Page 238 - Chemical process engineering design and economics

Compressors, Pumps, and Turbines 219

— = — (5.26)
Pi P 2
Similarly, after differentiating Equation 5.24 with respect to P, and setting
3
the derivative equal to zero, the pressure ratio for the second stage,

P 3 P 4
— = — (5.27)
P 2 Pa
Therefore,

P 2 PB P 4 PN
—• ——
— - — — — - — (p.zo;
—
7K\
d
—
Pi P 2 PS PN-I
Thus, the pressure ratio for each stage should be equal to obtain the mini-
mum work of compression. Then, the pressure ratio for each stage,
P , fp Y / N
S+
D
——— = — I (5.29)
PS U, )
Next, consider the case where the pressure drop across the intercooler and
connecting piping is significant. If the gas requires cooling between stages, the
pressure drop across the cooler, separator, and piping can be approximated by AP
= 0.1 PD°'? for centrifugal compressors except when compressing air [58], where
O?
P D is the discharge pressure for a stage. For air compressors AP = 0.05 PD [58],
and for reciprocating compressors AP = 0.3 P D ° 7 [58]. Now, we can develop a
procedure for calculating the compressor work if intercooling is necessary.
Assuming a two stage compressor, the pressure at the inlet of the second
7
stage is P 3 = P 2-0.1 P 2°' .
n /n
n i)/n
ZRT, rfp v - ( p 4 v -° i
2
W P = ————— II — I + 1 ———————— +•••••• (5.30)
0 7
(n-l)/n L l?i ) lP 2 -0.1P 2 ' ) J
Let 6 = (n - l)/n and then differentiate Equation 5.30 with respect to P 2. Then, set
the derivative equal to zero to obtain the minimum work of compression. Thus.

3
(l-0.07P 2 -°- )
7 2
P, Ip -o.ip 2 a7 j L (p -o.ip °- ) J
2
2
2
(5.31)
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