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(OP)
Hello Everyone ,
I'm trying to size a relief header to which three PSVs are connected on a gas compression package . I'm using the max capacity of the largest PSV (MMSCFD) and sizing the header for 0.7 Mach velocity .
Should I use the simple flow rate equation Q=V*A to find the pipe dia. or there is some more in depth equation that I should be using , since this is a compressible flow .
I have tried API 521 equation 27 with following conditions
flowrate = 173464 lb/hr , mach = 0.7 , pressure = 1111 psig , z = 0.868 , temp = 333k , k = 1.31 , MW = 18
but the pipe dia is coming as 1" which to me is wrong .

Any help will be much appreciated .

### RE: PSV relief header sizing

It is obvious you are new to this kind of work. Moreover this is a process safety critical engineering task, so it should be supervised and approved by some one experienced, who should show you how this calculation is to be done.

There is too much to say in this discussion forum to be of much help; for the benefit of others also who arrive at this discussion thread looking for help, the tasks are, briefly:

a) Determine the worst case combination relief load to be considered from this combination of PSVs'.
b) Determine the highest continous backpressure / flow resulting from normal flaring operations on the main header to which these PSVs' are connected.
c) Superimpose this worst case PSV load onto this continous load and rework backpressure at the PSV tail pipe, by working backwards from the flare tip, starting with the adjusted flare tip dp for this combined load.
d) Pipe size selection should be based on (i) Mach number not to exceed 0.5-0.6 anywhere in this relief path (ii) max developed backpressure at PSV exit not to exceed the permissible backpressure for the type of PSV selected and the PSV setpoint / accumulation permitted for your jurisdiction.
e) Backpressure estimates are to be based on isothermal compressible flow (or adiabatic compressible if you are particular)
f) The backpressure at the end of the main header, where your PSVs' are teeing in to, should not have a backpressure greater than the setpoint of the lowest set of all the PSVs' connected to this header.
g) Finally, for high relief rates, you may need to do a coarse screening AIV study to see if you need to increase pipe schedule beyond that which is used for this flare system piping class.

Be wary of multiple operating modes in your plant that may affect how you choose the max normal continous flaring load which is applicable to these PSVs. You should also check if other PSVs' will be operating at the same time as this set of PSVs', either due to some common failure mode, of if the backpressure on the relief header will set off some other PSV ( normal flaring PCV cannot operate), because of the absence of instrumented shutdown safeguards at that protected equipment.

### RE: PSV relief header sizing

What GV said.
But wouldn't the pressure of the relief header be 0 psig

### RE: PSV relief header sizing

For typical sub-sonic, open pipe flares, headers are designed for 0.5 Mach or less. The 0.7 Mach figure applies for PSV tailpipes.

You have considered relieving pressure equal to the header pressure, which resulted in a small-size line. In reality, the header pressure will be closer to 10-15 psig, not 1000+ psig. It is calculated as atmospheric pressure + flare tip dP + flare header dP + PSV tailpipe dP. You need to consider the maximum combined load (relief) to the flare, and then start calculating pressure drop backwards from the flare tip, for given maximum flow and given line size. This is the backpressure against which the PSV has to relief the system inventory.

For conservative calculation, you can consider sizing the header for 0.5 Mach at the maximum flow and at atmospheric pressure. In real world, the true Mach No. will be slightly less than 0.5 because of the built-in backpressure during relief. It is always a good practice to leave some margin for future upgrades/expansions - you don't want to find out later that the flare system is undersized.

Dejan IVANOVIC
Process Engineer, MSChE

### RE: PSV relief header sizing

tickle: the relief header probably is at 0 psig, but not necessarily. You would need to consider what other things are happening on site that are connected to that flare. I work for a compressor packager, and one of the first things we do when sizing our on-skid relief header is confirm with our customer what the expected backpressure is in the flare header. In my experience, most are 0 psig, but not all.

Guri77: I assume the three PSVs on your package are sized for blocked flow, and you have one per stage of compression. Keep in mind that all three of those PSVs are fed by the same gas, and in general, the source of overpressure is the compressor itself, combined with something blocking the line (commonly a frozen or otherwise blocked cooler). So if your first stage PSV is venting, unless you have a sidestream inlet, there's no way for more gas to get to the 2nd or 3rd stages (assuming it is sized correctly for the maximum flow your compressor can put out).

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