Environmental Engineering Reference
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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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