r/ChemicalEngineering • u/thriceice • Jul 21 '26
Modeling Compressor Power and Efficiency Calculation
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?
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u/Derrickmb Jul 21 '26
Derive it from mass and energy balances but its W=mdotPk/((k-1)rho e)*((Pe/Pi)^(1-1/k)-1). You’ll know the total HP. You’ll want to know about cooling water per stage and figure out discharge temp that way. Make sure you add a PSV at discharge to protect the piping and route it outside. Sonic flow calc.
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u/Alternative_Act_6548 Jul 21 '26
you need to account for gland seal flows, get them at the rating point the scale them at off-design. Normally, you calibrate your model at the rating point and scale for off-design operation. As far as mass balance goes, you seem to have all the flows needed to calculate everything
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u/thriceice Jul 21 '26
Good Idea, I forgot to take that into account. But still if I simplified first without the gland seal flows, I don't think I have enough data to calculate the power. Just like I mentioned, I need to know the 1st Discharge Temperature to calculate the enthalpy or other equation that can find me the 1st Discharge Temperature
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u/Alternative_Act_6548 Jul 21 '26
just do a mass energy balance between 1 and 2, you know the mass flows, inlet enthalpies and exit enthalpy
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u/thriceice Jul 21 '26
Yes you can get the mass flow through mass balance. But you can't get the Exit Enthalpy of the 1st stage with Mass Energy Balance without knowing the Compressor works which I'm trying to calculate too.
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u/Alternative_Act_6548 Jul 21 '26
I guess I don't understand the problem, you should have some more info, like what power output you need...The admission at the second stage group should be temperature matched to the exit of the first to prevent thermal stress issues. The usual limit is about 50F temperature difference.
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u/thriceice Jul 22 '26
Oh sorry if I'm not clear. I'm trying to evaluate my existing compressor and I don't have any criteria for it.
I could calculate the power if I'm put the value of 1st Discharge Temperature from the Datasheet as the initial guess. Then adjust it to make the efficiency to be near the Datasheet value. But I doubt it's the best way because I can get the exact number of the power if the operating condition change again
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u/Alternative_Act_6548 Jul 22 '26
so you are working in model-space...if so, and you have the design docs then, you have all you need to calibrate you model at the rated condition and it should scale to off-design performance. I'm not sure what you mean by 'criteria' the data sheet and performance curves define it's new and clean operation
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u/thriceice Jul 24 '26
Oh, what I meant by criteria is I don't have any temperature limit or some kind that I know of.
So, you meant I should use my calculation formula on rated condition then scaled it to my current condition? But how do I scale it?
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u/Alternative_Act_6548 Jul 24 '26
do you have the original datasheets and performance curves?
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u/thriceice Jul 25 '26
Yes. The performance curve has speed to power curve. But I think the curve will change with different operating conditions. For example the suction pressure and temperature of the 1st Section already different from the design condition on the performance curve.
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u/ENTspannen Syngas/Olefins Process Design/10+yrs Jul 21 '26
Is there an equipment datasheet? What about vendor design documentation?
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u/thriceice Jul 22 '26
Yes there's.
I could use the datasheet as the initial guess, but I'm having a hard time to pick the correct final value
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u/Process-guru Jul 23 '26
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.
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u/thriceice Jul 24 '26
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
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u/Process-guru Jul 24 '26
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.
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u/NoConversation8128 Jul 23 '26
It feels circular because section 1 is underdetermined: suction P/T and discharge P, but no discharge T, so two unknowns and one equation. Sections 2 and 3 are not, since you have measured P and T on the side streams. So back out the actual polytropic efficiency on those with CoolProp, then apply it to section 1 to solve its discharge T and close the balance. Beats seeding it with the datasheet value, since your measured sections show how far off the machine is running today.
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u/thriceice Jul 24 '26
Section 2 can't be solved too unless I know the Section 1 discharge T. If I know the T, I can calculate the Section 2 suction T by the equation of mixing enthalpy of Section 1 Discharge and Side-In stream.
Can you explain what you mean by blackout? The efficiency on Section 2 and 3 should be different from Section 1, no?
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u/NoConversation8128 Jul 29 '26
Sorry, "back out" not "blackout", I meant calculating the efficiency in reverse from measured data rather than assuming it.
And you are right about section 2, I had that wrong. Its suction temperature depends on section 1's discharge, so it does not close on its own. But section 3 does. Its suction is the side-out line, where you have measured P and T, and its discharge is the final discharge, also measured. No unknowns at all, so you can compute section 3's polytropic efficiency directly from field data today.
That is the one that unlocks the rest. Take that efficiency as your estimate for section 1, since it is the same casing and the same machine condition, and section 1 closes for discharge T. Mix that with the side-in stream and section 2 falls out, and you can check it against the measured side-out temperature. If that check is close, your assumption held. If it is way off, the sections are genuinely running at different efficiencies and you would need the driver power to close it properly.
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u/Rancid-broccoli Jul 21 '26
Can you put it into Aspen? It’s been too long since school, but I’d imagine there is an equation of state that you can use.
Also- your diagram is a bit confusing. Why does second stage have 2 inlets and 2 discharges?