Valve Sizing Equations: What is Correct?

[magusinp]

The Universal Gas Sizing Equation Q = SQRT(520/(SG*(Temp+460)))*Cg*P1*SIN((59.64/C1)*SQRT(P1-P2/P1)) establishes one Flow Rate. There is a Fisher simplified version Q = Cg*P1*SQRT(520/(SG*(Temp+460))) for critical flow. There is another simplified version from Moooney Q = P1*Cg*1.29. Finally, when I ask for a quote from any vendor, their flow rates will not match the flowrates I try to model using these equations. I am sure everyone else has noticed this. I realize these are empirical equations...but there are design issues and legal concerns. How do you balance these disparities? Which information is most accurate? Which information should be used for process design? Which information should be called Best Design Practice?

 

[TD2K]

How much difference are you seeing?

Fisher publishes a gas sizing equation which is for IDEAL gases (though they don't explain that very well) which looks very much what you have 'universal gas sizing equation' (sorry, don't have my reference books handy so I'm going from memory). They ALSO have another equation which is specifically for all gases at all pressures and temperatures. The two equations give you the same answer if you replace the SQRT (520/(SG*(Temp+460)) with SQRT (520/(ZSG*(Temp+460)) (Z being the compressibility factor). With a little alegrabic manipulation, you can show the two equations are virtually the same (the 520 coefficient back calculates to 521).

That's not very clear I realize, if you want a copy of the work, drop me an email at testdog2000@yahoo.com and I'll email you a copy of it. Why Fisher never included the Z term in their gas equation is a mystery to me.

I'm not familar with the Mooney equation (or that anyone else uses Cg) but if you go back to the true universal Fisher equation, you should be able to work out what gas and temperature this is based on (since there is no SG or T term, they must have assumed one. If you gas is different, this equation is not going to give you correct answers).

 

[TD2K]

I looked at my Fisher catalogue here at work. What you have called their 'universal' gas sizing equation is for ideal gases (though it's not called out as such) and is called simply the 'gas flow' equation in my copy of their catalogue 10. The equation for any gas under any pressure and temperature is Qs = 1.06*SQRT(d1*P1)*Cg*sin(as above) where Qs is the flow in lb/hr, d1 is the inlet density, lb/ft3.

You can convert Fisher's 'ideal' gas equation to be valid for any pressure and temperature by changing 520/GT to 520/ZGT where Z is the compressibility factor.

The 'simplied' version you refer to (for critical flow) is the same as the first equation except that the sin( ) term has been set equal to 1.0 (eg. where critical flow occurs) as under critical flow, the downstream pressure, and hence dP, has no effect on the flow. Essentially, you calculate the term inside the sin ( ) and if it is equal to or more than 90 degrees, you set the sine of it equal to a maximum of 1.0 (or as your equation is using radians, pi/2 radians and the sine of that is 1.0). If you don't have critical flow, you won't get obviously the same answer as the first equation.

For the "mooney' equation, I can't add anything to my previous comment. I'm not sure this helped you or not %-)

 

[manian]

The different flow conditions viz., liquid, gas, mixed are to be dealt with differently. While the liquid sizing is easier and straightforward, the gas sizing equations tend to get more complex due to the compressibility etc. The calculations are simpler as long as there is no choking. If a choked flow occurs, the equations are more complex and it is practically not feasible to predict the flow conditions. Even otherwise, you need a lot of data like the terminal velocity coefficient, Cv etc for the valves, pipes and fittings which most of the manufacturers do not clearly publish. Would suggest you look at the ISA Handbook of Control Valves to get a better picture. Wonder whether this is of some help.

Regards

Manian