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# Efficiency of a centrifugal compressor with 2 suction stages and 1 discharge

## Efficiency of a centrifugal compressor with 2 suction stages and 1 discharge

(OP)
Hi y'all,

I'm normally a fixed equipment guy (piping and vessels) but I've got a new role now, so apologies in advance for any ignorance I display.

I have a centrifugal compressor with 2 suction stages and 1 discharge stage. One shaft, one case, 3 impellers per suction stage. I have been asked to calculate and trend efficiency to monitor the performance of the machine. The 1st stage and 2nd stage suction are the same products but the 2nd stage is at a slightly higher temperature and pressure. So far I have calculated isentropic efficiency (using Mark's Standard Handbook for MEs) from 1st stage suction to the discharge, completely discounting the 2nd stage. In order to trend the performance, would that be "good enough?" Is it even correct to calculate the efficiency from 1st stage to discharge? Would the intermediate temperature and pressure in the compressor be required in the efficiency calculation? If so, how would I do that? Would it be possible using the 2nd stage suction pressure and temperature? The only data points I can pull are temperature and pressure of the 1st stage suction piping, 2nd stage suction piping, and discharge piping. I do not have temperature and pressure at the end of the 1st stage going into the 2nd stage inside the compressor casing.

Also to note, I need to do something similar for another compressor that has 3 suction stages and 1 discharge stage.

Thanks in advance. Let me know if there are any clarifications I can make.

### RE: Efficiency of a centrifugal compressor with 2 suction stages and 1 discharge

Look into ASME PTC-10 for a method.

since the compressor is existing, investigate the documentation from the mfg could be beneficial. if none exist, contact the mfg for their assistance. they will be glad to help you with which method, isentropic/polytropic, is best. this is best as you can compare original test data, if the data exists, with current conditions.

another method, with gas composition, P,& T at each section/stage and using an equation of state, the efficiency can be determined.

not sure what is meant by "3 suction stages and 1 discharge stage"; i would guess you meant to state 3 suction nozzles (3 different streams) and a single discharge nozzle (a single outlet stream)?

good luck.

### RE: Efficiency of a centrifugal compressor with 2 suction stages and 1 discharge

not sure what is meant by "3 suction stages and 1 discharge stage"

I am not sure either but I think you have a side stream application. Terminology you have used (suction stages) is not appropriate I believe.
On the first machine, I think you what you have is a single casing with straight-through arrangement and an injection stream.
That would explain the two suction nozzles with one final discharge. In this case you would have two sections as follows:

section #1: 1st inlet -> injection stream
section #2: injection stream -> discharge

In general you do not measure the "internal" pressures and temperatures. I am just surprised that you do not mention Delta P flow meters on main suction and injection streams (?). The injection stream should have an injection pressure slightly above the discharge pressure of the 1st stage (that is to permit the injection process). In regard to temperatures (1st stage discharge and injection stream) there should be some mixing that occurs (You may want to check if you have a lateral tangential or radial injection). The manufacturer states the intermediate condition in the datasheet and maps, so you have a reference case. This is what you need to use to figure out a mixing model (energy balance formula).

You would also be better off if you use a software package for the calculation, especially if you are dealing with offdesign conditions. I could recommend some if you wish.

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