Subsea Free Flooding 1

[rsdorn84]

Hello all,

Im trying to calculate the fill time for free flooding a subsea pipeline. However, when using Bernoulli equation for velocity, the result is very large. Here are my parameters.

Empty pipeline initial pressure: 1 bar
Water depth: 1,300 m
Pressure @ 1,300 m: 131.36 bar
Pipe length: 9,144 m
Pipe ID: 12.70 cm
Fluid density seawater rho: 1030 kg/m^3

v = sqrt(2*(P1 -P2)/rho))

When solving, the result is a velocity of 159.71 m/s (almost half the speed of sound!). I have confirmed this number manually and with online calculators. What assumption am I missing? At this rate it will fill a 9.144 km pipeline in 6 mins.

 

[Compositepro]

You have not considered the friction factor of fluid flowing in a pipe. There will also be considerable inlet losses. Bernoulli is an energy conservation equation and is not relevant to your problem. Are you planning to get an empty pipeline to 1300 m depth and then fill it?

 

[LittleInch]

Well at a full bore entry with 130bar entry pressure I'm surprised you don't reach sonic velocity (choked flow - look it up).

Bernoulli is the wrong equation to use here.

Unless your pipe is vertical the gas inside will start to compress as water enters. Otherwise where is the air going?

Normally flow in is controlled to stop this sort of thing happening.

What's the back ground here?



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[rsdorn84]

@Compositepro this makes sense. This is for an offshore pipeline installation and pre-commissioning problem. Pipelines are usually installed empty and then free flooded with seawater.

@LittleInch I´m looking up choked flow , thanks for the reference. Which equation should I be applying for this case? Air exits the pipeline through a check valve at the other end. T

At the end, I want to know how long it will take fill the entire line.

 

[itsmoked]

"The End" being on shore at atmosphere?

Keith Cress
kcress -

http://www.flaminsystems.com

 

[rsdorn84]

@itsmoked thats one example, through a riser to sealevel. But trying to keep it simple, just a straight pipeline on the seabed, free flooding from subsea to subsea (one direction).

 

[LittleInch]

The issue is more the max velocity your pipe can reasonably withstand.

Start there and work backwards.

But if your air exhaust pipe isn't ending at least a few metres above pipe level it won't escape.

The flow won't be constant so there is a transient analysis to be done here.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[miningman]

There is a nomograph in one of my old engineering text books that gives the flow associated with a head loss of 100 feet for every 100 feet of pipe. This is the absolute maximum flow that can be theoretically be expected with a pump powered by a motor with infinite HP, or more practically the flow to be expected thru a drill hole drilled from underground workings into the bottom of a lake........ and yes I have deliberately done this once during my career. For a 3 inch hole / pipe it is 500 gallons per minute, for a 6 inch hole it is 3000 gallons per minute and for a 5 inch hole it is 2000 gallons per minute.
This should be more than adequate to generate an initial estimate for the time to fill a 9000 metre pipe which has essentially an infinite quantity of water at infinite head available.

 

[itsmoked]

Check your numbers miningman?

Keith Cress
kcress -

http://www.flaminsystems.com

 

[miningman]

Sorry itsmoked, there are no numbers for me to check. The nomograph is taken from the Mining Engineers handbook by Peele, 1946 edition. It is still regarded as the premier text book within the mining industry......... I doubt it has been digitized yet. Obviously it is based on a number of assumptions as to pipe roughness etc , but it has proven its usefullness to me over the decades. If you'd like to post your estimates we might be able to have an intelligent discussion but otherwise I cant contribute much more.

Incidentally, it was remarkably accurate in predicting the final , actual flow from that incident in the gulf of mexico a few years ago, when the official estimates were all over map.

 

[georgeverghese]

Liquid inrush velocity will be so high it will shake the pipeline off its supports due to momentum changes at elbows.

 

[itsmoked]

miningman; LOL, You faked me out listing 3,6,5. I saw it as 3,5,6 and the flows don't make monotonic sense then.

Keith Cress
kcress -

http://www.flaminsystems.com

 

[LittleInch]

George, it's a pipe lying on the seabed!

The fact is that at 9km long this is a transient event so there is no simple formula and practical limits on velocity will prevail one hopes.

A flow speed of 3 to 5 m/ sec is what I would use.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[georgeverghese]

@LI,
Yes,am aware this is a subsea line. Free flooding a 0barg line at 1300metres depth with ? Dont need to run any calcs for this. Am presuming this 12.7inch line valve at 1300m depth is wide opened suddenly. It would take ages for the built up line pressure in a 9km line to build up to a point when the inflow velocity is reduced to 3-5m/sec.

 

[1503-44]

Limit the inflow to filling the pipeline to 3 to 5m/s max. I don't think that will be a problem with the 130 Bars of pressure you have available. Velocity across the inlet valve will be sonic, limiting press drop across the valve to what I estimate will be 1/2 of the pressure differential. It will take only 30 to 60 min to fill 9000 m at those filling velocities. Internal air pressure will not increase very much for awhile, only doubling by the time half of the pipeline has been filled and doubling again when you fill 3/4 of the pipeline. You should reach 20 Bar at 8000m filled and 130 Bar at around 8860 m filled. Don't open the vent valve at the end of the pipeline until then when the initial air internal pressure (assumed at 2 BarA) is nearing the 130 BarA outside pressure, or the pipeline will fill with water from both ends.

 

[rsdorn84]

Thank you all for your insights. They are steering me in the right direction. Just to clarify the problem, I´ve attached a diagram. I´ve added an inlet. Research has lead me to a coef. of discharge or resistace coef.

Assuming and infinite tank, smaller diameter inlet. Same pipe length and depth.

 

[1503-44]

Good. Inlet will let the water go in. Would be difficult without that.
Do not forget about outlet for air at other end.

 

[LittleInch]

you'll have choked flow for sure.

Better have some really hard material there or else your hole will end up rather bigger than it started....

And hope you don't suck in any rocks, sand, fish bits, crabs, plant material etc.

This sounds like a wholly bad idea. Is this a real project?

9km of pipe at 1300m deep is no joke and will have cost a lot. Why are you trying to break it before it even starts operation?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[georgeverghese]

Without a significant incline on this pipe, some or most of the air, when compressed to 130barg, will escape through the water inlet.

 

[1503-44]

Sea bed never perfectly flat