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1
0.9
L/V minimum
0.8
0.7
pinch
0.6
0.5
0.4
0.3
0.2
0.1
0
x
b
x
d
z
f
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x, mole fraction liquid
Figure 11.3
Minimum reflux.
to the feed line/
q
-line intersection, as shown in Figure 11.3. If the equilibrium curve
has an unusual shape, as in a methanol-water system, a different pinch point may be
located, as shown in Figure 11.4. A rule of thumb commonly used for the design of
distillation columns is that the operating reflux should be between 1.25 and 2.0 times
the minimum. An estimate of the minimum number of stages required, which occurs
at total reflux, is shown in Figure 11.5.
If a sidestream is required, a third operating line is introduced, as shown in
Figure 11.6. This operating line starts at the feed/
q
-line intersection and has a slope
L
/V
. After determining the operating reflux ratio, a McCabe-Thiele diagram can
be constructed and theoretical stages stepped off as described above. A detailed
McCabe-Thiele example follows.
11.3 A THREE-PRODUCT DISTILLATION EXAMPLE
A 20 mol % ethanol-water solution is to be distilled. Two products, 80 mol % and
40 mol %, are required. The feed is available as a saturated liquid. The composition
of the bottom product should not exceed 0.25 mol % ethanol. The external reflux ratio
is to be four times the minimum. The shape of the equilibrium curve necessitates a
relatively high reflux ratio, The sidestream draw-off is 10 lbmol/hr. Using a basis of
100 lbmol/hr, determine the number of theoretical stages required, the feed location,
the sidestream location, and the quantities of the products. The experimental data of
Kirschbaum and Gerstner (1939) are to be used.
The data are plotted in Figure 11.7, as is the minimum
L
/
V
of 0.5, which corresponds
to a minimum external reflux ratio
L
/
D
of 1.0. The enriching section operating line's
