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Calculating pinhole leak rates through a pipe under pressue
3

Calculating pinhole leak rates through a pipe under pressue

Calculating pinhole leak rates through a pipe under pressue

(OP)
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.

RE: Calculating pinhole leak rates through a pipe under pressue

2
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
 

RE: Calculating pinhole leak rates through a pipe under pressue

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

Paul
www.ostand.com

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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.


 

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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 www.curryhydrocarbons.ca

RE: Calculating pinhole leak rates through a pipe under pressue

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)
.

 

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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

Regards

RE: Calculating pinhole leak rates through a pipe under pressue

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 dTo/To

To = stagnation temperature used as a measure of the energy effects of heat transfer.
I think you know the other variables.

 

Good luck,
Latexman

RE: Calculating pinhole leak rates through a pipe under pressue

I'll still take the

 Q = D^2 * P

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

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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.

 

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

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

RE: Calculating pinhole leak rates through a pipe under pressue

.
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: Mass flow rate of a gas through an orifice during choked conditions 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

Quote:

... 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)
.

 

RE: Calculating pinhole leak rates through a pipe under pressue

mbeychok (Chemical)
Welcome back!
The first of your referenced equations must use stagnation conditions to be correct. Also, what is meant by real density?
The first equation is approximate, only if the upstream Mach numbers are low.
If the agencies that you reference, use other than stagnation conditions, they are misapplying choked flow equations.
 

RE: Calculating pinhole leak rates through a pipe under pressue

Finally, give us an exactly round, tappered pinhole and its diameter +/-.001%.  At some point, all the equations don't matter because of all the unknowns.

RE: Calculating pinhole leak rates through a pipe under pressue

.
dcasto:

Bravo! I am giving you a second star for being a voice of sanity. Not every problem requires a Ph.D. thesis.

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

 

RE: Calculating pinhole leak rates through a pipe under pressue

(OP)
Thank you all for your in-depth analysis, and I'm also glad I could come up with an interesting problem.  

I ended up using an equation from Chemical Process Safety Fundamentals by Daniel Crowl (4-40), and double checking my results with dcastos's and mbeychok's equations, and was close enough.  I was also fortunate enough to be able to see the leak for myself and visualize my answer to see if it made sense.  

I know that these are probably not to most accurate answers, but I was told to be conservative and use "engineering judgment".  

Thanks again!

RE: Calculating pinhole leak rates through a pipe under pressue

This is probably my stupid question, and you have certainly gotten some in depth responses.  To sort of verify all this comprehensive work that has been done and to obtain a meaningful answer(as I did not initially realize you had access to the leak), I was just curious if you could weigh a large rubber balloon on a sensitive balance, then hold it over the leak for a length of time e.g. measured with a stop watch (I would assume the gas @ 300 psi might blow same up, though without building a lot of backstop pressure), then weigh the balloon again to determine roughly how much agas escaped over that time period?    

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