I'm sizing PSVs and calculating the relief load on different scenarios. The discharge of the PSVs are collected to the flare header then routed to the Flare KO Drum. What should be the basis of calculating the superimposed back pressure?
For individual contingencies, most Flares have methods (such as liquid seal) that intensionally hold a constant back pressure on the Flare Header.
Some Flare systems have additional backpressure due to purge gas input.
You should figure out all this for your specific site.
For multiple contingencies (such as general Fire, power failure)you will need a specific study to determine the rating of the Flare header.
I have seen one systems that had 24-psig superimposed back pressure for multiple contingency during a generaL FIRE.
I have also seen 12-psig for power failure.