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In-Depth Information
1
equilibrium curve
0.9
0.8
stripping section
oper
a
ting line
0.7
L
x
B
x
b
y
=
-
V
V
enriching section
operating line
0.6
L
x
D
x
D
y
=
+
0.5
V
V
0.4
c-line
q
z
f
y
=
x
-
q
- 1
q
- 1
0.3
0.2
0.1
0
x
b
z
f
x
d
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 11.2
McCabe-Thiele diagram.
An overview of the method is given with reference to Figure 11.2, the
McCabe-Thiele diagram. The coordinates are the vapor and liquid mole fractions.
An equilibrium curve based on experimental data is plotted in the figure. There are
operating lines above and below the feed which are derived from the material balance
equations in terms of the vapor and liquid mole fractions. The equations of the two
operating lines are given in the figure. The two operating lines intersect with the
y
=
x
line at the column's respective end compositions and intersect with a feed line
that emanates from the feed composition,
z
f
, located on the
y
=
x
line. The slope of
the feed line,
q
, is calculated by
H
f
−
H
F
H
f
−
h
f
q
=
(11.7)
where
H
F
represents the molar enthalpy of the feed,
H
f
is the molar enthalpy of
saturated vapor, and
h
f
is the molar enthalpy of saturated liquid. For example, if
H
F
is a saturated liquid, the value of
q
is zero, which represents a horizontal line on the
McCabe-Thiele diagram.
The number of theoretical stages is obtained by drawing a vertical line from an
operating line to the equilibrium curve. This is equivalent to finding the equilibrium
compositions for a stage. A horizontal line from the equilibrium curve back to the
operating line gives the compositions of the passing streams (i.e., the material balance).
This is repeated from one end of the column to the other.
An important feature is the ability to determine the minimum reflux ratio,
L
/
V
,which
occurs at an infinite number of stages. This is known as the
pinch point
and usually
occurs when a line drawn from the overhead composition specification is connected
