Oxygen depletion in a fixed volume due to inert gas leak

NOTE

Also see an extension of this work which incorporates a recycle stream.

In a system where nitrogen leakage into a room results in oxygen depletion, the following may be used to determine the leakage rate resulting in a specified oxygen concentration at equilibrium.

Where: is nitrogen flow into room, is the no. of room change per hour due to HVAC, is room volume, is final room oxygen concentration at equilibrium, (vol frac)

Assumptions

• Assumes instantaneous perfect mixing. Whilst concentration will average out to some degree in large spaces, this method does not account for local oxygen depletion. This will be significant at the point of release.
• All flowrates given in at atmospheric pressure.
• Air into the system via HVAC unit is a constant volumetric flow and taken as 21 vol% oxygen.

Derivation

At equilibrium, oxygen in = oxygen out. Where: is air flow into the room, is final room oxygen concentration at equilibrium, (vol frac) is vent flow out of the room,

Since , we can substitute to find: Re-arranging for : The vent flow is related simply to the number of air changes per hour: Where: is the number of air changes per hour, is the room volume,

Substitute into :