Environmental Engineering Reference
In-Depth Information
6.6.3
Concentrated absorbers and strippers
For concentrated absorbers and strippers, the total flowrates are not constant. Solute
transfer is diffusion through a stationary component (
N
B
=
0). The amount of solute trans-
ferred is sufficient to change the total flowrates
and
the driving force for mass transfer as a
function of position in the column. Thus, a log mean driving force (
m) is the appropriate
choice.
The rate of mass transfer can be defined to look like the one given previously for dilute
solutions:
k
y
a
(
y
A
−
N
A
a
=
y
A
I
)
.
The mass transfer coefficient is now:
k
y
=
y
A
)
m
, where
k
y
can be thought of as
a mass transfer coefficient adjusted by using a mean (average) mole fraction. In this case,
the mean used is the log mean to account for the variation in driving force throughout the
column. Hence,
k
y
a
/
(1
−
(1
−
y
A
)
−
(1
−
y
A
I
)
(1
−
y
A
)
m
=
ln
1
.
(6.26)
−
y
A
1
−
y
A
I
Repeating the analysis for dilute solutions, but now accounting for variable total
flowrates,
L
=
L
(1
−
x
A
)
V
=
V
(1
−
y
A
)
,
(6.27)
where
L
and
V
are the constant flowrates of inerts in each phase.
In this case the differential in concentration is
d
V
V
d
y
A
y
A
d
y
A
d
y
A
V
d(
Vy
A
)
=
=
=
=
V
y
A
)
.
(6.28)
1
−
y
A
1
−
y
A
(1
−
y
A
)
2
(1
−
The resulting equation for the column height is (in terms of overall mass transfer
coefficient):
y
A
in
V
K
y
aA
c
d
y
A
y
A
)
y
A
−
y
A
.
=
(6.29)
(1
−
y
A
out
Rearranging,
y
A
in
V
K
y
aA
c
(1
(1
−
y
A
)
m
d
y
A
=
y
A
)
y
A
−
y
A
−
y
A
)
(1
−
m
y
A
out
y
A
in
V
K
y
aA
c
(1
(1
−
y
A
)
m
d
y
A
y
A
)
y
A
−
y
A
=
(6.30)
−
y
A
)
m
(1
−
y
A
out
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