How to calculate compressor discharge temperature by hand? 1

[roteng518]

Hi,

I came across a problem when calculating the compressor discharge temperature. When using the GPSA databook to calculate a single stage centrifugal compressor discharge temperature, the result is much higher than that we gained using the simulation software ProII or a compressor sizing program.

The formula in the GASP is:

T2=T1(P2/P1)^[(n-1)/n]
(n-1)/n=(k-1)/(k*Eta)
Eta - Polytropic efficiency

Who knows how to estimate the centrifugal compressor's discharge temperature? What is the actual formula most vendors use?

What is limitation of the formula in GASP databook?

Thanks.

 

[zdas04]

I've never had much luck with the simple multiplier approach to determining the polytropic coefficient. I've only been able to make it work with experimental values for "n" (and even then it seems to have starting temp ranges where it works better than others).

David

 

[dcasto]

TD = (TS + 460!) * ((Ratio ^ CON - 1!) * C1P10 * (1.0 + .078 / (R - .793)) + 1.0) - 460

C1P10 = 1.10675

CON = (VN - 1!) / VN

VN = e^(.35 - .188 * SPGR)

SPGR = specific gravity of the mostly hydrocarbon gas.

Ratio = Pd/Ps pressure discharge/pressure suction in absolute

TD & TS are temperatures in degrees F

 

[roteng518]

Hi DCASTO,

Where is your formula coming from? Can you please let me know the book or references?

 

[dcasto]

Mostly from 1970's Oil and Gas Journal an Hydrocarbon Engineering articles. I used these equations in my copyrighted program called SUPRC.

 

[Hippo]

I just performed this calc today, and the GPSA calculated discharge temperature was within 5 degrees of the vendor supplied discharge temperature. Hysys was also within 5 degrees. The vendor number was higher in both cases. I'm surprised you are getting a much higher number.

If you post the info, I can double check the numbers.

Mark

 

[roteng518]

I just found why this difference was happened. Although the calculation of the discharge pressure (polytropic process) in GPSA data book does not indicate the limitation of the equation, there is actually a limitation applied, which is the pressure ratio P2/p1 < 1.15. This means the GPSA equation is only suitable for lower pressure ratio <1.15 compressor. The higher the pressure ratio, the bigger the errors.

In my application, the pressure ratio is 4.6. This means that the GPSA equation will not work precisely. The simulation software like ProII or Hysis and my compressor software give more accurate result.

I don't know other limitation of the GPSA equation. Please comments if you have.

Hippo, is your pressure ratio near 1.15?

Frank

 

[Hippo]

I was around a 2.3 compression ratio. I wouldn't think the error would be too large, otherwise it would have likely had been noted in GPSA. I'm speculating obviously, but I just wouldn't expect the answer to be too different.

Mark

 

[dcasto]

Which equation in the GPSA data book? Eq 13-18 or 13-31? In older books I remeber they use to have curves for HP and discharge temperatures for reciprocation compressors.

What we tend to forget about is valve loss ends up in the equation for discharge temp. We try to simulate this loss as polytropic efficiency. Then when we do an anlysis of calculated versus observed we get excited when the calcs say 275 Degrees and the Observed is 280 degrees, this is less than 1% error (remember, use absolute temperatures).

I've attached some sample Td calcs from all sources posted here.

 

[tgmcg]

An isentropic efficiency of about 85% works well for most applications when calculating discharge temperature and gas power.

 

[tgmcg]

I'm sorry. Somehow I got the idea we were talking recip compressors, for which 85% is a good number. I've got recips on the brain these days.....

However, for centrifs it's a different case entirely. For lower flow higher ratio machines I'd use a polytropic efficiency on the order of 68-73%. The narrower the impellers, the lower the efficiency. The older the design (ie. 2D wheels) the lower the efficiency...that is, closer to the 68% number.

For higher flow, lower ratio machines, then I'd be looking at 76-82% polytropic ifficiency, the same qualifies applying as before re: impeller vintage and passage width.

Your best bet is to obtain the PTC-10 based performnace curves for the compressor, which should include a plot of efficiency vs speed and volumetric flow. And then subtract 3-4 percentage points for laby wear.

One well known manufacturer boasts polytropic efficiencies in the low 80's. However, these efficiencies fall off 5-7% in service to normal laby wear...they fall off further than you would expect an older design machine with lower initial efficiency to fall off. I'd recommend caution when using their as-new efficiencies for economic analysis.