Environmental Engineering Reference
In-Depth Information
V
0
,
y
A
0
V
1
,
y
A
1
V
2
,
y
A
2
1
2
O
1
,
x
A
1
Figure 5.10
Countercurrent cascade.
O
2
,
x
A
2
O
3
,
x
A
3
∆
O
2
O
1
V
1
V
2
V
0
y
A
2
y
A
1
y
A
0
Figure 5.11
Triangular diagram for countercurrent cascade.
V
0
V
1
V
2
V
j
−1
V
j
V
N
−1
V
N
1
2
j
N
O
1
O
2
O
3
O
j
O
j
+1
O
N
O
N
+1
Figure 5.12
Countercurrent cascade of
N
stages.
point” came directly from the mass balances. Therefore, we can write:
V
0
=
+
O
1
⇒
V
0
O
1
is a straight line and the composition of
V
0
will lie between
and
O
1
(if
is positive)
.
The same can be said for:
V
1
=
+
O
3
.
The compositions corresponding to
O
1
and
V
1
(as well as
O
2
and
V
2
) will lie on a tie-
line since they are outlet streams from a stage and they are assumed to be in equilibrium
with each other.
O
3
and
V
0
are not on a tie-line. This is shown graphically in Figure 5.11
(dashed lines are tie-lines).
A more general case consists of
N
stages (Figure 5.12).
O
2
and
V
2
=
+
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