Calculate Heat Capacity and Heat Capacity Ratio for a Real Gas

[Varden]

Hey all,

I am in the midst of a compressor monitoring project. One of the key parameters needed is the heat capacity ratio, i.e. Cp/Cv.

I am dealing with high pressures, such that gases cannot be treated as "ideal".

1st Stage Suction: T = 15 degC P = 3500 kPa Q = 95950 scfm

1st Stage Discharge: T = 128 degC P = 7405 kPa Q = 95950 scfm (less seal losses)

2nd Stage Suction: T = 10 degC P = 7000 kPa Q = 95350 scfm

2nd Stage Sidestream Inlet: T = 15 degC P = 14686 kPa Q = 310783 scfm

2nd Stage Discharge: T = 40 degC P = 15 000 kPa Q = 406133 scfm

I have done an extensive literature survey, and have only found one procedure for determining the heat capacity of a real gas in Perry's 8th Edition Section 2.22.8:

Eqn 2-44 Cp = Cp ideal - T * Integral from 0 to P of (d^2v/dt^2) * dP

Cp ideal is easy enough to find using Cp ideal = A + BT + CT^2 + DT^3

I used the Peng-Robinson EOS to determine my Z values, but cannot find it simplified in terms of V (molar volume), such that this integral in 2-44 could be satisfied.

Assuming I could complete the integral, I have not found a similar correlation for Cv. I saw in a previous post,

http://www.eng-tips.com/viewthread.cfm?qid=202403&page=5

A correlation for Cv given Cp, Tr and Pr:

ChE (March 14,1977) gave for real gases:

Cp - Cv = R [1 + (Pr/Tr2)[0.132+0.712/Tr)2]

then, k = Cp/Cv = Cp/[Cp-(Cp-Cv)]

Does anyone have any thoughts/ideas/opinions with respect to the solution of this problem?

Thanks in advance,

Varden

 

[israelkk]

See this NIST page

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

It has real gas measured data.

 

[davefitz]

It would seem that a straightforward test for determining Cp/Cv would be based on a choked flow or shock wave experiment. Since it is easy to measure Ti, To, Pi, Po, then Cp/Cv falls out easily.

 

[hacksaw]

you are probably working with a multicomponent stream with possibility of condensed phases, it is a tough problem even when you get answers.

Perry's method works well. Once you have the equation of state there are a lot of thermodynamic derivatives to take (numerically) and integrations to perform.

As soon as non-ideality sets in, however, the results are very approximate. Most firms use less rigorous estimates for design-less chance for error though hardly exact.