Tracer gas leak rate correction

A leak test almost never uses the service fluid. Helium is used because a mass spectrometer can see it, and the acceptance criterion is usually written for air, nitrogen or the process gas. The two rates are not the same number, and which correction applies depends on how the gas moves through the leak channel.

For very small leaks the channel is narrower than the mean free path of the gas, so molecules pass one at a time without colliding with each other — molecular flow. The throughput then depends on molecular speed, which goes as the inverse square root of molar mass: Q₁/Q₂ = √(M₂/M₁). Helium (M = 4.003) therefore passes about √(28.96/4.003) = 2.69 times faster than air through the same molecular leak. A helium rate must be divided by 2.69 to give the equivalent air rate, and an air-based acceptance limit must be multiplied by 2.69 before it is applied to a helium reading — getting that direction backwards is a factor of seven error.

For larger leaks the channel is wide compared with the mean free path and the flow is viscous (laminar). Throughput is then governed by viscosity, Q₁/Q₂ = η₂/η₁, and the ranking reverses: helium is more viscous than air (about 19.9 versus 18.5 µPa·s at 25 °C), so helium actually passes slightly more slowly than air, by roughly 8%. The molecular relation is the conservative one for the small leaks that matter in vacuum and pressure-equipment work, and is the correction assumed by most codes; the crossover sits broadly around 10⁻⁴ to 10⁻⁵ mbar·L/s, and in the transition region neither law is exact.

The pressure terms matter as much as the gas terms. Molecular throughput scales with the difference of the absolute pressures across the leak, Q ∝ (P₁ − P₂), while viscous throughput scales with the difference of their squares, Q ∝ (P₁² − P₂²) — so a rate measured at 1 bar differential understates a 10 bar service condition by an order of magnitude under the viscous law. Enter the absolute pressures for both conditions; with identical pressures the factors reduce to the pure gas-property ratios. One remaining limitation: the laws assume a clean, dry, open channel, and real leak paths that are wetted, blocked by product, or contain a liquid seal behave in neither regime.

Molecular flow:  Q₂ = Q₁ × √(M₁ / M₂) × (P₁′ − P₂′) / (P₁ − P₂)
Viscous (laminar) flow:  Q₂ = Q₁ × (η₁ / η₂) × (P₁′² − P₂′²) / (P₁² − P₂²)
unprimed = test condition, primed = service condition, all pressures ABSOLUTE
Helium → air, molecular, same pressures: Q_air = Q_He / 2.69