Diesel Leak rate through a buried pipe 1

[Atwerp]

I need to calculate the rate diesel would leak out of a 2" steel pipe buried 3' below grade. The hole was approx. 1/4" diameter and the pipe is under 20 psi pressure. I know the soil type will probably affect the rate. If it is easier, can I find the maximum leak rate assuming the pipe were not buried and then deal with how the pipe burial would affect the rate?

Thanks

 

[Ashereng]

Are you trying to figure out how big a spill you have?

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
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[Atwerp]

No, not exactly. I will figure that out with geological magic. I am trying to figure out at what rate diesel could have leaked from the pipe. An opposing consultant made an estimate and I am trying to check if their calculation is at all accurate.

Thanks

 

[Ashereng]

I would think not just soil type, but soil compactness and density would also matter.

Also, the orientation of the hole may have an effect. Not sure how, but it may.

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[Atwerp]

That is why I am starting with trying to find the leak rate without considering that it is buried. Assume the worst case scenario would be the pipe leaking onto the surface.

 

[Ashereng]

Assuming that the ratio of the hole size 1/4" to 2" (2" Sch.40 pipe has ID of about 2"), the flow going out the leak would be about 1.5% of the original flow rate.

If you assume the soil conditions outside the pipe will further retard that, by let say 80% (pure guess here), then the total leakage rate is 0.3% of the original total flow rate.

That's my unqualified off the top of my head guess.

What was the other consultant's number?

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[thermcool]

Well, if you use darcy law of diffusion thorough the porous structure to calculate the flow rate of the diesel through the buried pipe.

Hopefully it will give you valid approach and better results.

See the below link for detail:

http://biosystems.okstate.edu/darcy/LaLoi/basics.htm

 

[ornerynorsk]

I think with 20 psi, soil type would only be a factor for about a couple of minutes. Even very dense compaction is going to give way to the jetting action, especially a leak as big as 1/4 inch.

 

[Ashereng]

I was thinking actually of a longer period of time, after a pool forms. I thought maybe the pool will dampen the jetting action, and the pipe will just be leading into the pool, and hence, affected by the "backpressure" of the pool.

Maybe like areas with a lot of clays?

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[BigInch]

Any oil under 20 psi is not going to let soil resistance stop it until you get way down to 30 feet or more and the pipe was drilled into a solid clay.

Just figure your leak rate without the soil.

 

[itsmoked]

I would agree with BI. Certainly the "full leak" is the number to work with.

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[CarlB]

Until the flow creates a path to the surface to allow soil to migrate, I don't believe much "jetting action" will occur. Where would the soil particles go?

Only reference I came up with in a little searching discusses other factors that influence leak rate besides the size of the hole-

http://www.leakage2005.com/pdf/The Effect of Soil Properties on Leakage Economics.pdf

 

[itsmoked]

Interesting article CarlB!

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[BigInch]

CarlB. People seem to be confusing this with geological formations thousands of feet below surface where earth resistance is 8000+ psi. 20 lbs is a lot of force on a in3 of soil that is probably only 3 or 4 feet below ground surface level. Most soil particles, especially in a usually poorly compacted backfilled pipeline trench with broken rock, some gravel, soil and sand around the pipe will be compressed into adjacent void spaces and will easily yield a flow path allowing fluid to go wherever it wants to go. As soon as a grain of soil anywhere near the hole in the pipe tries to stop flow, flow backing up to the high pressure source brings the full pipeline pressure to bare to give it that extra needed little boost. I can tell you... (as sure as the Space Shuttle can fly) it doesn't take long for it to just go straight up. Later it may make its way down to an aquifer, but much much later.

 

[CarlB]

You may be correct, but I think people are more likely visualizing what happens when a water jet strikes the ground surface dislodging unconfined particles. Maybe someone will dig a 3 feet deep hole, bury the end of a garden hose, backfill and compact, let er rip, and see how long until it becomes a fountain.

 

[BigInch]

Ha! I was going to suggest they do the exact the same thing.

The reference you found seems to suggest that well compacted backfill is used over pipelines, which in general is very far from the truth. While it may be true at specific constructions in city street works and rural highway undercrossings, I can assure you that it is absolutely not the case for the thousands of miles of oil pipelines making their cross-country runs as they try to avoid those areas where extra care in backfilling is demanded by public works and highway authorities.

 

[BigInch]

Hit the post button too soon.

I was going to re-emphisize that full pipeline pressure can be felt by soil near a hole. If one looks at the equation for flow across across a nozzle, valve or hole, approximated by, Q = Cv * (Pi^2 -Po^2),
Pi = pressure inside pipeline
Po = " outside

you can see that when the flow is very small, as it is when it is just starting to develop and leave the pipeline through a new hole, the pressure drop from inside to outside = apx. 0, so full pipeline pressure is there. When flow through the leak reaches sonic velocity, both flow and the pressure drop across the hole are at maximums and you have the conditions to determine maximum flowrate possible from the leak.

So, IMO its very difficult for soil to stop a pipeline leak. On one hand maximum acceleration pressure will push a grain out of the way; on the other, it must resist full momentum from a maximum flow velocity. Energy (pressure head or velocity head) cannot be created or destroyed by soil trying to resist a pipeline leak flow. The only way soil grains have to reduce the total energy head is by providing friction to the flow, which would require very high cohesion between individual grains.

<OK, now hit post button>

 

[kyong]

Simple physics can apply to calculate maximum theoretical flow. dP=1/2 * rho * v^2
v= (2*dP / rho)^2
Q=A*v=9 gpm

In a short time of beginning of leakage, soil adhered to the pipe will be broken. It may be less than 1 second or so. Negligible. Once it happens, soil resistence will be zero and then only resistence will be the liquid back pressure formed by the diesel spilled. It will take long time and can't be higher than 3 ft head, so again not significant. Friction loss at the opening can be more significant, but not very big. My ball park guess is 10 to 50%.

 

[Atwerp]

Kyong, what does rho represent?

 

[BigInch]

I get 5.6 gpm, because kyong forgot the vena contracta area ratio of flow through a square edged hole which is 0.62, so Flowrate = 9.06 gpm * 0.62 vena contracta area ratio = 5.62 gpm.

192 bbls/day

Only some $14,000 a day if it was today's market crude oil. Price for diesel is on your local gas station pumps. Its a lot higher here I'm sure.