PSV Reaction Force Calculation - API 520 Static Pressure Term 1

[Pavan Kumar]

Dear Friends,

I have a PSV on Saturated steam service set at 306 psig that vents to atmosphere. The outlet pipe has one 90 Deg LR elbow and some 2 feet of vertical pipe. The PSV size is 4N6. The outlet pipe is 6"Sch 40 ( ID= 6.065 inches). I calculated the reaction force for the PSV for Steam service using the formula per API 520 part II 5th Edition, section 4.4.1.1. I considered that the static pressure is the pressure at the discharge point of the pipe before exiting the pipe to atmosphere. This I think is pressure at the PSV outlet flange minus the pressure drop in the 90 degree elbow and 2 feet vertical pipe. The pressure at the PSV outlet flange is critical pressure because the pressure at the outlet flange before PSV pops open is atmospheric pressure which is less than the critical pressure. Conservatively I assumed negligible pressure drop in the outlet pipe ans used the pressure at the PSV outlet flange as the static pressure P at the PSV outlet. Attached with this message is the calculation. I would like to hear from you if the approach taken is good enough.

https://files.engineering.com/getfi...=Steam_PSV__-_Reaction_Force_Calculation.xlsx

Thanks and Regards,
Pavan Kumar

 

[Latexman]

You calculated the pressure at the exit of the flow nozzle in the PSV, not at the outlet flange of the PSV body.

If flow is subcritical at the tailpipe exit, the pressure just inside the outet will be atmospheric pressure + 1 velocity head.

If the flow is critical at the tailpipe exit (and it is), the pressure just inside the outlet will be whatever it needs to be for the velocity to be Mach 1 + 1 velocity head.

Try this (from my handy dandy adiabatic compressible flow calculator):
Outlet Pressure = 15 psig
Outlet Temperature = 161 C

This should give you a Reaction Force:
Momentum Term = 1103.6 lbf
Pressure Term = 433.5 lbf

Reaction Force = 1537.1 lbf


Good Luck,
Latexman
Pats' Pub's Proprietor

 

[pierreick]

Hi,
You will find pointers using Crosby handbook , section 7 or Anderson, Greenwood , Crosby Technical seminar manual section 6 .
Same from the LESER engineering handbook using your favorite search engine .

https://www.leser.com/-/media/files/engineering/leser_engineering.pdf

http://www.iceweb.com.au/PressRelief/TechManual.pdf

Good luck
Pierre

 

[Vishal Kumar]

Why is the reaction force important sir?

 

[Latexman]

The reaction force is needed for the piping stress analysis.

Good Luck,
Latexman
Pats' Pub's Proprietor

 

[Pavan Kumar]

Hi Latexman,

The fluid velocity is already at Mach 1 at the PSV outlet and will not reduce any further. With the outlet piping being minimal the pressure at the inside of tail pipe outlet would be nearly same as that exit of PSV nozzle which is critical pressure, I used critical pressure for the "P" or static pressure term in the API 520 formula. Can you please show through a calculation how you got 433.5 lbf for the pressure term.

Thanks and Regards,
Pavan Kumar

 

[Latexman]

As high speed gas/vapor flows downstream in a pipe, it loses pressure to friction. As gas/vapor flow loses pressure, it gets more volumous/less dense. As gas/vapor flow gets less dense, it's velocity increases. So, if you have Mach 1 at the upstream end of this pipe, even though short, and the velocity increases as it goes downstream, do you have > Mach 1 at the end?

No. Your reasoning is flawed.

Here's what is going on. There is Mach 1 at the exit of the PSV flow nozzle, and you calculated the pressure just inside the flow nozzle using the critical pressure ratio. At the PSV flow nozzle exit (Mach 1) there is a shock wave, which is a "pressure discontinuity". Since we know gas/vapor flow increases velocity as it goes downstream, we know if it obtains Mach 1 in the pipe, it will be at the downstream end. So, you find the pressure just inside the exit of the pipe which gives Mach 1, then calculate the adiabatic compressible flow pressure drop backwards to the upstream end. Yes, you are kind of working backwards, but it's the easiest way to solve this. This pressure at the upstream end is also the "backpressure" at the PSV exit nozzle. The pressure discontinuity is the difference between your PSV nozzle pressure and the backpressure at the PSV exit nozzle.

I used your spread sheet with Outlet Pressure = 15 psig and Outlet Temperature = 161 C and some of your other information to calculate the Momentum Term = 1103.6 lbf and the Pressure Term = 433.5 lbf to yield the Reaction Force = 1537.1 lbf.

I also ran a different PSV sizing program with a 4N6 PSV and your conditions and it said the reaction forces were essentially the same as above.

Good Luck,
Latexman
Pats' Pub's Proprietor

 

[Pavan Kumar]

Hi Latexman,

What you said is perfectly correct. The gas will attain sonic velocity only at the exit of pipe as the gas cannot accelerate to more than sonic velocity if it already reaches sonic velocity at the pipe inlet as the pipe cross-sectional area is constant. Supersonic velocities can be reached if there was a divergent nozzle in place of the pipe.

Knowing the mass flow rate per PSV rated capacity, pipe ID, pipe absolute roughness, critical temperature the Reynolds number and hence friction factor can be calculated.

Knowing M2=1, friction factor f, pipe length L and pipe inside diameter D, the pipe upstream Mach number M1 can be calculated using the adiabatic compressible friction loss formula. Once upstream M1 is calculated the pipe upstream pressure P1 or the pressure at the PSV outlet can be calculated using isentropic flow formula. Once P1 is calculated, P2 can be calculated using the pressure ratio formula for adiabatic frictional flow.

I will complete my calculations in the method described above and post my spreadsheet in my next reply. I hope it will work out.

Thanks and Regards,

Pavan Kumar

 

[Pavan Kumar]

Hi Latexman,

For the above calculation I was trying to estimate the Superheat temperature of Steam after it expands from the PSV using Steam tables.

The PSV inlet Pressure Po= 336.6 psig
Saturation Temperarure, To = 222.272 Deg C,
Specific Enthalpy = 1204.23 Btu/lb

I assumed a Mach number = 0.57 and calculated pressure P1 after isentropic expansion across the PSV Nozzle, using the assumed Mach number of 0.57.

Pressure P1= 270.8 psig
Saturation temperature = 211.574 Deg C

Now using P1=270.8 psig and Specific Enthalpy = 1204.23 Btu/lb (assuming Isenthalpic expansion), the super heat temperature from steam tables = 212.713 Deg C. Now this temperature has to be higher than To, but I got T1 lower than To. This is not making sense. I wanted to hear your thoughts to solve this issue.


Thanks and Regards,
Pavan Kumar

 

[Latexman]

The temperature does not have to be higher than To. It does have to have the same enthalpy. I think you are thinking of how a gas behaves far from it's saturation temperature. This is riding close to the saturation line.

336.6 psig sat'd steam is 432.07 F with 1204.47 Btu/lb
270.8 psig sat'd steam is 412.85 F with 1202.92 Btu/lb

Difference = 1.55 Btu/lb

@ 270.8 psig Cp for steam = 0.65 Btu/lb/F = (1259.57 - 1202.92)/(500 - 412.85)

1.55/0.65 = 2.38 F

412.85 + 2.38 = 415.23 F = 212.91 C

You got 212.71 C

For all practical purposes, it's the same number.

Carry on.

Oh yeah, what's the signifigance of the assumed Mach number = 0.57?

Good Luck,
Latexman
Pats' Pub's Proprietor

 

[Pavan Kumar]

Hi Latexman,

I would like to understand the fundamentals used in determining the Steam temperature after pressure reduction. The pressure reduction over the PSV as you mentioned is iso-enthalpic. Textbooks however say the expansion across a PSV is iso-entropic, which I guess would give different temperature values. How about across the Control Valve. Is there any reference that I can study to understand this better. I am not clear about this.

Thanks and Regards,
Pavan Kumar

 

[Latexman]

Take a look at this - faq1203-1293 . I know the author.

Also, you may want to take future questions on relief devices to forum1203 . There's a lot of talent there.

Good Luck,
Latexman
Pats' Pub's Proprietor

 

[PaoloPemi]

Pavan,
with critical flow in nozzles the outlet temperature (normally) has some intermediate value between a isentropic and isenthalpic process,
that depends from several factors and it is difficult to predict accurately,
there are threads discussing this topic,
Paolo

 

[Pavan Kumar]

Hi Latexman,

Per your calculation mentioned below I am not sure how you estimated 15 psig as the outlet pressure. As per your note below, the fluid reaches sonic velocity at the pipe exit. The fluid will lose pressure once it exits the pipe through a series of shock waves. The formula from Crosby PSV handbook is giving 1527 lbf which is close to your value, but the formula used there is different from API 520 Part II and hence not confident on this number. I trying to calculate the Pressure P2 at pipe exit after calculating the pressure drop for adiabatic compressible flow in the outlet pipe. I am currently running into some issues. I would put my questions and the spreadsheet in my next query.

Thanks and Regards,
Pavan Kumar


---------------------------------------------------------------------------------------------------------
Latexman (Chemical)6 Jul 20 23:49
As high speed gas/vapor flows downstream in a pipe, it loses pressure to friction. As gas/vapor flow loses pressure, it gets more volumous/less dense. As gas/vapor flow gets less dense, it's velocity increases. So, if you have Mach 1 at the upstream end of this pipe, even though short, and the velocity increases as it goes downstream, do you have > Mach 1 at the end?

No. Your reasoning is flawed.

Here's what is going on. There is Mach 1 at the exit of the PSV flow nozzle, and you calculated the pressure just inside the flow nozzle using the critical pressure ratio. At the PSV flow nozzle exit (Mach 1) there is a shock wave, which is a "pressure discontinuity". Since we know gas/vapor flow increases velocity as it goes downstream, we know if it obtains Mach 1 in the pipe, it will be at the downstream end. So, you find the pressure just inside the exit of the pipe which gives Mach 1, then calculate the adiabatic compressible flow pressure drop backwards to the upstream end. Yes, you are kind of working backwards, but it's the easiest way to solve this. This pressure at the upstream end is also the "backpressure" at the PSV exit nozzle. The pressure discontinuity is the difference between your PSV nozzle pressure and the backpressure at the PSV exit nozzle.

I used your spread sheet with Outlet Pressure = 15 psig and Outlet Temperature = 161 C and some of your other information to calculate the Momentum Term = 1103.6 lbf and the Pressure Term = 433.5 lbf to yield the Reaction Force = 1537.1 lbf.

I also ran a different PSV sizing program with a 4N6 PSV and your conditions and it said the reaction forces were essentially the same as above.

---------------------------------------------------------------------------------------------------------

 

[Pavan Kumar]

Hi Latexman,

I estimated the pressure at the PSV outlet pipe exit and developed a spreadsheet. However I am finding that velocity calculated using the calculated Mach Number and that calculated from mass flow rate, density and pipe flow area is not matching. I wanted to understand the reason. Attached with this message is the spreadsheet with explanatory notes. Your inputs would be of great help to me.

I also calculated the reaction force per ASME B31.1 and get a value close to what you calculated.

https://files.engineering.com/getfi...Steam_PSV_Sizing_and_Reaction_Force_Calc.xlsx

Thanks and Regards,
Pavan Kumar

 

[Latexman]

The outlet pipe has one 90 Deg LR elbow and some 2 feet of vertical pipe.

Your current spreadsheet uses one 90 Deg LR elbow and 6 feet of vertical pipe. I used 2 feet of pipe as in the OP, so all I say below is based on that.

The critical pressure is calculated for the PSV inlet pressure and this value is compared to
the pressure(P3) of the location the PSV is discharging to. In this case the PSV discharging to
atmosphere through an outlet pipe. If P3 is less than the calculated critical pressure P*,
then PSV oultet presssure will be critical. But since there is an outlet pipe attached to the PSV,
the pressure will reach critical at the exit of the PSV outlet pipe instead at the PSV
outlet flange. If P3 is greater than critical pressure then the flow will be subsonic and hence
P2 =P3=Atm

My comments are:

The critical pressure is calculated for the PSV inlet pressure and this value is compared to
the pressure(P3) of the location the PSV is discharging to. In this case the PSV discharging to
atmosphere through an outlet pipe. If P3 is less than the calculated critical pressure P*,
then PSV flow nozzle exit will be critical. But since there is an outlet pipe attached to the PSV,
one must calculate if Mach 1 exists at the exit of the PSV outlet pipe instead at the PSV
outlet flange. If P3 is greater than critical pressure then the flow will be subsonic and hence
P2 =P3=Atm

In this problem, I (my software) found two occurrences of Mach 1, so there are two separate critical pressures to consider. The first occurrence of Mach 1 is at the exit of the PSV "N" flow nozzle (not the PSV exit flange). Btw, apply the critical pressure ratio to absolute pressures; not gauge pressures. I got 186.9 psia (351.3 x 0.532). Since the tailpipe exhausts to atmospheric pressure and it's so short, it's doubtful there is much backpressure, and the "N" flow nozzle is probably choked. You really have to calculate the backpressure on the PSV to know for sure though. You have components in series to be solved. A flow nozzle followed by an elbow and short pipe.

The second occurrence of Mach 1 is probably at the exit of the 6" tailpipe. This was/must be verified by calculation, which is iterative. With atmosperic pressure surrounding the exit of the tailpipe, for Mach 1 to occur at the tailpipe exit, the pressure just inside the tailpipe exit must be larger than or equal to 27.6 psia (14.7/0.532). This is a good first guess. Remember, adiabatic expansion applies in adiabatic, compressible flow (PV^k = constant). The mass flow rate comes from the PSV. You know the pipe ID. Calculate the T and P of the adiabatically expanding steam that gives Mach 1 at the tailpipe exit.

Now, calculate from the tailpipe exit to the PSV outlet flange (yes, this is backwards) and get the backpressure on the PSV.

You cannot calculate from the flow nozzle exit to the PSV outlet flange, or backwards from the PSV outlet flange to the flow nozzle exit. There is Mach 1 and a shock wave/pressure discontinuity between them. Your Step 2 is impossible to do. Rethink your methodology.




Good Luck,
Latexman
Pats' Pub's Proprietor