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High-pressure PSV discharge - backpressure and choked flow

High-pressure PSV discharge - backpressure and choked flow

Hello all,

I was asked to run some calculations on a PSV that was suspected to be installed with an undersized discharge line. I will be reviewing with our PE when he's free later in the month but wanted some theory double checking.

Specs -
Conventional spring-loaded PSV
Set pt 13,500 psig
0.250" orifice
Direct mount on pressure vessel (negligible inlet pressure drop)
Discharge to atmosphere 12.1 psia - total length 92", ID 0.62", 1 elbow, 1 branch-run tee, top terminates with a tee and longhorn vent (5" length in each direction)
Ambient temp on warm day (540 R)

References: ANSI API 521, AlChE "Sizing Pressure Relief Devices"
Calculations: Spreadsheet segmented calculations following API 521, with graphical table lookup from Fig. 14, recalcuating Z at each

Results - 38,866 SCFM H2 choked flow across PSV at 10% overpressure (matches manufacturer table)
Sonic chokes at both longhorn vent exits (Pcrit=316 psia)
Sonic choke at tee from main vent mast (Pcrit=1507 psia)
4672 psia at PSV outlet

So my questions here are:

The backpressure/(set pressure + overpressure) is at 31%. API 521 states that it should remain at 10% for conventional PSVs but the AlChE manual (Figure 7) does not show any reduction in capacity until about 55% backpressure for conventional PSVs in vapor service, and it is still under the Pcrit for choked flow across the PSV. What would the negative effects of having ~30% backpressure be on PSVs?

Does the secondary choke make sense in this context? I can see how there would be a choke at the vent exits (sonic boom as it exits the mast) but does the calculated result of another choke point at the tee (where the flow splits into two paths) mean that I need to re-iterate the calculations with a lower flow rate?

Cross posted to ME pressure vessel forum. Thanks all.

RE: High-pressure PSV discharge - backpressure and choked flow

That is an incredible pressure drop in the tail pipe - 4657psi!

The last time I saw this API, it showed the capacity corr factor Kb collapsing steeply as we cross the 10% backpressure line for conventional spring loaded PSVs. Not familiar with this AIChemE manual.

If you want to minimise exit line size, a balanced bellows or pilot op PSV ( which is possibly okay with this clean gas service) would be the choice.

At this pressure drop across the PSV, the JT effect would be considerable. Has this been taken into account in the tail pipe sizing also - there is a procedure in Perry for adiabatic compressible gas flow ( as opposed to isothermal compressible flow). The piping reducer on the PSV exit may be a big contributor to the exit dp. At very high pressure, hydrogen shows a negative JT effect with pressure drop - check if this applies here.

RE: High-pressure PSV discharge - backpressure and choked flow

Figure 7 in the CEP article "Sizing Pressure Relief Devices" (which, IMO, is NOT an AICHE Manual), comes directly from Figure 36 in API 520, Part 1. It is part of "Alternate Sizing Procedure for Conventional and Pilot-operated Valves in Subcritical Flow". Figure 36 carries the following NOTE:

NOTE This chart is typical and suitable for use only when the make of the valve or the actual critical flow pressure point for the
vapor or gas is unknown; otherwise, the valve manufacturer should be consulted for specific data. This correction factor should be
used only in the sizing of conventional (non-balanced) PRVs that have their spring setting adjusted to compensate for the
superimposed backpressure. It should not be used to size balanced type valves.

From your description, I believe your system is not subcritical, and the spring is not adjusted for superimposed backpressure, so it does not apply.

Good luck,

To a ChE, the glass is always full - 1/2 air and 1/2 water.

RE: High-pressure PSV discharge - backpressure and choked flow

mengh2 - I think I see the source of the confusion. That confusion stems from a logic error - one that's not obvious at first.

Your spreadsheet is calculating the flowrate based on fluid properties and the system (orifice, piping, etc.) through which the stream is flowing. Does the flowrate calculation depend on the type of PSV being used? No, the flowrate calculation is based on the PSV's orifice area, and not the PSV type. But here's the catch.....the orifice area which is used in the flow calculation isn't really available to you if the PSV is rapidly cycling open and closed. That is, the flow calculation assumes that the PSV operates in a stable manner - it remains open when needed - but that won't happen unless you choose the right type of PSV for the application. In this case the backpressure that is too high for a conventional PSV. It's too high to prevent a conventional PSV from rapidly cycling open and closed - thus rendering the flow calculation invalid. Because of this cycling, the "effective" orifice area is far less than the area that is assumed in the flow calculation.

In order for the flow calculation to be valid (in order for the orifice area to actually be available), the PSV must be one that remains open during the relief event. In this case you have ~30% backpressure, which is much too high for a conventional PSV.

RE: High-pressure PSV discharge - backpressure and choked flow

Thank you Latexman for the context! That note wasn't included! George, here is the article I was looking at - relevant text on pages 7/8. Notably it specifically talks about cases where the flow is critical. It seemed somewhat reasonable - backpressure doesn't matter if the flow is still critical right? - but it looks like it may directly contradict the code. I'll track down our copy of API 520 and review it in addition to API 521.

George, it's a good point you make about the J-T effect. I was using the isothermal calcs in API 521 and neglecting the J-T on the pipe exit since it's expanding to the atmosphere but with secondary chokes within the pipe I think adiabatic would be the best way to go here. For what's it worth I tried to reproduce the calculation in PIPE-FLO software for the same gas, full flow rate and pipe specs and came up with a backpressure of 2191 psi which is only 14% - closer to ideal. Not sure if PIPE-FLO uses adiabatic calculations but the difference is significant. Did get some errors with sub-zero static pressures at the choke points (tee, pipe exits), not much experience with PIPE-FLO software.

Don, wouldn't we be looking at the flow at the instant the PSV opens? Once it pops it's fully open and then the maximum flow rate is achieved - then it chokes and causes the PSV to chatter. Yes the overall relieving capacity is reduced over the full time required to vent and blowdown but wouldn't it be full flow for a few milliseconds? Would a backpressure correction factor apply in this case of instant full-open flow? I am not calculating the flow rate over time, only at the 10% overpressure case.

I'll try to reproduce my calculations with adiabatic equations taking the J-T expansion into account and using the Fanno lines to try to validate the PIPE-FLO model.

RE: High-pressure PSV discharge - backpressure and choked flow

Yes, have seen this graph in the API, but I dont think anyone actually uses this; there is no way of online compensation of set press as backpressure changes in a conventional PSV. Vaguely recall there is another graph in the API that ties in with what oil and gas process engineers use in practice.

There is a numerical trial and error procedure in Perry for adiabatic compressible flow - using the graphical Fanno line procedure is painful and somewhat prone to error when reading off the graph. Also, it is customary practice to keep velocities in tail pipes below 0.5Mach,and this includes the final exit to atm. (i.e press ratio at final exit should be less critical if you are not using a special sonic exit.)

RE: High-pressure PSV discharge - backpressure and choked flow

What this graph in the CEP doesnt tell you straight out is that in a conventional valve, the actual relieving pressure changes with backpressure. All it shows you is that relieving capacity drops off somewhat when backpressure exceeds 30-50% of the original set pressure. But by this time, the actual relieving pressure has moved up by the same amount that the backpressure has increased.

Hence the practice to limit the backpress to 10% of MAWP on conventional RVs, since a 10% exceedence on MAWP is all that is permitted per ASME for non firecase relief scenario.

Essentially , a conventional RV has zero capability to adjust relieving pressure - once its set pressure is fixed, relieving press just floats along with backpressure.

RE: High-pressure PSV discharge - backpressure and choked flow

Just looking at the base criteria, Set Pressure 13,500 PSIG, Orifice 0.25" (is this diameter or area in2 ?) need to see if a SRV design actually exists. It is way over API-526 etc. Also consider the material of the SRV in case sparking etc., can occur anywhere (H2 service). Without talking calculations, you need to be looking at a pilot operated SRV. The technology is out there to make a special (and it has been done). The pilot SRV selection would offer greater seat tightness, non metal seats, no back pressure and other options such as remote sensing, opening. Dependant on connection type, a solid forged main valve body would be the answer with an appropriate modulating pilot actuator.

Per ISO, only the term Safety Valve is used for all overpressure eventualities regardless of design.

RE: High-pressure PSV discharge - backpressure and choked flow

Thank you George. I understand clearer now. I was confused by the CEP article, which didn't specify that the graph was to be used only with superimposed backpressure, and from this section in a manufacturer of a conventional PSV similar to the one we were looking at - "At a backpressure equal to approximately 40% of set pressure, chatter / rapid-cycling may start.
Reduce backpressure by reducing flow rate or reworking outlet piping (increase size; shorten; reduce number of turns). It is recommended that outlet piping size be equal to or greater than the valve outlet size."

So within 10% to 40% the negative effects of backpressure would be an increase in the set pressure, likely causing it to close early. Higher than 40% the flow stops being choked and the capacity reduces (in addition to the increase in set pressure).

Valveman, yes it is a real valve. The capacities we calculated matched the manufacturer spec sheet. It's a .250" diameter orifice. The outlet is only a 3/4" size which is pretty much clearly too small for our applications. I wasn't involved in the sizing and selection of the valve and the tailpipe was selected based on the recommendation that it match the valve outlet size but I am going to recommend a step up to 1-1/2" piping to get the pressure under 10%.

George, the code appears to allow for sonic exits as long as the 10% backpressure is not exceeded. What would the reasons be to try to reduce the Mach to 0.5 to 0.7 other than tailpipe forces and sound?

RE: High-pressure PSV discharge - backpressure and choked flow

Beyond about Mach 0.7, the rate of change of upstream pressure with flow is very steep, hence large changes in P1 can occur for small changes in flow or in total equivalent length. In some cases, the rate of change can happen when Mach No is as low as 0.5. So, if you are in this mach no region, it is a good idea to run some sensitivity cases and see how much P1 changes with some variation in flow or temp or mol wt or total equivalent length. This then will help you find a more stable region to be operating in. It also buys you some insurance against variations in the currently perceived system as design proceeds further.

RE: High-pressure PSV discharge - backpressure and choked flow

With such a high set pressure, and processing hydrogen, I would get the opinion (i.e. pay for) of a recognised professional in relief. There are a number of consultants who specialise in this. This particular application is not for amateurs (Which I am).

RE: High-pressure PSV discharge - backpressure and choked flow

Im with Longintheyooth here. H2 will explode very easily, just a little spark (e.g. statics) and boom. I dont like idear of discharging a cloud of H2 (or two clouds) just 7-8 ft above the vesse - or is it just me?

RE: High-pressure PSV discharge - backpressure and choked flow

What could possibly go wrong? bugeyed

Good luck,

To a ChE, the glass is always full - 1/2 air and 1/2 water.

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