Polytropic efficiency for two compressors in parallel

[rafcu]

I am looking for calculating the overall polytropic efficiency for of two compressors in parallel.

I have the performance map from the supplier for both compressors with the polytropic head depending on the flow rate; the speed and the efficiency are also represented.

But for two different speeds with the compressor running in parallel, I wonder how calculated the overall efficiency if I have for example 78% for one compressor and 82% for second one. What is the overall efficiency?

regards,

Rafcu

 

[DickRussell]

I guess that would depend on your definition of "overall efficiency." If by that you mean the efficiency of a single machine that took the combined feeds and produced the combined discharge flows, then you could calculate that with any simulator by doing the two compressors separately, each with its own efficiency, mixing the discharges, and finally doing a third compressor calculation with efficiency varied until the discharge temperature matches that of the mixed discharge stream previously calculated.

 

[Montemayor]

Just what type of compressor(s) are we supposed to be talking about?

Nowhere does this thread mention what type of compressor(s) are being discussed. This is not the first engineer who assumes that every compressor in the world is a centrifugal. It just so happens that Polytropic efficiency is normally only attributed to centrifugals - but is everyone supposed to know that?

This is analogous to giving temperature readings as "degrees" without mentioning anything about which scale. Or how about discussing automobile engines without revealing that the engine in question is not a "clunker", but really a Mazda rotary?

 

[rafcu]

I have a performance curve of one stage centrifugal compressor. On this curve it is represented the pressure against the volume flow rate with the different speeds and the different efficiencies. This curve is for one compressor, I can obtain the curve for both compressors working in parallel: flow and pressures, but I do not know how obtain the efficiencies of both together. I do not ask to the supplier because they want more money…

How obtain the new efficiency to the group, knowing that I have just the curve and the table associated no polynomial models are available from the constructor.

Thanks,

 

[pmover]

re-iterating DickRussell's comment - what is your definition of "overall efficiency?" frankly, i do not know of any justification in determining "overall efficiency" for 2 centrifugal compressors in parallel operating mode. i can certainly understand why mfg wants more money for something that is likely difficult to provide.

if A compressor operates at X% and B compressor operates at X +/- 5%, i know of no known mathematical formula to determine "overall efficiency". the results for efficiency simply state how well the compressor is performing.

i would further ask you for the purpose/justification in wanting "overall efficiency". perhaps an explanation may be helpful . . .

now, if you want both centrifugal compressors operating at same efficiency, then that is a control system matter and can be address/handled as such.

goodl uck!
-pmover

 

[MariusChE]

The performance curves will not help you much; unless you have data set that fits exactly. Is it turbine- or electrically driven? Measure T1 and T2,i (i = 1 to n). Measure the amps on both. You can now calculate the mass flow and polytropic efficiency of each. The overall efficiency is the weighted average.

 

[MichaelPn]

I would suggest little bit more formal approach. Polytropic
efficiency for centrifugal compressor is defined as a
e=Wp/(Hs-Hd), where Wp is "net reversible process mechanical energy input"; Hs and Hp - enthalpy on the suction and discharge correspondingly. That's why I agree with DickRussell that you can talk about "overall efficiency" only if there are a junctions between the suction (s) and discharge (d) lines, may be drams or something like that. Then you can determine the polytropic
efficiency between those points or, more formal, for the "path of constant efficiency" between s and d points. You need to calculate temperatures in these points, Ts and Td. Discharge temperatures for each compressor you can calculate using given compressor maps and then calculate the temperature of mix flow. Suction and discharge pressures for both compressors are probably equal. So, you know Ts, Ps, Td, and Pd. Now you can calculate the polytropic efficiency. Easy way for ideal gas is e=(k-1)/k * ln(Pd/Ps) / ln (Td/Ts). Hard way for real gas - use the eq. e= v* dP/dH, where v is specific volume; solve it iteratively to find the efficiency. Or you can use method from PTC-10.
I used the article:
Journal of Engineering for Power; Vol 84; January 1962; J.M. Schultz; "The Polytropic Analysis of Centrifugal Compressors"