PSV Discharge Line Choking

[buelowj]

While validating the fire relief case for a propane drier, I came across a discharge pipe sizing issue that I'd like some advice on.

The drier has a balanced bellows style PSV with a set point of 445 psig. Using the API 521 guideline for vessel relief when exposed to external fire, I calculated the required relief capacity to be 26,412 pph. Allowing 121% overpressure in the fire case, I found that the Pcritical = 328 psia, the flow will be choked, and the PSV required an orifice of 0.595" to meet the required relief capacity assuming the backpressure is low enough that Kb = 1.0 (which I later verified). The current PSV has an H size orifice of 0.785" (which satisfies the >0.595" required).

The question I have centers on the discharge pipe backpressure. The discharge line from the PSV is ~100 ft effective pipe length that is 3" nominal diameter schedule 40. This 3" line connects to an 18" flare header that runs ~2 psig.

Using the required 26,412 pph mass flow along with the 2 psig downstream flare header pressure, I determined the outlet pipe pressure drop is large enough to cause the gas to choke a second time in the 3" PSV discharge piping. Can double choking like this occur?

Assuming that double choking can occur, I assumed adiabatic compressible choked flow through the pipe (since it is a short run and flowing quickly through the pipe) and iterated the adiabatic compressible pipe flow equation to determine what inlet pipe pressure would be needed in order to satisfy mass balance continuity. From this iteration, I found that once the discharge pipe inlet pressure reaches ~63 psig, mass balance continuity is achieved across the PSV choke flow and the pipe choke flow. Since the Pcritical for the PSV outlet is 328 psia (313 psig), the PSV is still choked so the increase in downstream pressure shouldn't affect the relief case, right? Furthermore, from the API 520 Kb chart for bellows backpressure the backpressure/set pressure isn't high enough to cause the Kb to drop below 1.0. It also should be noted, the 63 psig in the flare discharge piping is within the flare pipe design MAWP.

Anyway, I'm just curious if anyone else has ever come across such a second choke in flare outlet piping - and if you agree with the methodology I used (adiabatic compressible flow in discharge pipe) to determine backpressure and verify relief valve capacity. Personally, I don't think choking in the PSV discharge piping is a good idea and should be avoided in new designs - but this is a case where it is an existing design.

I am a young process engineer and somewhat new to this, so any advice from the experienced process engineers is much appreciated

 

[CJKruger]

buelowj,

1) Yes, it is possible to have two (or more) choke points in one circuit.

2) The choke points will always be at an expansion (or exit). An orifice choke not when the fluid enters the orifice, but when it leaves.

3) I think your logic is correct, apart from how you calculate the second choke flow/pressure. You should include the effect of the 100 ft of pipe.

4) In general we try not to have choke flow in the discharge piping. Would be best if you can increase the pipe size to get say 70-80% of sonic velocity.

5) To confirm your choke flow calcs, download the shareware version of Korf Hydraulics at

http://www.korf.co.uk

and simulate the problem.

Disclaimer, I am involved with Korf Hydraulics.

 

[buelowj]

I appreciate the advice DJKruger and thanks for the software link!

Also, I agree with you about using the pipe for the calculation in the second choke. I think my original post was confusing. I did include the effects of the 100 ft of pipe for the second choke. I used the compressible adiabatic flow equation through a pipe (which I obtained from my gas dynamics textbook). The inputs needed were the upstream conditions, the Cp/Cv ratio, and the pipe geometry data. I assumed choked flow and then verifed the downstream pressure was below Pchoke to ensure the choked flow assumption was valid.

Thanks again!

 

[meanderson3d]

buelowj,

When I design relief systems, I am generally less concerned with whether or not there is choked flow in the pipe than what the actual back-pressure at the valve is. For a balanced bellows or pilot operated valve, this is not usually an issue, but it still needs to be checked.

I agree with CJKruger that you need to take into account the 100 feet of 3-inch pipe. This can be somewhat tricky to calculate with a high pressure drop relative to the static pressure, but there are software packages out there to help.

Andy
New Orleans, LA
Petronyx Consulting Engineers, LLC

http://www.petronyx.com

 

[TD2K]

As others have said, you can get a double choke point in a PSV outlet line.

You can estimate what the pressure in the 3" line is where it ties into the main flare header (at 2 psig) by calculating what pressure gives you a Mach number of 1. You can then backcalculate what is the pressure at the outlet of the PSV to get the flow needed through the 3" line.

The last issue of API 520 or 521 however recommends you should use the PSV's actual capacity when doing the exit line losses, not the required capacity. Moot point because if your PSV is a balanced bellows, you will be able to accept up to over 200 psig backpressure before its capacity will start to be affected. You just need to make sure the bellows is designed for the calculated backpressure.

 

[Bill3752]

blue, a couple of items you may want to consider. First, refer to the API 521 and use the isothermal approach for doing your back pressure calcs, beginning at the discharge and working backwards. Per the literature I have seen, do not apply the typical Crane exit =1 in your calculation. Work your way back through the 3" leg (i.e. what is the pressure at that point). Second, continue the calculation back to the RV. Third, as stated above it is recommended that you use the capacity of the RV, not the required rate. However, you did not state whether this was a fire event - if so base the flow on 10% overpressure per "Guidelines for Pressure Relief".

You will invariably find that most of the dP is in the first (in your case 2") leg. Makes sense the the available area is 2 1/4" larger.

Hope this helps.

 

[4Pipes]

Bill3752

I admit that Process Engineers often use isothermal for high mach numbers but this is not necessarily correct. Isothermal starts to fall over for M>0.3 or thereabouts. Somebody will correct me on this.

 

[buelowj]

I used adiabatic compressible fluid assumption rather than isothermal assumption because I figured that for the short time it would take to travel through the tail pipe there would be very little time for heat transfer between the outside air surrounding the pipe and the relieving fluid.

I thought it wouldn't be isothermal since there would be significant temperature change due to the large pressure change in the compressible fluid.

Is this a poor assumption? Is isothermal the recommended method to use? Or maybe best to calculate both ways and take most conservative approach?

 

[Latexman]

For short pipes and high velocities in compressible flow, adiabatic is the best choice.



Good luck,
Latexman