Calculating pinhole leak rates through a pipe under pressue 3

[kcjBoiler]

I'm a little embaressed by the fact that I don't know how to do this, but as they say, "if you don't use it you lose it"

I have a pinhole leak in a 12" pipe that is pressurized at around 300 psi and has a gas flow of approximtely 300,000 lbs/hr. I just need to come up with a conservative estimate as to how much is leaking out of the pinhole. Are there any plug and chug calculations that I could use to get me within +/- 10%?

This seems pretty straight forward, and was wondering if someone with more experience could help.

Many thanks.

 

[dcasto]

Q = D^2 * P

Q is volume of gas in MCF/hr based on .6 gravity gas

D is the diameter in inches

P is pressure in line in psia

 

[mbeychok]

newbie89:

Read this FAQ by clicking on it: faq798-1196

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[proinwv2]

Crane TP410 is an excellent resource, and you can purchase it online for a small charge.

Paul

http://www.ostand.com

 

[tdlai]

Using PHAST software from DNV you can earn more than a pinhole leak. It covers almost hydrocarbon release cases.
But only if you are so rich.

Process Engineer in Vietnam

 

[sailoday28]

mbeychok (Chemical)
In the second of your referenced formulas with respect to using Z, please explain how one obtains Cv or Cv or k.
My reason for the question is that with constant Z, the ratio of the specific heats k is not equal to Cp/Cv.
You know that I have raised this issue previously.

 

[sailoday28]

Correction, should read
using Z, please explain how one obtains Cv or Cp or k

 

[owg]

I would like to see this thread closed. The hardest part is estimating the diameter of a pin. Wayne's world says it is about 0.02 inches. Note this is a pinhole leak not a pinhead leak which would be about twice the diameter. Using dcasto's excellent formula and noting that the diameter of the pipeline and the rate through the pipeline have nothing to do with the question, unless the pipeline diameter is approaching that of a pin, the leak rate through the pinhole is about 120 SCFH.

HAZOP at

http://www.curryhydrocarbons.ca

 

[mbeychok]

sailoday28:

Now that you have chipped in, I am no longer needed and I am "outa here". Bye!

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[Latexman]

I confirmed owg's flow using a different equation with ammonia gas as a basis. Ammonia is a 0.6 s.g. gas whose properties were handy for me.

Good luck,
Latexman

 

[sailoday28]

Has anyone tried isothermal choked flow of a perfect gas?

G/P=[sqrt(Mol/(RT)]*exp[U^2*Mol/(2RT)-1/2]

Where G = mass flux ie kg/m^2/s
R=universal gas const
and upstream conditions where
T=absolute static temp
P=static pressure
U=velocity

Regards

 

[Latexman]

No, but since the last time you asked (end-May), I think I found an equation and table of "influence" factors in Shapiro that will yield the differential equation for isothermal choked flow of a perfect gas. Would you be interested in seeing that?

Good luck,
Latexman

 

[sailoday28]

Latexman (Chemical)
Thanks, I'd like to see the equations.

Regards

 

[Latexman]

Chapter 8 develops equations for area change, wall friction, drag of internal bodies, external heat exchange, chemical reaction, change of phase, mixing of gases, and changes in molecular weight and Cp given the basis of one dimensional flow, continuous stream properties, and semiperfect gas (obeys Boyle's and Charles' laws and Cp varies only with composition and temperature).

So I do not reproduce the entire chapter, I assume you are interested in area change and external heat exchange to achieve isothermal choked flow. The equation that appears it may be beneficial to you is:

dT/T = 0 = (k-1)M^2/(1-M^2) x dA/A + ((1-kM^2)x(1+(k-1)/2 x M^2))/(1-M^2) x dT[sub]o[/sub]/T[sub]o[/sub]

T[sub]o[/sub] = stagnation temperature used as a measure of the energy effects of heat transfer.
I think you know the other variables.



Good luck,
Latexman

 

[dcasto]

I'll still take the

Q = D^2 * P

And get just as close, in engineering terms.....

 

[Latexman]

For a short run of pipe, you'd probably be right, but for a 100 mile pipeline, you'd probably be wrong.

Good luck,
Latexman

 

[dcasto]

What does distance have to do with it. As amatter of fact, the basic assumption is P=constant and on a very short piece of pipe, that may not be true.

 

[Latexman]

True, for the OP's application. I'm not 100% sure of sailoday's application. Traditionally, long pipelines were modelled as isothermal compressible flow. I really shouldn't assume what his application is and how he intends to model it, but that's apparantly what I mentally did. I am a victim of my experience!

Good luck,
Latexman

 

[sailoday28]

The pin hole blowdown is not necessarily adiabatic and could lie between that process and isothermal. I'm not sure of what the process stated by dcastro represents, although it may satisfy the original question of being with 10 percent.

Regards

 

[mbeychok]

.
I believe that many of us would agree that the U.S. EPA, the Federal Emergency Agency and the U.S. Department of Transportation are very interested in evaluating the risks incurred from accidental leaks of pollutants or flammable gases. The equation (referred to earlier in this thread) in
FAQ798-1196 has been recommended for use by all three of those agencies. See the two references below and read them online at the links provided:

(1) ''Handbook of Chemical Hazard Analysis Procedures'', Appendix B, Federal Emergency Management Agency, U.S. Dept. of Transportation, and U.S. Environmental Protection Agency, 1989. Handbook of Chemical Hazard Analysis, Appendix B. Click on the PDF icon, wait quite a bit and then scroll down to page 391 of 520 PDF pages.

(2) "Risk Management Program Guidance For Offsite Consequence Analysis", U.S. EPA publication EPA-550-B-99-009, April 1999. Guidance for Offsite Consequence Analysis. Look at Appendix D: Equation D-1 in Section D.2.3 and Equation D-7 in Section D.6

... calculations that I could use to get me within +/- 10%.

As noted by by others in this thread, the original poster asked for calculation methods that would provide his needs within +/- 10 percent. The equation recommended by the above agencies will do just that ... and it is all that is really needed for a great many engineering problems. In such cases, practical engineers (as differentiated from physicists and research scientists) are not interested in spending endless hours trying to determine how many angels would fit on the head of a pin.

Milton Beychok
(Visit me at www.air-dispersion.com)
.