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Pipe burst and transient analisis

Pipe burst and transient analisis

Pipe burst and transient analisis

(OP)
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 ..

RE: Pipe burst and transient analisis

This problem sounds similar to a common lab test in compressible gas dynamics, studying shock waves, etc. using a shock tube. In those lab tests, they deliberately punch a hole in a membrane that isplaced at the end of a tube, and this membrane fails instantaneously , releasing the gas  ( similar to a "bursting disc" in chemical plants)and leading to a shock wave in the downstream channel.

For the conditions upstream , they probably use the "method of characteristics" to solve the wave equation for how fast the message is transmitted upstream.

To get the proper search terms, you would visit with a professor or grad student of compressible gas dynamics and ask them for some background on these shock tubes.

RE: Pipe burst and transient analisis

I don't think you need transient analysis yet, but your problem statement is still not too clear to me, so let's look at that for a minute. If you do need a transient analysis, we'll do that after we clarify the situation.

A.) If the gas line is closed in when the leak develops, then you will only need a method to estimate the 10 Km pipeline blowdown time through a given diameter leak.  Is that what you need?

B.) If the line is flowing and you develop a leak somewhere between pipeline inlet and outlet, then you want to know what the pressure loss is at some other point in the line, transient analysis can determine that.

So, is it A, or B or something else?

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

(OP)
Situation is described under B).


More detailed description;

PipeLine is sectioned with some valves each 10 km. Let's look only one section between two valves - valve A and valve B.

After steady flow there is some pipeline break (rupture) at point C, somewhere between point A and B. This starts pressure drop. Pressure drop travels through pipeline. Let's say that inlet and outlet (points A and B) still have same mass flow for some time.

Pressure sensor (transmiter) is put in some place on pipeline (usualy at points A and B). They need to detect pressure drop.

Problem for me is to determine this pressure drop in points A and B. How big is it, and how is distributed through time; pA=f(t)and pb=f(t).





RE: Pipe burst and transient analisis

Dario2002 (Petroleum)
There should be a steady state pressure drop between points A and B.
If rupture is instantaneous you must specify other boundary conditions which maintain the assumption of constant flow at points A and B. Do you realistically expect flow at A and B to be constant throughout transient.

One approach with MOC would be to specify a boundary conditon at A,
For approximation purposes, assume frictionless flow AND infinite line.  Your choice on adiabatic or isothermal. For slow process Isothermal.
Rupture area can be considered with a coef of discharge.
Is gas considered perfect?  If so, is ratio of specif heats also constant?
Is rupture instantaneous?

Regards
  




RE: Pipe burst and transient analisis

(OP)
Sailoday, may You misunderstand me.

Steady state flow was only before rupture. After INSTANT rupture, pressure drop wave expands through pipeline, and there is no steady flow any more.

So, one state is before rupture (steady flow downstream), and another state after rupture.

RE: Pipe burst and transient analisis

Dario2002 (Petroleum)
I understand you.  What I was trying to say is that prior to the rupture there is a steady state pressure drop.
Clearly pressure, flow, etc will vary at points A and B.

RE: Pipe burst and transient analisis

Now the nature of the leak.  Is it a full complete line break across the entire diameter or will you need to run various scenarios of different diameter leak holes?

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

(OP)
Well, leak is NOT full diameter leak.
Leak should be through some smaller diameter. This diameter should be variable.

Also position of this hole (distance from A or B) should be variable. Another big influance is IMHO speed of mainflow or massflow.

RE: Pipe burst and transient analisis

Got your diagram, its nice.

If you're willing to do some estimation, rather than a full sim, I've had reasonable success with these, IF the leaks are to be relatively small leaks where a steady state condition can eventually be reached, by assuming various leak rates and figuring the pressure drop (using Weymouth or whatever) from inlet to leak point at flow Q0, then from leak point to outlet using the flow Q0-Q_leak_rate.

The time it takes to reach the steady state condition can be approximated by the usual blowdown equation arriving at the time to blowdown the difference between the volume contained in the segment at initial steady state condition and the volume contained at the final steady state condition.

If you do want to do a full sim, get my e-mail details off my web pages/contact page, and we'll see what we can do, so I'll need the gas gravity, temps, pressures, intial flows etc.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

Pipeline studio is quite good with the kind of problems described. Take a look at:

http://www.energy-solutions.com/

It can do both full line rupture and partial.

Best regards

Morten

RE: Pipe burst and transient analisis

Dario2002 (Petroleum)
If your initial steady state pressure drop is small, I again suggest you neglect friction in the piping.
You could model the break area as an orifice with quasi-steady flow dependent upon its upstream stagnation conditions.
I don't believe for the size break 200mm to full pipe diam of 500mm that a quasi steady analysis for the whole pipe will be realistic. Therefore a method of characterisitics analysis should be done.

From your sketch, you need the boundary conditions at the upstream and downstream source/sink conditions.
As I stated in prior response, try and approximate stagnation condions at Point A and assume the pipe is extremely long downstream of point B.
If Point A boundary condition is to vary with time, then you should specify a boundary condtion upstream of Point A, and not worry about what conditions are at Point A.
Regards

RE: Pipe burst and transient analisis

There has been some misunderstandings.  Please do not take my offer of personal help as a solicitation of work.  Since the OP included, "I would prefer freeware solution, because its a private investigation.", I obviously assumed there was no money there anyway.  Leak detection is just something that I am interested in.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

(OP)
Ok, tnx BigInch and Sailoday.

It looks that I will have to make some aproksimation. I will neglect pipe friction.

I'll try only to calculate pressure drop on point C (leak point) as closed volume (blowdown), and then time until wave of this pressure-drop travels until point A and B (upstream, downstream).

Any equations for this two effects (blow down, speed of pressure change wave) ?


On the other hand maybe I will try demo of PipeLine stuidio (k56 modem here for 160Mb :=(()



RE: Pipe burst and transient analisis

Dario2002

For blowdown its Tm =[.0588 x (P1)^0.33(G)^1/2 x D^2 x L x Fc] / (di^2n), where

Tm = time (minutes)
P1 = line pressure (psi)
G = specific gravity
D = nominal pipe dia (inches)
L = length (miles)
n = number of blowdown valves
Fc = Choke factors (1.8 for a gate valce and 2.0 for a plug valve)

Greg Lamberson
Consultant - Upstream Energy
Website: www.oil-gas-consulting.com

RE: Pipe burst and transient analisis

GregLamberson (Petroleum)
Could you provide the basis for your formulation? That is, major assumptions and governing equations.

Regards

RE: Pipe burst and transient analisis

Sailoday28

The formula comes from a nomograph published in an engineering manual form the old Butler Engineering company (then Willbros-Butler Engineers), the nomograph was based on this formula and derived from Weymouth.  I have used it since to determine blowdown  velocities, reaction forces, volumes, and to design thrust blocks.

Pipeline Rules of Thumb Handbook have another simple method for calculating blowdown volumes (3rd Edition, Page 260):

Q = D^ 2 x P1, where

Q = volume in Mcf/hr
D = diameter of nipple or orifice (inches)
P1 = absolute pressure in psi at some point upstream of the blowdown

The resultant is gas volume in Mcf/hr

Greg Lamberson
Consultant - Upstream Energy
Website: www.oil-gas-consulting.com

RE: Pipe burst and transient analisis

GregLamberson (Petroleum)
It seems to me that your references are for steady state or quasi-steady flow/energy equations.

Generally,I would expect the solution equations to be based on conservation of mass/energy/momentum-all of which would be time related.  

For the max size rupture stated, I don't think quasi-steady flow analyses are appropriate.
I would expect a method of characteristics or similar approach to be used.

regards.

RE: Pipe burst and transient analisis

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.

RE: Pipe burst and transient analisis

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.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

"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

RE: Pipe burst and transient analisis

(OP)
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 ..



RE: Pipe burst and transient analisis

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.

RE: Pipe burst and transient analisis

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.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

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.

RE: Pipe burst and transient analisis

(OP)
Yes, dcasto

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

Can You upload it somewhere, please ..

RE: Pipe burst and transient analisis

(OP)
Dcasto,

I have found some definition of Panhandle B equation at www.lmnoeng.com. 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"?

RE: Pipe burst and transient analisis

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

RE: Pipe burst and transient analisis

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









RE: Pipe burst and transient analisis

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.  

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pipe burst and transient analisis

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

RE: Pipe burst and transient analisis

(OP)
I have tried Panhandle B model in Excell:
http://rapidshare.com/files/15502659/PanhandleB_-2.xls.html
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.

RE: Pipe burst and transient analisis

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

RE: Pipe burst and transient analisis

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)

RE: Pipe burst and transient analisis

Exactly, It is a curve fit of the GPSA Data book.  I added the generalized equation for Tc and Pc from another article.  I have another more complex z factor that required 1 iteration and I used the previous direct to get the "seed" and it improves the first by less than 3%, but its upper pressure limit is over 1600 psia, so I don't use it in my spread sheets.

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