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Compressor power requirement

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Section summary
1. Formula to calculate the compressor power required
2. Usual values for calculation
3. Example of calculation
4. Compressor power free Excel calculation tool

1. Formula : compressor power calculation

For 1 compressor stage, the isentropic compression is the following :

Pis = 2.31*(k/(k-1))*(Tdis-Tsuct)/M*Qm


Calculation of power required for a compressor

A compression is said isentropic when it is carried out by an ideal compressor, without friction, without internal leakage and while being perfectly insulated. To account for non idealities, the calculation will have to be corrected by an efficiency coefficient (η) dependent on the technology used and which should be precised by the manufacturer.

Compressor power requirement calculation

With :

Pis=Power (kW)
Tsuct=Temperature inlet compressor (K)
Tdischarge=Temperature outlet compressor (K)
M=Molar weight of gas (g/mol)
Qm=Compressor throughput (t/h)
k=Gas isentropic coefficient

One will note that a key unknown in the equation above is the discharge temperature. The discharge temperature Tdischarge can be determined thanks to an abacus or by calculation, for an isentropic compression, please have a look to this page.

2. Usual values for calculations

  • For air k=1.4
  • Reciprocating compressor high compression rate η=0.75
  • Reciprocating compressor low compression rate η=0.75
  • Rotary compressors η=0.7

Centrifugal compressors : η is calculated from the polytropic efficiency given by the manufacturer. A chart is then used to calculate the polytropic coefficient of the gas, then the discharge temperature calculated and then the actual power needed thanks to the formula above.

3. Example of calculation of the compression power

A compressor has to deliver 2000 Nm3/h of air at 6 bar g, from air at atmospheric pressure and 20°c. The efficiency of the compressor is known and is 0.72.

Step 1 : calculate the mass flow rate

The compressor is to deliver 2000 Nm3/h of air. Normal conditions are here defined as 101325 Pa and 0°c [1], at this pressure gas ideality is mostly verified thus the specific gravity is PM/RT/1000 = 1.294 kg/m3. This gives a mass flowrate of 2000*1.294 = 2587 kg/h.

STEP 2 : calculate the discharge temperature

The discharge temperature for an isentropic compression can be calculated with :

Calculation Temperarure Elevation in Compressor

In this case Tdischarge = (20+273.15)*((101325+6*100000)/101325)^((1.4-1)/1.4) = 509.5 K

Which gives 509.5 - 273.15 = 236.4c

STEP 3 : calculate the isentropic power requirement

Use the formula given above : Pis = 2.31*1.4/(1.4-1)*(236.4-20)/29*2587 / 1000 = 156 kW

STEP 4 : calculate the actual power requirement

The efficiency of the compressor must be taken into consideration and is equal to 0.72 which gives a required power of 156*0.72 = 216.8 kW.


Note : for a centrifugal compressor, the same calculation is done as above, but the isentropic coefficient is replaced by a polytropic coefficient that can be found on charts, knowing the gas isentropic coefficient and the compressor polytropic coefficient as given by the manufacturer

4. Free Excel calculation tool

You can access a free Excel calculation tool to make the compressor power calculation explained above : Compressor Power Calculator


Source
[1] https://en.wikipedia.org/wiki/Standard_cubic_feet_per_minute