Page 102 - Coulson Richardson's Chemical Engineering Vol.6 Chemical Engineering Design 4th Edition

for use in equation 3.31; and a polytropic temperature exponent m for use in the following
equation: FUNDAMENTALS OF ENERGY BALANCES 85
m

P 2
T 2 D T 1 3.35
P 1
ZR 1
where m D C X for compression, 3.36
C p E p
ZR
m D E p C X for expansion 3.37
C p
E p is the polytropic efficiency, defined by:
polytropic work
for compression E p D
actual work required
actual work obtained
for expansion E p D
polytropic work
An estimate of E p can be obtained from Figure 3.6.
1
n D 3.38
Y m 1 C X
At conditions well removed from the critical conditions equations 3.36, 3.37 and 3.38
reduce to:
1
m D 3.36a
E p
1 E p
m D 3.37a

1
n D 3.38a
1 m
These expressions can be used to calculate the polytropic work and outlet temperature
by substitution in equations 3.31 and 3.35. They can also be used to make a first estimate
of T 2 in order to estimate the mean reduced temperature for use with Figures 3.9 and 3.10.
The use of Schultz’s method is illustrated in Examples 3.11 and 3.16.

Example 3.11
Ž
Estimate the power required to compress 5000 kmol/h of HCl at 5 bar, 15 C, to 15 bar.

Solution
For HCl, P c D 82 bar, T c D 324.6K
2
6 2
3
9
Ž
C D 30.30 0.72 ð 10 T C 12.5 ð 10 T 3.9 ð 10 T kJ/kmol K
p
Estimate T 2 from equations 3.35 and 3.36a.
For diatomic gases ' 1.4.
C p C p
Note: could be estimated from the relationship D D
C v C p R