small proportion
of helium can be readily sensed.
This fractional concentration is given Mean Free Paths of Gas
by Eq. 13 in terms of the number of Molecules
molecules of tracer gas as a fractional part
of the total number of molecules in a The mean free path is the average
gaseous mixture. The percentage distance a gas molecule travels between
concentration by mass would depend also successive collisions with other molecules
on the molecular masses of each gaseous in the gas or vapor state. The mean free
constituent. The partial pressure PT of path is important in leak testing because
tracer gas required to provide a specific it determines the type of gas flow that will
percentage of tracer gas molecules, occur through leaks or other passageways
percent T, is given in terms of total traversed by tracer or pressurizing gases.
system pressure Ptotal by Eq. 14: The mean free path can be calculated
from the pressure, temperature and
(14) P T = %T × Ptotal molecular properties by means of Eq. 15:
100
Partial Pressures of Gaseous (15) λ = 116.4 n T
Constituents of Earth’s P M
Atmosphere
where λ is mean free path (meter) under
The composition of atmospheric air is static pressure; n is gas viscosity (pascal-
78 percent nitrogen, 21 percent oxygen, second); P is absolute pressure of gas
0.9 percent argon and about 0.1 percent (pascal); T is absolute gas temperature,
of other gases and vapors (including water (kelvin); and M is molecular mass of gas,
vapor, whose concentration varies with (g-mol–1).
the temperature and relative humidity of
the atmosphere). The partial pressures of Table 4 lists the mean free paths of
atmospheric constituents at sea level, common gases at 20 °C (68 °F) and
where the total pressure of 100 kPa 1.0 mPa (7.6 µtorr).
(1 atm) is equal to that of 760 torr, are
given in Table 3. Simple Approximation Formula
for Mean Free Path of Common
The partial pressure in kilopascal is Gases
about the same as the percentage of each
constituent gas, at standard atmospheric An easily remembered relation for
pressure. The partial pressures of approximating the mean free paths of
atmospheric constituents at an altitude of common gaseous molecules is presented
3600 m (12 000 ft), where the total in Eq. 16:
pressure is equal to 64.4 kPa (9.3 lbf·in.–2
absolute), are given in Table 2. (16) λ = NF
P
The percentage composition of
atmospheric air changes very little until where λ is mean free path length (meter),
very high altitudes are reached. When test P is gas pressure in pascal and NF is a
systems are pressurized with air pumped numerical factor (meter-pascal) given in
from the atmosphere, the percentage Table 5. An NF value of 6.8 × 10–3 permits
composition is also not changed from
TABLE 3. Partial pressures of atmospheric constituents at sea level, 100 kPa (1 atm).
kPa at (torr at kPa at (torr at
Gas Percent sea levela sea level)a 3.6 km 12 000 ft)b
Oxygen (O2) 21.0 21.28 (159.6) 13.52 (101.4)
Nitrogen (N2) 78.0 79.03 (592.8) 50.22 (376.65)
Argon (Ar)
Other 0.9 0.91 (6.84) 0.58 (4.35)
Total air 0.1 0.10 (0.76) 0.06 (0.45)
100.0 101.325 (760.00) 64.4 (483.0)
a. Atmospheric pressure at sea level = 101.325 kPa (1 atm).
b. Percentage × atmospheric pressure of 64.4 kPa.
Tracer Gases in Leak Testing 41
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TABLE 4. Mean free path lengths of Relation of Mean Free Path
various atmospheric gases at 20 °C Lengths to Viscosity and
(68 °F) and at absolute pressure of Molecular Mass of Gas
1.0 mPa (7.6 µtorr).
The ratio of mean free path lengths for
__M__e_a_n__F_r_e_e__P_a_t_h___ two different gases at the same
Gas m (in.) temperature and pressure are given by
Eq. 17:
Air 6.8 (268) (17) λ1 = n1 M2
Argon (Ar) 7.2 (284) λ2 n2 M1
Carbon dioxide (CO2) 4.5 (177)
Hydrogen (H2) 12.5 (492) In Eq. 17, n indicates the gas viscosity
Water (H2O) 4.2 (165) and M indicates its molecular mass. The
Helium (He) 19.6 (771) subscript 1 indicates the first gas and
Nitrogen (N2) 6.7 (264) subscript 2 indicates the second gas. (This
Neon (Ne) 14.0 (551) relationship is derived from Eq. 15 when
Oxygen (O2) 7.2 (284) T and P are held constant.) For a leak or
an orifice across which there is a sizable
use of Eq. 16 for estimating the mean free pressure differential, the mean free path
path lengths for air, argon, nitrogen and length within the orifice is typically
oxygen molecules. Table 5 lists the estimated from the average pressure in the
numerical factors used in the numerator orifice (the mean value of inlet and outlet
of Eq. 16 for several other common gases. pressures).
However, it is seldom necessary to know
mean free path lengths to precisions Effective Viscosity of Mixtures of
better than one order of magnitude. For Gases
example, the molecular mean free path at
20 °C (68 °F) at atmospheric pressure is of In a mixture of various species of gases,
the order of 30 to 300 nm. At a pressure the effective viscosity nmixture is assumed
of 1 Pa (1.5 × 10–4 lbf·in.–2), the mean free to be proportional to the sum of the
path is in the range from 3 to 30 mm products of viscosity and concentrations
(0.12 to 1.2 in.). for each individual gaseous constituent, as
indicated by Eq. 18:
TABLE 5. Physical properties of common gases used in leak testing.
Numerical Diffusivityd
in Air at
Densitya Factorb for Dynamic Thermal
0 °C (32 °F) Conductivitye
Molecular at Mean Free Viscosityc and 101 kPa
at 20 °C (68 °F)
Mass 100 kPa Path at 20 °C (68 °F) (m2·s–1) (W·m–1·K–1)
Gas Formula (g·mol–1) (g·L–1) (m·Pa) (µPa·s)
Airf Mixture 29.0 1.21 6.8 × 10–3 18 13.9 × 10–6 26.2
Argon 40 1.79 7.2 × 10–3 22 15.8 × 10–6 17.9
Carbon dioxide Ar 44 1.97 4.5 × 10–3 15 16.0
Refrigerant-12 121 5.25 13 63.4 × 10–6
Helium CO2 0.179 19.6 × 10–3 19 9.8
Hydrogen CCl2F2 4.0 0.090 12.5 × 10–3 17.8 × 10–6 149.0
Krypton He 2.0 3.74 9 23.9 × 10–6 183.0
Neon 84 0.90 5.36 × 10–6 25
Nitrogen H2 20 1.25 14.0 × 10–3 31 9.4
Oxygen Kr 28 1.43 18 48.0
Sulfur hexafluoride 32 6.60 6.7 × 10–3 20 25.6
Water Vaporg Ne 146 0.83 7.2 × 10–3 15 26.2
Xenon 18 5.89 2.5 × 10–3 13.0
N2 131 4.2 × 10–3 9 18.7
O2 3.8 × 10–3 22
SF2 5.5
H2O
Xe
a. Density in oz·ft–3 = g·L–1 = mg·cm–3 at 20 °C (68 °F) and 100 kPa (1 atm).
b. Numerical factor for calculating mean free path using Eq. 16. Mean free path in meters at 20 °C (68 °F).
c. Independent of pressure under conditions for viscous flow.
d. Diffusivity in m2·s–1 in air at 0 °C (32 °F) and 101 kPa (1 atm).
e. Thermal conductivity in W·m–1·K–1 at 20 °C (68 °F). Thermal conductivity is independent of pressure under conditions for viscous flow.
f. N2, 78 percent; O2, 21 percent; argon, 0.9 percent; others, 0.1 percent.
g. Vapor pressure of H2O at 20 °C (68 °F) is 2.3 kPa (17.5 torr).
42 Leak Testing
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(18) nmixture = N1 n1 + N2 n2 masses of common gases and some vapors
are tabulated in Table 6.
+ … + Nk nk
Vapors resulting from evaporation of
where n1 is viscosity of the first gaseous liquid hydrocarbon compounds have
constituent and N1 is fractional molecules containing relatively large
concentration of the first gaseous numbers of atoms. Molecular masses of
constituent, as defined by Eq. 14. such organic chemical compound vapors
increase as the macromolecules increase
Molecular Masses of Gases in complexity and contain more atoms.
and Vapors
Stratification of
Any combination of atoms in a chemical Constituents in Mixtures of
compound is called a molecule. The Gases
molecular mass equals the total number
of nucleons in the atoms forming the If a tracer gas is added to air already
molecule. Most elements in the gaseous within a vessel or system under test, a
state form diatomic molecules that consist uniform mixture of gases is often difficult
of two atoms of that element loosely to achieve. The tracer gas will settle
bound by electronic forces. The molecular toward the top or toward the bottom of
mass of diatomic gases is twice the atomic large containers, depending on the
mass. For example, the element oxygen O density of the tracer gas relative to the
has an atomic mass of 16; gaseous oxygen density of the air or other pressurizing
O2 has a molecular mass of 32. Exceptions gases within the system. This stratification
to this diatomic arrangement in gases of mixed gases is more pronounced with
include most metallic vapors and the high molecular mass gases and with gases
noble gases. The noble gases (argon, with low diffusion coefficients.
helium, neon, krypton, radon and xenon) Precautions should be taken to avoid or
have extremely stable electronic structures correct stratification effects during leak
and typically do not combine with any testing by (1) premixing of tracer gas with
other atom species. The molecular masses diluent gases before injection, during
of the monatomic gases are identical to pressurization of the test system or
their atomic masses. enclosing hood or chambers and
(2) providing some means for circulating
In chemical compounds containing and mixing the gases within large volume
different elements (for example, carbon chambers or test systems.
dioxide) the molecular mass is the sum of
the atomic masses of the constituent Usually, there should be no problems
atoms. One carbon atom (atomic mass 12) with pooling or stratification inside test
combines with two oxygen atoms (atomic systems, if precautions are taken to mix
mass 16 each) to form CO2 with a the tracer gas thoroughly with the diluent
molecular mass of 44. The molecular gas in pressurization of the test system.
However, if the test pressure is to be about
TABLE 6. Viscosity and molecular masses atmospheric pressure in the test system,
of typical gases and vapors used in leak the system should first be evacuated to
testing. remove air at atmospheric pressure and to
replace it by the thoroughly mixed
Viscosity at Relative combination of tracer gas with diluent
gas.
15 °C (60 °F) Molecular
Equilibrium Distribution
Gas (µPa·s)a Mass (u)b Law for Gas Concentration
Ratios with Gravity Effect
Hydrogen 8.7 2.02
Helium 19.4 4.00 The preferred technique is that in which
Methane 10.8 16.0 both the tracer and diluent gases used in
Ammonia vapor 17.0 pressurization of test systems are
Water vapor 9.7 18.0 premixed or added simultaneously
Neon 9.3 20.2 through a screened aperture or rake so as
Nitrogen 31.0 28.0 to be mixed rather uniformly from the
Air 17.3 28.7 start. There should then be no problem of
Oxygen 18.0 32.0 pooling of denser constituents inside the
Hydrogen 20.0 system under test, provided that
36.5 precautions are taken to mix the tracer
chloride vapor 14.0 39.9 thoroughly with diluent gas in the
Argon 21.9 44.0 pressurization of the system. The
Carbon dioxide 14.5 equilibrium distribution law of Eq. 19
a. One µPa·s = 10 micropoise.
b. One unified atomic mass unit (u) ≅ 1.6605 × 10–27 kg.
Tracer Gases in Leak Testing 43
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gives the ratio Ch of tracer as
concentration at the top of a tank relative
to the concentration Co of the same
gaseous constituent at the bottom of the
tank:
− Mgh
(19) Ch = Co e RT
where M is molecular mass of gaseous
constituent, h is height of interior volume
of tank, R is universal gas constant, T is
absolute temperature and g is local value
of acceleration due to earth’s gravity.
From Eq. 19, it is evident that with a
specific tracer gas in equilibrium
distribution, the concentration of tracer
gas diminishes exponentially as height
within the chamber increases. The
greatest concentration of the gaseous
constituent is at the bottom of the tank
and the lowest concentration exists at the
top of the tank. However, this effect takes
no account of the relative densities of the
tracer gas and diluent gas. If the tracer gas
were lower in density than the diluent gas
(as with helium tracer gas in air),
stratification effects could have a
predominant effect, with helium
collecting at the top of the tank after a
period of time. If the tracer gas were
higher in density than the diluent gas (as
with refrigerant-12 gas in air),
stratification effects could also
predominate and the denser tracer gas
would tend to collect at the bottom of the
tank after a period of time. In large test
chambers or enclosing hoods, it would be
desirable to provide constant internal
circulation and mixing of the internal
contents of tracer gas and diluent gas, as
with a fan.
44 Leak Testing
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PART 2. Mechanisms of Gaseous Flow through
Leaks
Modes of Gas Flow Depending of the material and the type of
through Leaks of gas, a rubber O-ring usually represents a
Restrictions permeability of about 5 × 10–7 Pa·m3·s–1
(5 × 10–6 std cm3·s–1) for every 100 kPa
To clarify the problem of leakage, it is (760 torr) of pressure differential per
necessary to consider gas flow through linear centimeter of exposed O-ring
small restrictions. It is extremely surface. This permeability does not have
important to know something about the to be taken into consideration during
basic modes of flow: viscous, transitional routine leak testing if the leakage
and molecular. Viscous flow may be measurement occurs in a time too short
further divided into laminar flow or to permit the saturation and mass transfer
turbulent flow. Other special modes of of gas through the O-ring.
leakage or flow are permeation and
choked flow. The factors that influence Mean Free Path of
gaseous flow through leaks are (1) the Gaseous Molecules
molecular mass of the gas, (2) the
viscosity of the gas, (3) the pressure Molecular flow occurs when the mean
difference causing the flow, (4) the free path of a tracer gas is greater than the
absolute pressure in the system and cross section dimension of the leak. The
(5) the length and cross section of the mean free path is the average distance a
leak path. molecule travels between successive
collisions with other molecules in vapor
An understanding of leakage state. The mean free path is of some
mechanisms and controlling factors is importance in leak testing because it
vital to the proper interpretation of leak establishes the type of gas flow that will
tests. A simple description of gaseous flow occur. The mean free paths of several
through leaks is presented here for leak gases are given in Table 4.
testing operators and supervisory
personnel, followed by a theoretical In flow systems encountered in leak
approach to leakage. testing, knowing the mean free path
allows one to know, or at least estimate,
Permeation of Gases through the type of flow occurring. Table 4 shows,
Solids in general, the relationship of mean free
path to pressure and the information may
Permeation is the passage of fluid into, be used as a guide to determine the nature
through and out of a solid barrier having of the flow.
no holes large enough to permit more
than a small fraction of molecules to pass Characteristics of
through any one hole. The process also Molecular Flow of Gases
involves diffusion through a solid and
may involve many phenomena such as It should especially be noted that in
adsorption, dissociation, migration and molecular flow the leakage rate is
desorption. proportional to the difference of the
pressures. Molecular flow occurs quite
The first implication of permeation is often in vacuum testing applications. In
that if the system is to be relatively molecular flow, molecules travel
leaktight, the materials of construction independently of each other. It is possible
have to exclude leakage by permeability. for random molecules to travel from a
As an example, the permeation rate at part of a system at low pressure to
room temperature of a natural rubber another part of the system at a higher
gasket (2.5 mm thick, with a 2.5 mm wide pressure. When an ultrahigh vacuum
rim and a 125 mm diameter) with a system is being tested by a mass
100 kPa (1 atm) hydrogen pressure spectrometer leak detector, the mass
differential is 1.6 × 10–6 Pa·m3·s–1 spectrometer leak detector operates at a
(1.6 × 10–5 std cm3·s–1). In some uses, this pressure of about 10 µPa (0.1 µtorr)
permeation might represent an whereas the ultrahigh vacuum system
unacceptable leakage rate. might be operating at a pressure of
Another similar example of this type of
permeation involves a rubber O-ring.
Tracer Gases in Leak Testing 45
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0.1 µPa (1 ntorr). When a tracer gas enters measured are in the laminar flow range,
the ultrahigh vacuum system through a the simplest means of increasing test
leak, it will eventually travel from the sensitivity is by an increase of pressure
0.1 µPa (1 ntorr) vacuum system to the across the leak.
mass spectrometer operating at 10 µPa
(0.1 µtorr) by the process of molecular Viscous Flow of Gases
flow. This does not imply that the total through Leaks
flow is from a system at low pressure to
one at high pressure. The mass Laminar flow is one of the two classes of
spectrometer operating at 10 µPa viscous flow; the other class is turbulent
(0.1 µtorr) sends some gas molecules into flow. Because turbulent flow is rarely
the system at the lower pressure. encountered in leaks, the term viscous flow
However, when summing flows, total net is sometimes incorrectly used to describe
flow is from the high-pressure to the low laminar flow in leak testing. Viscous flow
pressure region. The high pressure system implies that the flow occurs when the
is contributing gas molecules to the mean free path of the gas is smaller than
ultrahigh vacuum system. The tracer gas the cross section dimension of the leak. It
flow in the direction opposing the major should especially be noted that the
flow of molecules is possible because of viscous flow leakage rate is proportional
the random mode of molecular flow. The to the difference of the squares of the
gas molecules, when traveling from one pressures. Viscous flow leakage occurs in
system to the other, do not come in high pressure systems, such as are
contact with molecules traveling in the encountered in detector probe leak tests.
other direction. It is often related with the Reynolds
number. The dimensionless Reynolds
Characteristics of number is the ratio of the inertial to the
Transitional Flow of Gases viscous forces acting on the medium. In
the case of tubes (or leak paths), the
Transitional flow occurs when the mean Reynolds number NRe is expressed by
free path of the gas is about equal to the Eq. 20:
cross section dimension of the physical
leak. It occurs under conditions (20) N Re = vd
intermediate between laminar and η
molecular flow. The transition from
laminar flow to molecular flow is gradual. where v is velocity (m·s–1), d is diameter of
The mathematical treatment of this opening (meter) and η is kinematic
region is extremely difficult; however, a viscosity (m2·s–1). However, any set of
treatment of this region is necessary consistent units may be used in this
because leakage from an enclosed volume equation. Above a critical value of the
to a vacuum necessarily involves a Reynolds number (about 2100 in the case
transition from laminar to molecular flow. of circular tube flow), flow becomes
unstable. This results in innumerable
Characteristics of Laminar eddies or vortexes in the flow. The partial
Flow of Gases path in turbulent flow leaks is very erratic.
In laminar flow, the particles flow nearly
The laminar flow of a fluid in a tube is straight line paths.
defined as a condition in which there is a
parabolic distribution of the fluid velocity Characteristics of Choked
in the cross section of the tube. The two (or Sonic) Flow of Gases
most important characteristics of laminar
leaks are (1) the flow is proportional to Choked flow, or sonic flow as it is
the square of the pressure difference sometimes called, occurs under certain
across the leak and (2) the leakage is conditions of leak geometry and pressure.
inversely proportional to the leaking gas Assume there exists a passage in the form
viscosity. Table 1 shows that the viscosity of an orifice or a venturi, and assume that
of most gases varies by less than one order the pressure upstream is kept constant. If
of magnitude. Changing the tracer gas the pressure downstream is gradually
will not markedly increase the sensitivity lowered, the velocity through the throat
of the leak test unless this change of gas or orifice will increase until it reaches the
implies a change of instrument sensitivity. speed of sound through the fluid. The
However, increasing the pressure downstream pressure at the time the
difference across the leak by a factor of a orifice velocity reaches the speed of sound
little over three will increase the flow rate is called the critical pressure. If the
through this leak by a factor of ten. downstream pressure is lowered below
Obviously then, when the leaks to be this critical pressure, no further increase
in orifice velocity can occur, with the
46 Leak Testing
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TABLE 7. Composition and partial pressures of dry air at sea level (101.325 kPa or
1.00 atm). Note the similarity of partial pressures with the percentages. When less
precision can be tolerated, use percentages × 103.
Content Partial Pressure
________________________ ________________________________
Constituent Percent µg·g–1 Pa (torr)
Nitrogen 78.084 —— 7.9119 × 104 (4.9343 × 102)
Oxygen 20.946 —— 2.1224 × 104 (1.5919 × 102)
Argon —— 9.460 × 104
Carbon dioxide 0.934 —— 3.34 × 101 (7.10)
Neon 0.033 18.18 (2.50 × 10–1)
Helium 1.8 × 10–3 5.24 1.84 (1.38 × 10–2)
Krypton 5 × 10–4 1.14 5.3 × 10–1 (3.98 × 10–3)
Xenon 1 × 10–4 0.087 1.16 × 10–1 (8.66 × 10–4)
Hydrogen 0.5 8.8 × 10–3 (6.61 × 10–5)
Methane —— 2.0 5 × 10–2 (3.80 × 10–4)
Nitrous oxide (N2O) —— 0.5 2 × 10–1 (1.52 × 10–3)
—— 5 × 10–2 (3.80 × 10–4)
——
consequence that the maximum mass be used. Table 7 lists the standard
flow rate has been reached. This condition composition of dry air at sea level.
is known as choked or sonic flow.
The physical properties of gases and
Leaks Dependent on a Critical Gas vapors are also important, including the
Temperature or Pressure molecular mass, the molecular diameter
and the viscosity. The gas streaming
Both pressure dependent leaks and through a narrow bore tube experiences a
temperature dependent leaks have been resistance to flow so that the velocity of
observed, but in extremely limited gas flow decreases uniformly from the
number. Pressure dependent or temperature center outwards until it reaches zero at
dependent leaks denote a condition where the walls. Each layer of gas parallel to the
no leakage exists until a critical pressure direction of flow exerts a tangential force
or temperature is reached. At this point, on the adjacent layer, tending to decrease
the leakage appears suddenly and may be the velocity of the faster moving layers
appreciable. Further changes in pressure and to increase that of the slower moving
or temperature cause the leakage to vary layers. The property of a gas or liquid by
in the prescribed manner. When the virtue of which it exhibits this
pressure or temperature is reversed, the phenomenon is known as internal
leakage follows the prescribed course to viscosity.
the critical point at which leakage drops
to zero. No adequate explanation for this The internal viscosity is directly
phenomenon is advanced, but in view of proportional to the velocity gradient in
the very few times this occurs, such leaks the gas. Furthermore, the viscosity must
can generally be ignored. Temperature depend on the nature of the fluid. In a
and pressure are not normally applied in more viscous fluid the tangential force
the course of leak testing for the purpose between adjacent layers for constant
of locating such leaks. Instead, they are velocity gradient will be greater than in a
used to force existing discontinuities to less viscous fluid. For any gas at constant
open, so as to start or increase the leakage temperature, the gas viscosity is
rate to a point of detection. independent of the pressure. However, gas
viscosity increases as gas temperature
Physical Properties of rises. Conversely, the viscosity of all
Tracer Gases Used in Leak ordinary liquids decreases with increased
Testing temperature.
When performing any leak test it is
important to have some knowledge of the
residual gases present in the test area
because this will have a bearing on the
choice of tracer gas and test technique to
Tracer Gases in Leak Testing 47
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PART 3. Practical Measurement of Leakage
Rates with Tracer Gases
Principles of Leakage Criteria to Determine Type
Measurement of Gas Flow through Leaks
All leak detection with tracer gases The type of flow that occurs through leaks
involved their flow from the high pressure depends on the factors listed earlier. In
side of a pressure boundary through a flow systems encountered in leak testing
presumed leak to the lower pressure side with gases, the length of the mean free
of the pressure boundary. When tracer path of the gaseous molecules can be used
gases are used in leak testing, instruments to estimate the type of flow occurring
sensitive to tracer gas presence or through leakage paths. (The mean free
concentration are used to detect outflow path lengths for various gas molecules can
from the low pressure side of the leak in be calculated by means of Eq. 15 or 16.
the pressure boundary. Tables 4 and 5 give data on mean free
path lengths for several gases and pressure
Where leak tests involve measurements ranges.) When determining the nature of
of change in pressure or change in flow of gases through leaks, use is made of
volume of gas within a pressurized two parameters: (1) the mean free path
enclosure, the loss of internal gas pressure length λ is determined by using the
or volume indicates that leakage has average pressure in the leak flow system.
occurred through the pressure boundary.
When evacuated or low pressure test The criteria that determine the mode of
systems or components are surrounded by gas flow through leaks, given in terms of
higher pressure media such as the earth’s the mean free path length λ and the leak
atmosphere, or a hood or test chamber dimensional constant d, are as follows.
containing gases at higher pressures,
leakage can be detected by loss of pressure 1. When the ratio λ·d–1 is less than 0.01,
in the external chamber or by rise in the gas flow is viscous.
pressure within the lower pressure system
under test. 2. When the ratio λ·d–1 has values
between 0.01 and 1.00, the gas flow is
Modes of Gas Flow transitional.
through Leaks
3. When the ratio λ·d–1 is greater than
For each type of leak test, it is essential 1.00, the gas flow is molecular.
that the test operator have a basic
understanding of the types of flow that In molecular flow, the mean free path
might occur in a leak. Different basic laws length is greater than the largest linear
relate leakage rate to pressure difference dimension of the cross section of the leak.
across the leak, the range of absolute
pressure involved and the nature of the Relation of Viscous
gaseous fluid escaping through the leak. Leakage Flow to Pressure
There are three basic types of gas flow Differential across Leaks
through leaks.
Viscous flow occurs when the mean free
1. Viscous flow typically occurs in probing path length of the gas is significantly
applications with gases leaking at smaller than the cross section of a leak.
atmospheric or higher pressures. This condition is implied by the first
criterion above, where λ is at least 100
2. Molecular flow usually occurs in leaks times smaller than the leak’s cross
under vacuum testing conditions. sectional diameter d. Viscous flow occurs
in high pressure systems such as in
3. Transitional flow occurs under test probing applications where tracer gases
conditions intermediate between leak into air at atmospheric pressures.
vacuum and pressures higher than With viscous flow through leaks, the flow
atmospheric pressure. rate or leakage Q is proportional to the
difference in the squares of the pressures
Figure 7 shows the range of conditions of acting across the leak. This relationship is
gas pressure and leak radius under which shown by Poiseuille’s law for viscous flow
each of these types of flow is typically through a cylindrical tube, in Eqs. 21 and
encountered, for leakage flow of air. 22 for the leakage rate Q:
48 Leak Testing
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( )π r 4 in the discussion above. Molecular flow
usually occurs through leaks in vacuum
(21) Q = 8 n l Pa P1 − P2 systems or systems that have vacuum
applied to the lower pressure side of the
or pressure boundary for purposes of leak
testing. With molecular flow through
( )(22) Q = π r4 leaks, the leakage rate Q is proportional to
16 n l the difference in pressures applied across
P12 − P22 the leak. This relationship is shown by
Knudsen’s law for molecular flow through
where Q is gas flow rate (Pa·m3·s–1), r is a cylindrical tube, neglecting the end
effect, as shown in Eq. 23 for the leakage
radius of leakage tube (meter), l is length rate, Q through a tubular leak with
molecular flow:
of leakage tube (meter), n is viscosity of
(23) Q = 3.342 r3
leaking gas (Pa·s), P1 is upstream gas l
pressure (pascal), P2 is downstream
pressure (pascal) and Pa is average pressure
within leak path, (P1 + P2)/2 (pascal).
RT (P1 − P2 )
M
Relation of Molecular where Q is leakage rate (Pa·m3·s–1), r is
Leakage Flow to Pressure
Differential across Leaks radius of leakage tube (meter), l is length
Molecular flow occurs when the mean of leakage tube (meter), M is molecular
free path length of the gas molecules is
greater than the largest cross sectional weight of gas (kilogram per mole), P1 is
dimension of a physical leak. This upstream pressure (pascal), P2 is
condition is implied by the third criterion downstream pressure (pascal), T is
absolute temperature (kelvin); and gas
constant R = 8.315 J·mol–1·K–1.
FIGURE 7. Types of flow characteristics of tracer gases though leaks as function of leak channel
radius and gas pressure. Graph illustrates air at 25 °C (77 °F).
105 (4 × 103)
104 (4 × 102)
103 (4 × 101) Viscous
102 (4 × 100)
Radius of tube, mm (in.) 101 (4 × 10–1) Transition
100 (4 × 10–2)
10–1 (4 × 10–3) Molecular
10–2 (4 × 10–4)
10–3 (4 × 10–5)
10–4 (4 × 10–6)
10–5 (4 × 10–7)
10–4 10–3 10–2 10–1 100 101 102 103 104 105
(15)
( 1.5×10–8)(1.5×10–7)(1.5×10–6)(1.5×10–5)(1.5×10–4)(1.5×10–3)(1.5×10–2)(1.5×10–1) (1.5)
Absolute pressure, Pa (lbf·in.–2)
Tracer Gases in Leak Testing 49
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If this value is substituted for R in ( )(29) Q = 3.342 r3 RT
Eq. 23, the leakage rate in SI units is given lM
by Eq. 24: P1 − P2 FT
( )(24) Q = 9.637 r3 T For Eq. 28 and 29, the symbols are
lM
P1 − P2 explained below Eq. 23, with the
exception of the mean free path length λ,
If the molecular mass M is given in units which is determined at the average
of grams per mole. All other quantities are
in SI units as listed above. The leakage between upstream and downstream
rate in SI units of Pa·m3·s–1 is given by Eq.
25: pressures acting across the leak, namely
(P1 + P2)/2, from Eq. 15 or 16 and Tables 4
and 5.
( )(25) Q = 304.8 r3 T
lM
P1 − P2 Analogy between Electrical
Conductance and Gaseous
In cgs (centimeter-gram-second) units, Conductance
with tube radius and length given in
centimeter and molecular weight in gram Conductance is a term describing the
per mole, the rate of leakage (L·s–1) is property of a gas flow system that permits
given by Eq. 26: gas to flow. It is defined analogously to
electrical conductance G, the reciprocal of
( )(26) Q = 30.48 r3 T electrical resistance R. Ohm’s law for
lM direct current flow i through a
P1 − P2 conductance or resistance is stated in
Eq. 30:
This flow rate is related to the flow rate Fo
for zero thickness orifice:
(27) F = 8 r Fo (30) i = V = V G
3 l R
where both F and Fo are flow rates (L·s–1). In Eq. 30, the quantity V equals the
voltage drop across the resistance R or
Relation of Transitional conductance G. Electrical conductance
Leakage Flow to Mean could be described as the property of an
Free Path Length of Gas electric circuit that permits current to
and to Pressure flow. In steady state direct current circuits,
Differential Applied across the conductance G is the ratio of the
Leak Path current i flowing in the resistive element
to the drop in electrical potential (or
electrical pressure) across the resistive
element, as in Eq. 31 for the electrical
conductance G:
Transition flow occurs when the mean (31) G = 1 = i
free path length of the gas molecules is RV
about equal to the cross-sectional
dimension of the leak. Transitional flow With gas flow through the
occurs under leakage conditions conductance of a leak path, for example,
intermediate between those for viscous the flow rate Q is analogous to the electric
flow and those for molecular flow. For current i. The pressure drop (P1 – P2) is
transitional flow, Knudsen’s law (see analogous to the voltage drop V. Leak
Eqs. 23 to 27) for molecular leakage is conductance C is analogous to the
modified by an additional term that electrical conductance G. The electrical
depends on the ratio R equal r/λ or current could be considered as the leakage
leakage tube radius r to the mean free of electrical charge through a resistive
path length λ that applies for the average element such as a length of wire of given
pressure (P1 + P2)/2, existing within the diameter and specific conductivity. The
leakage path. This correction term for gaseous conductance of a tubular
transitional flow in leakage paths is given passageway permits the leakage of a
as the factor FT, defined by Eq. 28 where gaseous constituent when a pressure drop
Rt = r/λ: exists between the ends of the tubular
hole. The gaseous conductance is the
(28) FT = 0.1472 R t + 1 + 2.507 Rt reciprocal of the resistance of the leak
1 + 3.095 Rt passageway, as indicated by Eq. 32 for the
gaseous conductance C:
The leakage rate Q in SI units of Pa·m3·s–1
is given by Eq. 29: (32) C = 1 = Q
R gas P1 − P2
50 Leak Testing
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The equivalent of Ohm’s law for a gas The conductance for molecular flow of
conductance would be the linear gases through a long cylindrical tubular
relationship of Eq. 33 for the rate Q of leak channel can be calculated from
leakage or of gas flow: Eq. 36:
( )(33) Q = P1 − P2 = (36) C = 3.342 r3 RT
R gas l M
P1 − P2 C
However, Eq. 33 is only true for the case The conductance of a leak that can be
of molecular flow, as shown in Eqs. 23 approximated by an ideal orifice subject
to 27. to molecular flow at low pressure is
calculated by Eq. 37:
It is very important to keep in mind
that, by definition, the relationships of (37) C = 3.613 r 2 T
gaseous conductance calculations always M
include a term describing a property of
the flowing gas. This property usually is The conductance of a long tubular leak
the gas viscosity that influences viscous with transitional gas flow can be
flow through leaks or is the gas molecular calculated from Eq. 38:
mass that influences molecular flow
through leaks. (38) C = 3.342 r 3 T
P M
FT
Equations for Calculating In Eq. 38, the factor FT is the correction
Conductances of Leaks term for transitional flow defined earlier
with Various Modes of
Flow by Eq. 28.
The following equations give basic Gas Conductance with Two Leaks
relationships required to calculate leak in Series
conductances under various conditions of
leak geometry and of modes of gas flow If two different diameter leaks with
and to estimate variations of leakage rate different conductance values are
with different gas pressures. connected in series as in Fig. 8, the total
conductance of the connection between
The conductance of a leak exhibiting extreme ends decreases (resistance
viscous flow of gas can be calculated by increases). From Eq. 33, the conductance
Eq. 34, assuming that the physical leak of the leak between the outer ends of
channel approximates a straight, sections 1 and 3 may be expressed as in
cylindrical tube: The viscous conductance Eq. 39:
C of a tube is expressed as follows:
(39) C1−3 = Q
P1 − P3
πr4
(34) C = 8nl Pa The total pressure drop across the two
leaks in series is given by Eq. 40:
In Eqs. 34 through 38 for calculating
FIGURE 8. Diagram of typical leak paths connected in series.
the conductance of leaks, C is gas
conductance (m3·s–1), r is radius of bore of Wall of
system
tube (meter), l is length of tubular leak
Inside P2 chamber Atmosphere
passageway (meter), n is viscosity of P1 of P3
leaking gas in Pa·s, P1 is upstream pressure system C23
(pascal), P2 is downstream (pascal), Pa is
average gas pressure within leak channel C12
(pascal), Pa = (P1 + P2)/2, M is molecular Tracer Outer
mass of gas g·mol–1 and T is absolute capillary
Inner
temperature (kelvin). capillary
If viscous leakage occurs through an
ideal orifice where the ratio P2/P1 of
downstream to upstream pressures is
smaller than or equal to 0.52, the
approximate conductance for viscous flow
through an ideal orifice can be calculated
by the empirical Eq. 35:
(35) C = 6.4 r 2 T Legend
1 − P2 M
P1 C = channel connecting points
P = point where fluid is present
Tracer Gases in Leak Testing 51
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( ) ( )(40) P1 − P3 = P1 − P2 + P2 − P3 ( )(46) Qa = Ca P1 − P2 = Ca ∆ P
The pressure drop across each ( )(47) Q b = Cb P1 − P2 = Cb ∆P
individual leak is shown in Eq. 41:
(41) P1 − P2 = Q, The total conductance through the
C1−2 pressure boundary between Points 1 and 2
is given by Eq. 48:
P2 − P3 = Q (48) C1−2 = Ca ∆ P + Cb ∆ P
C 2 −3 ∆P
Now, by combining Eqs. 39 to 41, the Simplifying Eq. 48 gives Eq. 49:
conductance C13 for the two leaks in (49) C1−2 = Ca + Cb
series is given by Eq. 42:
(42) C13 = Q In its general form, the total
Q +Q conductance for n individual leaks
C1−2 C 2 −3 connected in parallel is given by the sum
of the individual conductances as in
or, in its reciprocal form, Eq. 50:
Q +Q (50) CT = C1 + C2 + C3 + … + Cn
(43) 1 = C1−2 C 2 −3
C13 Q
= 1+1 Graphical Determination
C1−2 C 2 −3 of Conductance for
Molecular Flow through
In its general form, Eq. 43 may be written Tubes and Orifices
as Eq. 44:
The preceding equations give the
(44) 1 = 1 + 1 +…+ 1 relationships required to calculate
CT C1 C2 Cn conductance under various conditions. In
practice, calculation of the exact
where the subscript T denotes the total conductance often is not required in leak
testing. Also, it has been found that most
conductance of a number of conductances needed conductance values are for
molecular flow through cylindrical tubing
C1, C2, C3 … Cn connected in series. and orifices. Figures 10 and 11 have been
In the case of only two conductances provided to allow quick determinations.
Note that the curves are plotted for air at
connected in series, Eq. 44 should be 20 °C (68 °F) and values must be corrected
if another gas or temperature is used.
written in the form of Eq. 45:
(45) CT = C1 × C2
C1 + C2
This case applies for two successive leak FIGURE 9. Diagram of typical leak paths connected in
conductances connected in series. This is parallel.
analogous to the case of two electrical
resistors connected in parallel or of two
electrical conductances connected in series.
Leak Conductance for Two Inside of Wall of system Atmosphere
Leaks Connected in system P2
Parallel P1 Ca
Cb
Figure 9 shows the case of two leaks
connected in parallel. With this situation, Legend
the total leakage through two parallel
leaks divides between the two leakage C = channel connecting points
paths from the high pressure side to the P = point where fluid is present
low pressure side of the pressure
boundary. The division of flows depends
on the conductance of the individual
leaks as indicated in Eqs. 46 and 47:
52 Leak Testing
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Improvement of Viscous Effect of Variations in
Flow Leak Test Sensitivity Tracer Gas Concentration
by Increasing Pressure
Differential Under viscous flow conditions, which are
usually encountered when leak testing
The change in leakage rate obtained by pressurized systems, the flow rate increase
resulting from higher pressure differentials
increasing the pressure applied to a leak may also be used to conserve tracer gas. In
a mixture of two gases such as helium and
to atmosphere is used to great advantage nitrogen, each gas will flow through a
leak at the same rate regardless of their
in leak testing under conditions where the concentrations in the mixture. Thus, if a
10 percent tracer gas in 90 percent carrier
leakage flow is viscous in nature, as gas mixture is used, the test sensitivity
will be 10 percent of what it would be if
illustrated in Fig. 12. For example, 100 percent tracer gas were used at the
same working pressure. To bring the test
suppose that the leakage rate is sensitivity back to a leakage rate increase
1 × 10–8 Pa·m3·s–1 (1 × 10–7 std cm3·s–1) ratio of 1, the pressure would have to be
from a system with an internal gage raised enough to increase the flow by a
factor of 10. Suppose that a tank must be
pressure of 1 atm (absolute internal brought to an absolute pressure of 10 MPa
(1.5 × 103 lbf·in.–2) and leak tested with
pressure of 200 kPa or 2 atm), as indicated helium. To save money, it is desired (1) to
use the smallest amount of helium that
by point P1 in Fig. 12. It is desired to will give adequate sensitivity and (2) to
determine the new absolute internal
pressure P2 needed to make the leakage
rate 50 times higher, or 5 × 10–7 Pa·m3·s–1
(5 × 10–6 std cm3·s–1). From Fig. 12, the
new flow rate at Point P2 is seen to be
obtained with an absolute internal
pressure of 1.23 MPa (12.3 atm), as shown
on the horizontal scales.
FIGURE 10. Conductance of cylindrical tubes of different lengths and inside diameters for air
at 20 °C (68 °F). 1 L = 1 dm3 = 0.028 ft3.
Conductance (L·s–1)
10–2 10–1 1 10 102 103
0.01
0.02
0.04
0.06
0.08
0.1
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
20
40
60
80
100
200
400
600
800
1000
20 Inside1do00if8a9tmmu7mbme5temem6(5s4r20(sm3immn.53(.mm3)8i.n0m((.2)2imn..502.)5(ii2nn1m2...)5)mm2in0m1.()61m(.m00m1.3mi8n(71m.0)5(0.07mi.m5n6.(2im)0n5..56)(in0im.n.)3.m5)75m(0imn4.2.)m5(0m3i.n1m.8()08m.1in6(0.)i.n1.2)5 in.) 1000
Length of tube (m)10 800
Length of tube (in.) 600
5 400
10–4 10–3 10–2 10–1
2 200
1
0.5 100
80
0.2 60
0.1 40
0.05
20
0.02
0.01 10
0.005 8
0.0025 6
4
10–5
2
1.0
0.8
0.6
0.4
0.2
0.1
100
Conductance (m3·s–1)
Tracer Gases in Leak Testing 53
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FIGURE 11. Conductance of orifices for air at 20 °C (68 °F), molecular flow. For curve A read
left vertical scale; for curve B read right vertical scale (1 m3 = 35 ft3).
10–1 100
Conductance (m3·s–1)10–2 A B 10
Read left scale10–3 1.0
Read right scale
Conductance (m3·s–1)
10–4 0.1
10–5 0.01
2.5 25 250 2000
(0.1) (1 . 0 ) (10) (100)
Orifice diameter, mm (in.)
FIGURE 12. Viscous leakage rate as function of internal pressure of system leaking to
atmosphere when pressurizing with 100 percent gas. For curve A read left vertical scale, for
curve B read right vertical scale.
Internal absolute pressure (atm) at 1 atm
1 10 100 1000
100 100 000
50 P2 = 1.23 MPa (12.3 atm)
A
10
Leakage rate increase ratio B
Leakage rate increase ratio10 000
1.0 1000
P1 = 200 kPa (2 atm)
0.1 103 104 100
(147) (1470)
102 2 × 102 105
(14.7) (14 700)
Internal pressure, kPa (lbf·in.–2), outside of part at 100 kPa (1 atm)
54 Leak Testing
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pressurize the rest of the way with Effect of Increasing
Pressure Differential across
nitrogen. The minimum detectable Molecular Leak Flow
leakage should be at least Figure 14 shows the effect of changing the
1 × 10–8 Pa·m3·s–1 (1 × 10–7 std cm3·s–1) at pressure differential across a leak when
100 kPa (1.0 atm) pressure differential. It the flow conditions are molecular. As
would be predicted by Eq. 23, the increase
is desired to calculate the percentage of of gas flow is a linear function of pressure.
Under conditions of molecular flow, the
helium that should be used after reaching amount of tracer gas flowing through a
leak is not a function of the total pressure.
an absolute pressure of up to 10 MPa It depends only on the partial pressure of
(1.5 × 103 lbf·in.–2). the tracer gas. Therefore, there would be
no advantage in raising the total pressure
The specified minimum detectable difference without raising the tracer gas
leakage rate of 1 × 10–8 Pa·m3·s–1 pressure.
(1 × 10–7 std cm3·s–1) requires that the leak
test sensitivity be standard or the same as Conversions between
Leakage Rates with
it would be if 100 percent tracer was used Different Tracer Gases
at 100 kPa (1 atm) pressure difference. Many occasions will arise where it will be
necessary to express a leakage rate (flow
From Fig. 12 it is seen that an absolute rate) or conductance in terms of a
particular tracer gas when it has been
pressure of 10 MPa (100 atm) results in a measured using a different tracer gas. For
leakage rate increase factor of 3300. Thus,
the helium concentration after pressuring
up should be 1/3300 or 0.03 percent.
Figure 13 is very similar to Fig. 12 and is
used in the same manner. The difference
is that Fig. 13 is plotted for conditions
where high vacuum is on the low pressure
side of the pressure boundary. Figure 13
still assumes viscous flow conditions.
FIGURE 13. Viscous leakage rate as function of pressure differential during vacuum testing,
pressurizing with 100 percent tracer gas. Read left vertical scale for curve A and right vertical
scale for curve B.
1 Internal absolute pressure (atm) 1 000
10 100 1 000 000
1 000
800 500 000
600
400
Leak rate increase ratio
200
Read left scale
Read right scale100
Leak rate increase ratio
80 A 100 000
60
50 000
40 B
20
10 10 000
8
6
5 000
4
2
1 103 104 1 000
(147) (1470)
102 105
(14.7) (14 700)
External pressure, kPa (lbf·in.–2 ) inside part at high vacuum
Tracer Gases in Leak Testing 55
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example, a specification may state that a n2 is viscosity (same units as gas 1) for
certain part cannot leak more than a gas 2.
given amount for air, but helium tracer
gas is used in testing. To be able to Conversion of Viscous
convert a measured helium leakage rate to Conductance between Different
an equivalent air leakage rate, the type of Gases
flow must first be identified. After the
flow type is determined, the conversion Dividing both sides of Eq. 51 by the
may be made. Also, many times the pressure drop will give conductance C
conductance for a piece of tubing or other rather than flow Q. Any two conductances
item must be determined. Conductance is C1 and C2 will then have a relationship
the part of the flow equations that given in Eq. 52:
contains the term describing either
molecular mass or viscosity of the gas that (52) C2 = n1 C1
is flowing. The conductance of a given n2
system will be quite different for two
gases having different properties. In leak where C1 is conductance (any units) for
testing work, this situation is encountered gas 1, C2 is conductance (same units as
where the pumpdown time of a system gas 1) for gas 2, n1 is viscosity (any units)
for air must be determined and then for gas 1 and n2 is viscosity (same units as
response and cleanup times for helium gas 1) for gas 2.
must be determined.
A few comparisons that may be used
Conversion of Viscous Flow Rates
between Different Gases for converting higher conductance or flow
from helium flow rates to flow rates for
other gases are shown in Table 8.
If a flow rate has been identified as TABLE 8. Comparison of viscous flow rates
viscous for one gas, the viscous flow for of other gases with helium flow rates.
any other gas may be determined using
the expression given in Eq. 51:
(51) Q2 = n1 Q1 To Convert to Multiply Helium
n2 Flow by
where Q1 is flow rate (any units) for gas 1, Q of argon 0.883
Q2 is flow rate (same units as gas 1) for gas Q of neon 0.626
2, n1 is viscosity (any units) for gas 1 and Q of hydrogen 2.23
Q of nitrogen 1.12
Q of air 1.08
Q of water vapor 2.09
FIGURE 14. Molecular leakage rate as function of pressure Conversion of Molecular Flow
differential in vacuum leak testing, pressurizing with Rates between Different Gases
100 percent tracer gas.
If molecular flow occurs, the flow rate for
1000 one gas may be compared to the flow rate
800 for any other gas by Eq. 53:
600
400
200 (53) Q2 = M1 Q1
M2
Leak rate increase ratio 100
80 where Q1 is flow (any units) for gas 1, Q2
60 is flow (same units as gas 1) for gas 2, M1
is molecular mass for gas 1 and M2 is
40 molecular mass for gas 2.
20
10 Conversion of Flow Rates for
8 Molecular Conductance
6
4 The conductance under conditions of
molecular flow for one gas may be
2 compared to the conductance for another
by using the expression of Eq. 54:
1 1.0 10 100
0.1
(10) (100) (1000) M1
(1) M2
Absolute external pressure inside of part (54) C2 = C1
at high vacuum, MPa (atm)
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where C1 is conductance (any units) for Test Variables Limiting
gas 1, C2 is conductance (same units as Leak Testing Sensitivities
gas 1) for gas 2, M1 is molecular mass for
gas 1 and M2 is molecular mass for gas 2. Some factors that prevent leak testing
devices from attaining their ultimate
A few comparisons that may be used sensitivities include geometry, sampling
efficiency, tracer economy and noise (or
for converting either conductance or flow contamination). Geometry enters the
picture because any instrument should
are given in Table 9. and must respond only to local
conditions at its sampling inlet. Two
TABLE 9. Comparison of molecular flow things are of interest in the leak
rates of other gases with helium flow evaluation process: the space coordinates
rates. of the leaking orifice and the mass rate of
leakage. The effects of leak location and
To Convert to Multiply Helium leakage rate on the concentration of tracer
Flow by at the instrument depend on convection
and diffusion of the tracer gas.
Q of argon 0.316
Q of neon 0.447 Sampling efficiency may be thought of
Q of hydrogen 1.410 both as a measure of how nearly all of the
Q of nitrogen 0.374 quantity to be measured is used in
Q of air 0.374 making the measurement and as a
Q of water vapor 0.469 measure of how well extraneous responses
can be excluded. Many leak detectors
Effect of Temperature on Gas must operate with their active parts in a
Conductance with Molecular Flow partial vacuum. This limits the rate at
which samples of the surrounding air can
The effect of temperature on conductance be ingested for analysis. Other leak testing
when the flow is molecular should not be instruments may take in the sample so
overlooked. As can be seen in Eq. 35 and violently that extra turbulences are
36, the conductance changes in direct created near the sampling point. The
proportion with the square root of gas sampling problem is somewhat
temperature. The expression of Eq. 55 is interrelated with the noise and
for a variation in gas conductance contamination problem.
resulting from a change in temperature
only, with pressure and dimensions The ultimate sensitivity of most leak
remaining constant: testing instruments is quoted on the basis
of 100 percent tracer concentration in the
(55) C2 = T2 C1 system or, equivalently, on the amount of
T1 tracer leaking. In a practical situation this
concentration is necessarily kept down for
where C1 is conductance at temperature reasons of safety or economy and
T1; C2 is conductance at temperature T2; sometimes because of corrosiveness of the
T1 is starting temperature, kelvin; and T2 tracer. With reduced tracer concentration,
is new temperature in kelvin. T1 and T2 the leakage sensitivity is reduced
must be absolute temperatures. proportionately. With 1 percent tracer
concentration the sensitivity figure is
Relative Sensitivities of correspondingly reduced by a factor of
Leak Testing Techniques 100.
When choosing a test technique it is Control of Ambient
advantageous to have an insight into the Concentrations of Tracer
relative sensitivities of the various Gases
techniques. Obviously, the test sensitivity
does not equal the published ultimate Changes in tracer gas concentration due
sensitivities of the various detecting to leaks are self obscuring in the presence
devices because of many variables. of random variations in the ambient
Table 10, showing relative sensitivities, tracer gas concentration. Background
may be used to assist in choosing levels of tracer gas in the atmosphere
potentially satisfactory leak testing disturb the predicted gas concentration
techniques. pattern. The problem of distinguishing
leaks from increasing and randomly
varying background contamination may
reduce instrument sensitivities by orders
of magnitude or even destroy test
sensitivity altogether.
Tracer Gases in Leak Testing 57
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TABLE 10. Relative ultimate leakage sensitivities of various leak testing methods under
ideal conditions with very high concentrations of tracer gases. (These numbers are not
intended to be used as guides in practical leak testing.)
______________L_e_a__k_a_g_e__R_a_t_e________________
Minimum Detectable Leakage Test Technique Pa·m3·s–1 (std cm3·s–1)
Pressure drop using liquids Depends on volume tested and gage range
Pressure drop using gases
Pressure rise Depends on volume tested
Ultrasonic leak detector
Volumetric displacement (gas flow meter) Depends on volume tested
Gas discharge
Ammonia and phenolphthalein 10–2 (10–1)
Ammonia and bromocresol purple
Ammonia and hydrochloric acid 10–3 (10–2)
Ammonia and sulfur dioxide
Halide torch 10–3 (10–2)
Air bubble in water
Air and soap or detergent 10–3 to 10–4 (10–2 to 10–3)
Thermal conductivity
Infrared 10–3 to 10–4 (10–2 to 10–3)
Hydrogen Pirani technique
Hot filament ionization gage 10–3 to 10–4 (10–2 to 10–3)
Mass spectrometer detector probe
Halogen diode detector 10–3 to 10–4 (10–2 to 10–3)
Hydrogen bubbles in alcohol
Palladium barrier detector 10–4 (10–3)
Mass spectrometer envelope
Radioactive isotopes 10–4 to 10–5 (10–3 to 10–4)
10–4 to 10–5 (10–3 to 10–4)
10–5 (10–4)
6 × 10–4 to 6 × 10–5 (6 × 10–3 to 6 × 10–4)
10–7 (10–6)
10–7 to 10–8 (10–6 to 10–7)
10–6 to 10–8 (10–5 to 10–7)
10–7 to 10–9 (10–6 to 10–8)
5 × 10–7 (5 × 10–6)
10–8 to 10–9 (10–7 to 10–6)
10–10 (10–9)
10–9 to 10–13 (10–8 to 10–12)
Any gas tracer system, no matter how gas concentration that are caused by
sensitive, that responds to the simple accumulated leakage or by venting tracer
absolute level of concentration will soon gases. The need for controlled
become incapable of detecting leakage environment and ventilating systems is
when the ambient tracer concentration minimized. The reference intake of the
rises to the level capable of giving differential detector is prevented from
spurious signals. This is the major failing sampling in the immediate area of the
of the simple halogen leak detector. leak to avoid fast transients and confusing
indications. However, the differential
Two solutions to the background detector leak sensor is less sensitive than
problem immediately present themselves: either the heated anode halogen leak
(1) keep the ambient concentration low detector or the helium mass spectrometer
and (2) use a gradient sensor (differential leak detector.
detector). One such instrument actually
has two separate detection cells
(Chambers where the temperature
compensator detects are mounted). Each
cell has an individual intake port. The
dual detectors continually compare the
thermal conductivity of the sample gas
(from potential leakage sources) with that
of the ambient atmosphere. When the
sample cell intake is not near a leak, the
two detection cells are sampling the same
gas concentration and their combined
output is zero, giving no output reading.
Only when the leak area is encountered
by the leakage sample intake does the
instrument respond.
The differential detector prevents
interference from gases in the atmosphere
and working area. It eliminates the need
for selectivity to any particular gas. Leak
testing can be performed in areas of high
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PART 4. Mathematical Theory of Gas Flow
through Leaks
Mechanisms of Mass Because turbulent flow is rarely
Transfer in Gas Flow encountered in leaks, the term viscous
flow is sometimes incorrectly used to
Mass transfer attributed to leakage can describe laminar flow in leak testing work.
occur in two modes: pneumatic flow and
permeation. Pneumatic flow occurs when The most familiar laminar flow
leakage is by passage of fluid through equation was developed by Poiseuille.
finite holes. Permeation is passage of a Poiseuille’s equation for laminar flow
fluid into, through and out of a solid through a straight tube of circular cross
barrier having no holes large enough to section is given in Eqs. 21 and 22.
permit more than a small fraction of the Poiseuille’s equation has been
molecules to pass through any one hole. substantially verified experimentally and
is applicable where the length and
Leakage Rates for diameter of the flow passage are known.
Different Modes of This is not the case for most leaks.
Pneumatic Flow of Gas in Equation 21 can be rewritten in the form
Leaks of Eq. 56:
Pneumatic gas flow in leaks may be (56) Q = K Pa P1 − P2
placed in five categories: turbulent, n
laminar, molecular, transition and choked
leakage flows. The approximate ranges of K represents the constants of the two
flow rates for various pneumatic modes of geometry factors of length l and diameter
gas flow follow. d of the tubular leak passage, as shown in
Eq. 57:
1. Turbulent flow occurs with leakage
rate above 10–3 Pa·m3·s–1 (57) K = πr4
(10–2 std cm3·s–1). 8l
2. Laminar flow occurs with leakage rates Laminar flow takes place when the
in the range from 10–2 to 10–7 Reynolds’ number of flow is lower than
Pa·m3·s–1 (10–1 to 10–6 std cm3·s–1). the defined critical value. The Reynolds’
number is a unitless quantity that defines
3. Molecular flow is most probable with the flow conditions and is given by
leakage rates below 10–6 Pa·m3·s–1 Eq. 58:
(10–5 std cm3·s–1).
(58) N Re = d ρF
4. Transition flow occurs in the gradual n
transition from laminar to molecular
flow. where NRe is Reynolds’ number, p is fluid
density, n is gas viscosity, F is average flow
5. Choked flow occurs when the flow
velocity approximates the speed of velocity across a plane in the tube and d is
sound in the gas.
diameter of the leak (compare with
Laminar and molecular flows are the
predominant modes of leakage flow in the Eq. 20).
range of leakage rates of interest in most
leak testing. Reynolds’ Number for Ideal Gas
Characteristics of Laminar By substituting the ideal gas equation (see
(or Viscous) Flow Eq. 9) into Eq. 58, the expression for the
Reynolds’ number for an ideal gas
The laminar flow of a fluid in a tube is becomes Eq. 59:
defined as a condition where the velocity
distribution of the fluid in the cross (59) N Re = Q 4M
section of the tube is parabolic. Laminar d πn RT
flow is one of the two classes of viscous
flow, the other class being turbulent flow. where M is molecular mass, R is molar gas
constant, T is absolute temperature, Q is
leakage rate, d is leak diameter and n is
gas viscosity.
The critical value of Reynolds’ number
has been shown to depend on the
Tracer Gases in Leak Testing 59
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entrance conditions, roughness of the will increase the flow rate through this
walls of a tube and shape of the flow leak by a factor of ten. Obviously then,
path. In general, for smooth tubes with when the leaks to be measured are in the
well rounded entrances, the critical value laminar flow range, the simplest way to
is about 1200. increase leakage sensitivity is by an
increase of pressure across the leak.
Equation for the Viscosity
of a Gas Equations for the Mean
Free Path of Gaseous
The kinetic theory of gases states that the Molecules
viscosity of a gas is given by the
relationship of Eq. 60: The mean free path length is the average
distance that a molecule travels between
(60) n = m Fa successive collisions with the other
molecules of an ensemble. The mean free
3 2 π σ2 path λ of gas molecules is given by Eq. 64:
where Fa is a average velocity of the TABLE 11. Mean free paths at 25 °C (77 °F), molecular
individual molecules, m is molecular diameters, and viscosities for gases and vapors used in
leak testing.
mass, σ is molecular diameter and n is
viscosity of gas. The average velocity of a
gas molecule is given by Eq. 61:
(61) F = 8RT Mean Free Molecular
πM
Path Diameter Viscosity
The mass m of the individual molecules is Gas (mm·Pa) (pm) (µPa·s)
given in terms of the molecular mass M of
a specific gas: Acetylene 9.2
Air 16.9
(62) m = M Ammonia 7.23
N Argon 1.53 9.4
Benzene 4.49 358 20.8
In Eq. 62, N is Avogadro’s number, i.e., Carbon dioxide 765 6.9
number of molecules per mole. Carbon disulfide 3.21 465 13.5
Substituting Eq. 61 and 62 into Eq. 60 Carbon monoxide
results in Eq. 63 for the viscosity of a gas: Dichloromethane 19.5 8.9
Ethane 12.2 17.1
2 M RT Ethyl alcohol
(63) n = Ethylene 5.27 537 8.5
Refrigerant–11 1.86 8.2
3 π3 N σ2 Refrigerant–12 1.51 9.3
Refrigerant–21 1.31
Equation 63 shows that the viscosity of a Refrigerant–22 13.70 10.3
gas is independent of pressure and is Refrigerant–113 11.8
proportional to the square root of Refrigerant–114 6.99 10.8
absolute temperature. Refrigerant–134a 2.32 12.0
Helium
Characteristics of Laminar Hydrogen 4.23 9.8
Gas Leaks Hydrogen sulfide
Methane 218 17.8
The two most important characteristics of n–Butane 275 8.3
laminar leaks shown by Eq. 21 and 22 are n–Pentane
(1) the flow is proportional to the n–Hexane 11.8
difference between the squares of the Neon 419 10.0
pressures upstream and downstream of Nitric oxide 706 10.0
the leak and (2) the leakage is inversely Nitrogen 782
proportional to the leaking gas viscosity. Nitrous oxide 842
Table 11 shows that the viscosity of most Oxygen 260
gases is similar. Therefore, a change of Propane
leaking gas will not markedly increase the Sulfur dioxide 17.8
sensitivity of the leak testing technique Sulfur hexafluoride 16.8
unless this change of gas implies a change Water 13.3
of instrument sensitivity. Xenon 364 19.1
632 7.7
However, as shown in Fig. 15, 11.6
increasing the pressure difference across
the leak by a factor of a little over three 468 8.8
21.0
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(64) λ = 1 The molecular diameters and mean free
2 π n1 σ2 paths of typical leak testing gases and
vapors are listed in Table 11. As a
where n1 is number of molecules in 1 cm3 convenient calculation guide, the mean
volume and σ is molecular diameter. The free path, in meters, of air at room
temperature is given by Eq. 67:
molecular density n1 of gaseous molecules
per unit volume is given by Eq. 65: (67) λ air = 6.8 × 10−3
P
mN
(65) n1 = MV The pressure P is expressed in pascal in
Eq. 67 (compare with earlier Eq. 16).
where m is mass of gas, M is molecular
Equation for Molecular
mass of gas, N is Avogadro’s number, i.e., Flow of Gases
6.023 × 1023 molecules per mole; n1 is
number of gaseous molecules per unit Molecular flow is flow through a duct
under conditions where the mean free
volume; and V is volume containing the path is greater than the largest dimension
of a transverse section of the duct. In such
gas. Replacing the volume V in Eq. 65 by a flow, each atom moves independently
by random movement. Net flow is from a
its value mRT/P from the ideal gas law of volume of high concentration to one of
low concentration. The original
Eq. 9 and substituting it in Eq. 64 results mathematical derivations of molecular
flow are attributed to Knudsen (see
in the equation for the mean free path Eqs. 23 to 27). The rate of gas flow in a
length λ of Eq. 66: long tube is given by Eq. 68:
(66) λ = MRT
2 πPN σ2
which shows that at constant pressure the (68) Q = d3( )2π RT
mean free path is proportional to absolute 6lM
temperature. However, if the amount of P1 − P2
gas in a volume is kept constant, the
mean free path is independent of
temperature, as indicated in Eq. 64. In
Eq. 66, R is the specific gas constant and
MR equals the molar gas constant.
FIGURE 15. Relation of leakage to pressure differential with where d is diameter of the tube, l is length
laminar flow of helium gas in typical hardware leak. of the tube and P2 and P1 are pressures at
the two ends. For the formula of Eq. 68 to
Pressure across leak (lbf·in.–2) apply, the tube must be of a circular cross
section. For tubes and ducts of a
1 2 5 10 20 50 100 noncircular cross section, the conductance
(10–1) is less than for tubes of circular cross
10–2 section and equal area. Equation 68
applies only if the tube is much longer
than its diameter. Any difficulty
experienced by a molecule in entering the
tube must be negligibly small compared
to the difficulty in transversing its length.
Leakage rate, Pa·m3·s–1 (std cm3·s–1) 10–3 (10–2) Equation for Free
Molecular Entry of Gases
10–4 (10–3) into a Small Aperture
If gas molecules experience difficulties in
entering a small leak opening, the kinetic
theory shows that the rate of free
molecular escape of gas from the
container into a small aperture of area A is
given by Eq. 69:
(69) Q = ( )RT
2πM
A P2 − P1
10–5 (10–4)
10 20 50 100 200 500 1000 In the case of an aperture, the leak
opening does not have to be circular for
Pressure across leak (kPa) this equation to apply.
Legend
= Theoretical values
= Measured values
Tracer Gases in Leak Testing 61
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Flow Characteristics of 1. the flow is not turbulent in any part of
Molecular Leaks the pipe and
The conductance of lines and apertures in 2. the pressure difference between the
molecular flow is independent of pressure. ends is not so great that the
Calculations may be made of the effect of mechanism of the flow, i.e., laminar or
turns, apertures and change in tube molecular, changes along the pipe.
diameter to calculate the overall flow in a
leak. Although the first of these conditions
is usually satisfied in the leak, the second
Equations 23 to 27, 68 and 69 generally is not: that is, the transition
demonstrate the general form of relations from laminar to molecular flow does take
for molecular flow through leaks. They are place within a leak. Equation 70 at low
not applicable in most leakage situations pressures becomes an equation of
because the leak length and diameter are molecular flow, whereas at high pressure
not known. The molecular flow of each this equation reduces to one of strictly
individual species in a gas mixture is laminar flow.
inversely proportional to the square root
of the individual masses. Therefore, a Knudsen used Eq. 70 to represent his
certain amount of separation of gaseous experimental data. This equation has the
species takes place during flow through a effect of molecular flow added to the
leak. In molecular flow, the gas molecules effect of laminar flow; consequently, it is
travel independently of each other. Thus, not an actual representation of the flow
it is possible for random molecules to mechanism taking place in the leak. The
travel from a part of a system at low phenomenon is better visualized by
pressure to another part of the system at a realizing that both are occurring at the
higher pressure. same time.
Burrows Equation for Transitional
Flow
Knudsen Equation for Burrows combined Eq. 23 to 27 for
Transition Flow laminar flow with that of Eq. 68 for
molecular flow to obtain the general
The transition from laminar flow to relation for transitional flow given in
molecular flow is gradual. The Eq. 71:
mathematical treatment of this region is
extremely difficult, but is necessary π d4 Pa
because a leak from a volume to a vacuum 8 2 nl
necessarily involves a transition from =( )(71) Q
laminar to molecular flow. Equation 68 P1 − P2
shows that the conductivity of a passage
in molecular flow is proportional to the 2π RT d3
cube of the passage diameter and M 6l
independent of pressure. Conversely, ( )+
Eq. 21 and 22 show that the conductivity P1 − P2
of the same passage in laminar flow is
proportional to the pressure. In a way, Eq. 71 accurately represents the
events occurring in the leak. Both laminar
Knudsen derived a semiempirical and molecular flow always occur in a leak.
formula for the conductance of gas However, laminar flow is insignificant at
flowing through long tubes in the low pressures. The molecular flow mode
transition flow region: contributes little to total flow at high
pressures.
(70) C = Cviscous + ZCmolecular
Equation 71 is not completely accurate
= π d 4 Pa because of a slipping of molecules in
8 2 nl transition flow. In laminar flow, the
velocity of the molecular layers is
+ 1 2 RT d3 proportional to their distance from the
M l wall, the first layer being stationary. In
6 the transition region, slipping of the gas
over the walls of the tube occurs; that is,
1+ M Pa d the flow velocity at the walls is not zero.
RT n At pressures below the viscous limit, the
× slip correction becomes an appreciable
contribution to the total conductance.
1 + 1.24 M Pa d
RT n With further reduction in pressure, the
dependence of flow conductance on
In this case, the gas flow rate Q = pressure becomes more complex. The flow
characteristics begin a progressive change
C(P1 – P2), where C is defined by Eq. 70. from those of viscous slip flow to those of
Equation 70 is valid providing that: molecular flow, where the conductance
becomes independent of the pressure. The
complete transition from viscous to
molecular flow takes place over roughly
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two orders of magnitude change in γ
pressure. This effect of slip can change the
predicted flow rate by at least 20 percent. (73) rc = P2 = 2 γ −1
Because of this effect, Eq. 70 better P1 γ + 1
represents flow in the transition region
but cannot handle the total transition The term γ is the ratio of specific heats
region. defined by Eq. 75 below. The velocity of
sound through a gas can be written as in
Other authors have attempted to derive Eq. 74:
equations to represent this phenomenon
of transition from one type of flow to (74) Fc = 2γ RT1
another. One simple way is to calculate γ +1 M
laminar flow through one section of the
tube, calculate molecular flow through where Fc is velocity of sound and T1 is
another and approximate the region absolute temperature upstream of the
between them. orifice where the velocity is low. The ratio
of specific heat at constant pressure to
Characteristics of that at constant volume is described by
Turbulent Flow of Gases gamma (γ), the ratio of specific heats
defined in Eq. 75:
In viscous flow above a critical value of
the Reynolds’ number (about 2100 in the (75) γ = C p
case of circular pipe flow), flow becomes Cv
unstable, resulting in innumerable eddies
or vortexes in the flow. Any particle in where Cp is heat capacity at constant
turbulent flow follows a very erratic path, pressure and Cv is heat capacity at
whereas in laminar flow the particle constant volume.
follows a smooth line. Turbulent flow
occurs only in rather large leaks because it The mass flow rate under a choked
requires relatively high velocity.
flow condition is given by Eq. 76:
The laws for turbulent flow are quite
different from the laws for laminar flow. πd 2 P1Co
The equation relating mass flow rate Q in
units of pressure × volume/time may be (76) Q = 4M
written as Eq. 72:
RT1 γ 2 γ +1
+ 1 γ −1
γ
(72) Q = π d5 ( )RT P12 − P22 where d is orifice diameter, P1 is upstream
pressure and Co is orifice discharge
16f Ml coefficient.
The friction factor f depends on The value of γ for an ideal monatomic
roughness of the channel walls and can gas is 1.67. For polyatomic molecules, the
be considered a constant in fully
developed turbulent flow. heat energy supplied is used for increasing
Theory of Choked (or not only the kinetic energy of translation
Sonic) Flow of Gases
through Leaks but also the kinetic energy of rotation and
The phenomenon of choked flow (also vibration. Because the same amount of
known as sonic flow) of gases is described
above. Two conditions required for extra energy is required at both constant
choked flow to occur are: pressure and constant volume, γ decreases
with molecular complexity. Characteristic
1. The flow passage must be in the form values of γ are listed in Table 12.
of an orifice or venturi in which only
negligible fractional losses occur TABLE 12. Specific heats of gases at constant pressure Cp,
upstream of the orifice or throat of the at constant volume Cv, and as the ratio γ of Cp·Cv–1, in
venturi. joule per mole of gas at 25 °C (77 °F) and 100 kPa
(1 atm) pressure.
2. The ratio of downstream to upstream
pressure must be below a certain Gas Cp Cv Cp·Cv–1 = q
critical value.
Argon 20.8 12.5 1.67
The critical ratio rc of downstream Helium 20.8 12.5 1.67
pressure P2 of upstream pressure P1 Hydrogen 28.8 20.5 1.41
required for choked flow is given by Oxygen 29.5 21.1 1.40
Eq. 73: Nitrogen 29.0 20.7 1.40
Carbon dioxide 37.5 28.9 1.29
Ammonia 36.1 27.5 1.31
Ethane 53.1 44.5 1.19
Propane 73.6 65.2 1.13
Tracer Gases in Leak Testing 63
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Because of the stringent requirements, (82) N Re > 2100
choked flow is rarely encountered as the
predominant flow mode except in very for turbulent flow,
large leaks.
(83) N Re < 1200
Criteria for Distinction
between Modes of Gas for viscous flow and
Flow in Leaks
(84) 1200 < N Re < 2100
Equations have been presented for the
various possible modes of flow that can be for either turbulent or viscous, depending
encountered in a leak. The following rules on duct conditions.
may be used to predict the mode most
likely to occur. In distinguishing between Choked flow takes place when the
laminar and molecular flow, the size of pressure ratio between outlet and inlet
the passage and the mean free path are reaches a certain minimum value. This, of
the two important parameters. The course, depends on other characteristics,
distinction may be specified by a such as aperture dimension. The formula
dimensionless parameter called the for the critical pressure ratio for choked
Knudsen number. The Knudsen number is flow depends on the ratio r defined in
defined as the ratio of the mean free path Eq. 73. The critical ratio below which
of the molecule to a characteristic choked flow takes place is given by
dimension of the channel through which Eq. 73. Choked flow cannot take place
the gas is flowing. The Knudsen number is when P1 is so low that molecular flow
defined by Eq. 77: exists.
(77) NK = λ General Formula for
d Gaseous Permeation Flow
Rate
where NK is Knudsen number, λ is mean
free path and d is channel diameter. Permeation is passage of a fluid into,
through and out of a solid barrier having
The type of flow encountered in the no holes large enough to permit more
various Knudsen number ranges is than a small fraction of the molecules to
described by Eqs. 78 to 80: pass through any one hole. The process
always involves diffusion through a solid
(78) λ < 0.01 and may involve other phenomena such
d as adsorption, solution, dissociation,
migration and desorption. The general
for laminar flow, formula for permeation is given by Eq. 85:
(79) λ > 1.00 A ∆P SD A ∆P
d l l
( )(85)q=Kp =
for molecular flow and
(80) 0.01 > λ > 1.00 where Kp = SD; q is rate of mass flow
d (Pa·m3·s–1·m2); S is solubility coefficient;
for transition flow. D is diffusion coefficient; Kp is permeation
Flow in the viscous region is rate constant (per second); A is area
normal to flow (square meter); ∆P is
determined by the Reynolds’ number pressure drop along the flow path
described earlier in Eq. 58 and 59 and
repeated in Eq. 81: (pascal); and l is length of flow path
(meter). The ∆P in Eq. 85 does not
(81) N Re = d ρF = Q 4M represent absolute pressures, but the
n d πnRT
difference in partial pressure of the
leaking fluid between the two sides of the
barrier.
where d is channel diameter, ρ is fluid Permeation of Helium through
density, F is flow velocity, n is gas Rubber
viscosity, Q is leakage rate, M is molecular
mass, R is gas constant and T is absolute Permeation presents a problem in leak
temperature. testing equipment where the construction
materials have a high permeability to the
The distinction between laminar and tracer gas. For example, if a component
turbulent flow is shown by the numerical containing a rubber diaphragm 1 mm
criteria of Eqs. 82 to 84: (0.04 in.) thick and 650 mm2 (1.0 in.2) in
surface area is leak tested using helium
64 Leak Testing
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gas, a leakage of about 1 × 10–6 Pa·m3·s–1 material to be saturated with gas. This
(1 × 10–5 std cm3·s–1) will be measured is only possible if the material is
across the diaphragm. relatively thick. For example, a rubber
diaphragm will rapidly saturate and
This leakage is due to permeation of almost immediately show leakage. On
helium through the diaphragm and not to the other hand, O-rings are relatively
any actual holes. It represents the thick and will not saturate rapidly
maximum sensitivity of helium leak enough to give a reading within a
testing that can be performed on this reasonable period of time (5 min). If
component. However, if the component is the diffusivity and solubility of the
to be used with another fluid to which fluid in the material are known, it is
the membrane is impermeable, the possible to calculate the rate of
apparent leakage due to permeation increase of leakage. However, in many
measured during the leak testing has little cases (where the leakage path is long),
meaning under operating conditions. this calculation is not necessary.
Rather than calculations, experimental
Another example of this type of false results can determine very quickly if
reading is a rubber O-ring. Depending on leakage through a thick gasket is
material, a rubber O-ring usually inconsequential for short time periods.
represents a permeability of about 2. The maximum permeability of all
5 × 10–7 Pa·m3·s–1 per centimeter of O-ring components and the resulting mass
surface exposed for every 100 kPa transfer produced by permeability
(14.5 lbf ·in.–2) of differential pressure. during leak testing may be calculated
Figure 16 is an example of the permeation (refer to Eq. 85, below). In this way,
rates of O-ring of various materials. This the permeability value will be known
permeability does not have to be taken and only leakage above this value will
into consideration during routine leak be considered as leakage flow.
testing if leakage measurement occurs in a 3. The last and most difficult way is to
time too short to permit the saturation quantitatively measure the leakage at
and mass transfer of helium through the various pressure differentials. If gas
O-ring. leaks through a hole in the
component so that the leak being
Procedures for Reducing Gas measured is pneumatic and laminar,
Permeability Effects during Leak the flow is proportional to the square
Testing of the pressure differential across the
leak. However, if the flow is strictly
To reduce permeability as a factor in due to permeation, then the flow
leakage measurement, three procedures through the leak will be directly
may be used: proportional to the difference in tracer
gas concentration across the leak. In
1. The leakage measurement may be this way, the presence of holes in the
taken rapidly, not allowing the component can be differentiated from
permeation.
FIGURE 16. Permeation rate of helium at differential pressure
of 100 kPa (1 atm) through O-rings of 4 × 4 mm (0.16 × General Guide to Estimating Gas
0.16 in.) cross section, per 25 mm (1 in.) of length at 25 °C Flow Rates through Leaks
(77 °F) in units of pascal cubic meter per second (left vertical
scale) and torr liter per second (right vertical scale). Table 10 lists the theoretical ultimate
leakage sensitivities of various leak testing
Silicone (composition: 20 percent) techniques under ideal conditions with
very high concentrations of tracer gas. It
10–6 10–5 is derived from the various flow equations
10–7 presented in the text. As may be seen
Permeation rate (Pa·m3·s–1)10–8 from Tables 8 to 10, the influence of
permeation rate (torr·L·s–1) varying the gas is not so great as that of
Natural (composition: 10 percent) 10–6 varying the flow mode. Once the flow
Hydrocarbon (composition: 10 percent) mode is determined, the conversion to
another gas should be relatively easy to
Synthetic rubber (composition: 10 percent) make, providing the relationships in Table
10–7 10 are in fact correct. The major difficulty
is identifying the predominant flow
10–9 10–8 mode.
0 30 60 90 120 150 180 200 The data necessary for the conversion
Time (min) of leakage rates between various gases are
relatively easy to obtain. For example, the
viscosity of many gases is published. Even
if the viscosity is not known,
approximation should not produce a large
Tracer Gases in Leak Testing 65
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error. As shown in Table 11, the viscosity 1. If pressure is increased, correlate as
of gases at constant temperature varies by laminar.
less than half an order of magnitude
between the most viscous and the least 2. If pressure is decreased, correlate as
viscous. molecular.
For molecular flow, data on the 3. If gas is changed, correlate as
molecular mass of the gases is easily molecular.
available and should cause no problem in
the conversion (see Table 5). If choked Correlation should be performed so
flow does occur, the gamma of Eq. 75, that, if an error is made, actual leakage
necessary for conversion of choked flow will be no greater than that predicted in
leakage, is 1.67 for monatomic gases and the correlation. Correlation of leaks
rapidly approaches 1 as the complexity of resulting from increased pressure across a
the gas molecule increases. leak is not recommended. An actual
measurement should be made whenever
Effect of Leak Size on Mode of possible to verify leakage rate.
Gas Leakage Flow
Equation for Gas Leakage
By working with a variety of leaks of Flow Rate in Laminar Flow
different sizes and under different
conditions, some of the flow modes may Assuming the flow mode has been
readily be eliminated. For example, if the identified, the following are sample
leakage rate is small, it is relatively easy to calculations for correlation of flow rates
assume that no turbulent flow will take with the use of different gases and
place. If the leakage goes from high pressure. The first sample calculation is
pressure to a slightly lower pressure, but for laminar flow. The general equation for
not to a vacuum, it is likely that laminar flow of gases is given by Eq. 86:
molecular flow is not the flow
mechanism. In this case, the flow may be π d4
of a laminar nature and therefore 8nl 2
conversion to a second flow pressure is ( )(86) Q=
relatively easy. Choked flow is rarely Pa P1 − P2
encountered in small leaks.
where Q is leakage (mass flow in units of
Another example is that of converting pressure × [volume/time]), d is average
the leakage rate for gas flowing into a diameter of leak hole, P2 is pressure on
vacuum to an anticipated rate for a the entrance side of the leak, P1 is
different pressure driving gas into the pressure on the exit side of the leak,
same vacuum. If the leak is of relatively average leak inlet and leak outlet pressures
small size, 10–6 Pa·m3·s–1 (10–5 std cm3·s–1) Pa = (P1 + P2)/2, n is viscosity of the
or less, molecular flow will play a major leaking fluid or fluid mixtures and l is
role in such a leak. However, should the leak length. Note that Eq. 86 is equivalent
leak be relatively large, 10–4 Pa·m3·s–1 to Eq. 21 given earlier.
(10–3 std cm3·s–1) or greater, the leakage
will be predominately laminar. If one can The leak dimension of d and l are
accurately predict the type of flow that usually not known. An apparent
will predominate in a leak, one could conductance C may be calculated by the
therefore make accurate conversions to a formula, where this apparent conductance
different set of conditions. Unfortunately, is the product of π(d/2)4/8 l and any unit
the state of the art is such that these conversion factors. From this calculation,
predictions are usually not possible. an apparent leak geometry factor can be
calculated from Eq. 87:
Estimating Mode of Gas
Leakage Flow from (87) C = π d4
Leakage Rate and Pressure 128 l
Many authors have predicted the following If C is calculated only for conversion
predomination flow modes in leaks of from one flow to another, the constant
various sizes: turbulent flow, 10–3 Pa·m3·s–1 does not have to be in compatible units,
(10–2 std cm3·s–1); laminar flow, 10–2 to providing that the same units are used
10–7 Pa·m3·s–1 (10–1 to 10–6 std cm3·s–1); both in solving for C and using the C in
transition flow, 10–5 to 10–7 Pa·m3·s–1 (10–4 correlation equations.
to 10–6 std cm3·s–1); molecular flow,
10–7 Pa·m3·s–1 (10–6 std cm3·s–1) . When Using the apparent conductance C
there is doubt about the correctness of flow calculated above, the flow of any gas at
identification, the following procedure is operating pressure may be predicted by
recommended. using Eq. 88:
( )(88) QC
= n P12 − P22
A similar apparent conductance may be
calculated for other flow modes using the
66 Leak Testing
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equations given earlier in this section. leak cannot be seen below a critical
Such calculations are correct only if the pressure.
flow mode has been correctly chosen.
Effects of Geometry Change in
Categories of Anomalous Leaks
Leaks
The shape of a leak may change with
Four types of leaks have been encountered changes in system pressure. As pressure
that do not fit in the categories already increases, the expansion of system parts
discussed: (1) check valve leaks, (2) surface resulting from stresses induced by the
flow leaks, (3) geometry change leaks and increased pressure can cause leakage rates
(4) self-cleaning leaks. of known leaks to increase beyond the
The errors in leak measurement because of predictions of laminar flow theory. Figure
these types of leaks could be greater than 18 illustrates this increase of leakage rate
any errors inherent in the preceding with geometry change.
equations for flow conversions.
Effects of Self-Cleaning Leaks
Effects of Check Valve Leaks
If gaskets under compression are subjected
Examples of check valve and geometry to a high helium pressure and the leakage
change leaks have been found during rate is determined quantitatively, the
studies of leakage phenomena. Figure 17 slope of the pressure leakage line is found
is a plot of the leakage-pressure to be greater than two. No flow regime
differential obtained on a damaged needle would produce such a slope. However,
valve. It was observed that although the these curves consist of a series of lines
typical laminar flow curve was obtained at with a slope corresponding to that for
a high pressure differential, below this laminar flow.
pressure, the leakage abruptly stopped. On
increasing the pressure, the leak Because the increase in leakage could
reappeared. This phenomenon was result from a permanent deformation of
repeatable. This type of leak would be the gasket, an experiment was run using
particularly hard to detect because the an aluminum gasket too sturdy to be
deformed. Figure 19 shows the data
obtained during this experiment. During
the original increase in pressure, the
leakage increased at a rate greater than the
FIGURE 17. Check valve leakage effect in hardware leak.
Pressure across leak (lbf·in.–2) FIGURE 18. Effects on leakage of geometry changes in
gasket.
12 5 10 20 50 100 Pressure across leak (lbf·in.–2)
103 104
10–4 (10–3)
102
10–6 (10–5)
10–5 (10–4)Leakage rate, Pa·m3·s–1 (std cm3·s–1) 10–7 (10–6) Broken lines indicate
10–6 (10–5) Leakage rate, Pa·m3·s–1 (std cm3·s–1) 10–8 (10–7) theoretical laminar flow slopes
Leakage drops to less than 10–9 (10–8)
10–4 Pa·m3·s–1 (10–3 std cm3·s–1)
10–7 (10–6) 12 5 10 20 50 100
10 20
50 100 200 500 1 000
Pressure across leak (kPa) Pressure across leak (MPa)
Tracer Gases in Leak Testing 67
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square of the pressure increase. However, solid provides binding sites for the gas
on releasing the pressure, the leakage atoms and the electronic structure of the
decrease was proportional to the square of solid permits the formation of a
the pressure decrease. A second increase chemisorption bond. The nature of the
in pressure produced an increase that binding sites, the bonds between the gas
retraced the leakage encountered during atoms and the surface all influence the
the pressure decrease. It is believed that degree of surface migration of the atoms.
the original pressure increase cleaned the
leakage passages. Further pressure cycling The flow along a fine capillary or
did not affect the maximum leakage. This micropore is assumed to consist of two
suggests that whenever possible, leak mechanisms working simultaneously:
testing should be done at the proposed (1) molecular flow along the bore of the
operating pressure, in order that potential capillary, whereby molecules are supposed
leaks may be formed and observed. to collide with the wall, reevaporate and
collide with the wall again without
Characteristics of intermolecular collisions; and (2) surface
Absorbed or Surface Flow flow along the wall of the capillary,
Leaks whereby molecules are adsorbed and
diffuse along the surface of the wall. Both
The flow of gases and noncondensing these mechanisms promote gas flow from
vapors through fine capillaries and regions of higher gas concentrations to
micropores cannot be dealt with by regions of lower gas concentrations.
means of simple techniques analogous to
those applicable to molecular and laminar Factors Influencing Surface Flow
flow. The narrow passages and large of Gases
surface areas involved cause surface
adsorption and surface flow to become For a given set of conditions, the
important factors. proportion of molecules that follow the
mechanisms of adsorbed or surface flow
The adsorption may be physical, where leakage depends on a variety of factors,
only relatively weak van der Waals including (1) the sticking probability (the
attractions are involved. However, the probability that a molecule sticking the
adsorption may also be regarded as surface will become adsorbed), (2) the
chemical. In this case, the surface of the length of time the molecule remains
adsorbed (the mean surface lifetime of the
FIGURE 19. Leakage curves showing self-cleaning effects in gas molecules) and (3) the coefficient of
leaks. surface diffusion of the gas molecules.
These features are, in turn, influenced by
Pressure across leak (lbf·in.–2) other characteristics, such as the number
of sites occupied by the adsorbed
10 20 50 100 200 500 1000 molecules or whether a complete
10–5 (10–4) monolayer is involved.
Leakage rate, Pa·m3·s–1 (std cm3·s–1) 10–6 (10–5) The nearer the properties of a gas
approach those of a condensable vapor,
10–7 (10–6) the greater the proportion of surface flow.
Therefore, a reduction of temperature or
10–8 (10–7) an increase of pressure may sometimes
promote a total flow in excess of that
0.1 0.2 0.5 1.0 2.0 5.0 10 predicted by the laminar molecule theory.
Pressure across leak (MPa) Although the final leakage rate
achieved with a condensable gas may be
Legend higher than predicted from flow theory,
there may be an initial delay of flow
= Pressure decrease because of condensation of the tracer gas
= Second pressure increase on the leak surfaces. This delay is
= Initial pressure increase important if a tracer probe technique is
used for testing. For example, if butane, a
readily condensable gas, is used in the
tracer probe, some small leaks will be
missed because of the delay caused by the
adsorption. Two remedies can be
suggested to counter this problem: use of
a noncondensable gas and use of a
detector probe with condensable gases.
With use of a detector probe, the gas is
continually in contact with the leak and
equilibrium is established.
68 Leak Testing
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References
1. Nondestructive Testing Handbook,
second edition: Vol. 1, Leak Testing.
Columbus, OH: American Society for
Nondestructive Testing (1982).
2. Slattery, J.C. and R.B. Bird.
“Calculation of the Diffusion
Coefficient of Dilute Gases and of the
Self-Diffusion Coefficient of Dense
Gases.” AIChE Journal. Vol. 4, No. 2.
New York, NY: American Institute of
Chemical Engineers (1958): p 137-142.
Tracer Gases in Leak Testing 69
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3
CHAPTER
Calibrated Reference
Leaks1
Mark D. Boeckmann, Vacuum Technology,
Incorporated, Oak Ridge, Tennessee
Charles N. Sherlock, Willis, Texas
Stuart A. Tison, National Institute of Standards and
Technology, Gaithersburg, Maryland
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PART 1. Calibrated Reference Leaks
Terminology Applicable to specification requires some arbitrary
Reference, Calibrated or standard. However, if any doubt exists,
Standard Leaks one need only reduce the leakage of this
arbitrary standard physical reference leak
Physical leaks suitable for checking leak by a sufficient safety factor to ensure that
detector performance and leak test test sensitivity meets the practical leakage
sensitivity are a vital component of requirement within some estimated
instrumentation for leak testing. The confidence interval.
terms reference, calibrated and standard
leaks have been used in the past to Classification of Common
identify these physical leaks. To many Types of Calibrated or
people, the term calibration implies the Standard Physical Leaks
existence of a universally accepted
standard such as those at the National Calibrated physical leaks are designed to
Institute of Standards and Technology. deliver gas at a known rate. The most
common use of such leaks is in the
The National Institute of Standards and measurement of sensitivity of leak
Technology has performed calibration of detectors. However, calibrated leaks are
helium leaks (capillary and permeation) also used to measure the speed of vacuum
over the range of 10–14 to 10–6 mol·s–1 pumps and to calibrate pressure gages. A
(2.3 × 10–11 to 2.3 × 10–3 Pa·m3·s–1) on a standard physical leak makes feasible the
routine basis. The uncertainties in leak establishment of leakage rate
rate vary from less than 1 percent at requirements for specifications. It also
10–6 mol·s–1 (2.3 × 10–3 Pa·m3·s–1) to as provides a uniform reference standard for
much as 5 percent at 10–14 mol·s–1 calibrating leak detectors at different
(2.3 × 10–11 Pa·m3·s–1). Additionally, the locations where products are inspected.
National Institute of Standards and This ensures more uniform agreement of
Technology will calibrate leaks with other all tests.
gases over this range on a special test
basis. All of these calibrations are Calibrated leaks may be divided into
performed while the gas is exhausted into two distinct categories: (1) reservoir leaks
a vacuum. Leaks may also be calibrated by that contain their own tracer gas supply
commercial companies that derive their and (2) nonreservoir leaks to which tracer
measurement uncertainty from either of gas is added during testing. Figure 1
two techniques. The first is that they shows a classification of physical leaks
derive their measurements from leaks used for reference, calibration or standard
calibrated at the National Institute of leaks.
Standards and Technology and perform
calibrations using a comparison Accuracies of Reservoir Calibrated
technique. The second technique uses Leaks
secondary techniques that derive the leak
rate through measurements of pressure, The uncertainty in the leak rate of fixed
volume, temperature and time with reservoir leaks is due to a combination of
instruments whose calibration can be calibration uncertainty, leak rate decay
traced to the National Institute of because of calibration, temperature effects
Standards and Technology. The and leak instability. Of these, uncertainty
appropriate type of calibration will in the stability of the leak is hardest to
depend on particular measurement quantify. Changes in the leak rate may
requirements including the required occur in capillary leaks because of partial
accuracy, traceability or regulatory issues. blockage of the capillary. Changes in the
leak rate of glass permeation leaks may
In some cases, accuracy in leakage occur because of the development of
measurement is not of prime importance. microcracks in the glass. In general, these
Rather, most practical situations require leaks are more stable than leaks without
that some particular leakage value not be closed reservoirs, particularly for
exceeded. It need only be established that calibrated leaks with values less than
no leakage in the tested system is greater 10–9 mol·s–1 (2.3 × 10–6 Pa·m3·s–1).
than this allowable maximum leakage
rate. This practical approach to leakage
72 Leak Testing
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Accuracies of Nonreservoir correction for pressure, temperature and
Calibrated Leaks other environmental factors. In the tracer
probe mode of leak detection, tracer gas is
The nonreservoir type of leak provides sprayed on the calibrated leak under the
only a hole or a series of holes and same conditions that exist when the leak
passages that permit gas to pass through detector is used to measure a leak in any
at a known rate. The users of this type system or enclosure under test.
calibrated leak must provide gas at a
known concentration, purity and In the case of a leak containing a
pressure. reservoir, the measured sensitivity of the
leak detector is independent of the test
The uncertainty in the leak rate of gas pressure and of the tracer gas
nonreservoir leaks is due to a contamination of ambient air surrounding
combination of calibration uncertainty, the leak testing area. If the calibrated leak
temperature effects, leak instability, is to be used for the measurement of an
pressurizing gas purity and uncertain absolute value, as in the case of the
measurements of gas pressures and calibration of a pressure gage or
temperatures. Most if not all nonreservoir measurement of the speed of a pump, a
leaks are physical leaks and are susceptible leak carrying its own gas supply is
to plugging. Because of this it is very desirable.
important that the input gas be free of
particulates and hydrocarbons. In Basic Categories of
addition the output should be exposed to Calibrated Gas Leaks
as little contamination as possible,
especially when the leak is not Generally, leaks may be grouped into
pressurized. Nonreservoir type leaks are either of two categories: (1) leaks that
typically used for higher leak rates, greater depend on the permeation of some
than 10–9 mol·s–1 (2.3 × 10–6 Pa·m3·s–1), materials by certain gases and (2) leaks in
where the depletion rate of reservoir leaks orifices that permit the flow of any gas
becomes greater than 20 percent per year. when a pressure differential is exerted
The temperature coefficients of leaks can across the element.
be measured to account for changes in the
leak rate as a function of temperature. Variation of the material composition,
the membrane dimensions and the partial
Comparison of Standard Leaks pressure differential of gas across the
with and without Tracer Gas element permit the attainment of an
Reservoirs almost infinite range of flow rates. The
temperature coefficients of the
In proper leak testing practice, the permeation leak systems are appreciable.
sensitivity of leak detectors is checked This provides an additional means of
frequently by calibrated leaks of reservoir extending the flow range, particularly
types with internal gas supply. For system when the other parameters are fixed or
sensitivity checks, a calibrated leak limited.
without a reservoir is preferable because it
closely imitates the behavior of an actual Leaks that permeate through a
leak in the object or system under test. fluorocarbon resin membrane are also
The calibrated leak without a reservoir is available with properties similar to those
open to local atmospheric pressure; of gas leaks. The second category of orifice
therefore, it requires no sensitivity leaks permits the attainment of a wide
range of flow rates by modification of the
FIGURE 1. Categories of artificial physical leaks commonly spoken of as “reference,”
“calibration” or “standard” leaks.
Leaks
Reservoir Nonreservoir
Permeation Capillary Porous Capillary Porous
plug plug
Glass Fluorocarbon
resin Fixed Variable Fixed Variable
value value value
value
Fixed Variable
value value
Calibrated Reference Leaks 73
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element dimensions and the pressure reservoir standard leaks with low leakage
differential across the element. rates of the order of 2 × 10–7 Pa·m3·s–1
Temperature is not as great a factor (2 × 10–6 std cm3·s–1) or less.
because the temperature coefficients are
small with glass orifice standard leaks. During manufacture of calibrated leaks,
additional effort and weight can extend
Properties Designed in Calibrated the upper limit of flow by as much as a
Gas Leaks factor of 50 without allowing the
depletion of the gas supply to cause a
The range of possible flow rates of falloff in leakage rate greater than
calibrated leaks is rather severely limited 10 percent per year. Greater increases of
by practical considerations in the the upper limit call for nearly linear
selection of parameters for the increases in volume of the leak gas
construction of leaks for quantitative reservoir and even greater increases in
standards. An ideal calibrated leak should weight. These reduce the portability and
have the following properties. ease of installation of standard leaks.
1. The leakage rate should be constant Limitations of Flow Rate
and should remain unaffected by Calibration of Standard Gas Leaks
ambient conditions.
The lower limit of flow rate that is
2. The calibration should be accurate. practical for direction calibration is about
3. The physical size should be 10–11 Pa·m3·s–1 (10–10 std cm3·s–1). The
degassing of the system becomes a
convenient. problem as the size of the leak is decreased.
4. The calibrated leak should not be too In this range the changes of both true
leakage and virtual leakage caused by
delicate or fragile. pressure increase are nearly equal.
5. The calibrated leak should have its
Two indirect techniques may be used,
own gas supply. either separately or in combination, to
calibrate with reasonable accuracy in the
Temperature Coefficients of low ranges; both techniques have been
Calibrated Leaks experimentally justified. The calibration
may be made by comparison with a
Unfortunately, those parameters useful in standard of greater flow rate by means of
extending the possible range of flows are a mass spectrometer. The actual rate is
not conducive to constancy. The high extrapolated (assuming linear response of
temperature coefficients of the membrane the instrument). Alternatively, the leakage
leaks are particularly disturbing when the rate may be increased in a manner in
changes in ambient temperatures are which the response is predictable (i.e., the
frequent and there is no way of pressure response of membrane leaks is
determining whether or not the linear) and calibration made at the higher
equilibrium flow rate is reached at any flow rate.
one temperature. Even the relatively small
temperature coefficients of orifice leaks Limitations of Glass Membrane
are appreciable when the temperature Standard Gas Leaks
varies over wide ranges.
Construction of all-glass membrane leaks
The National Institute of Standards and that vary in flow range at ambient
Technology measures the temperature temperatures from 0 to 50 °C (32 to
coefficients of leaks as a normal part of 122 °F) is rather simple. Larger flows
their calibration service over the range of require either higher pressures or
0 to 50 °C (32 to 122 °F). Some modification of membrane parameters
manufacturers of calibrated leaks may also that tend to make them excessively
be able to measure temperature fragile.
coefficients. Normally manufacturers
assume a linear temperature coefficient of It is possible to combine a number of
3 to 4 percent per 1 °C (2 °F) for glass the large leak elements in parallel to
helium permeation leaks. For the lowest obtain greater flow when necessary.
uncertainties the temperature coefficients Advantage has been taken of the relatively
should be measured. sturdy nature of glass tubing of very small
cross section and correspondingly thin
Size, Weight and Portability of walls. Elements have been made using
Calibrated Gas Leaks literally miles of such tubing in systems
designed for use at relatively high
The convenience of the physical size is a temperatures to separate low
property that would vary considerably, concentrations of helium from natural
depending on the use to which the gases. However, these elements do not
calibrated leaks is applied. In general, seem suitable for use under high vacuum
complete and convenient portability of conditions.
standard leaks is desirable and is usually
available in nonreservoir standard leaks.
Portability is easily attainable with
74 Leak Testing
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Limitations of All-Glass Orifice Basic Characteristics of
Standard Leaks Orifice Standard Leaks
All-glass orifice leaks are more difficult to The orifice standard leaks share several
produce with flow rates smaller than characteristics.
5 × 10–9 Pa·m3·s–1 (5 × 10–8 std cm3·s–1)
unless precautions are taken to maintain 1. They may be used with almost any gas
the pressure differential significantly under conditions sufficiently removed
positive in the downstream direction from liquidus conditions.
while the upstream pressure is made
subatmospheric. 2. They have relatively low temperature
coefficients.
The upper limit in flow rate is
determined mainly by the maximum 3. They are relatively sturdy, being able
acceptable physical size. Glass reservoirs to stand high pressure differentials, in
become bulky when they are of adequate excess of 10 MPa (100 atm).
size to supply a leak of the order of
1 × 10–6 Pa·m3·s–1 (1 × 10–5 std cm3·s–1) 4. They have pressure responses that vary
without having the leakage rate fall off from linear response for very small
more than 10 percent per year. leaks, about 1 × 10–9 Pa·m3·s–1
(1 × 10–8 std cm3·s–1), to direct
Improving Calibrated proportion to the square of the
Leakage Rate Stability by pressure for very large leaks, about
Increasing Envelope 5 × 10–4 Pa·m3·s–1
Pressure (5 × 10–3 std cm3·s–1).
Stability of leakage rate may be improved 5. They are subject to plugging by solids
greatly without sacrificing compactness by or by condensation of vapors of
enclosing the leak element in a metal materials close to liquidus conditions.
envelope and filling the envelope to a
significantly greater pressure. Membranes Precautions with
that leak 5 × 10–8 Pa·m3·s–1 Calibrated Gas Leaks
(5 × 10–7 std cm3·s–1) at a pressure
differential of 100 kPa (1 atm) will raise For maximum accuracy in the use of
their leakage 20× to a rate of calibrated leaks, the following precautions
1 × 10–6 Pa·m3·s–1 (1 × 10–5 std cm3·s–1) should be taken.
when used with a partial pressure
differential of 2 MPa (20 atm). 1. Leakage rates should be defined as
mass units per unit time. When
The leakage rate will fall off one volume units are used, they must be
twentieth as much as that of a membrane defined by specification of the
that will leak 1 × 10–6 Pa·m3·s–1 temperature and pressure conditions
(1 × 10–5 std cm3·s–1) at atmospheric under which they are to be measured.
differential, with the same volume
reservoir. Maximum envelope membrane 2. The temperature at which the
leak pressures are limited by their nature calibration is made and the
to not more than 2.8 MPa (400 lbf·in.–2 temperature at which the calibrated
gage). Orifice leaks have been used with leak is used should be specified. If they
maximum pressures in the envelope of are not identical, the temperature
12 MPa (1700 lbf·in.–2).1 coefficient should be used to correct
the leakage rate. For best results the
Basic Characteristics of leak should be calibrated and used
Membrane Standard Leaks under constant temperature
conditions.
Membrane standard leaks share several
characteristics. 3. A considerably higher than ambient
temperature surrounding the element
1. They are restricted to usable gases, of the orifice leaks will tend to
even at elevated temperatures. decrease the possibility of plugging by
condensation of liquid.
2. They have relatively high temperature
coefficients. 4. If a leak is not equipped with an
integral gas supply, care should be
3. They are relatively fragile when taken to use dry gas with orifices and
constructed with glass. to maintain a positive pressure
differential across the element in the
4. They normally have a response linear downstream direction if possible.
with respect to reservoir Membrane leaks should be given
concentration. adequate time to reach an equilibrium
rate if the partial pressure differential
5. They are almost impossible to plug. of the tracer gas is changed.
Calibrated Reference Leaks 75
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Design and Construction leakage temperature coefficient is large
of Permeation Physical (three percent or more per degree kelvin).
Leaks
Permeation Leak for Helium
Permeation leaks use the principle of gas Tracer Gas
diffusion through a thin wall. Tracer gas
permeates from the high leak reservoir A common helium permeation leak is
concentration through the wall to air or shown in Fig. 2. The helium permeation
vacuum. Leakage is governed by the leak consists of a small helium filled metal
permeability of the thin membrane. The or glass cylinder with an integral glass
major advantage of permeation leaks is membrane at one end. Helium diffuses
that they deliver extremely small through this glass at a measurable rate.
quantities of gas. The commercially Each leak should be calibrated and labeled
available helium leak standard range with the following information: (1) name
extends from 10–7 to 10–11 Pa·m3·s–1 (10–6 of manufacturer, (2) model number,
to 10–10 std cm3·s–1). Because a long period (3) type of leak (glass permeation, orifice
of time is necessary to achieve permeation etc.), (4) serial number, (5) composition of
equilibrium, these leaks usually come fill gas, (6) leak rate, (7) calibration
with a self-contained gas supply. However, temperature, (8) estimated uncertainty of
at small leakage rates, the leakage remains leak rate, (9) date of calibration,
constant over a long period of time. The (10) temperature coefficient and
two disadvantages of calibrated (11) reservoir pressure, date of fill and
permeation leaks are (1) that they can estimated depletion rate.2
only be made for gases that permeate
through membranes and (2) that their The leak may contain two valves: a
vacuum valve downstream of the leak
element and a pressure (or reservoir
valve). The reservoir valve is used for
FIGURE 2. Helium permeation leak with self-contained reservoir: (a) photograph of standard helium leak and
cut away model; (b) schematic cross section.
(a)
(b) Standard Helium Permeable 38 mm
vacuum reservoir glass/quartz (1.5 in.)
63 mm coupling membrane outside diameter
(2.5 in.) Filling
maximum port
32 mm
(1.26 in.)
Leak shutoff
valve
280 mm
(11.0 in.)
76 Leak Testing
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refilling of the leak reservoir. The vacuum changed to change the leakage rate at
valve is used for briefly shutting off the which tracer gas flows out of the physical
helium flow for purposes of zeroing a reference leak.
helium leak detector during the process of
calibration. The vacuum valve should not Variable Value Orifice Physical
be shut off for extended periods of time Reference Halogen Leaks
(greater than 10 min) or the stability of
the leak may be affected severely. The variable value physical halogen vapor
leak shown in Fig. 4 is available for
Porous Plug Calibrated Leaks different ranges, such as 10–5, 10–6, 10–7
Providing Molecular Flow of Gas and 10–8 Pa·m3·s–1 (10–4, 10–5, 10–6 and
10–7 std cm3·s–1). A schematic flow
Porous plug calibrated leaks are not
commercially available but have FIGURE 3. Reservoir variable rate physical orifice leak standard
frequently been cited in literature. They (top) and fluorocarbon resin permeation leak standard
consist of a metal, ceramic or glass plug (bottom) for calibration of detector probe instruments.
containing extremely fine pores. The
major advantage of this type of calibrated
leak is that molecular gas flow occurs
through the plug. Therefore, the change
of leakage flow resulting from a change of
tracer gas can be calculated from the
kinetic theory of gas flow. Porous plug
leaks can be either reservoir or
nonreservoir type, with the choice of
materials cited above.
Design and Characteristics FIGURE 4. Variable leak rate halogen refrigerant leak standard
of Capillary Calibrated or with physical (capillary) leak element: (a) photograph of leak
Standard Physical Leaks standard with internal reservoir of refrigerant gas and
another of refrigerant liquid and (b) schematic flow
Another type of commercial calibrated diagram.
leak is a single orifice in heat resistant
glass or metal, encased in a stainless steel (a)
fixture. Tracer gas leaks through the
orifice at the rated leakage, when the leak (b) Gage
is placed under a specified gage pressure
(relative to atmospheric pressure). Such (Pressure Vapor Calibrated
capillary leaks are available in two types, increase) reservoir leak Detector
fixed value leaks and variable value leaks, probe
as next described. Liquid
reservoir Vapor
Fixed Leakage Value Orifice reservoir
Capillary Leaks fill valve Vent (pressure decrease)
Capillary type calibrated leaks are made Fill valve for
from constructed glass tubing or collapsed liquid halogen/refrigerant
thin metal tubing. These orifice leaks can
be produced from large sizes down to
about 10–8 Pa·m3·s–1 (10–7 std cm3·s–1).
Although smaller leaks of this nature can
be made, they become extremely difficult
to handle because of leak clogging.
Capillary leaks can be calibrated to deliver
one or a variety of tracer gases. Some leaks
are to be used with an independent tracer
gas supply, i.e., they simply consist of a
capillary leak attached to the system
under test. In the tracer probe method of
leak testing, tracer gas is simply sprayed
over the capillary. Alternatively, a physical
reference capillary leak can be made with
a self-contained gas supply that can be
permanently attached to the leak. Figure 3
shows a physical capillary orifice leak
with its own tracer gas reservoir and a
leak factor gage. The gage pressure may be
Calibrated Reference Leaks 77
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diagram of its system is shown in Fig. 4b. room temperature would be much too
This leak contains a reservoir of liquid slow). The leak is designed to yield a
Refrigerant-134a halogenated point source of helium to simulate a pin
hydrocarbon tracer to be valved into a hole leak. The point source of leakage
ballast tank in gaseous form. Also may be used to calibrate the detector
connected to the ballast tank is a glass probe of a helium mass spectrometer leak
capillary tube and pressure gage. The rate detector. The helium detector probe
of gas leakage through the calibrated leak calibrator may also be used as a training
depends on the pressure in the ballast tool to train operators on the distance and
tank. Laminar gas flow occurs through the speed a probe must be from a certain size
leak. This permits the pressure gage to be leak to detect the leak. The major
marked in leakage units, where leakage is disadvantage of the helium detector probe
proportional to the ratio of the difference calibrator is that it requires an external
between the squares of the absolute tank of helium for refilling, unlike
pressures. The halogen leak standard is refrigerant calibrators that can store extra
commonly used with heated anode refrigerant in an on-board liquid tank
halogen leak detectors. It is an excellent (Fig. 4).
leak standard to use with probe
instruments because the probe may be Other types of variable value reference
passed directly across the leak exit. The leaks are controlled by elegant needle
calibration then approximates detector valve or crushed tubing whose
probe operating conditions. conductance is changed by flexing.
Although the conductance of these leaks
Variable Leak Rate Helium can be made quite repeatable, they should
Reference Leaks not be considered calibrated leaks because
of a complete lack of standardization of
Variable reference leaks have been leakage rates in these artificial orifice
designed to leak helium for use with types of physical leaks.
helium mass spectrometer leak detectors
equipped with a detector probe. The leak Sources of Inaccuracy of
arrangement is shown in Figs. 3 and 5. Leakage Measurements
The leak standard in Fig. 5 uses either a with Standard Leaks
capillary or fluorocarbon resin permeation
membrane as the gas flow restriction (the The inaccuracy of leak detector
time response for a glass membrane at measurements made with physical
standard leaks can be caused by factors
FIGURE 5. Variable rate helium leak standard such as: (1) inaccuracy in calibrating the
(capillary style sniffer). leak, (2) nonlinearity of the leak detection
instrument, (3) variation in pressure
Fill and flush differential applied across the leak,
valve (4) impurity of gas applied to the leak and
(5) variation in the amount of gas
6 mm (0.25 in.) reaching the detector.
male pipe thread
Accuracies of Calibrations of
Gas reservoir Commercially Available Physical
Reference Leaks
Capillary pinpont
helium source Beginning in 1987, the National Institute
of Standards and Technology established a
6 mm leak calibration program that calibrated
(0.25 in.) leaks over the range of 10–11 to
10–3 Pa·m3·s–1 (10–10 to 10–2 std cm3·s–1).
In a 1980 study, tests of standard leaks
from various manufacturers have shown
that their accuracies could differ by more
than ±50 percent of a mean value.1 This is
shown by the experimental plot of Fig. 6,
which shows the calibrated leakage
reading compared to the response of a
linear mass spectrometer. The straight line
drawn in the graph is the least mean
square value of leakage as a function of
spectrometer response. This line does not
imply the correct value, but the general
pattern around which the values of the
leaks congregate.
78 Leak Testing
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Even the leaks made by any single A typical leak detector response error
manufacturer vary by about 10 percent. curve is shown in Fig. 7. The instrument
This is usually the guarantee that is response is not linear with leakage. This
presented on purchase of the permeation error is added to the error that occurs
calibrated leak. Leaks of a variable type, because of the difference in leak
such as that shown in Fig. 4, are claimed calibration. Because of this lack of
to be accurate only to ±20 percent. linearity, the farther apart the two leaks
are in nominal value, the greater the error
Beginning in 1987, many in the calibration. Because such deviations
manufacturers of leaks began deriving exist it is recommended that, when the
their measurements directly from leaks leakage measurement is done to a
calibrated by the National Institute of specified high tolerance, a calibrated leak
Standards and Technology. The existence to the exact specified value be used as a
of national standards in leak standard.
measurement should improve the relative
agreement between the manufacturers of Effect of Barometric
leaks and may also reduce the Pressure on Leakage
uncertainties that manufacturers provide Measurements
for calibrated leaks.
Leakage depends on the pressure
Errors in Response of Commercial differential acting across the leak. When
Electronic Leak Detectors leak detection is done by a tracer probe,
the pressure differential is usually 100 kPa
Most commercial leak detectors display (1 atm). The gas is sprayed over the
the response to a detected leak as a suspected area without aid of additional
current reading on a sensitive pressure. Should leak detection be
microammeter. It is usually assumed by performed at high altitudes, the
the operator that current reading twice atmospheric pressure is less than 100 kPa
the magnitude of a previously observable (1 std atm). The magnitude of this
one represents a leak of twice the size. reduction is as much as 20 percent in
This assumption of linearity in response is places such as Boulder, Colorado. If the
not necessarily correct; nonlinearity may leaks that are being located are of a
result from the structure of the pumping laminar nature, the laminar flow through
system, the background usually associated
with the leak testing practice, the FIGURE 7. Typical range of error possible in actual leakage
electronic circuitry associated with the measurements with a leak detector. Variations with
detection system and the mode of gas magnitude of leakage increase the difficulties of correlating
flow through the leak. measured leakage rates with standard reference leaks.
FIGURE 6. Comparison of leakage values for leaks supplied by
various vendors, measured by linear mass spectrometer.
Resulting ion current depends on mass spectrometer
configuration.
10–2 (10–1)
Stated leakage, Pa·m3·s–1 (std cm3·s–1)10–3 (10–2) Possible variation
Actual leakage (relative units)10–4 (10–3) in measurement
10–5 (10–4)
10–6 (10–5)
10–7 (10–6)
10–8 (10–7)
10–9 (10–8) Measured Calibrated
leak leak
Measured leakage
10–10 (10–9) (relative units)
10–14 10–13 10–12 10–11 10–10 10–9
10–8 10–7 Legend
Ion current (A) = range of deviation due to nonlinearity of instrument response
= error due to comparison and instrument linearity
Calibrated Reference Leaks 79
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the leak is proportional to the square of Effect of Position of Calibrated
the pressure differential. The values Leak on Test System
obtained for leakage readings at the
altitude of Boulder, Colorado, are Tracer gas may be absorbed on test system
40 percent less than those obtained with a surfaces as it travels to the detector. This
100 kPa (1 std atm) pressure during use. would decrease the response of the leak
Therefore, a leakage rate measured to detector. Therefore, calibrated leaks
atmosphere in Boulder, Colorado will be should be positioned on the system as
only 60 percent as large as with the same near as possible to suspected leak sites to
leak measured at Cape Kennedy on the improve accuracy. Alternatively, they may
seashore of Florida. be positioned as far away from the
detector as possible to show minimum
Certain calibrated leaks contain their sensitivity. Both of these positions are
own gas supply, whereas others have the conservative choices that ensure that
tracer gas sprayed onto the entry orifice of leakage from test object discontinuities
the leak at 100 kPa (1 atm) pressure will not be underrated.
during use. Calibrated leaks with a self
contained gas supply always deliver to the Specifying Maximum Allowable
detector a fixed amount of gas that can be Leakage Rate
used to measure the sensitivity of the leak
detector. On the other hand, leaks where Because of the variations discussed here,
gas is added during use produce the the accuracy of any leakage measurement
calibrated amount of leakage only when a probably varies from half to twice the
100 kPa (1 atm) pressure differential is actual value. This implies that, if a leak is
supplied. These nonreservoir physical measured as 1 × 10–6 Pa·m3·s–1
reference leaks therefore deliver less than (1 × 10–5 std cm3·s–1), the actual value of
the calibrated amount of leakage when this leak is between 2 × 10–6 and
used at high altitudes where the 0.5 × 10–6 Pa·m3·s–1 (2 × 10–5 and
atmospheric pressure is lower. However, at 0.5 × 10–5 std cm3·s–1). Therefore, if the
these altitudes, the pressure of the tracer maximum allowable leakage rate of a
gas across the leak is lower. In such cases, particular system is 2 × 10–6 Pa·m3·s–1
a physical reference leak without its own (2 × 10–5 std cm3·s–1), the specification
gas supply describes more accurately the may be written with a leakage tolerance of
sensitivity of the leakage test. It is this test 1 × 10–6 Pa·m3·s–1 (1 × 10–5 std cm3·s–1),
sensitivity that is important in practical knowing that the accuracy of the leakage
leak testing. measurement is a factor of two. There is
reasonable assurance that if the measured
Effect of Tracer Gas Purity leakage is not higher than that stated on
on Accuracy of Leakage the specification, 1 × 10–6 Pa·m3·s–1
Measurements (1 × 10–5 std cm3·s–1), the actual system
leakage will be no greater than the
Another source of inaccuracy is the allowable rate, 2 × 10–6 Pa·m3·s–1
impurity of the tracer gas used for leakage (2 × 10–5 std cm3·s–1). This technique of
measurement. If a tracer probe technique specifying leakage is much more sensible
of leak location is used, the gas is sprayed than specifying a slightly higher leakage
over the suspected area in the value, such as 2 × 10–6 Pa·m3·s–1
environmental atmosphere. In such a (2 × 10–5 std cm3·s–1), and thereby
case, it is quite possible that the tracer gas requiring an unreasonably high accuracy
is diluted with air as it approaches the (such as ±10 percent) during leak testing.
leak. Therefore, the response of the leak
detector operating on the internal
vacuum of the test system will be reduced
by the amount air impurity entering the
detector with the tracer gas. In this case, a
calibrated leak with a self-contained gas
supply is undesirable because it would not
reproduce the leakage measurement
technique. In other words, the gas should
be sprayed onto the calibrated leak in the
same manner as onto the tested leak. The
gas in a self-contained calibrated leak
would be purer than the gas encountered
by simple spraying from a tracer probe.
80 Leak Testing
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PART 2. Operation of Standard (Calibrated)
Halogen Leaks
Functions of Known Halogen Leak Calibrator
Leakage Standards without Reservoir
The halogen gas leak detector (known also Figure 8 shows a leak calibrator that has
as the alkali ion diode halogen leak no reservoir for halogen tracer gas. It
detector) is a transfer agent or compactor. contains a single orifice in heat resistant
Leak testing with halogen tracer gas glass. When a reservoir of refrigerant-134a
requires use of a known reference halogen is attached, the pressure of the
leak to calibrate the leak testing operation refrigerant-134a gas is 165 kPa gage
properly. The halogen leak detector is (24 lbf·in.–2 gage) and that gas will leak
adjusted to produce an alarm or meter through its orifice at a fixed rate.
indication of the panel indicator when
exposed to a known leakage rate. The Calibrated Halogen Leak
detector is then used to compare with Gas Reservoir
unknown leakage rates to the specific
known leakage rate of a calibrated The calibrated halogen leak of Fig. 3 has
reference leak. its own refrigerant-134a reservoir plus a
leak factor gage. The gage reads in
The maximum acceptable leakage rate, multiplying factors, used when the
however, must first be determined, either pressure is changed to vary the leakage
by the user or from specifications that the rate. The gage is set at a factor of 1 at the
user must meet. The type and range of factory (165 kPa or 24 lbf·in.–2 gage).
leak standard then may be selected, but These leak capsules, used when a precise
only after this has been accomplished. leakage rate is required, are frequently
Three types of halogen leak standards are mounted in the halogen leak detector
(1) the calibrated standard leak (no gas), control unit.
(2) the leak capsule (single gas reservoir)
and (3) the halogen leak standard (reserve
gas supply).
FIGURE 8. Calibrator for halogen leak standards with small Adjustable Halogen Leak
bore capillary tube orifices for leaks from 3 × 10–5 to Standards with Ballast
3 × 10–8 Pa·m3·s–1 (3 × 10–4 to 3 × 10–7 std cm3·s–1) or Tank
with larger bore capillary tube orifices for leaks from
3 × 10–4 to 3 × 10–7 Pa·m3·s–1 (3 × 10–3 to The halogen leak standard shown in
3 × 10–6 std cm3·s–1). Movement of a colored liquid within Fig. 4a contains a reservoir of liquid
the calibrated capillary tube over a specific period of time refrigerant-134a, which is valved in
gaseous form into a ballast tank.
permits calculation of the rate of leakage from the standard Connected to the ballast tank is a glass
capillary tube and pressure gage. The
leak, when the calibrator is attached to the standard amount of leakage is dependent on the
amount of refrigerant-134a tracer gas
through a vent valve. pressure in the ballast tank. Pressure is
indicated by a Bourdon gage and
controlled by two valves (Fig. 4b).
Applications of Calibrated
Halogen Leaks and
Capsules
Predetermined standard halogen leaks are
of great advantage to quality control
engineers in refrigeration, air
conditioning and space vehicle
Calibrated Reference Leaks 81
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manufacturing, where critical checks of second (std cm3·s–1) and also in ounce per
lines, valves and hydraulic systems are of year (oz·yr–1) by the manufacturer of these
the utmost importance. They afford great standard leaks. The SI units are mole per
accuracy wherever halogen leak detectors second (mol·s–1) and pascal cubic meter
are used and where a leak of one specific per second (Pa·m3·s–1).
value is required.
Components of Adjustable
The adjustable halogen leak standard Halogen Leak Standard
in Fig. 4 provides the same advantages as
the calibrated leaks and capsule but has The adjustable halogen leak standard is a
the additional advantage of being compact instrument consisting of the
adjustable to the full scale rating. Thus, following seven functional components
they can be used more easily for (see Fig. 4):
quantitative measurements of actual leaks
and of background contamination. Leak 1. direct reading leakage rate indicator
standards also enable the establishment of (calibrated in ounces of
leakage rate specifications and provide refrigerant-134a per year);
uniform standards for calibrating leak
detectors at each location of product 2. probe fitting in the center of which is
inspection. a glass leak capillary (a different
capillary for each leakage rate);
Halogen Leak Standards to
Prolong Life of Alkali Ion Diode 3. leakage increase valve and control
Sensing Element knob;
All three leak standards can be used to 4. leakage decrease valve and control
extend the useful life of the alkali ion knob;
diode sensing elements in heated anode
halogen leak detectors. Users frequently 5. vent (with protective cap) for
replace the detector’s sensitive element exhausting refrigerant-134a gas;
long before the end of its useful life. A
sensing element can be used until it no 6. tank for holding liquid
longer responds to the desired setting of refrigerant-134a (the tank contains
the leak standard. Additionally, any leak some refrigerant-134a when shipped
standard permits use of the lowest from the factory); and
possible anode heater current to provide
adequate leak detector sensitivity. This 7. a reservoir for holding refrigerant-134a
practice increases element life and results gas at a pressure corresponding to the
in reduced maintenance and lower desired leakage rate.
replacement costs.
Principles of Operation of
Accuracy of Adjustable Adjustable Halogen Leak
Halogen Leak Standards Standard
Typical accuracy of the adjustable halogen The adjustable halogen leak standard
leak standard of Fig. 4 is about ±20 (Fig. 5) operates as discussed below. The
percent of scale setting on the upper two filler tank provides a supply of
thirds of the scale and ±30 percent of refrigerant-134a liquid under its own
scale setting on the lower one third of the partial pressure. The increase valve
scale. controls the amount of refrigerant gas fed
from the filler tank to the ballast tank, the
Description of Adjustable leakage rate meter and the leak capillary.
Halogen Leak Standard The pressure in the system is maintained
by the ballast tank. With the increase and
The leak standard of Fig. 4 is a simple, decrease valves closed, the system is
accurate instrument that expels a halogen practically in a static state, except for the
compound gas, refrigerant-134a through a minute amount of refrigerant gas that
glass capillary marked probe to the escapes through the leak capillary. The
atmosphere at a known rate. This known decrease valve provides a means of
rate is adjustable when using certain decreasing the pressure built up in the
halogen leak standards. The leak standard system. With the decrease valve opened,
is intended primarily for use with halogen refrigerant gas is allowed to escape
sensitive leak detectors. The leakage rate through the vent opening on the front of
for each unit is marked on the scale plate. the leak standard. The rate of refrigerant
Leakage rates are customarily labeled in gas escaping through the leak capillary is
units of standard cubic centimeter per a function of the pressure in the system
and is indicated on the leakage rate meter.
82 Leak Testing
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Preparation for Operation 1. To check the operation and sensitivity
of Adjustable Halogen of the halogen leak detector. The
Leak Standard probe of the detector to be checked is
moved past the probe fitting of the
The following procedure is used with leak standard, which is set at the
adjustable halogen leak standards. maximum leakage rate allowable for
any single leak on the item being leak
1. Remove the protective caps from the tested. If an adequate signal is
leak capillary in the probe fitting and obtained, the leak detector has
from the vent. sufficient sensitivity (or more) to
detect this rate of leakage.
2. To increase the leakage rate, turn
increase valve knob counterclockwise 2. To determine size of leaks. If the leak
slowly until the instrument pointer standard is set so that the leak detector
starts to move upscale. As the pointer gives the same signal for the leak
approaches the desired leakage rate, standard as for the leak, the leak
gradually close the increase valve so standard then indicates the size of the
the pointer will stop at the desired leak, only if 100 percent pure
leakage rate. If the instrument pointer refrigerant-134a is in the test system.
continues to go upscale, this indicates
that the increase valve is not firmly 3. To extend the useful life of the sensing
closed. Always make sure the increase element of the halogen leak detector.
valve is closed firmly. (Avoid running Users frequently replace the detector’s
the instrument pointer off scale. This sensing element long before the end
can subject the instrument to as much of its useful life. A sensing element
as 500 percent over pressure. Although can be used until it no longer
the unit can withstand the overload, responds to the desired standard leak
repeated abuse may damage it.) setting. Additionally, the leak standard
permits use of the lowest possible
3. To decrease the leakage rate, turn the heater current to provide adequate
decrease valve knob counterclockwise leak detector sensitivity. These
slowly until the instrument pointer practices increase element life and
starts to move downscale. As the result in reduced maintenance and
pointer approaches the desired leakage lower replacement costs.
rate, gradually close the decrease valve
so that the pointer will stop at the 4. To simplify establishment of leakage
desired leakage rate. If the instrument rate specifications. The leak standard
pointer continues to go downscale, makes feasible the establishment of
indication is that the decrease valve is leakage rate specifications and
not firmly closed. Make sure the provides a uniform standard for
decrease valve is closed firmly. calibrating leak detectors at each
location of product inspection.
4. After increasing or decreasing the
leakage rate, be sure both valves are 5. To improve product quality. By
closed by turning knobs clockwise. calibrating leak detectors with the leak
standard, it becomes possible to locate
5. After increasing or decreasing the and repair all significant leaks. This
leakage rate and noting that the valves ensures that products are
are firmly closed, wait about 60 s for manufactured in accordance with
the leakage rate to stabilize before leakage specifications.
calibrating the leak detector. When the
leakage rate is being decreased, Precautions for Adjustable
refrigerant-134a gas is allowed to Halogen Leak Standard
escape through the vent to
atmosphere. During this operation it is The following precautions should be
best to remove the leak standard from applied when using the adjustable
the test area to avoid building up a halogen leak of Fig. 4. Never allow any
background of halogen vapor at the grease or liquid to enter the leak capillary,
test site. If this is not possible, attach as it may plug the leak or alter its leakage
the vent tubing to the vent and rate. When the leak standard is not in use,
discharge the gas from the test area it is recommended that the instrument
through a window or other vent. pointer be set up scale and that the
protective caps be placed over the vent
6. The leak standard is now ready for use. and leak capillary. This must be done to
prevent plugging of the capillary.
Applications of Adjustable
Halogen Leak Standard
The adjustable halogen leak standard of
Fig. 4 may be used in several ways.
Calibrated Reference Leaks 83
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Operational Procedure 100 percent tracer gas probe intake
When Pressurized System and the signal obtained during normal
Contains 100 Percent probing procedure.
Refrigerant
Interpretation of Unknown
With the leak standard prepared for use, Leakage Rate from
proceed as follows. Comparable Standard Leak
1. Turn on the leak detector and let it A leak that gives the same leak signal as
warm up for the time prescribed in the the standard is the same size as that
applicable leak detector instruction indicated by the leak standard. A larger or
book. Set the leak detector in the same smaller signal indicates a larger or smaller
mode of operation as that to be used leak, respectively. If it is desired to
during leakage testing. determine the size of any leak that is
located, adjust the leak standard in small
2. Place the probe squarely against the leakage rate increments (waiting about
probe fitting on the leak standard (see 60 s after each change) until the signal
Fig. 4) and observe the indicator caused by the leak standard is the same as
reading. Remove the leak detector that caused by the leak. The leak standard
probe tip from the leak standard probe then indicates the size of the leak in
fitting. When the leak detector reading question, in terms of its leakage rate.
has settled to a stationary indication,
pass the tip of the leak detector probe Operational Procedure
past the probe fitting on the leak When Pressurized System
standard at a rate of about 25 mm·s–1 Contains Less than 100
(1 in.·s–1). The tip of the probe should Percent Refrigerant
just graze the front circular edge of the
probe fitting and pass across the Halogen leak standards can also be used
center of the probe fitting as shown in to calibrate a leak detector when the
Figs. 4 and 9. system being checked contains less than
100 percent refrigerant-134a. For
3. Repeat the procedure of step 2 above, applications using mixed gases in
reducing or increasing the sensitivity pressurized components, the leak standard
setting of the leak detector each time, may be used to calibrate a leak detector.
until the leak detector signal is However, a leak from the vessel (such as a
adequate for the specified leakage rate. tank, pipe or steam condenser) that
The results of this test will indicate the produces the same leak signal as does the
allowed probing speed and the safety leak standard will have a total leakage rate
factor required and provide the that is approximately inversely
operator with a feeling for the proportional to the percentage of
difference in indications between a refrigerant-134a tracer gas in the
enclosure. For example, suppose that,
FIGURE 9. Technique for checking leak with 10 percent refrigerant-134a in the
testing sensitivity with sniffer probe tip vessel, the leak standard indication is 30 g
moving past the orifice of an adjustable leak per annum (1 oz·yr–1). The total leakage
standard. rate is then 100/10 × 30 = 300 g·yr–1
(10 oz·yr–1).
Tip of sniffer probe leak detector
Halogen leak standards are also used to
calibrate a leak detector when test systems
contain a halogen tracer gas other than
refrigerant-134a, such as refrigerant-22,
refrigerant-114 or refrigerant-11. The
leakage rates for these other tracer gases
may be read directly in standard cubic
centimeter per second. Leakage rates in
ounce per year can be obtained by
multiplying the readings in standard
cubic centimeter per second by 5.5 × 104.
Readings in pascal cubic meter per second
can be obtained by dividing the reading
in standard cubic centimeter per second
by a factor of 10.
84 Leak Testing
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Measuring Atmospheric Use of Calibrator for
Contamination with Halogen Leak Standard
Adjustable Halogen Leak
Standard The calibrator is an accessory designed to
check the accuracy of calibrated leaks,
To measure the amount of atmospheric leak capsules and halogen leak standards.
contamination with a heated anode Three models of the calibrator differ in
halogen vapor leak detector, the the bore size of the calibrated glass
equipment required includes an capillary tube, which is the major
adjustable halogen leak standard, a component of the calibrator. A small bore
halogen leak detector and a pure air capillary tube is used for leaks from
supply. The procedure recommended by 3 × 10–5 to 3 × 10–8 Pa·m3·s–1 (3 × 10–4 to
the leak detector manufacturer is as 3 × 10–7 std cm3·s–1). A larger bore
follows. capillary tube is used for leaks from
3 × 10–4 to 3 × 10–7 Pa·m3·s–1 (3 × 10–3 to
1. In contaminated test areas, with the 3 × 10–6 std cm3·s–1). Another model is
leak detector operating at an air flow supplied with both capillary tubes.
of 4 cm3·s–1 (0.5 ft3·h–1), allow the leak
detector to breathe pure air for about The major component of the calibrator
1 min, then allow the leak detector to is a calibrated glass capillary tube.
breathe air from the contaminated Accessories are provided allowing the
area. If the leak detector gives a signal, capillary tube to be connected to and
the area is contaminated. Note the supported by the halogen standard leak
magnitude of the leak detector signal. under test. To perform a calibration, the
Do not adjust the sensitivity setting of calibrator is attached to the standard leak
the leak detector between this through a vent valve. A colored indicating
measurement and that which follows. liquid is inserted into the open end of the
capillary tube and the vent valve is
2. Move the leak detector and leak opened. The indicating liquid is drawn
standard to an area where there is no into the capillary tube by applying a
atmospheric contamination. Adjust slight suction to the plastic suction tube
the leak standard so that when the connected to the vent valve. The vent
leak detector sniffs the reference leak, valve is then closed, retaining all the
the leak signal is the same as when the escaping halogen vapor in the capillary
leak detector sniffed air in the tube of the calibrator. By noting the
contaminated area. Note the leakage amount of movement of the indicating
rate shown on the dial of the leak liquid in the capillary tube for a specific
standard. This is a measure of the level period of time, the magnitude of the leak
of atmospheric contamination with from the standard can be calculated and
halogen vapors in the original compared with the reading of the leakage
contaminated area measured in step 1. rate gage on the standard.
3. If it is desired to determine
(approximately) the degree of
contamination of the contaminated
area in parts per million (µL·L–1) of
halogen gas, the reading of the leak
standard from Step 2 in ounces per
year can be multiplied by 16. For
example, if the indication on the
reference leak is 1.5 oz·yr–1 the
contamination level is 1.5 × 16 =
24 µL·L–1. (For a leakage in grams per
year, divide the number by 1.8 to
arrive at the number of parts per
million.)
4. When using a leak detector that has its
own integral pure air supply, an
indication of the degree of
atmospheric contamination with
halogens can be obtained by holding a
finger over the probe tip for 30 s and
then switching the leak detector to
manual zero with the other hand. If
the leak detector reading is then
greater than the indication received
with leakage of the rejection level, the
halogen contamination of the air in
the test area is excessive.
Calibrated Reference Leaks 85
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PART 3. Operation of Standard (Calibrated)
Helium Leaks
Functions of Calibrated tracer gas or gas mixture flowing through
Helium Reference the leak and (3) the pressure differential
Standard Leaks acting across the leak.
Calibrated helium standard leaks are In the viscous flow range, the mass
essential when helium is used as the tracer flow rate is inversely proportional to the
gas in leak testing for quantitative leakage gas viscosity and directly proportional to
rate measurements. Calibration serves to the difference in the squares of the
determine the user’s ability to detect upstream and downstream pressures. In
leakage and to perform quantitative the molecular flow range, the mass flow
measurement of leakage rates. It is rate is inversely proportional to the square
imperative that the entire leak testing root of the mass of the gas molecule and
system be calibrated. It is not sufficient directly proportional to the difference in
merely to calibrate the leak testing partial pressure. Leakage at rates of
instrument. In the case of a detector probe 1 × 10–5 Pa·m3·s–1 (10–4 std cm3·s–1) or
test, for example, the detector probe must greater will be most likely to be viscous
be included in the leak testing system flow. Leakage at rates between 10–5 and
during the calibration operations and used 10–8 Pa·m3·s–1 (between 10–4 and
in the normal manner as during testing. 10–7 std cm3·s–1) will usually be
transitional in nature, exhibiting
The difficulty of repeating exact characteristics of both molecular and
detector probe techniques virtually viscous flow. Leakage at rates in the range
precludes the detector probe method as a of 10–8 Pa·m3·s–1 (10–7 std cm3·s–1) or
way of measuring leakage rates smaller will probably be molecular.
quantitatively, although detector probe
tests are good qualitative tools. In vacuum Membrane or Diffusion
pumped systems, the system leak and the Calibrated Reference
artificial reference leak must be located Helium Leaks
very close to each other for the
quantitative measurement to be valid. Two types of helium standard leaks or
calibrators are in general use, namely the
Rating of Calibrated Helium Leaks membrane type and the capillary type.
The design of a membrane or diffusion
Calibrated helium leaks are usually type standard leak is shown in Fig. 2. This
measured in units of pascal cubic meter standard leak has a reservoir filled with
per second (Pa·m3·s–1) or standard cubic helium surrounding a sealed glass tube
centimeter per second (std cm3·s–1). It is through which helium diffuses at a very
expected that standards in the future will low rate, usually from 10–8 to
be calibrated in mass flow units of mole 10–10 Pa·m3·s–1 (10–7 to 10–9 std cm3·s–1).
per second. However, when discussing the The standard calibrated helium leak
flow of a compressible fluid, it is necessary shown in Fig. 2 is fitted with a shutoff
to state not only the volumetric flow rate valve that uses a metallic seal rather than
(V/t) but also pressure P and temperature an elastomeric seal. This avoids spurious
T. Note that the units of leakage are changes in leakage rate due to helium
identical to the units of throughput (the hangup. The reservoir is filled with
product PS of pressure P and pumping 100 percent helium at 100 kPa (1 atm or
speed S). Both leakage and throughput 14.7 lbf·in.–2 absolute) of pressure. During
describe the mass flow rate or, actually, calibration of this leak, the pressure
the number of gas molecules escaping per differential feeding helium tracer gas into
unit time if the temperature is given. an evacuated test system is therefore from
100 kPa to 0 kPa (14.7 to 0 lbf·in.–2).
Characteristics of Gaseous Flow Because the partial pressure of helium in
Involved in Leakage Calibrations air is only about 0.5 Pa (4 mtorr), the glass
membrane calibrator of Fig. 2 continues
At least three additional variables must be to leak helium even when it is not under
considered when using standard vacuum.
calibrated leaks: (1) the nature of flow
(viscous, transitional or molecular) of gas
passing through the leak, (2) the specific
86 Leak Testing
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Capillary Standard (1) Q2 = M1 Q1
Calibrated Helium Leaks M2
The capillary helium leak consists merely where Q1 is flow rate for gas 1 (any units
of flattened tubing or glass capillary of leakage rate), Q 2 is flow rate for gas 2
enclosed in a protective metallic sheath. (same units of leakage rate) and M1 is
They are generally calibrated with one molecular mass for gas 1 (relative atomic
end at vacuum and the other end at
atmospheric pressure. Capillary leak mass).
standards are available with fixed leakage
rates varying from 10–3 to 10–6 Pa·m3·s–1 Computation of Viscous
(10–2 to 10–5 std cm3·s–1). These capillary Flow Leakage Rates for
leaks may have self-contained helium Other Gases from Helium
reservoirs. They are more susceptible to Leakage Rates
drastic changes in leakage rate caused by
clogging or by foreign agents such as dust If the flow rate has been identified as
or condensation than are membrane leaks. corresponding to viscous flow for one gas,
the viscous flow rate for any other gas can
Computation of Molecular be determined by use of Eq. 2:
Flow Leakage Rates for
Other Gases from Helium (2) Q2 = n1 Q1
Leakage Rates n2
Although helium is commonly used as the where Q1 is flow rate for gas 1 (any units
tracer gas for mass spectrometer leak of leakage rate), Q 2 is flow rate for gas 2
testing, it is usually necessary to determine (same units of leakage rate), n1 is viscosity
the rate at which air would leak through a of gas 1 (pascal second) and n2 is viscosity
similar discontinuity. In the molecular of gas 2 (pascal second).
flow range (and only in the molecular
flow range), the air leakage rate will be Table 1 lists the viscosities and
about 35 percent of the helium leakage
rate through the same pressure differential. molecular masses of helium, argon and
When molecular flow occurs, the flow rate
for one gas can be compared to the flow neon inert tracer gases, air, nitrogen,
rate of any other gas by use of Eq. 1:
ammonia and other gases and vapors
commonly encountered in leak testing.
The values of the viscosities and
molecular masses from this table can be
used in Eqs. 1 and 2 to compute leakage
TABLE 1. Physical properties of certain gases and vapors.
Relative Gas
Chemical Molecular Constant _V_i_s_c_o_s_it_y__a_t_1_5__°_C__(_5_9_°_F_)_
µPa·s (millipoise)
Gas Symbols Mass (Mr) (J·kg–1·K–1)
174 (1.74)
Air NH3 29.00 287 97 (0.97)
Ammonia Ar 17.03 488.22
Argon 40 207.86 220 (2.20)
Carbon dioxide CO2 44.01 188.89 145 (1.45)
Dichlorodifluoromethane CCl2F2 120.93 127 (1.27)
Dichloromethane CH2Cl2 84.83 68.75
Helium He 98 192 (1.92)
Hydrochloric acid 4.00 2078.60 140 (1.40)
Hydrogen HCI 36.50 227.79
Krypton 4116.04 86 (0.86)
Methane H2 2.02 99.22 246 (2.46)
Neon Kr 83.80 518.35 107 (1.08)
Nitrogen 16.04 412.01 309 (3.09)
Nitrous oxide CH4 20.18 296.84 173 (1.73)
Oxygen Ne 28.01 188.96 143 (1.43)
Refrigerant R-134a 44.00 259.91 199 (1.99)
Sulfur dioxide N2 31.99 81
Sulfur hexafluoride N2O 102.03 129.91 123 (1.23)
Water vapor O2 64.00 57 152 (1.52)
C2H2F4 146 461.40
SO2 18.02 93 (0.93)
SF6
H2O
Calibrated Reference Leaks 87
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