High-pressure PSV discharge - backpressure and choked flow
High-pressure PSV discharge - backpressure and choked flow
(OP)
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
Hydrogen
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 7.3.1.3.3, 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.
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
Hydrogen
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 7.3.1.3.3, 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
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
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,
Latexman
To a ChE, the glass is always full - 1/2 air and 1/2 water.
RE: High-pressure PSV discharge - backpressure and choked flow
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
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
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
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
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
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
RE: High-pressure PSV discharge - backpressure and choked flow
RE: High-pressure PSV discharge - backpressure and choked flow
RE: High-pressure PSV discharge - backpressure and choked flow
Good luck,
Latexman
To a ChE, the glass is always full - 1/2 air and 1/2 water.