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Pipe burst and transient analisis 1

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Dario2002

Dario2002

Petroleum
Aug 25, 2006
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I lost 2 days searching for this on google, etc.


I need method, or better yet software for transient flow analisis for following problem;

Gasline with nautral gas (f.e. lenght 10 km, diameter 500 mm, pressure 30 bar). Gasline is broken is some point and loosing known flow (depending of hole size, f.e. 200 mm hole).

What is pressure drop through time at some other point?


I would prefer freeware solution, because is private investigation. I would like to answer some of those questions: can this pressure drop be good detection of pipeline break? What pressure drop should be used for this use?


Thank You for all inputs ..

 
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Having been around a couple leak detection systems, everthing said here is right as a starting point. The real problem is getting the data into a program running all the equations mentioned (even a transient similation series of equations). If this post is leading down a path of building a leak detection for free (I can't see what else it could be doing other than a review of pressure drop), you'll need a larger computer system just to analyze the input data Pressure, temp, flow, ect.. than the actual pressure drop equations. Just a warning and I may be off track.

The diagram sent later by the OP isn't possible, unless the end point is feeding gas backward into the line. If the feed pressure doesn't change, the the pressure at the leak point will be the same just before the leak happened. There will be sudden drop and a rebound of the local pressure as long as the inlet pressure is kept constant (by way of flow control at the outlet end. If the outlet pressure is held constant, then there will be a drop in pressure at the leak point and at the inlet point. There are so many varibles that need looking at and those varibles are the data I mentioned above, a 1% error in apressure transmitter can be a 10% error in location or flow of the leak.

 
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I think the diagram is valid for the nanosecond as the leak occurs, and the flows are shown in the positive direction for convention, not to say that they could not reverse depending on the leak flowrate and how the upstream and downstream boundry conditions are managed. There is nothing to say that they would have to stay constant, unless a simple model was desired for convenience.

An (expensive) pipe sim program can easily handle this type of analysis.

BigInch[worm]-born in the trenches.
 
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"BigInch (Petroleum) 7 Feb 07 9:57
I think the diagram is valid for the nanosecond as the leak occurs"
At the instant of pipe break, the conditions at A and B
are boundary conditions which (probably will vary over time)but as boundary conditions they are valid at the instant of the break. It not a question of at that nanosecond-why confuse the issue?

Regards
 
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Ok guys, now when you pointed out .. sketch/diagram might not be too appropriate, that's true. It is ok for some "nanoseconds", but not then mainflow will change this picture compleatly.

I do not need situation in those nanoseconds. I need developement of pressure measured by seconds in point A and B. Devices which "detect" leaks are on point A and B, and they monitor for some pressure drop. I would like just calculate pressure drop over time for those points.

It looks to complicated for me, I can make some models, but I will never be sure that is correct, because I have no good theoretical background. Therefore, I must proceede with original idea of finding good simulation software (some of demos will arrive any day now). On the other hand, I would like better "formula" soultion inside Excell, but.. no luck there ..



 
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You can similate it with excel, but you have one equation and two unknowns. Like I pointed out, it depends on how the line is operated, is it constant volume, constant input pressure, constant output pressure, or what combination? Her is how I did a small pipeline model. You take 1 row in a sheet and you build the Panhandle B formula in the cells across. You'll have inlet pressure, flow, lenght, z factor, ect.. and you'll solve for the outlet pressure.

In the next row, duplicate the the row from above, this time make the inlet pressure the outlet from abouve. You can also make a coulumn where you add or subtract gas.

You replicate this pattern 100 time. If you make each segment .1 km, you'll have a model that you can simulate a leak at .1Km intervals.

You can also stop with just two segments. The first is the upstream of leak, the second downstream ok leak. If you make the lenght of the up stream say 1 km, you leave the lenght of the downstream as 10 - upstream. The do a goal seek and solve for the right split of distance that gives you the desired output value of say the pressure out.

It's not calculus derived solution, but what use to be a hard numerical solution, just love the digital age to keep me away from intergals.
 
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The equation of state makes for a few more unknowns.

To do it right it should be an iterative solution at each timestep (which itself may take 50 to 100 iterations) to assure the pressure errors are within allowable error tolerance for each timestep.

BigInch[worm]-born in the trenches.
 
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I've got a direct solution equation for hydrocarbons to calculate density (zfactor) that gets great results for gas lines under 1600 psig. It was from an OG&J article in the late 70's. I use it as a EOS to get density required for pressure drop. I've replicated the line by line outlined above and after about .25 mile steps, the end point doesn't change much.
 
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Yes, dcasto

I would also like to see this article from OG&J,
and also this Excell worksheet.

Can You upload it somewhere, please ..
 
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Dcasto,

I have found some definition of Panhandle B equation at One of sentences in definition is:

The equations were developed for turbulent flow in long pipelines. For low flows, low pressures, or short pipes, they may not be applicable.

This means that this equations are not aplicable for my example? We have in almost all conditions/points laminar flow (L=10 km, Q=1000m^3/hr, D=20"). In other words, some parts of pipeline in first moments are not afected, and still have laminar flow. Also if pressure drop is not too high, main flow could stay lamar, except in "pressure-change-wave"?
 
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Dcasto:

Are the results great because they are validated against actual data - or because they are easy to calculate and dont "misbehave"? Back in the '70 simplicity was definately an issue.

Best regards

Morten
 
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At the time of an instantaneous break/rupture, the locations A and B will not sense things until the effects of the depressuization (at C) reach A and B. For isentropic flow of perfect gas, this is calculated from the characteristic equation
dx/dt =u+(-)a where x is distance along pipe, t is time
u, the local velocity along the "characteristic and a, the sound speed.
"If" the distance from A to break is 20 meters,a =300 m/s and u =10 m/s then A will not sense break unitl after
dt=t=(u-a)/dx = -20/-290seconds
Similarly for the same type conditions at B, dx/dt=u+a
dt=t=+20/+310 seconds.
The above calculations are simply using a method of characteristics (MOC)approach.

For relatively large ruptures, over "relatively" short lengths, the effects of friction are generally small compared to momentum effects.
For simplicity, with no heat transfer, MOC with isentropic flow will give a good handle on the transient.

At the instant of break, a centered rarifraction wave will eminate from the lower pressure region of the break.
Flow, from the rupture can be modeled using an "orifice" approach and stagnation conditions at inlet to the orifice. These are quasi-steady conditions.
Within the pipe --FROM MOC ---
Along a plus + characteristic dx/dx =u+a
AND 2a/(gamma-1) + u = 2ai/(gamma-1) + ui (1)
where gamma =ratio of sp. heats and subscript i refers to initial conditions.

FROM QUASI-STEADY AT ORIFICE and assuming choked flow thru orifice.
Consv of mass, rho* area*u and isentropic flow
alpha*u= athroat*(atrhroat/a)^[2/(gamma-1)] (2)
where alpha is A pipe/A rupture

Consv of energy using stag. conditions
a^2 + u^2*(gamma-1)/2 = athroat^2 * [gamma +1 )/2] (3)

3 equations, 3 unknowns a, u, athroat.

Please let me know of questions relating to above. If there are any, refer to equation number. I will give basis, etc.

Regards









 
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Morten and Sailoday are both correct. Its obvious that an accurate simulation must realize that laminar flow stops and Pan A won't apply, but that could be accomplished by substituting those for appropriate equations incorporating momentum effects.

The question really is, how accurate a simulation do you need? What is the purpose of the study? Is it for finding the time to sense a pressure drop and begin and complete a valve closure to shut-in to find the total volume of gas lost before shut-in has completed? If that's the case, it may be better to wait for your demo CD and hope the demo will get you as far as you need to go.



BigInch[worm]-born in the trenches.
 
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CORRECTION OF TYPO IN MY PREVIOUS POST

"If" the distance from A to break is 20 meters,a =300 m/s and u =10 m/s then A will not sense break unitl after
dt=t=(u-a)/dx = -20/-290seconds

SHOULD READ
"If" the distance from A to break is 20 meters,a =300 m/s and u =10 m/s then A will not sense break unitl after
dt=t=dx/(u-a) = -20/-290seconds

Regards
 
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I have tried Panhandle B model in Excell:
That is not really what I need.

Last model from Sailoday is more like my solution.
I will try with this one in new Excell worksheet.

At this point, I have to admit that I do not understand all, but I'll google to get some background.

If You have will to explain, it could save me some time;
- what is MOC stands for ?
- what is parameter athroat means ?


I know that is probably stupid questions, but I'm not proffesional in this area, and we have different theoretical approch - naming conventions, fomula preparations, etc ..

B.R.
 
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The method of characteristics (MOC)is a technique to generally transform partial differential equations into ordinary differential equations.
In fluid dynamics
Generally used for two dimensional gas flows for mach>1 in steady state and
one dimensional transient fluid flows

Excellent texts are those written by Fredrck Moody(Of ASME fame) Joseph Foa, George Rudinger and lastly in Volume 2 of Shapiros text.

For transients, moc, transforms momentum, conservation of mass in conjuction with consv of energy equations,
Note these equations include transient terms. A number of engineers somehow, mistakenly will use quasi-steady analysis to solve transients. Quasi-steady is generally reasonable if the transient is "slow".

Regards
 
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The articles long gone but here are the equations used. They work wonderfully.

Tc =169.01+314.001*Spgr
Pc = 708.75-57.5*Spgr
Pr = PSIA / Pc
Tr = T rankin / Tc
z = 1 + (0.0703 *Pr / Tr) * (1 - 6 / Tr ^ 2)
 
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