CHEMICAL ENGINEERING

112 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

and substituting forV 1 V 4 ,gives:

WDP 1 Vs[1CccP 2 /P 1 ^1 /

][

/

 1 ][P 2 /P 1 

^1 /

1] (equation 8.43)

D 110 , 000 ð 0. 0157  1. 4 / 0. 4 [ 10. 45 ^0.^286 1]D5781 J

The theoretical power requirementD 3 ð 5781 D 17 ,340 W or 17.3kW

The capacityD 3 ð 0. 0157 D 0 .047 m^3 /s

PROBLEM 8.4

Methane is to be compressed from atmospheric pressure to 30 MN/m^2 in four stages.
Calculate the ideal intermediate pressures and the work required per kilogram of gas.
Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on
a temperature – entropy diagram the effect of imperfect intercooling on the work done at
each stage.

Solution

The ideal intermediate pressures are obtained when the compression ratios in each stage
are equal. If the initial, intermediate, and final pressures from this compressor areP 1 ,P 2 ,
P 3 ,P 4 ,andP 5 , then:

P 2 /P 1 DP 3 /P 2 DP 4 /P 3 DP 5 /P 4 DP 5 /P 1

as in problem 8.1.

P 5 /P 1 D 30 , 000 / 101. 3 D 296. 2

and: P 5 /P 1 ^0.^25 D 4. 148

Hence: P 2 D 4. 148 P 1 D 4. 148 ð 101. 3 D420 kN/m^2

P 3 D 4. 148 P 2 D 1 .74 MN/m^2

P 4 D 4. 148 P 3 D 7 .23 MN/m^2

The work required per kilogram of gas is:

WDnP 1 V 1

 1

[(

P 5

P 1

)

 1 /n



 1

]

(equation 8.46)

For methane, the molecular massD16 kg/kmol and the specific volume at STPD
 22. 4 / 16 D 1 .40 m^3 /kg.
If D 1 .4, the work per kilogram is:
WD 4 ð 101 , 300 ð 1. 40  1. 4 / 0. 4 [ 296. 2 ^0.^4 /^4 ð^1.^4 1]
D 710 ,940 J/kg or 711 kJ/kg

The effect of imperfect cooling is shown in Figs 8a and 8b.