Hi all,

apologies if this process is described elsewhere but I have tried a search and can't seem to find the precise answer that I want.

Background:

A vessel has existing PSVs installed, these were designed for fire relief. As part of a modification there is a new relief case greater than the existing sizing case (vapour).

The steps I need to do are:
1) Calculate new relief case - done
2) Calculate what size orifice is required from relief valve sizing calc - done.
I used GPSA (5-7) for vapour relief.
The answer from 2) above meant that for the new relief case I would need to increase the orifice size from D to E. This is possible in the 1"x2" valve body, so no limitation physically there.
3) I need to determine if the existing installed tailpipes are adequately sized for the new rated relief case (max flow E orifice at relief conditions).

What are the steps I need to do to do this? I have API 520 (I/II) and 521 but to be honest I can't seem to get my head round it.

I have calculated the overall K factor (fl/d) for the downstream pipework using Crane "Flow of Fluids - Through valves, fittings and pipes". Though not sure if that will be useful or where the Mach number equations come into play that are provided in API 521 pages 106-108.

Any help in spelling out exactly what steps I now need to follow to 'size/rate' the existing tailpipes will be gratefully received!

Thanks.

I can happily provide specifics if it helps with clarification.

You are almost there.

Since you have a copy of Crane, take a look at example 4-21 'gases at sonic velocity'

You need to calculate the pressure required at the outlet of the PSV to flow the capacity of the PSV to atmosphere at 10% overpressure.  You can have chocked flow in an atmospheric tailpipe so this is a good example showing how to check for choked flow and how to correct for it.  Most of your losses will likely be the exit loss to atmosphere (K = 1).

You then compare that to the allowable backpressure for your PSV (for example, conventional PSVs are limited to 10% of backpressure).

You also need to check at the inlet line losses are less than 3% of set pressure.  Since the capacity of the PSV has increased, the inlet line losses will also have increased.

It really depends on the length and size of the tailpipe.  If it is bigger than the orifice (which it certainly is) and shorter than about 10D then you can safely assume that it is "infinitely wide and infinitely short" which means that the choked flow exiting the orifice stays at near sonic velocity until it has exited the tailpipe.  

The important fact is that friction loss in the tailpipe does not push up the outlet pressure at the orifice to more than the critical pressure for choked flow.

At about 10D the infinite  assumption starts getting a bit flaky and you have to do real work.  Above 0.6 Mach, the flow is compressible and cannot use any of the incompressible equations.  The simplifying assumption that I use is that the transonic region is 10D and that I'm below 0.6 Mach after that point.  This is not assured, but I've found it to be a reasonable approximation.  At that point I can look at the pressure at the exhaust (atmospheric pressure), the mass flow rate through the orifice, and use the Isothermal Gas Flow Equation to calculate the upstream pressure (i.e. the pressure at 10D downstream of the PSV).  If that pressure is "well under" the critical pressure for choked flow at the orifice then I call it good.  If not, then the tail pipe is too long and/or too small.

"Well under" is more than a bit mushy, but for 6 ft tail pipes I usually find that this exercise results in a pressure at 10D that is less than half of critical, sometimes a lot less.  If I'm going to a flare, then I often find that I need more care.  In those cases I use <95% of critical pressure is acceptable and don't feel very good about it.

I've always found that in these gray areas it is crucial that you document your assumptions and calculations.  I've been audited several times and this calculation has withstood serious scrutiny.  The key seems to be that you've applied an objective criteria consistently.  I find the "guidance" in the standards to be so full of exceptions that it isn't much help.

David   

Exellent advice zdas04.......  as always..!!

For the sake of comparison, there is also a method of sizing "tailpipes" for steam relief valves in an appendix to ASME B31.1.

(By "tailpipes" I am assuming that you mean fairly short, mostly vertical, pipe segments that relieve the process fluid to atmosphere.....is that correct ?)

Regards

MJC