Environmental Engineering Reference
In-Depth Information
Equilibrium line
1.0
y
A
e
y
Operating line
A
x
z
1.0
A
A
e
x
A
Figure 3.18
x-y
analysis of a single equilibrium-limited stage.
Therefore, the feed mole fraction
z
A
is known, since the operating line intersects the
y
F
ratio can be specified and the equilibrium values obtained,
or vice versa. This is shown in Figure 3.18.
The same calculation can be performed analytically using an equation that relates
y
A
e
and
x
A
e
. For a constant relative volatility,
=
x
line at
z
A
. Then, the
V
/
α
AB
,
y
A
/
x
A
y
A
/
x
A
α
AB
=
x
B
=
(3.24)
y
B
/
(1
−
y
A
)
/
(1
−
x
A
)
α
AB
x
A
e
y
A
e
=
1)
.
(3.25)
1
+
x
A
(
α
AB
−
With two equations and two unknowns one can solve for
x
A
e
and
y
A
e
.
An alternative graphical solution uses a
T
-
x
-
y
phase equilibrium diagram. First, the
mass balance equation is rearranged:
x
A
1
V
F
y
A
V
F
z
A
=
−
+
(3.26)
z
A
−
x
A
V
F
.
x
A
=
(3.27)
y
A
−
If the mole fractions are plotted on a
T
-
x
-
y
diagram (Figure 3.19),
V
F
can be calculated
from the ratio of line segments. This is an example of the lever-arm rule (described in
to next section). Note that the mass balance could be rearranged to solve for
L
/
/
V
or
L
F
using the same approach of the ratio of the length of line segments. Note also that
once
T
is fixed, the
x
A
e
and
y
A
e
are fixed. The ratio of flowrates
V
/
/
F
can be varied by
changing
z
A
.
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