Estimate leak rate through pit hole in a pipeline

[vpg]

Does anyone know how to estimate the Leak Rate through a pitted hole of a pipeline?

The key point here is that the hole diameter is not a fixed value. It grew from 0 at the begging of the leak to a final size of 0.25". The leak rate varies with time.

Given the following data, I would appreciate if anyone can give an insight into the problem. I need to estimate the total time (from the start of leak) to have a leakage amount of 108 cubic meters.

Pipe diameter: 3.5" (88.9 mm)x 0.125" (3.2mm) wall thickness
Diameter of leak hole: 0.25" (6 mm)
Volume flow through pipe: 340 cubic meter/day
Total volume of leak: 108 cubic meters
Normal operating pressure: 138 psi (950 KPa)
Pipeline: buried 2 meters underground (clay)
Fluid: 98% salt water + 3% oil

Thanks in advance,

 

[RWF7437]

It is a nearly circular orifice. See Kings Handbook of Hydraulics for orifice coefficents.

 

[hacksaw]

since you have critical flow conditions the flow is proportional to the area. you can use an "average" area or you can integrate the flow with a hole diameter that changes with time.

The disch. coefficients are available from many sorces.

 

[vpg]

Thanks RWF7437 and Hacksa for your suggestions.

I still have a question regarding the effect of mostly clay soil surrounding the pipeline.

Will the permeabiltiy or seepage through clay affect the leak rate? If yes, how do I account for the effect in the calculation?

I know this question may be slightly out of piping and fluid mechanics area.

Any suggestions will be apprecitated.

 

[BobPE]

yes vpg, the soil will affect the initil leakage rate until such time that the leak removed the soil. It is a real pain to calculate the soil factor. Yo would use Darcy's law to overlay a tortous flow path on the orifice discharge to induce additional headloss. This will have the net effect of keeping actual flows below what you calculate using the orifice equation.

What is your goal here though, it seems like you are trying to use math to justify and event. Like if your pipe leaks it wont leak that much. This is true for a short period of time, but the true defination of a leak is that it will approach orifice flow. The effect of the soil will only increase the time it takes the leak to reach maximum flow.

I guess I would sume it up as.....a leak is a leak, of course, of course.....or is that a horse??? LOL

BobPE