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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 |

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

P_{is} = 2.31*(k/(k-1))*(T_{dis}-T_{suct})/M*Q_{m}

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.

With :

P_{is}=Power (kW)

T_{suct}=Temperature inlet compressor (K)

T_{discharge}=Temperature outlet compressor (K)

M=Molar weight of gas (g/mol)

Q_{m}=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 T_{discharge}
can be determined thanks to an abacus or by calculation, for an
isentropic compression, please
have a look to this page.

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- 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.

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 :

In this case T_{discharge} =
(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 : P_{is} =
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.

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