Environmental Engineering Reference
In-Depth Information
y
T
x
x
A
z
A
y
A
Figure 3.19
T-x-y
phase equilibrium diagram for a single-stage process.
For liquid-liquid extraction systems, the approach is the same to analyze a single
equilibrium-limited contact. A mass balance (operating) line is plotted on a phase equi-
librium diagram. In this case, the phase equilibrium diagram is a ternary diagram.
3.5.2
Lever-arm rule
Each equilibrium stage in extraction has two distinct steps, mixing of the two phases for
solute partitioning and separation of the phases to form exit phases with altered solute
concentrations. The goal of analysis for any system is, as before, to determine the number
of equilibrium stages required for a specified separation. The lever-arm rule described in
this section provides a way of analyzing a tertiary system by breaking it down into mixing
and separating steps.
The analysis begins with mixing of the solvent and diluent streams, as follows. Imagine
two liquid streams (
O
and
V
) which may contain any or all of components
A
,
B
and
C
. These
two streams are mixed to form a third stream, (
F
). The streams
O
,
V
and
F
may be single
phase or two phase. Note that the control volume isn't necessarily an equilibrium-limited
stage. The compositions and flowrates of the two feed streams are known (remember that
for
O
:
x
A
+
1). [
Do
not be confused about the notation: the x's and y's are used to differentiate between the
compositions of the two feeds, but the y's do not mean that stream V is vapor. Both feed
streams are liquid
.]
Referring to Figure 3.20:
x
B
+
x
C
=
1, for
V
:
y
A
+
y
B
+
y
C
=
1, and for
F
:
z
A
+
z
B
+
z
C
=
V
=
total mass (or flowrate) of
V
phase
O
=
total mass (or flowrate) of
O
phase
F
=
total mass (or flowrate) of
F
phase
Assumptions:
x
A
i
=
fraction of component
A
in
O
phase
1 no chemical reactions
y
A
i
=
fraction of component
A
in
V
phase
2 isothermal system
z
A
o
=
fraction of component
A
in F phase
3 system is at steady state.
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