Estimating the area of a slot in a pipe

[amiket]

Hi everyone,

I'm currently trying to estimate the area of a crack in a pipe based on the pressure difference and leakage rate out of the crack. I've been assuming that the crack is a rectangular slot and trying to use a variation of the orifice eqution, but the results I've been getting seem ridiculous (1400 L/min through a slot area of 0.000583 square meters). I have the following data:

Pressure difference: 1300 psi (8.96 MPa)
Leakage Flow Rate: 1600 L/min (0.026667 cubic meters/sec)
Viscosity: 1750 cP
Specific Gravity: 1.2
Pipe is capped at the end so all flow must be going through slot

If anyone has any ideas they would be much appreciated.

 

[LittleInch]

Kind of has the right feel to me - that size equates to about a 1" square hole.

even given your rather high viscosity, with 89 bar across it, getting 85 m3/hr to 96 m3/hr through it sounds in the right order of magnitude to me - why the difference between your two flow rates by the way?)

Is this real or just homework?

My motto: Learn something new every day

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

 

[amiket]

Thanks for the reply. Yes this is a real problem. We are trying a different method of estimating crack area in an underground formation. The different flow rates was a typo thanks for catching it. The reason why this estimate seems off to me is because we have some photographic evidence that these cracks are larger than this.

 

[LittleInch]

I suspect if this is buried system that the real pressure drop across the tube is rather less than what I assume you have quoted as a shut in condition. whilst you would get some initial high flow, there should be a gradual rise in pressure as your rather thick gloopy material doesn't just magically flow away ad infinitum with no pressure rise.

what is the fluid and what sort of depth is this / type of ground etc? "underground formation" sounds more like reservoir rock than sand and gravel...

A photo would be good!

My motto: Learn something new every day

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

 

[amiket]

It is a brine solution, so that should be 1.75 cP not 1750 cp sorry. It is a rock formation, but I can not provide the picture. The 1300 psi is an estimate of the pressure before the wellbore comes to refusal. This is all just an estimate, but we are trying to figure out a suitable model so we do not have to do a full scale test.

 

[Duwe6]

Those calc results may be accurate. A 3-meter crack may only be 0.01mm open in the middle, and of course tapers to NIL on both ends. That is why there is a differentiation between 'crack' 'split', and 'tear'. They are attempting to quantify the size.

 

[LittleInch]

That's making a bit more sense now. As said before, the problem will be what is the true differential pressure across the crack / slot / tear? initially it might be the static pressure, but as soon as you start to "inject" liquid into solid rock, the local formation pressure increases and hence your differential pressure reduces.

As this is quite likely then to get the same flow your open area would need to increase. A bit of site testing would seem to be the best way to match your actual size / results to the theoretical one.

My motto: Learn something new every day

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

 

[3DDave]

I am trying to understand why crack size is important. If the goal of the pipe is to keep material inside, then the rate at which it leaves seems like the important factor. After that it would seem that increased dP causes the crack to elastically enlarge so it's not as if the crack is a fixed area; it varies with dP and may be closed near 0 dP. If it's a fatigue problem then the crack length grows with time.

The complicating factor is that the crack is a labyrinth that is formed by the fractured crystal boundaries where the crack is formed, so the passage is not only narrow at it's maximum, it is, potentially, very rough. Discontinuities on the order of the width of the crack opening, for comparison.