How can I calculate flow rate for leaking pressure vessel during maintenance?

[atc250r]

I work in the oil and gas industry and frequently encounter an issue involving isolation valves that do not seal 100%, and that begs me to ask the following question...

I often need to isolate particular sections of piping so that a segment can be opened/disassembled for maintenance. When I have isolated a particular section of pipe (by closing valves and diverting the flow) from an operating system, I then bleed off the pressure in the isolated section (volume of isolated pipe varies from 3 cubic meters up to about 18 cubic meters). I often bleed the isolated section's pressure down to about 10psi and company procedures dictate that I then I observe a digital pressure gauge (for a period of 5 minutes) to confirm that the closed valves are infact holding, and that mainline pressure has been 100% diverted. There is often upwards of 300-800 psi of crude oil still flowing in the system which I have diverted by the earlier closing of certain valves. Occasionally, the pressure in the isolated section climbs slowly, maybe 10 psi/minute (give or take). Sometimes the valves hold completely and no pressure rise occurs in the isolated section and then we're all happy. But when the pressure does climb, how can I get a "liters/minute" flow rate so that I know how much product will be leaking past the valves after I have drained the isolated section and I open that isolated section for maintenance? I need to know if the leakage will manageable or not, while the isolated section is disassembled. I assume the variable numbers you need to know are:
isolated pipe volume: 5 cubic meters
time: 60 seconds
pressure rise: 10 psi
mainline pressure: 500 psi
incoming flow rate (leakage past closed valve): ?? Liters/minute

Is there a formula for this that will work on various sizes of isolated pipe sections? Maybe mainline pressure is irrelavent? Do you need more info?

Thanks!

 

[Rx7man]

Easiest way I could think of is to bleed off as much as necessary after 1 minute into some container until you're back down to your original (10 psi) reading.. Perhaps do it a couple times and average it? Mainline pressure is pretty irrelevant because the flow difference between a 490 psi leak and a 500 psi leak is negligible.

It's really hard to solve this without knowing how much air is in the system, or mixed in with the crude.. a big air bubble in the system could DRASTICALLY change how 'compressible' the whole system is, as the air is easy to compress... With no air at all, a small leak will raise pressure quickly, while with air (lets say 50L of air space), the same leak may not show hardly at all

I'm no expert, but I don't think there's a 'neat', reliable mathematical solution to this.. Bleeding off to maintain a given pressure and measuring is about the most reliable way, if it's feasible.

 

[atc250r]

The air quantity in the pipeline would be zero, so that variable can be eliminated. Hence why I only bleed the pressure down to approximately 10 spi, rather than zero; I want to eliminate the possibility of introducing air into the system.

But I've searched the web for hours and I agree, that unfortunately, there appears to be no mathematical formula yet established for this exact scenario. I suppose bleeding off the measure into a bucket and measuring the quantity is the only way. Thanks for your help.

 

[Rx7man]

If you knew the compressiblity of the oil (which will be very small) you could do it, but you'd have to know the exact volume of the closed pipe.. Sometimes the simple solutions are still the best ones.

Perhaps if you had a pressure relief valve set at 10PSI or so and you installed it on the drain, it would make it easier to keep a consistent pressure over a time period to measure the leakage

 

[Nidum]

This problem is not significantly different to testing a pressure vessel hydraulically .

With vessel already completely full additional fluid is pumped into raise the pressure .

Pumping in more fluid has three basic effects :

Compressing the fluid itself .
Compressing any gas inclusion in the fluid .
Expanding the vessel walls .

Given the analysis of the fluid and technical details of the vessel a calculation of pressure rise relative to amount of additional fluid pumped in is possible .