Page 181 - Chemical Process Equipment - Selection and Design

7.6. THEORY AND CALCULATIONS OF GAS COMPRESSION 253

Theoretical methods allow making such calculations for ideal and
real gases and gas mixtures under isothermal and frictionless
adiabatic (isentropic) conditions. In order that results for actual
operation can be found it is neecessary to know the efficiency of the
equipment. That depends on the construction of the machine, the
mode of operation, and the nature of the gas being processed. In
the last analysis such information comes from test work and its
correlation by manufacturers and other authorities. Some data are
cited in this section.
DIMENSIONLESS GROUPS
The theory of dimensionless groups of Section 7.2, Basic Relations,
also applies to fans and compressors with rotating elements, for
example, Eqs. (7.8)-(7.10) which relate flow rate, head, power,
speed, density, and diameter. Equivalent information is embodied
rU, .SPEtlFiC SPEED (CFS) in Table 7.5. The concept of specific speed, Eqs. (7.11) and (7.12),
also is pertinent. In Figures 7.21 and 7.25 it is the basis for
Figure 7.25. Efficiency and head coefficient qad as functions of identifying suitable operating ranges of various types of compressors.
specific speeds and specific diameters of various kinds of impellers
(Evans, 1979). Example: An axial propeller has an efficiency of
70% at Ns = 200 and 0, = 1.5; and 85% at N, = 400 and LIS = 0.8. IDEAL GASES
See Table 7.4 for definitions of gad, N,, and 0,. The ideal gas or a gas with an equation of state

pull a vacuum of 28in. of mercury. A two-stage unit can deliver PV = zRT (7.18)
250psig. A generous supply of lubricant is needed for the sliding
vanes. Table 7 9 shows that power requirements are favorable in is a convenient basis of comparison of work requirements for real
comparison with other rotaries. gases and sometimes yields an adequate approximation of these
Liquid-liner compressors produce an oil-free discharge of up to work requirements. Two limiting processes are isothermal and
125psig. The efficiency is relatively low, 50% or so, but high isentropic (frictionless adiabatic) flows. Changes in elevation and
enough to make them superior to steam jet ejectors for vacuum velocity heads are considered negligible here. With constant
service. The liquid absorbs the considerable heat of compression compressibility z the isothermal work is
and must be circulated and cooled, a 200HP compressor requires
v
lO0gpm of cooling water with a 10°F rise. When water vapor is w = 6 = zRT ln(p2/pl). (7.19)
dP
objectionable in the compressed gas, other sealing liquids are used;
for example, sulfuric acid for the compression of chlorine. Figure
7.19(e) shows ihe principle and Table 7.10 gives specifications of Under isentropic conditions and with constant heat capacities, the
some commercial units. pressure-volume relation is
O
l
~
7.6. THEORY AND ~ ~ L ~ OF ~GAS ~COMPRESSION ~ S PV~ = P,V~ = const, (7.20)
The main concern of this section is how to determine the work where
requirement aind the effluent conditions of a compressor for
which the inlet conditions and the outlet pressure are specified. k = C,/C, (7.21)
TABLE 7.7. Some Sizes of One- and Two-Stage Reciprocating Compressors
(a) Horizontal, One-Stage, Belt-Driven
~~~
Diameter Brake Openings (in.)
Cylinder Stroke Displacement Air Pressure HP at Rated
(in.) (in.) (cuft/min.) rpm (Ib/sq in.) Pressure Inlet Outlet
74 6 106 310 80-100-125 15.9-17-1 8 2; 23
B
8, 9 170 300 80-100-125 25-27-29 3 3
IO 10 250 285 80-100-125 36-38.5-41 3; 3;
71 12 350 270 80-100-125 51-57-60 - 4
sf 6 136 350 40-60 1 5-1 8.5 - 3
10 9 245 300 40-75 27-34 3; 3;
11 10 312 285 40-75 34-43 4 4
13 12 495 270 40-75 54-70 5 5
42 9 350 300 20-45 30-42 4 4
83 10 435 285 30-45 42-52 6 6
45 12 660 270 30-50 59-74 7 7

(Worthington Corp.).