Environmental Engineering Reference
In-Depth Information
V
,
y
A
i
,
y
B
i
Equilibrium
stage
F
,
z
A
o
,
z
B
o
O
,
x
A
i
,
x
B
i
Figure 3.22
Equilibrium-limited stage for a three-phase system.
V
o
,
y
A
o
V
i
,
y
A
i
F
,
z
A
o
Mixing
Equilibrium
O
o
,
x
A
o
O
i
,
x
A
i
Figure 3.23
Mixing and separating stages in an extraction process.
4 To use the graphical method:
-
remember that there are two streams on one side of the mass balance and one stream
on the other side (
V
F
);
-
note that the same method can be followed for one inlet stream which separates into
two outlet streams (the reverse process).
(a) Given the ratio
V
+
O
=
O
and the inlet compositions
x
A
i
and
y
A
i
,
z
A
o
could be located
by solving the equation or measuring line segments:
/
V
O
=
x
A
i
−
z
A
o
line segment
FO
line segment
VF
.
y
A
i
=
z
A
o
−
(b) Measuring line segments would locate
F
, and then
z
A
o
could be found.
(c) Given
x
A
i
,
y
A
i
and
z
A
o
(the
inle
t and outlet compositions), one could solve for
V
/
O
by measuring
VF
and
FO
and substituting into the above equation.
Special case: equilibrium stage
A special case of the lever-arm rule, which renders it applicable to extraction analysis, is
an equilibrium-limited stage for a three-phase system (Figure 3.22). Everything stated for
the lever-arm rule still applies here since the mass balances around the control volume
(equilibrium stage) are still the same. The compositions of the three streams will still lie
on a straight line, and stream ratios can still be calculated as before.
The second extraction step, separation of the two phases into the raffinate and extract
streams, will be considered next. This step, when combined with the previous mixing
analysis, constitutes one ideal equilibrium stage. Imagine (Figure 3.23) that a mixing is
followed by an equilibrium stage which allows
F
to separate into two streams:
V
o
and
O
o
,
which a
re in eq
uilibrium.
Now
O
o
FV
o
will also be a
straight
line based on a mass balance. Because the second
stage is an equilibrium stage,
O
o
FV
o
will be a tie line, which represents the equilibrium
between
y
A
o
and
x
A
o
.
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