Environmental Engineering Reference
In-Depth Information
Boundary condition:
x
m
=
x
F
(feed composition) for
n
=
0 (note: this only counts
stages in enriching section):
1
x
F
−
1
C
1
=
h
+
2
h
.
a
+
b
+
a
+
b
+
2
h
Smoker equation:
x
n
=
h
+
a
−
n
in enriching section.
+
b
+
h
+
x
F
a
+
h
−
1
x
F
−
h
b
+
h
[This equation can also be modified for a stripping section:
x
n
is replaced by
x
B
,
R
V
by
the reboiler ratio.]
The stage number is from fe
ed pl
at
e dow
stripping section
n instead of fe
ed p
la
te u
p
enriching section
.
Let
x
e
,
y
e
be the interaction of the operating and equilibrium lines:
Equilibrium line
y
y
=
x
Operating line for enriching
section
x
α
x
Equilibrium curve:
y
=
1
+
x
(
α
−
1)
Operating line:
y
=
xR
V
+
x
D
(1
−
R
V
)
Equating:
x
e
+
x
e
(
a
+
b
)
+
c
=
0(
a
,
b
,
c
defined previously)
x
e
=
h
(see defining equation for
h
).
∴
h
must be positive,
b
negative and greater than
a
or
c
.
The variable
h
shifts the coordinate system to the intersection of the operating and stripping
curves. One special case is that of total reflux. In this case
D
=
0 as no product is being
withdrawn and the reflux ratio
R
V
=
becomes 1. This also corresponds to the minimum
number of equilibrium stages required for a separation when this is the case,
1
α
−
−
α
α
−
a
=
1
;
b
=
1
;
c
=
0
1
C
1
1
α
x
n
=
n
1
.
+
When
n
=
0
,
x
n
=
x
B
(composition at bottom of enriching section):
1
x
B
−
C
1
=
1
.
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