Page 185 - Chemical Process Equipment - Selection and Design

7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 157

EXAMPLE 73 The isentropic enthalpy change becomes
Compression Work with Variable Heat Capacity
Hydrogen sulfide heat capacity is given by 441.1
AH, = C, dT = 1098.1 cal/g mol
310.1
C, = 7.629 -1 3.431(E - 4)T t 5.809(E - 6)T2 * 1098.1(1.8)/34.08 = 58.0Btu/lb,
- 2.8:18(E - 9)T3, cal/g mol,
compared with 59.0 from Example 7.7. The integration is
with T in K. Thie gas is to be compressed from 100°F (310.9 K) and performed with Simpson's rule on a calculator.
14.7 psia to 64.7 psia. The actual final temperature will vary with the isentropic
Assuming the heat capacity to be independent of pressure in efficiency. It is found by trial from the equation
this low range, the isentropic condition is
r,
1O98.l/qs = 1 C, dT.
As = (c, / d~ - R ln(P2/Pl) 1098.1
= \ Tz (C,/T) dT - 1.9871n(64.7/14.7) = 0. Some values are
310.9
7s 1 .o 0.75 0.50 0.25
By trial, with a root-solving program, T2 441.1 482.93 564.29 J91.72

T2 = 441.1 M, 331.4"F (compared with 345°F from Example 7.7).

WORK ON NONIDEAL GASES General Method. The effects of composition of mixtures and of
pressure on key properties such as enthalpy and entropy are
The methods discussed thus far neglect the effect of pressure on deduced from PVT equations of state. This process is described in
enthalpy, entropy, and heat capacity. Although efficiencies often books on thermodynamics, for example, Reid, Prausnitz, and
are not known well enough to justify highly refined calculations, Sherwood (Properties of Liquids and Gases, McGraw-Hill, New
they may be worth doing in order to isolate the uncertainties of a York, 1977) and Walas (Phase Equilibria in ChemicaI Engineering,
design. Compressibility factors are given for example by Figure Butterworths, Stoneham, MA, 1985). Only the simplest correlations
7.29. Efficiencies must be known or estimated. of these effects will be utilized here for illustration.
For ideal gases with heat capacities dependent on temperature,
the procedure requires the isentropic final temperature to be found
Thermodynamic Diagram Method. 'When a thermodynamic by trial from
diagram is available for the substance or mixture in question, the
flow work can be found from the enthalpy change,
AS =/TT(Cp/T) dT - R ln(B,/P,)-+O, (7.43)
W = hH. (7.40)
and then the isentropic enthalpy change from
The procedure is illustrated in Example 7.7 and consists of these
steps: =a
AH=I C, dT. (7.44)
1. Proceed along the line of constant entropy from the initial
condition to the final pressure P2 and enthalpy (H2)s.
2. Evaluate the isentropic enthalpy change (AH)s = (E& -HI. The final temperature T2 is found by trial after applying a known
3. Find the actual enthalpy change as isentropic efficiency,

AN = (Ah%/qS (7.41) (7.45)
and the final enthalpy as
The fact that heat capacities usually are represented by empirical
polynomials of the third or fourth degree in temperature accounts
for the necessity of solutions of equations by trial.
Example 7.5 applies this method and checks roughly the
4. At the final condition (P2, H,) read off any other desired calculations of Example 7.7 with the thermodynamic diagram of this
properties such as temperature, entropy or specific volume. substance. The pressures are relatively low and are not expected to
generate any appreciable nonideality.
Thermodynamic diagrams are known for light hydrocarbons, This method of calculation is applied to mixtures by taking a
refrigerants, natural gas mixtures, air, and a few other common mol fraction weighted heat capacity of the mixture,
substances. Unless a substance or mixture has very many
applications, it is no's worthwhile to construct a thermodynamic c, = XiCpi. (7.46)
diagram for compression calculations but to use other equivalent
methods. When the pressure range is high or the behavior of the gas is