Time for pressure to drop through Relief Valve

[grego68]

I appologize for the stupid question in advance but I am not very well versed in fluids. I have a system which actuates a relief valve when the air pressure falls to 60 psi. I am looking for the method of finding out how long it takes to exhaust that pressure to atmosphere. The pipe runs about 100 ft with various bends and valves. Is there an easy way to find the time for this? Thanks

Please let me know if any further information is needed.

 

[dcasto]

I set up an excel spread sheet. In the first row I pick a time period. Then calculate the vent volume rate at the start pressure based on relief valve flow coefficient or API equation. Take that rate time the selected time period to get lost volume. Then calculate new pressure in line based on lowered volume (std volume or do it on a mass basis).
Then just replicate that series of calculations across the row to new rows, The inut for row two pressure will come from row 1.

Then you can adjust the time increments and see if 1 minute changes are any less accurate than 1 sec time periods.

Its digital integration.

 

[grego68]

thanks dcasto,

Earlier today I actually calculated the exit flow rate by use of Darcys Formula. Is this a valid method for this problem? I can't seem locate the API equation that you speak of.

So I now have the flow rate and initial volume and can get to that point of your given method. Then I get lost again. What do I use to find the new pressure based on the lower volume? Using boyles won't work as far as I can tell since if my volume lowers my pressure increases, which is opposite of what is happening here. Or am I just looking at it incorrectly?

Thank again

 

[jistre]

The ideal gas law may be more suited to that kind of calculation, grego. Boyle's law only holds for a fixed amount (mass basis, not volume basis) of gas, which isn't what you have here. Plus, the volume of the gas in the system doesn't change anyway. As gas escapes the system, the number of gas molecules (the mass) in the system drops, but the physical volume of the piping system remains unchanged and the gas will always spread out to fill it completely.

 

[dcasto]

The formula for relief valve capacity from API is:

(DESIGN FLOW, MSCFD)= (AREA,SQ. IN.)/(((TEMP+460)*(SET PRESS*1.1+15)/(OPER PRESS*1.1+15)*(SP. GR.)*(Z))^0.5/((1.692)*(C1)*(K)*(P1)*(Kb)))

 

[MortenA]

Im not certain that i understand the problem described - but from the headline: "Time for pressure to drop through Relief Valve" then if you have a spring loaded relief valve the pressure shouldnt exceed the set pressure (+10 or whatever %) - and a PSV will not reduce pressure but re-seat when pressure drops below set-pressure again. Yes there is a %blowdown but that for mechanical reasons the way i understand it and typically only 7.5% of the set point.

Relief may continue for as long as the event that causes the pressure to exceed MAWP (fire, open block valve etc).

Best regards Morten