Challenge calculation 2

[elaineabc]

Can you tell me hours required to drop the following pipeline from high pressure to low pressure?

8.5 miles of isolated 12” pipeline @ approx. 595 psig to equalize @ 40 psig thru a 1.5 sq. inch open valve.

Please explain to me if you have sometime how to come up with a solution to this question. Thanks a bunch!!!

 

[Montemayor]

Go to:

http://www.air-dispersion.com

There, you will see how Milt Beychok walks you through the logic and the equations supplied to calculate the time and flowrates expected from a gaseous release. Make sure you scroll down to the bottom of Milt's opening page and there you will find the index to accidental releases. Although yours is not an accident, it is still a release.

 

[zdas04]

Art,
Great reference. I've been calculating blowdown times for 20 years by recomputing critical flow at the new pressure every 20 seconds or so. I got good results, but it was a pain with most of the tools that I had available. I'm updating my MathCad sheet with this information.

David

 

[zdas04]

The Bird, Stewart, and Lightfoot model looked to be the most usable (since it directly calculates a time to reach a specific proportion of original mass) and I put it into my MathCad file first.

To verify the numbers, I was varying input values to see the elapsed time to some small proportion of original mass. When I changed pressure nothing happended to blowdown time. I assumed I had fat-fingered it until I saw in the first term within the radical has P(0)/rho(0) since rho(0) can be stated as (P(0)*SG)/(R(air)*T(0)) it is easy to see the only pressure term in the equation just vanish.

My experience shows that blowdown time has a strong reliance on initial pressure. Since the Bird model doesn't have a pressure term surviving and it yeilds identical results to the Rasouli model, I think I'll stick to my brute-force iteration model.



David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[sailoday28]

I would check the assumptions in the blowdown analysis model.

For example, the model probably neglects the velocity along the length of the chamber or pipe. With 8 or so miles, -over 40000 ft- of pipe length and say 1000 to 2000 fps for a sound wave, there will be a delay of 20 to 40 seconds for pressure and velocity differential to reach one end from the other end.

If that can be neglected-- great. Othewise use a method of characteristics (MOC) transient analysis. The compressible flow text of Shapiro, Vol II (and other texts) illustrate the approach.
Wave duct analysis by Rudinger, illustrates blowdown from a guillotine break of a pressurized duct (pipe).

My main point is that major assumptions in an analysis should be considered. Otherwise one gets GITGO- garbage in-gabage out.

Regards

 

[MortenA]

elaineabc

The essence of these advice: Your request is actually quite a lot to ask for! This site is not "free consultacy". Besides if its "for real" how would you QA data from a "non descript" web page?

Contact a professional consultant if you company does not have inhouse expertise.

I BTW think that sailorday has an importnat point - but the importance of the increase in gas velocity will partially depend on the leak size.

Best regards

Morten

 

[katmar]

David,

This seems a real dumb question, but did you vary the B,S & L factor F as you varied the initial pressure? Looking at their equation it seems to make intuitive sense that for any given initial pressure you will get to much the same percentage remaining after the same time. To get to the 40 psi specified by Elaine you would have to decrease F as you increased the initial pressure.

The two different analyses on Milton Beychok's site are both based on rupturing vessels, rather than on pipelines and I agree with Sailoday that the pressure drop down the pipe could be important. I suppose this depends on the ratio of the diameters of the vent and the pipeline, as well as the length to diameter ratio of the pipeline. How do you deal with this in your iterative solution - or maybe that is proprietary knowledge?

regards
Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[zdas04]

I treated the "F" term as a target for iteration since it is the proportion of original mass remaining. I took the Bird equation as meaing "time to X% remaining". It didn't matter if I was starting at 1,000 psi or 100 psi, 1% remaining was still 1% (of a widely differing total mass).

Saloday's issue is really a boundary-condition issue. As long as the pressure near the leak is above the critical pressure required for choked flow, you'll have choked flow out the hole. In pipe above 10-inch, the friction drop from choked flow out a 2-inch blowdown is small enough to be negligible (i.e., at 100 psi the choked flow flowing out a 2-inch full-port ball valve is 8.9 MMCF/d which is about 12 psi/mile pressure drop in a 10-inch; at 30 psi the flow rate is down to 3 MMCF/d which is 2 psi-mile in 10-inch). If I use the pressure a mile from the blowdown to calculate the mass leaving, then at 100 psi I'm flowing 8.9 MMCF/d and at the valve I'm flowing 7.8 MMCF/d--this has always been close enought to tell me whether I needed to mobilize for a blowdown at 3:00 am or could let the guys sleep in till 4:00 am to have a line blown down by daylight.

David

 

[sailoday28]

zdas04 (Mechanical)states".....In pipe above 10-inch, the friction drop from choked flow out a 2-inch blowdown is small enough to be negligible".
Even with frictionless flow, there is a pressure drop due to the inertia of the fluid. And if the pipe is long enough a quasi steady analysis will at best lead to approximate results.
With frictionless flow and slamming a valve shut, one would not use a quasi steady analysis (I hope they would use MOC or a water hammer type approach which incorporates fluid inertia).

Main point again--Fluid inertia should be considered in long pipes- or where flow conditions cause rapid changes. AND user should understand major assumptions of program s/he uses.

Regards

 

[zdas04]

Sailoday,
You are right. As I said the pressure drop in 10-inch pipe caused by blowing a line down through a 2-inch valve is 12 psi/mile if you have 100 psi 1 mile upstream. That is not zero, but a rigerous inclusion of all of the pressure drops results in an answer that is very close to the answer you get when you ignore them. The important practical question is "how close is close enough?". If I'm trying to get a line blown down by daylight I have a lot of wiggle room. If I have a pressure recorder two miles from a leak and I'm trying to predict the leak size from the pressure profile I'd better account for both inertial losses and friction losses.

If I'm estimating a trail length I use the "pace" for measuremnt, if I'm building a house I use a tape measure, if I'm building a race-car engine I use a micrometer. I've found few concepts in engineering more important than "good enough".

David