Pressure drop in sealed pipes

[alxh]

Hi everyone,
This is about water pipes, but in a sealed system so I think pressure vessel mechanics may be more applicable.

I have been testing PEX (polyethylene) water pipes by assembling short lengths with a gauge at one end, and pumping water in through the other. When filled and pressurised to about 1500kPa, the inlet is shut off, and the pressure gauge is monitored.

In an ideal sealed system, this shouldn't show any change in pressure, which is what my bosses expected. Instead, there is a sharp drop in pressure that tapers off and appears to level off. This may be 300kPa in the first 10 minutes, and another 500 over a few hours. Left for days, this could end up around 500kPa and appear to still be slowly dropping.
Pumping up the system again at any point would result in a similar looking pressure drop curve, but not as significant in magnitude.

Metal pipes were similarly tested for comparison. These showed a more linear and much reduced pressure drop, eg after a few hours they be around 1200kPa. Left for days, this drop generally appears to continue, but with variations up and down that follow temperature (low pressure when cold, high when hot).

The bosses are stumped about all this, because beyond guessing that a leak would cause a pressure drop they don't really know anything about fluid or material physics. This has led to many repeated tests with thorough searches for leaks, with none found and the same results repeated. I haven't looked at either field too much lately, but I was always more familiar with materials than fluids and thermodynamics.

I believe that this pressure drop is primarily due to pipe expansion, with a small change in volume leading to a big change in water pressure (thermal effects are clear enough to be accepted, and don't apply in the short term). But they seem to need a solid proof to be convinced, which is why I'm reaching out to you guys.

So, is my assumption sound? Anything else I'm missing and need to look for or consider?
How would I best correlate pipe/vessel expansion with water pressure? I am thinking cylinder stress with PEX Youngs modulus for expansion, but what do I use to explain water pressure and volume change? It's often considered incompressible, but that isn't the case here.

Also what would be the effect of air trapped in the system? My thinking is that more air would allow more total volume change without much pressure change, and that's about it. One of the bosses thinks that air and water will mix into each other and perhaps allow the pressure to drop even in the absence of any change to volume and mass. This sounds strange to me and I think he is confusing water vapor pressure which doesn't apply anyway, but I'm a bit rusty in this area, and he's very convinced that they will mix and that this may do something. So I'd like to double check before correcting this point.

Sorry for the wall of text. Thanks for your help
Cheers guys

 

[LittleInch]

Sounds like clastic PE creep to me.

Look at something like this

http://www.eng-tips.com/viewthread.cfm?qid=19388

our search PE creep here and on the Web.

When testing pe, it's keeping to the known creep decay that proves your pipe is sound.

Air will slowly diffuse into water under pressure.




My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[alxh]

Cheers, that looks good. Creep is exactly what I was thinking, yet somehow I managed to use this simple keyword in a search and missed the rich vein of information on exactly this topic.

Diffusion makes a lot of sense too when I think about it. But what effect would water and air diffusion have on system pressure and volume, if any?
I was thinking that the specific volume of air and water under pressure, as the total volume changes, would be worked out individually and proportionally regardless of mixing. That is, changes in pressure of the sealed air-water system would be affected by the amount of total air trapped in the pipe, but not by the amount of trapped air that then diffuses into the water.

Thanks for the help

 

[LittleInch]

I'm kind of curious as to what the purpose is of this work /why you're doing it, but to answer your question.

Air and water diffusion affects the pressure by changing the volume. Although water is often regarded as incompressible, it isn't, but compared to air is many more times less compressible. Hence even if only 10% of the air volume is diffused into the water under pressure (the air volume should be small) that has a disproportionate effect on the pressure of a sealed system. Usual test procedures call for a air volume of less than 0.1%. For a small scale small bore pipe this is not a lot.

You might also be finding that the initial test water is somehow cooling down after initial pressurisation. In large scale pressure testing it is normal after the fill to allow some time (a few hours) for the water, pipe and surroundings to all equalise in temperature before you start the pressure test.

See this FAQ for the expansion due to temperature / expansion.

http://www.eng-tips.com/faqs.cfm?fid=1339

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[alxh]

Thanks LittleInch

To clarify what you're describing as 10% of the air volume diffused in water:
eg 10m3 total volume
At some point during the test after the system is sealed,
9m3 is water
1m3 is air, fully diffused through the water
This could make the water volume appear to be 10m3, but compressibility of air means this mixture expands/compresses much more than water alone.
Is this what you mean?


But, will this total resultant compressibility be different if the air were not diffused, but existed just as a separate pocket of air above the water. Maybe imagine some thin membrane separating the air and water and preventing diffusion, does the total solution show any difference in pressure response?

Thanks for the link about temperature expansion. I tried to work that out myself a while ago, and I'm pretty sure I got a similar result. When I'm back at the office I'll check my notes and see if I got that correct, it would be very satisfying to confirm that.

As for cooling down, would that just be due to initial difference between the water and air temperature? We had been doing small scale tests using an exposed tank of water, which should be at the same temperature as the surrounding air.
But I had been wondering if pressurization would raise the water temperature in the pipe, significantly or not. You would be adding energy to the water, does some of that become heat?


As for the purpose, my (small) company director took on the job of independent testing of pipes despite no background in the field or anything fluid related, believing that it was a simple matter of no leak=no pressure drop.
He has stubbornly stuck to this assumption and his desired method of further analysis was essentially to repeat the test with some minor changes here and there, such as different pipe lengths, adding in joints, using different sealing compounds etc. Anything that might give the result he wanted to see, but all pretty arbitrary and doomed to fail without understanding the existing results. Essentially trying to solve the problem without identifying the cause, and it became incredibly frustrating, especially since I've had to carry out these tests myself (I'm not long out of uni and pretty junior) with a fairly firm conviction that it was probably pipe expansion and that we should consider the fluid and material physics.

So my aim is to be sure about the causes of pressure drop and have evidence so that I can clearly explain it to him and not waste any more time carrying out flawed tests.
Your help has also led me to existing test methods and criteria developed for standards, which would have been useful to know earlier as it negates much of the work, but at least means I can suggest we just use that rather than try to create our own criteria.


So, hopefully this problem is solved and I can steer the project in the right direction. The other questions above are probably then more for my own learning than anything else, as I don't expect things to get that detailed for the job, but always useful to know more

 

[LittleInch]

No, that wasn't what I meant.

What I meant was that, say, out of your 10 units of volume, 1 of them was air. After compressing it 10% of the 1 unit of air would probably diffuse into the water, maybe a bit more depending on temperature and pressure. However small this is it does make a difference to the pressure in a static environment. that's why most test specifications state a very low amount of allowable air.

The issue with air in the system is that it becomes very difficult to calculate the impact of temperature on pressure as the air basically acts as a bladder and you don't see the pressure increase or decrease you should if the system was wholly water. If you stay at exactly the same temperature from start to finish, it doesn't matter so much, but this is quite rare for any test more than an hour or two. Also the more air, the more water you need to pressurise and it all takes longer as most pressurisation pumps are quite small volume.

If your boss needs some paperwork try these guys

http://www.water.org.uk/publications/WIS-IGN/general

Look up / download IGN 4-01-03 and any of the others. There are similar procedures, but this one is particularly good.

The temperature is the temperature of the pipe and its surroundings. Yes the water from the pressurisation pump might be hotter - even a few degrees makes a difference.

I am quite frankly amazed anyone gave you the work if you've never done it before or didn't tell you what specifications to use...

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[alxh]

I feel like we may be describing the same thing, but now I want to make extra sure. Lets try this

EXAMPLE 1
-Initial conditions-
Pressure P0,
Total Volume V0,
Water volume W0=0.9V0,
Air volume A0=0.1V0.
System is sealed
Assume air is not diffused into water, and is a distinct pocket above the water.

-Total volume is then compressed to V1, lets say V1=0.9V0
V1=W1+A1
Most of the compression will be due to change in air volume, so lets say (roughly)
W1=0.89V0
A1=0.01V0
Pressure=P1 (P1>P0)
The air has now diffused into the water.

EXAMPLE 2
-Same initial conditions as EX1, with the addition of a flexible, impermeable membrane between water and air that takes up no volume.

-Total volume is compressed to same volume. ie V2=V1=0.9V0
V2=W2+A2
Most of the compression will be due to change in air volume, but in this case no diffusion has occurred.
Could we assume that:
W2= W1 = 0.89V0
A2= A1 = 0.01V0
Pressure=P2 = P1

Or would W2, A2, and P2 differ from W1, A1, and P1. The only difference would be that the air remains a distinct pocket above the water, and has not diffused.


My gut tells me that this would be the case. That the total resultant P-V relationship depends on the amount of air and water in the system, but not on where they are within the system.

I am quite frankly amazed anyone gave you the work if you've never done it before or didn't tell you what specifications to use...

You and me both... I think the work came from a friend or associate of the director
I was told that the standards they referenced were poorly described and expected very those very simple, steady results
I'm sure if I look into it I'll find that what they looked at was for copper pipes or something else entirely inapplicable

Thanks again, it's nice to engage with someone who knows what they're talking about

 

[racookpe1978]

I suspect more that the plastic pipes are themselves expanding under pressure.

Sure - Vent the system carefully, and fill it slowly so the original air in the pipes does have time to rise to the high spots so it can be vented.

But. The poly plastic does yield differently at that high a stress point on its stress-strain curve for the same water pressure than steel does!

Thus, do the specific calc for the actual measured wall thickness of the poly pipe: What is the actual psi in the pipe wall (and ANY other surfaces like valves or cover plates or flanges!) when at maximum water pressure? (If you have any sections of pipe at larger or smaller diameters, repeat - all pipe will at the the same psig water pressure, but each different pipe wall will at a different material stress point - some will be further than others down the stress-strain curve.)

A steel pipe of the same diameter and wall thickness as your poly at the same water pressure will be substantially lower, probably not approaching a yield point at all.

 

[LittleInch]

alxh,

Re-reading my post I think I got it a bit wrong also, but lets look at your version.

First in testing the volume doesn't usually change, it's the pressure which increases, but lets put that to one side for a moment.

In the initial instance there is no difference between your two formulas. The point is that the diffusion of air into the water is a time dependant thing, which is why for a sealed system with no leaks and no change in temperature the pressure goes down as your A=0.01Vo turns into (say)A=0.005VO

The point is that added volume of water to the test piece does not result in the same increase in pressure per unit volume added when there is air in the system. Thus instead of a straight line on a pressure versus added volume graph, you get a curved line at the start before it gradually becomes straight as the air becomes pressurised and it's volume smaller.

racookpe - the PE doesn't "yield", it creeps at hydrotest pressure for a certain amount, which is less than yield stress. Thus yes the pipes expand, but do so at the same pressure on a time dependant basis. There are many known equations and curves for PE so that by measuring the pressure decay you can see if there is a leak on a big system if the pressure decay is worse than predicted without constantly having to add more water.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way