CHEMICAL ENGINEERING

SECTION 8

Pumping of Fluids

PROBLEM8.1

A three-stagecompressor is required to compress air from 140 kN/m^2 and 283 K to
4000 kN/m^2. Calculate the ideal intermediate pressures, the work required per kilogram of
gas, and the isothermal efficiency of the process. It may be assumed that the compression
is adiabatic and interstage cooling is provided to cool the air to the initial temperature.
Show qualitatively, by means of temperature – entropy diagrams, the effect of unequal
work distribution and imperfect intercooling, on the performance of the compressor.

Solution

It is shown in Section 8.3.4 that the work done is a minimum when the intermediate
pressuresPi 1 andPi 2 are related to the initial and final pressuresP 1 andP 2 by:

Pi 1 /P 1 DPi 2 /Pi 1 DP 2 /Pi 2 (equation 8.45)

P 1 D140 kN/m^2 andP 2 D4000 kN/m^2.

∴ P 2 /P 1 D 28. 57

∴ Pi 2 /Pi 1 DP 2 /Pi 2 D^3

p

28. 57 D 3. 057 ,

Pi 1 D428 kN/m^2 ,

and: Pi 2 D1308 kN/m^2

The specific volume of the air at the inlet is:
v 1 D 22. 4 / 29  283 / 273  101. 3 / 140 D 0 .579 m^3 /kg
Hence, for 1 kg of air, the minimum work of compression in a compressor ofn
stages is:

WDnP 1 v 1

(

 1

)[(

P 2

P 1

)

 1 /n



 1

]

(equation 8.46)

Thus: WD 3 ð 140 , 000 ð 0. 579  1. 4 / 0. 4 [ 28. 57 ^0.^4 /^3 ð^1.^4 1]D 319 ,170 J/kg

The isothermal work of compression is:

WisoDP 1 V 1 lnP 2 /P 1  (equation 8.36)

D 140 , 000 ð 0 .579 ln 28. 57 D 271 ,740 J/kg

The isothermal efficiencyD 100 ð 271 , 740 / 319 , 170 D 85 .1%

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