Environmental Engineering Reference
In-Depth Information
V
y
i
F
z
i
L
x
i
Figure 3.17
Continuous equilibrium flow system.
the separation. There are various staging modes and they will be described in more detail
in later chapters on specific separation technologies. The main purpose here is to show a
basic example for a single stage that will form the basis for analyses of various sequences
of equilibrium stages.
3.5.1
One equilibrium stage
Figure 3.17 represents a continuous flow system where streams
V
and
L
are in thermo-
dynamic equilibrium. This system can be evaluated by using thermodynamic equilibrium
information with the appropriate number of mass balances. This will be illustrated first
graphically and then analytically for a binary system. To analyze the system graphically,
an equation must be obtained
y
f
(
x
) from mass balances (operating line) and plotted on
an
x
-
y
equilibrium diagram. The intersection of the mass balance and equilibrium line is
the solution.
Component mass balance:
=
z
A
F
=
x
A
L
+
y
A
V
.
(3.20)
Total mass balance
:
=
+
→
=
−
.
F
L
V
L
F
V
(3.21)
Combining and rearranging:
x
A
[(
V
/
F
)
−
1]
1
y
A
=
+
z
A
F
.
(3.22)
V
/
F
V
/
When
y
A
=
x
A
:
x
A
[(
V
/
F
)
−
1]
1
x
A
=
+
z
A
F
→
x
A
=
z
A
.
(3.23)
V
/
F
V
/
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