Gas lost calculation in Choked Flow

[jhamil1]

Could someone verify that I am doing this correctly. The number calculated seems excessive. I am new to the industry and have been looking over equations and have nothing to compare my answer. In advance, I appreciate the help.

Problem Statement: An 8" nominal Rockwell dynamic balance plug valve was left open approximately 19 minutes. The inlet pressure was 825 psig and the valve was open to atmosphere.

Find: How much gas was lost to the atmosphere.

Knowns:

- Valve properties -
Cv=2680
Critical pressure drop ratio=0.42

- Supply Line -
8" NPS schedule 80

- Fluid Properties -
SG=0.595

- Choked flow conditions -
Expansion coefficient (Y)=0.667
Compressibility Factor (Z)=0.8728

Comments: I have read the post at Milton Beychok's site at

http://www.air-dispersion.com/feature2.html,

which is very good by the way. I understand the equation, but is there a way to relate the flow coefficient (Cv) to the discharge coefficient (Cd)? All most all of the information I deal with has everything based on the flow coefficient.

My Solution: I researched the ANSI/ISA-75.01.01 standard, "Flow Equations for Sizing Control Valves". Using Eq. 14B

Cv=(Q/Y*1360*Pi)*sqrt[(SG*T1*Z)/(Fy*xT)] (English Units)

Where,

Cv=2680 (from manufacturers data)
Q=? cf/h
Y=0.667
Pi=825+14.73=839.73 psia
SG=0.595
T1=60F=520R
Z=0.8728
Fy=k/1.4=1.27/1.4=0.9071
xT=0.42 (from manufacturers data)

Calculated flow rate, Q=1,279,847 scf/min.

In terms of 1000 of cf:

Q/1000 = 1,280 Mscf/min

Total lost over a 19 min period:

Total lost=Q*t --> 1,280*19min=24,317 Mscf

Questions:

Is this the correct equation to use for this situation?
If not, which equations are appropriate? (in terms of the flow coefficient (Cv))
How accurate is this equation?
If this is wrong could someone do an example of how to properly calculate this situation?

Again thank you for all the help and comments.

 

[BigInch]

Try this,

http://www.spiraxsarco.com/resources/calculators/orifice/flow-coefficient-to-orifice-diameter.asp

"If stupidity got us into this mess, then why can't it get us out?" - Will Rogers (1879-1935) ***************

http://virtualpipeline.spaces.live.com/

 

[CJKruger]

jhamil1, for a large valve like this the pressure loss through the pipe/entrance may be appreciable. And you may have choke flow at the pipe outlet, not the valve.

So, can you maybe describe the entire circuit, and I will simulate it for you (using Korf, from

http://www.korf.co.uk)

?

 

[jhamil1]

BigInch,

Thanks for the link, may be handy in the future.

CJKruger

This is an emergency blowdown valve. On the inlet side of the valve there is only about 50 feet of pipe which is connected to a series of pipes (i.e., compressors, etc...). In the case of an emergency, this valve is opened to atmosphere and the gas pressure is relieved (pressure decay). This is NOT the case for this situation (constant pressure). The valve opened accidentally and the supply line feed the valve at 825 psig for 19 minutes before personnel were notified. On the outlet side of the valve is only a small, maybe 2-1/2 foot of piping where the end is to atmosphere. If you could model this situation, it would be interesting to see the results and compare to ANSI/ISA standard equations. If you need any more information, let me know. Again thank you guys for the help.

 

[CJKruger]

jhamil1, like I suspected, the pressure drop through the pipes are significant and you have choke flow at the pipe outlet.

Results are:
Flow = 1,768,824 lb/h or 650,620 SCFM
Inlet pipe = 50 ft + one Tee
Valve dP = 76 psi

ANSI/ISA equation does not really help you much, as you don't know what the valve/orifice dP is without doing the entire system.

 

[jhamil1]

CJKruger, can you tell me if I am understanding you correctly. Instead of concerning myself with the Cv rating of the valve, and valve properties. Since it is choked flow at the end of the pipe anyway, just use that cross sectional area and the mass flow equations used at air-dispersions.com.

--------
If this is the case, take the reverse situation.

If the line was blown down to atmospheric conditions. I NOW shut the emergency valve and start filling the system back up with pressurized gas (purging the system). In this case, you would have a smaller valve, 2.5" to 4" for example. This would be supplied by the same 825 psig line and will be in sonic flow across the valve. Thus, I would need to be concerned about the valve properties. Since you are saying that the ANSI/ISA are inadequate what equations would be applicable?

 

[CJKruger]

jhamil1,

1) Yes, for the 8" line size valve case you could in theory only look at the pipe exit. But this doesn't really help you, as you don't know what the pressure is at the pipe exit (before the choke).

2) If you had a small restriction in the pipe (say 3" valve or orifice), then it will probably only choke there, and not at the pipe outlet. Using the ANSI/ISA equation is all you need then.

3) It is also quite possible for a system to choke at two different points (say the valve and the pipe outlet).

To correctly solve the problem you have, is very difficult by hand (there have been article published on it though). I recommend you get a program that can solve it.

 

[jhamil1]

CJKruger,

1) Wouldn't the pressure at the exit be atmospheric?

2) So for a small valve in a system purge situation the ANSI equation is alright to use. Why is it NOT alright to use the ANSI equation on a blow down situation?

3) How would you calculate this effect or would you have to model the situation?

Can you point me to some articles? Sorry, about all the questions, this problem has been irritating and I am trying to find some help. Thank you for your time.

 

[dcasto]

you have choked flow, so the flow rate is constant once the outlet pressure is below 420 psi. You calculation is correct for that rate. Next, a few feet of 8" pipe has about 50 psig drop to atmosphere, so all the drop is through the valve.

You have a typical PSV scenerio with 4 - 8T10 relief valves all opening up at once.

 

[CJKruger]

dcasto, it depends on whether the 825 psig is at the valve inlet or at the header.

If it is at the header, then the majority of the pressure drop is NOT though the valve. The bulk of the pressure drop is through the 50ft inlet pipe and the choke at the pipe outlet to atm.

It would only be the same as 4-8T10 (or did you mean 2) relief valves if he had 4x8" pipes to his valve and 4x10" pipes from his valve and the valve xT matched that of the relief valve.