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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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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.
 
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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?

BigInch[worm]-born in the trenches.
 
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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).





 
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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





 
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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.
 
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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.

 
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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.
 
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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.



BigInch[worm]-born in the trenches.
 
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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

 
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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.

BigInch[worm]-born in the trenches.
 
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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 :=(()



 
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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:
 
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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:
 
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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.
 
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