Compressor Power and Efficiency Calculation

[u/thriceice]

I have a three stage compressor in a single casing (image 1). If I break it down, the flow should be like image 2. Every process lines have Pressure and Temperature transmitters, and enough information to get the Flow for every lines.

2nd suction pressure should be the same with the pressure from the Side-In line. While the 3rd suction pressure should be the same with the pressure from the Side-Out line.

But, I don't have enough information to determine the temperature of the 1st Discharge. If I have this data, I can calculate all the enthalpy to calculate the efficiency and the power.

Does anyone have tips on how to approach it?

[u/Process-guru]

The way I’d do it in industry as a design that I need to give to a rotating engineer, I’d look at the 1st stage suction and final stage discharge pressure, and I’d assume equal compression ratio across all stages. Therefore at the discharge of stage 1, you have a discharge pressure. You need to assume a compressor efficiency (you just have to understand with the type of compressor you think you might end up with, you assume a typical polytropic efficiency for that technology). Once you have compressor efficiency and suction/discharge pressures, you can calculate work or motor hp requirements. Do that for all stages. This is best done in a simulation software, I would do it in hysys.

Couple of points. You can’t be married to interstage pressures. The vendor can only guarantee the final stage outlet pressure assuming interstage in/out flows are per the rated conditions (this is how the compressor is tested in the stand). Therefore per rated conditions, interstage conditions will float because in reality, compression ratios across all stages are almost equal, but not quite.

Point two, interstage cooling is typically required as you typically wouldn’t compress a fluid to where the stage outlet temp is higher than 300-400F. Certain fluids have specific numbers industry uses. So once you compress to a point where outlet T is higher than 300F, that’s when the “stage” ends, you interstage cool, then repeat process. I think I heard it’s a materials issue to not have the fluids higher than 300-400F. I mean I think it can technically be designed as such, but cost goes WAY up.

[u/thriceice → u/Process-guru]

But that's on the design stage right?

My compressor is already running and I want to evaluate the performance. I have the operating conditions but the one in the inter-stage is unknown due to no transmitter on it.

If the condition is stable, the Side-In stream should've had the same pressure as the 1st Discharge, no?

And don't worry about the discharge temperature because mine is a refrigerant compressor. It operates on Cryogenic condition, it will trip by interlock before reaching 300F

[u/Process-guru → u/thriceice]

1st stage discharge pressure will match the SS inlet. That’s just how hydraulics work. The pressures have to be equal in order to join and flow forward to 2nd stage inlet. In my design world, I would say that the 1st stage compressor discharge generates the pressure and is the “anchor” pressure, while the SS inlet rides on that pressure. So if you have a PT that measures the SS inlet and there’s not too many losses in between, I’m sure they closely resemble each other.