Page 239 - Chemical process engineering design and economics

220 Chapter 5

Multiply both sides of Equation 5.31 by P and rearrange the result to obtain
2

0 3
f P 2 V ( P 4 V 1-0.07P 2- '
a7
(Pi) ( P 2 -0.1P 2 ) 1-0.1P 2 ~ 03

Because

1-0.07P 2" 03
———————— « ! (5.33)
1-0.1P 2~°" 3

we find for the first stage that

— = ———————— (5-34)
PI P 2 -0.1P 2 a7

Also, the pressure at the inlet to the second stage is given by P 3 = P 2 - 0.1
7
P 2°- .Thus,P 2/Pi=P 4/P 3.
Similarly, for the third stage,

P 4 P 6
—- = ——————— (5.35)
P 4 -0.1P 4 °' 7
P 3
7
and the pressure at the inlet to the third stage is given by PS = P 4 - 0.1 P 4 °' . Thus,
P/P = Pe/Ps- Because P * P and P ^ P etc., the pressure ratio across any stage
4 3 2 3 4 5
and across the entire compressor are not simply related to the number of stages as
given by Equation 5.29.
The maximum allowed temperature determines the number of intercoolers.
This limit is determined by the stability of seals, lubricants, and other materials
that contact the gas. The gas temperature may have to be even lower than this
limit if the gases are corrosive; undergo chemical reactions at high temperatures,
possibly exploding; or react with the lubricating oil. High compressor operating
temperatures lead to high power consumption and may promote polymerization of
gases such as ethylene, acetylene and butadiene. In this case, the gas temperature
should be limited to 107 °C (225 °F) [2] If the stability of the materials are the only
constraint, then use the temperature limits listed in Table 5.4. If the discharge
temperature exceeds this limit, then the pressure ratio across a stage must be re-
duced. Ulrich [23] recommends that the temperature be no greater than 200 °C

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