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# Question about absorbed energy calculation of cooling discharge air

## Question about absorbed energy calculation of cooling discharge air

(OP)
I haven't took any courses about fluid mechanics before. Currently I have a question about compressor power & calculation of cooling discharge air.

The situation is like that:
For a one stage rotary compressor

Changes of state P2/P1 = (V1/V2)k = (T2/T1)k-1/k
Power P, kW {(k / k - 1)* P1*100000*Q1*[ (P2/P1)(k - 1/k) - 1 ]}/1000

Inlet Air is 20°C, 101 kPaa, 3700 m3/hr or 1.03 m3/s
Discharge Pressure is 790 kPaa

Per the adiabatic compression of air, the calculated results show: Discharge Temp is 256°C, the power of the compressor is 290 KW.
k P1, barA P2, barA T1, °C T1, K Q1, m3/s P, kW T2, K T2, °C
1.4 1 7.9 20 293.15 1.03 290.18 529.12 255.97

As there is a heat exchanger within the compressor kit to cool the discharge air to 20°C, I need to calculate how much cooling water is needed per hour. But interestingly, I found if I cool the air to 20°C, the absorbed power is:
Air density * air volume * Specific Heat of air * delta T == 1.2041 kg/m3 * 1.03 m3/s * 1.005 kJ/kg.K * 236K == 294 kJ/s ==294 kW

It is same as the power of the compressor....

I think I definitely have something wrong, as after cooling the discharge air to 20°C, the air pressure is still supposed to be 790 kPaa, the absorbed energy by the cooling water shouldn't be 294 kW.

Can anybody briefly told me where I am wrong in the 2nd part of the calculation and how to fix it? Thanks.

MSc. Mechanical Engineering;
4 years EPC experience;
Oil & Gas industry in Canada.

### RE: Question about absorbed energy calculation of cooling discharge air

A masters in Mechanical Engineering without having took any fluids courses? That seems odd. Did you skip the thermodynamics part of the curriculum too?

The format of the data you provided is very difficult to work with, but it looks like you are doing about 7.9 compression ratios. To get that kind of temperature on the discharge I would probably rule out an oil flooded screw, and any dry rotary equipment would fail long before reaching 256C (nearly 500F). Something is not computing here.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

### RE: Question about absorbed energy calculation of cooling discharge air

(OP)
Thanks. But still not very clear where the mistake of my calculation is.

Back in my country, the mechanical engineering at colleges are classified as mechanical design & manufacture engineering and Process Equipment & Control Engineering. The 1st one which I took mainly focus on design and manufacturing process and methods. I found I have a few important General courses missing after years which I need to learn them by myself now.

MSc. Mechanical Engineering;
4 years EPC experience;
Oil & Gas industry in Canada.

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