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218 Chapter 5

10 i l l

Isothermal Compression

Second-stage Adiabatic Compression

I i I i i i l i i t
0 24 6 8 10 12 14 16
Specific Volume of Gas

Figure 5.17 The effect of operating mode on compressor work.

phase separator after the condenser to separate the gas from the liquid. The total
work of compression is equal to the sum of the work for each stage of compres-
sion. Assuming that the compressed gases are cooled to the inlet temperature of
the compressor after each stage, we can use Equation 5.18 for each stage. If it is
also assumed that the pressure drop across intercoolers, phase separators, and
piping is negligible, then the total compressor work,
n
zRTi [ f P 2 Y ~ 1
Wp = ————— | | ———| + ..... (5.24)
(n-l)/n L IP, )

where z is the average of the inlet and discharge compressibility factors.
Because the work of compression should be a minimum, differentiate
Equation 5.24 with respect to P, and then set the derivative equal to zero.
2

1
5W P p 3
(5.25)
5P 2 P 2 J
Next, solve for the pressure ratio for the first stage, P/Pi.
2

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