Multiple valves flow Coefficient Cg

[soma0324]

Hi,
I am trying to depressure a plant piping system where we have multiple valves to depressure. i have divided the plant in various sections based on check valve locations and calculated the depressuring time for each section. now I have been told that if we remove all the check valves and let say the whole system is at the same pressure of 800 psig and we open all the blowdown valves at the same time how long it will take to blowdown the whole piping system. now i am struggling with this calculation. i am trying to calculate an equivalent Coefficient for all the blowdown valves (there are three of them) and then use that coefficient to calculate the blowdown time. the formula i am using is 1/Ce^2 = n (1/Cg1^2 + 1/Cg2^...). anyone knows if this formula is can be used to calculate the so called equivalent flow coefficient for valves? is this approach correct or should i use anyother way to calculate that. it is similar to situation where for example we have multiple holes in a vessel or pipe and how long will it take for the pipe or vessel to reach to a lower pressure.

Thanks,

 

[BigInch]

No. That method would only be halfway close, if the volumes blowing and hydraulic paths to each valve were equivalent and completely balanced. Highly unlikely, so each segment must be looked at separately, with pressures and flow continuity maintained at any joining points throughout the total blowdown time. I'd really think you'd want to do a transient flow simulation for all but the most basic simplistic system.

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[davefitz]

With an 800 psig initial system pressure , you will have choked flow , but only thru one of the many valves. The valve that chokes is the one with the smallest net free open area. This is the same as the theoretical situation of choked flow with multiple orifices in series .

I'll have to think about this to remember how this was handled many years ago.

 

[davefitz]

As I can recall, one solution is to iteratively solve for each assumed flowarate, as follows:

a) pick an initial pressure of the upstream reservoir, Pr.
b) assume a max wide open flowrate (Wn) thru the multiple valves.
c) working backwards from the exit nozzle to atmosphere, calculate what the pressure must be at the nozzle for the assumed flowrate.
d)Then calculate the pressure drop from the exit of the final valveto this nozzle, to determine the pressure at the exit of the final valve.
e) using that final valve's otulet pressure, Cv, Cd, Xt, etc calculate the minimum pressure upstream of the final valve that would pass the assumed flowrate.
f) likewise calculate the minimum pressure upstream of all preceeding valves.
g)If the pressure upstream of the first valve ( Pu1) does not match the known pressure of the upstream reservoir( item a, above), then correct the next iteration as W,n+1 = Wn * Pr/Pu1.

Once the iterations converge on a correct upstream pressure , then calcualte how much the upstream reservoir pressure would drop in ( 10 seconds) at this known flowrate. Revise the reservoir pressure accodingly and obtain a plot of reserovir pressure vs time and valve system flowarate vs time.