Environmental Engineering Reference
In-Depth Information
Remember that this balance assumes that the system operates adiabatically such that no
heat gains or losses occur between the distillation column and its surroundings.
Referring to Figure 4.3, we can evaluate the thermal energy inputs and outputs. At
steady-state, just as with mass balances, the energy inputs (gains) must equal the outputs
(losses):
Fh
F
+
Q
R
=
Dh
D
+
Bh
B
+
Q
C
,
(4.25)
where
F
,
D
, and
B
=
molar flowrates of the feed, distillate, and bottoms
h
F
,
h
D
, and
h
B
=
molar enthalpies of these streams
Q
C
=
energy requirement of the condenser
Q
R
=
energy requirement of the reboiler.
The enthalpies can be determined from an enthalpy-composition diagram or from the heat
capacities and latent heats of vaporization. In the case of a total condenser, the composition
of the stream is not changed (not true in a partial condenser!) and a mass balance around
the condenser can be written:
V
=
L
+
D
,
(4.26)
or, in terms of the external reflux ratio (
R
D
), as
L
D
D
V
=
+
D
=
(1
+
R
D
)
D
,
(4.27)
and, with a given value of
R
D
,
V
can be calculated.
The condenser energy balance is:
VH
=
(
D
+
L
)
h
D
+
Q
C
,
(4.28)
where
D
and
L
are at the same conditions, and
H
is the enthalpy of the vapor stream going
to the condenser or, combining equations,
Q
C
=
V
(
H
−
h
D
)
.
(4.29)
Substitution then gives:
Q
C
=
(1
+
R
D
)
D
(
H
−
h
D
)
.
(4.30)
Now this value can be used with the overall energy balance for the entire column to find
the reboiler duty,
Q
R
.
Feed line
As we have seen, the McCabe-Thiele diagram for a distillation column with rectifying
and stripping sections will have two operating lines, usually referred to as top and bottom
operating lines, respectively. When stepping off stages from the top, you use the top
operating line (mass balance) until the mass balance changes. This will occur when feed
enters the column. You want the feed to be introduced such that its composition and
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