|1. Formula to
calculate the compressor power required
|2. Usual values for
|3. Example of calculation
|4. Compressor power free Excel
For 1 compressor stage, the isentropic compression is the following :
Pis = 2.31*(k/(k-1))*(Tdis-Tsuct)/M*Qm
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.
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.
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.
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 , 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 :
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 =
You can access a free Excel calculation tool to make the compressor power calculation explained above : Compressor Power Calculator