Specific Heat Ratio in Compressor Calculations

[ChemEngSquirrel]

I'm carrying out compressor sizing calculations.

Which value of specific heat ratio should i use for max accuracy? My options are either actual cp/Cv from an EOS as calculated in process simulator or ideal figure where Cv = Cp-R.

 

[pmover]

conduct your analysis using both specific heat values and compare the results. chances are that the differences between the two results will not result in a difference in compressor frame/cylinder or impeller depending upon type of compressor you are seeking.

the alternative is to provide the gas composition (?) & process condition data to the compressor mfg and let them conduct sizing criteria. of course, a skilled engr needs to review and confirm the mfg analysis to ensure compliance.

good luck!
-pmover

 

[zdas04]

If your EOS results in a value more than 2-3% different from looking it up in NIST (which uses an EOS by the way), then there is a problem with your EOS. Tabulated values are subject to rounding errors. That is why a couple of editions ago the GPSA Engineering Field Data book stoped including c_v data, now they just include the equation

k=c_p/(c_p-R_gas)

You just have to be careful to use R_gas=R_universal/MW_gas instead of R_universal

David

 

[Montemayor]

Squirrel:

You don’t furnish much basic data, such as:

Is your gas pure, or a mixture? Is it dry or wet?
What are your suction and discharge conditions?
Is your compressor a recip or a centrifugal?
Is your compressor a single stage – or multi-stage?
What do you define as “Max accuracy”?
What EOS are you using? What simulator?

As Pmover and David have done, I can only address your concern in generalities – but I can add some experienced advice:

By “sizing” I assume you are calculating the adiabatic head / horsepower requirements, and discharge temperatures;
As Pmover infers, leave the rest of the “design” to the proven experts – the compressor’s manufacturer;
Refer to Royce N. Brown’s book, “Compressors - Selection and Sizing”; 2nd Edition; Gulf Professional Publishing. Read the section titled “Real Gas Exponent”. Even Brown fails to explicitly go into the details of finding and applying specific heats of gases in compressor calculations. However, he at least does mention some of the important details left out of most academic Thermodynamic text books.

Understand and accept the fact that the relationship

MCp - MCv = R = 1.986 Btu / (lbmol - °F)

Is a purely theoretical one based on “ideal” gas conditions – which are not realistic and unavailable in the real world. The same facts apply to the specific heat ratio derived from it. Reflect on the definition of ideal gas conditions: 1.0 atmospheric pressure and approximately 70 oF. Even if you are fortunate to calculate an accurate specific heat value for an ideal gas, what do you do with it when your compression conditions are probably various atmospheres of pressure and your average stage compression temperature is around 150 -160 of?
Accept the fact that the specific heat at constant pressure is NOT A CONSTANT – nor is the Cv. Also accept the fact that both gas specific heats will be varying from the suction port to the discharge port on the compressor in question – and you have no way to calculate that path, except to estimate it. Most manufacturers – including myself – have tried to identify the specific values at suction and discharge and then simply averaged them to obtain the “realistic” k that can then be used in the applicable equations to calculate, for example, the discharge temperature. This has been a sore subject with me for the past 50 years as I have not yet found or heard of a Thermodynamic paper dealing and explaining this fact as it relates to compressor calculations. I have found that University profs and text book authors simply prefer to avoid this subject.
As the GPSA has always stated – and even Brown also – use Mollier diagrams (in the case of pure gases) to obtain the maximum in accurate compressor calculations. Mollier diagrams are derived from reliable EOS, so an accurate and proven EOS will also work – as David also suggests.

Some gases - such as ethylene - can be mavericks, varying in specific heat values in strange ways without any respect for the academic relationship predicted by academics.

I hope these comments are of some help to you.

 

[zdas04]

Art,
I agree with everything you said. I just wonder about the materiality of it after the machine is designed and built. For example, in a recip compressor doing 4 compression ratios with 98% methane with 2% other stuff I've regularly used the published constituent constant values (at STP) and gotten estimated discharge temperature within 1% of measured data. Horsepower calculations are bit farther off since there is no way of knowing the exact valve losses or seal leakage, but I've often gotten within 3-4% of an electric meter and 8-10% of hp calculated from engine manifold pressure--numbers that are generally good enough for the engineering evaluations that I do.

Usually when the theoretical numbers are more than about 10% different from measured values there is something broken on the compressor. Published data gets me easily within the 10% and when I've needed better numbers I've gone to NIST and for the gases I work with the suction/discharge c(p)/c(v) ratio is very close.

A problem I was working on yesterday had k=1.3102 at STP. Suction conditions (60F and 25 psia) were k=1.3122 and discharge conditions (261F and 100 psia) were k=1.2650. Average of suction and discharge k valves was 1.2866 which is 1.7% lower than STP. Using published values estimated discharge temp at 262F. Using average of suction/discharge would have estimated 248F which gets the error up to 5%.

Maybe I've answered my own question.

Seeing an estimated value of 262F and a measured value of 261F gave me a warm fuzzy feeling. Seeing a measured value of 261F and a theoretical value of 248F would make me start to question my suction valve stiffness. To match measured conditions I have to drop my suction pressure to 23 psia. Now I'm wondering if an extra 2 psi dP across the suction valve is enough to change them. Usually not, but sometimes it is.

Maybe it really is material.

David

 

[ChemEngSquirrel]

David (Zdas04),

Thanks for taking time to respond (& others also).

In your example, you state discharge pressure is 100 psia. This is fairly low pressure so i'm not surprised you managed to get close to actual measured results i.e. discharge temperature. I'd be interested to know if using the ideal specific heat ratio for natural gas at 870 psig on compressor suction and 2175 psig at compressor discharge also gives accurate results.

At 870 psig, ideal k = 1.3 while actual k can be around 1.6. As a result, compressor calcs such as discharge temperature estimation can vary significantly dependent on the specific heat capacity ratio selected.

Any further thoughts from anyone would be much appreciated.

 

[SNORGY]

Forgive me for not researching completely before posting...

See also:

thread391-30277


Regards,

SNORGY.

 

[apetri]

it depends from process,
for contrifugal compressors I have a Excel page to estimate adiabatic or polytropic efficiencies starting from real gas data calculated with Prode Properties, the results (usually) are in agreement with manufacturer's data,
also I am able to predict a new operating point starting from a measured point (which is perhaps the most common problem), you can find the correlations in any good textbook, however do not forget that contrifugal compressors are complex pieces of equipment and you should ask the manufaturer to get the most accurate estimates.
About gas properties I use preferably the equations of state models available in Prode Properties, I have verified that calculated values are close to those estimated by our manufaturer's software (BWR with custom parameters), by the way Prode Properties calculates cp and cv from rigorous evaluation of departures and derivatives not easy to solve by hand...

 

[sheiko]

See also this article from JM Campbell to clarify the matter:

http://www.jmcampbell.com/tip-of-th...tivity-of-k-values-on-compressor-performance/

"We don't believe things because they are true, things are true because we believe them."

 

[dcasto]

you can do all the sizing you want, anywhere from GPSA, to the freebie wheels and tables, but until you you use the actual simulator by the people that manufacturer the equipment, you'll always be "close".

I'll give you an example. Run out pure propane compression on your model, then run it on the ariel compressor program with some set up. Run it at maximum frame RPM, then run it at 50% of max rpm.

Compare the sidcharge temps and HP/MMSCFD.

they don't look the same!