Page 99 - Chemical engineering design

82
The work produced (or required) is given by the general expression (see Volume 1,
Chapter 8): CHEMICAL ENGINEERING
n 1 /n n 1 /n
n P 2 RT 1 n P 2
W D P 1 v 1 1 D Z 1 3.31
n 1 P 1 M n 1 P 1
where Z D compressibility factor (1 for an ideal gas),
1
R D universal gas constant, 8.314 JK 1 mol ,
T 1 D inlet temperature, K,
M D molecular mass (weight) of gas,
W D work done, J/kg.
The value of n will depend on the design and operation of the machine.
The energy required to compress a gas, or the energy obtained from expansion, can be
estimated by calculating the ideal work and applying a suitable efficiency value. For recip-
rocating compressors the isentropic work is normally used (n D )(seeFigure3.7); and
for centrifugal or axial machines the polytropic work (see Figure 3.6 and Section 3.13.2).

3.13.1. Mollier diagrams

If a Mollier diagram (enthalpy-pressure-temperature-entropy) is available for the working
fluid the isentropic work can be easily calculated.

W D H 1 H 2 3.32
where H 1 is the specific enthalpy at the pressure and temperature corresponding to
point 1, the initial gas conditions,
H 2 is the specific enthalpy corresponding to point 2, the final gas condition.
Point 2 is found from point 1 by tracing a path (line) of constant entropy on the diagram.
The method is illustrated in Example 3.10.

Example 3.10

Methane is compressed from 1 bar and 290 K to 10 bar. If the isentropic efficiency is 0.85,
calculate the energy required to compress 10,000 kg/h. Estimate the exit gas temperature.

Solution

From the Mollier diagram, shown diagrammatically in Figure 3.5
H 1 D 4500 cal/mol,
H 2 D 6200 cal/mol (isentropic path),

Isentropic work D 6200 4500
D 1700 cal/mol