Environmental Engineering Reference
In-Depth Information
Solution:
(see Figure 4.8)
Given:
F
=
250 mol
/
hr
x
F
=
0.10
x
B
=
0.005
x
D
=
0.75
2.0.
Mass balances around the entire column:
R
D
=
mol
hr
=
F
=
D
+
B
⇒
250
D
+
B
250
mol
hr
moles EtOH
moles feed
x
F
F
=
+
⇒
.
x
D
D
x
B
B
0
10
0
D
0
B
moles EtOH
moles distillate
moles EtOH
moles bottoms
=
.
75
+
.
005
.
=
/
=
/
Two equations and two unknowns gives
B
218 mol
hr and
D
32 mol
hr.
Top operating line:
L
V
=
L
/
D
R
D
R
D
+
2
2
3
;
Slope
=
1
=
1
=
1
=
L
/
D
+
2
+
one point
=
y
=
x
=
x
D
=
0.75.
Feed line:
q
1
Slope
=
1
=
1
=∞=
vertical line;
q
−
1
−
x
F
=
one point
=
y
=
x
=
0.10.
Bottom operating line:
First point
=
intersection of feed and top operating line;
Second point
=
y
=
x
=
x
F
=
0.005.
Stepping off stages:
The separation will take eight equilibrium stages (the last stage will be the reboiler)
and the optimum feed plate will be the fifth from the top. The liquid composition on the
fourth stage from the top is
∼
0.28 mole fraction ethanol, and the vapor composition
on this stage is
∼
0.56 mole fraction ethanol.
Minimum reflux
Minimum reflux is defined as the external reflux ratio,
R
D
, where the desired separation
could be obtained with an infinite number of stages. Obviously, this is not a real condition,
but the concept is useful because actual reflux ratios are often defined in terms of minimum
reflux ratios.
The number of stages becomes infinite at a “pinch point” on a McCabe-Thiele diagram,
as shown in Figure 4.9. A “pinch point” occurs at the intersection of the operating and
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