Page 231 - Chemical process engineering design and economics

Compressors, Pumps, and Turbines 213

Then, for a real gas the isentropic work of compression is approximated by
k iyk
ZRT, rfp Y - i
2
W s = ————— II —— I - 1 I (5.12)

where z is taken as an average of the inlet and discharge compressibility factors.
To obtain the actual work of compressing a gas, W A, divide the isentropic
work by an isentropic efficiency.

W s
W A = —— (5.13)

Equation 5.9 cannot be use to obtain the gas-discharge temperature for a real
compression because it was derived for an isentropic compression. Instead, use
the macroscopic energy balance which applies for any process. Thus,

(5.14)
Ah = c P (T 2 -T,)=W A
where it is assumed that CP is a constant.

Polytropic Compression

When adiabatic conditions are not attained, the process is called a polytropic
change of state. Such a change of state is described by the Equation 5.15.

n
P V = a constant (5.15)
Thus,

PV" = PiV! n (5.16)

The exponent n depends on the amount of cooling, mechanical friction, and fluid
friction during compression. It is determined experimentally for any particular
compressor. By integrating Equation 5.8 over a polytropic path, using Equation
5.16, it can be shown that the polytropic work of compression for an ideal gas,
n i)/n
rrp v - i
2
W P = ————— M —— I - 1 I (5.17)
(n-l)/n K Pj J

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