Cp/Cv for Relief Valve Sizing

[chemdesign]

I am wondering if anyone can offer guidance on the proper reference conditions (i.e. temperature and pressure) for k (Cp/Cv) for use in the API 520 critical vapor flow equation for multi component mixtures? In most of the examples in API520, they reference a table that lists k values at standard conditions (60F, 1 atm), but the conditions at the inlet to the relief valve are significant departure from standard.

 

[MortenA]

If you know Cp then for an ideal gas:

k=Cp/Cv=M*Cp/(M*Cp-R)

This is a reasonable approximation even at relatively high pressure.

Best regards

Morten

 

[25362]

If you wish to obtain the Cp, Cv values for individual hydrocarbons at differing P,T conditions consult the NIST webbook:

http://webbook.nist.gov/chemistry/

For example the Cp/Cv ratios obtained for pentane are

1 atm 10 atm

200 deg C 1.052 1.083
300 deg C 1.044 1.056

 

[hacksaw]

you are on the right track, you use the worst case estimate of k for valve siziiing.

you can estimate it more rigorously using the methods listed in Perry's.

 

[chemdesign]

For complex hydrocarbon mixtures containing H2S and H2 at moderature pressures (25 atm), Hysis predicts a significant difference between the actual Cp/Cv ratio and MCp/(MCp-R). I believe this is due to the low compressibility factor (i.e. the gas is not ideal).

I don't disagree with the approach of using a conservative Cp/Cv ratio for new installations, but am concerned that this could lead to unecessary modifications when the size of existing relief valves are re-validated. Comments?

 

[EGT01]

Chemdesign,

See if you can get a copy of the following:
Shackelford, Aubry, "Using the Ideal Gas Specific Heat Ratio for Relief Valve Sizing", Chemical Engineering, pp. 54-59, November 2003.

I thought this was a reasonable discussion of your issue. The article starts out by saying
"In API Recommended Practice 520, the basis for evaluating the ideal gas specific heat ratio has been modified from standard conditions (in the sixth edition) to relieving conditions (in the seventh edition)."

You should also review the appendix in API RP-520 Part I covering "Review of flow equations used in sizing pressure relief valves for gas or vapor" and be aware of the isentropic expansion coefficient as well.

 

[TD2K]

"to relieving conditions (in the seventh edition)."

And I believe to add to EGT01's, it's at relieving conditions for an ideal gas.

 

[chemdesign]

Thanks EGT01. Shackelford's article "Using the Ideal Gas Specific Heat Ratio for Relief Valve Sizing", clears this up. It clearly states that one should use the ideal gas specific heat ratio evaluated at the relief conditions.