The leak rate of gas from a pressurized storage vessel or a pipeline will depend on the following factors:
- Leak size
- Gas composition and physical properties
- Pressure of gas
- Temperature of gas
- Volume and geometry of the containment
- Whether condensation will occur or not
If the pressure drop at the release point is critical, i.e.
where
p1
= ambient pressure
p2
= pressure inside containment
γ
= cp/cv ratio of spec.heat
the velocity of the escaping gas will be sonic at the leak point. Otherwise it will be subsonic. The sonic gas rate may be calculated as
where
mog
= initial gas leak rate (kg/s)
A
= release area (m2)
CD
= coefficient of discharge
γ
= cp/cv, gas spesific heat ratio
cp
= specific heat of vapour, constant pressure(J/kg oC)
cv
= specific heat of vapour, constant volume(J/kg oC)
p2
= pressure inside containment(N/m2)
T
= temperature in containtment (K)
R
= gas constant=8314(kg m2/K kmol s2)
M
= molecular weight (kg/kmol)
For the case of subsonic gas rate a correction factor ψ has to be included in equation above, defined as
A constant gas leak rate can be used only for releases from containments where the energy loss
due to friction is negligible (e.g. from storage tanks). It is also only valid for the first minutes
of the release, after the onset of the leak. As the leak continious the pressure inside the vessel
will decrease, as will the leak rate. The release rate decay will basically be dependent on two factors:
initial (constant) leak rate and mass of gas inside the vessel.
The decay of the leak rate will be exponential and can roughly be described by the following equation:
where
mg
= leak rate as a function of time (kg/s)
mog
= initial leak rate (kg/s)
w
= total mass of gas in the vessel (kg)
t
= time after onset of the leak (s)
Reference: Scandpower A/S,SINTEF-NBL"Handbook for Fire Calculations and Fire Risk Assessment in the Process Industry" 3rd Edition 1997
