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The primary criterion for determination of a snuffing condition is the flammability of the total mixture.
Most gases have published flammable limits which can be used to assist the assessment of inert requirements for snuffing.
The Lower Flammable (or Explosive) Limit is a measure of the leanest practical concentration of gas which will continue to propagate a flame in Air.
Find LEL from tables or theory
Ratio of Air to Gas at the Low (Lean) Limit
= RL = ( 100 - LEL ) / LEL
Theoretical Air (Stoichiometric) Ratio
= RST from tables or theory
Excess Air at Low Limit ( = dilution)
= RXS = ( RL - RST )
Nitrogen Equivalent of the required Inert = NE
N2 = 1.00 N2
CO2 = 1.82 N2
H2O = 1.35 N2
SO2 = 2.10 N2
He = 0.65 N2
Minimum Ratio of Inert to Flammable Gas
= RI = RXS / NE
Safety Factor FOS > = 1.5
Snuffing Ratio = RSN = RI * FOS
Burning Ratio = RBN RI / FOS
The calculated value of RSN represents the recommended minimum amount of Inert to be mixed with the Flammable Gas to just exceed the Low Limit condition and achieve a snuffing concentration.
The calculated value of RBN represents the recommended maximum amount of Inert which can be mixed with the Flammable Gas to without a concern that the mixture will achieve a non-flammable concentration.
Note that these are volume Ratios, and depend on the concurrent flow rate of Flammable material.
Some snuffing systems take advantage of the fact that, as a mixture becomes leaner, the intrinsic stability of the flame gets less (which is what you imply). At the tip of the discharge, air is entrained into the mixture by the dynamic velocity of the stream. This air acts as an added diluent and so the maximum velocity which will "hold" a flame reduces as the mixture gets leaner. This is a much more complex calculation than the above and can be easily disturbed by turbulence, which tends to help flame stability. Also, hydrogen (particularly) has very wide limits of flammability and relying on the velocity destabilization is not a great solution (in my view).
For either of the above solutions, you should sustain the flow of inert for long enough to fill up the down stream line with non-flammable mixture to reach the discharge.
OR, if you quickly introduce the inert into the line it can form a temporary "plug" of non-flammable material. The effectiveness of this is a function of the total system volume and how quickly the incoming flow can build a pressure able to "burst" through the plug. Consequently such calculations are system and case dependent and not easily simplified. You would need the plug to sustain its effect for longer than the normal burning time of the flame on the tip, which depends on the flow rate, heat release and wind speed but could be 1 to 5 seconds (sometimes more).
Your best bet is to design for the non-flammable mixture as the other conditions will all be less and you may get lucky in the real case.
Remember that, if you use steam, you have to think about the condensation and how to handle the drainage (and corrosion issues). Also, when you turn off the steam, the cooling and condensation will generate a suction effect in the system and suck air down the line. If you are still relieving hydrogen you then have a flammable mixture with hydrogen in the pipe and that can flash back if there is still a source of ignition, so there are procedural things to think about.