With ideal mixing, oxygen falls exponentially as inert gas is added: the number of vessel volumes needed is the natural log of the starting concentration divided by the target. Bringing 21 % down to 1 % takes about 3.0 vessel volumes; down to 0.1 % takes about 5.3. Real vessels need more if they do not mix well.
A dilution purge assumes the vessel is perfectly mixed. Displacement purging of a long pipe can need fewer volumes; a vessel with dead pockets can need many more. Always confirm with an oxygen analyser.
How it is calculated
In a well-mixed vessel, each increment of inert gas dilutes the oxygen in proportion to how much oxygen is present. That gives an exponential decay in concentration with the volume of inert gas added.
C(n) = C0 x e^(-n) n = ln(C0 / Cf) time = n x V / flow
Here n counts vessel volumes of inert gas, C0 is the starting concentration and Cf the target.
Worked example
A 10 m3 vessel is purged from 20.9 % to 1 % oxygen: n = ln(20.9) = 3.04 vessel volumes, so 30.4 m3 of nitrogen. At 20 m3/h that takes 91 minutes.
Taking the same vessel to 0.5 % needs n = ln(41.8) = 3.73 volumes, about 37 m3 and 112 minutes. Each halving of the target costs about 0.7 more volumes.
The curve flattens: the last decades of oxygen are expensive, which is why the target should come from the limiting oxygen concentration and a safety margin, not from habit.
Limits
- Perfect mixing is an ideal. Vessels with baffles, dead legs or stratification need more gas.
- Displacement of a long pipe by a plug of nitrogen can reach the target in about one pipe volume plus mixing.
- Confirm the end point by measurement. See Inerting and purging: how they work and how to prove them and What is limiting oxygen concentration (LOC).
Frequently asked questions
How many volumes does it take to purge a tank with nitrogen?
For good mixing, about 3 vessel volumes to go from air to 1 % oxygen and about 5 volumes to reach 0.1 %.
How do I choose the target oxygen for purging?
Start from the limiting oxygen concentration of the flammable material, then subtract a safety margin set by your safety assessment.
Why does my purge take longer than calculated?
Poor mixing, dead legs, leaks or incorrect inert gas flow. An oxygen analyser on the vent shows what is actually happening.
Can I purge to below 100 ppm oxygen?
Yes, but it takes more volumes and the leak tightness of the system becomes the limit, not the purge calculation.