PD pump sizing for pipeline hydropressure. 1

[gbratis]

Hi folks,
Here's a good one for you. We are trying to size a pump in order to perform a hydraulic test in a pipeline system.
We have the following data :
1) Pipe size - 18 " (SA 106 Gr.b)
2) Straight Pipe length - 5.000 mt
3) Hydraulic test pressure - 41,25 Barg
4) Fluid - Potable Water
5) Pressure rise rate - 0,25 Barg / min.
How can I calculate the pump capacity in order to incorporate all the above mentioned data? Is our current positive displacement pump with Q=50 lit/min and max. pressure 50 Barg, adequate?
Thanks in advance!!

 

[gbratis]

Sorry everybody, I meant HYDROTESTING!!!!!!

 

[BigInch]

Your use of "." and "," indicates 5000 meters length, which is 821 m3, 821000 L3 / 50L/m = 16417 min = 274 h = 11.4 days. And that's pumping 24/7.

I certainly wouldn't want to wait around to see if the pump holds up that long, unless you're paying time + expenses in cash.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[gbratis]

Dear Biginch,
Thanks for your fast reply.
I was informed that the pipeline will be filled with water and after that the PD pump will take action.My superior needs my evaluation on the correct PD pump that incorporates the pressure rise rate of the 0,25 barg/min, noting that from his experience the rise rate is different from a pressure rise interval to another i.e from 0-10 barg to 10-20 barg and so on. Is this valid.? If yes, which is the best approach to handle this issue.? Is it a transitional phenomenon?How can I size this pump? Which formula should be utilized for this circumstance?
Regard,
George

 

[djack77494]

George,
Once your system is filled with water, and a low head pump can easily accomplish this task, then all you're adding is pressure. The additional volume of water that will enter the system is very small indeed, since water is nearly incompressible. Very small pumps are typically used for hydrotesting. For small to moderate sized systems, they can even be hand pumps.

 

[BigInch]

Good.

Once the pipeline has been filled to its standard volume, (the pipe dimension tables figures are based on 60ºF) at 0 psig, the pipe expands elastically with wall stress/Young's modulus = [σ]/E = P*D/2/t/E. If the pipe is not restrained, there is axial shortening = Poissons ratio * [σ], however usually, during hydrotesting, pipelines are considered to be mostly axially restrained, due to continuous ground contact. (You can multiply by a factor Fr, less than 1, to include an estimate of axial restraint).
where 1 = full restraint.

New Area (from radial pressure expansion),
((?/4)^0.5*D +(?/4)^0.5* P*D^2/2/t/E-(?/4)^0.5*2*t )^2

New Length = L (1- (v*[σ])*(1-Fr)/E)
[&sigma] = P*D/2/t
v = Poisson's ratio [default = 0.3]

New Volume due to pressure = Vp = new Length * new Area

Usually of more significant concern is the volume change of the pipe due to temperature.

For steel this is New Volume, Vt = Vo (1 + 3*? * [δ]T)
where ? = 0.000006 in/in/Fº
[δ]T = change in temperature Fº

The volume of the Pipe must be equal to the volume of water, which also changes with pressure and temperature. The water volume factors for T and P can be found in tables, or there are some equations which are also around.

Now just find P such that volume of water @ P & T = volume of pipe @ P & T.

Usually the Pressure to Water volume response observed during an actual hydrotest depends more on how much air was left in the pipe, the temperature of the water entering vs the temperature of the water in the pipeline already and the temperature in the morning and during course of air temperature change into the afternoon than the actual pressure response of pipe expansion. For that reason, one can see a lot of different effects, depending mostly on the weather, and how long your pipeline has had a chance to stabilize before beginning the test.

Note, the equations are based on an initial volume at 60ºF, so if your test temperature is different, you must first translate your initial pipe and water volumes to your base test temperature.

If you get large volumes of water added and small changes in pressure, you usually have air that needs to be vented. If you make a running plot of volume water added vs pressure, its pretty obvious how long you need to settle and vent air.

Without all those variable conditions considered, and for a 400 mm pipe diameter, you would probably only need around 1 to 1.5 cubic meters of water added to raise the pressure 7000 kPa. Throw in a temperature expansion allowance of 20ºF change volume for day-night temperature difference.






BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[dcasto]

most testing use a small hydraulic pump they pump by hand. it doesn't take much once the water is in and all the air out.

 

[gbratis]

Thanks everybody,
BibInch your info was most explainable. The only thing I dont seem to understand is the ? parameter in the formula
((?/4)^0.5*D +(?/4)^0.5* P*D^2/2/t/E-(?/4)^0.5*2*t )^2. Which is the source of this formula? Do we have to consider the limitation of the 0,25 barg/min or is it an extraneous factor? Would you say that our pump 50 lt/min is adequate?
Sorry for my continuous questions, I'm only trying to learn from the wisdome distilled from your experience.
Thanks for all your precious time.
George

 

[BigInch]

Looks like [alt]+227 etc. doesn't translate to [π] (Pi) when copied from my word processor and pasted here, although the [alt]+ 1xx series does seem to work.

And I don't like the pi symbol here [π], looks like a "n".

Here's the corrected symbol version,

New Area (from radial pressure expansion),
(([π]/4)^0.5*D +([π]/4)^0.5* P*D^2/2/t/E-([π]/4)^0.5*2*t )^2

New Length = L (1- ([ν]*[σ])*(1-Fr)/E)
[σ] = P*D/2/t
[ν] = Poisson's ratio [default = 0.3]

New Volume due to pressure = Vp = new Length * new Area

Usually of more significant concern is the volume change of the pipe due to temperature.

For steel this is New Volume, Vt = Vo (1 + 3 * [δ]* T)
where [α] = 0.000006 in/in/Fº
[δ]T = change in temperature Fº


BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[vitalis77]

Yea Big Inch,
You hit the jackpot again.
What can I say!!!

 

[BigInch]

"You're hired", would be good.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[zdas04]

Not to detract from quality arithmetic, but I've done many dozens of hydrostatic tests and never once used Poison's ratio. When you compare the compressiblity of disolved air in the water to the elasticity of the pipe you aren't even in the same order of magnitude. This is only 5 miles of 18-inch pipe after all (just for the general fund of knowledge, test water requirements in bbl/1000 ft are ID^2 so this should take 5265 bbl or 850,000 l).

If you can get the air out of the water (I fill a line and let if sit for 24-72 hours with a vent open, adding water every few hours), then the big issue will be keeping the rate of pressurization down to 1/4 bar/min. The test will eat the elasticity of the pipe in a couple of seconds and then pressure will increase with every stroke of the pump.

Once you have a line filled with deaerated water and close it up, don't leave it unattended for any reason. Every degree F temperature change will change line pressure about 100 psi (call it 3.8 bar/degree C). A big temperature drop can go a long ways towards reaerating the water through vacuum leaks, a big temperature rise can easily break stuff.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[BigInch]

That's exactly why I included it. Made you think, right? Poisson's ratio is there just to make sure the sum of all volume changes are approximately = 0, if the temperature doesn't change. Actually there are additional secondary terms I neglected in the derivation too, but ...

As I've noted, the Poisson effect is often never seen due to natural axial restraint being the overpowering force, and if there is any temperature difference at all, those effects obscure it immediately.

Actually what's distrubing my Saturday morning is, "eat the elasticity of the pipe". I think what that should be something more like "compress any remaining air into dissolution", or something similar. I would say that pipe elasticity does not go away... until the pipe yields, then its plasticity.



BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[zdas04]

As the steel approaches the yeild point the rate of change in pipe volume will slow down if I remember the stress/strain curve correctly. During the pressurization stage of a test with properly deaerated water, the pressure change per stroke is much greater late than toward the beginning. I've always assumed that that this is because of the pipe becoming less elastic as the stresses approach SMYS.

David

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[BigInch]

As I recall the slope of stress vs strain for steel is relatively constant (but does bend a little) up to Young's modulus, changes to another constant slope and then curve and almost levels off at ultimate. I attributed the effects to the result of water's decreasing compressibility with pressure at constant temp and perhaps the increasing rate of thermal expansion of water with temperature.

Maybe its the Poisson stress finally overcoming a longitudinal restraint... maybe its...

P (psi) Compressibility 1/psi
0 3.17 10^-6
2500 3.03
5000 2.90
7500 2.78
10000 2.67

Sixty-three Anomalies of Water. Water is indeed a strange substance.


BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

Forgot to post the link to 63 Anomalies of Water.

here it is,

63 Anomalies of Water



BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

Make that "slope = Young's modulus up to the elastic limit". I'm not having a good day so far. TG its Saturday.

For convenience here's a typical steel stress strain diagram, which for all grades shows near linearity up to at least the elastic limit. I think that would include most pipeline steels, at least up to 60-70 ksi. There is a bit of a bend around 75 ksi.

I have not found any data so far on exactly how much [α] increases with pressure, but I'm still looking.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[BigInch]

The coefficient of expansion for water is given in "Pipeline Rules of Thumb" as , B, for which an equation appears as,

BxE6 = -64.268 + 17.0105 * T - 0.20369 * T^2 + 0.0016048 * T^3

T is ºC

It also states that Poisson's ratio was used to develop the pressure change with temperature charts.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com