Ankur is right to say that in most cases, the real k is higher than the ideal k value, and using the ideal k value in the API equation results in a larger calculated area, which is thus conservative.
However,about 12 years ago I was looking into this subject and I found that this is not always the case. I checked the data for propane vapour, and it turns out that the real k value for propane, over a range of pressures and temperatures, is less than the ideal value, and in fact is less than 1.0 . Thus, a relief valve for propane vapour would be undersized if the ideal k value was used. The undersizing was between 2% and 8% over the range 10 to 40 bar, my old results show.
I also tried various blends of propane and methane, and the effect was still there, though smaller, with a 70% propane - 30% methane mix.
The Hysys version available to me at the time did not calculate the real Cp/Cv, so I derived the isentropic exponent k using a property table and the definition k = ln(p1/p2)/ln (rho 1/rho 2)isentropic.
The same effect may also be true for other vapours near the dewpoint, but I did not check any other cases. Likewise, I don't know the comparison for non-hydrocarbon gases.
I did some relief valve sizing calculations for the propane cases using the derived real k values and the API equation, and as a check I also used the HEM method for sizing, which uses rigorous thermodynamics explicitly, without an input for k, and the API method came out very close, about 2% to 3% higher in calculated area than HEM. This difference can be attributed to the API discharge coefficient of 0.975, whereas in the HEM, I used 1.0.
HEM was developed for two-phase flow, but the principle is to treat the two phases as a single phase (Homogeneous Equilibrium), so applying the same method to a single phase is quite consistent.
Imperial College has verified HEM experimentally in a research programme in 1998 and 1999, I have the tables of results. The discharge coefficient of 1.0 for propane is taken from these. Basically this means that the measured flows exactly matched the HEM calculations.
It is this work that is my basis for recommending the use of the real k value in the API equation. If the ideal k is known to be
higher correction- LOWER
, then that value can be used, but if the resulting larger area then triggers the next standard size of orifice to be selected, that outcome is not necessarily optimum engineering, as the piping and block valves will all end up a lot larger.
Edited by paulhorth, 17 October 2011 - 05:06 PM.