Environmental Engineering Reference
In-Depth Information
C
A
,i
C
A
,i
C
A
,o
C
A
,2
C
A
,o
C
A
,4
C
A
C
A
C
A
,3
C
A
,1
x
Cocurrent
x
Countercurrent
Figure 2.3
Concentration profiles.
barrier and
C
A
,
4
can be larger than
C
A
,
o
. Therefore, countercurrent operation is usually
the preferred method.
To account for the variation in driving force, a log-mean driving force is used instead
of a linear one:
C
1
−
C
2
ln
C
1
C
2
.
C
lm
=
(2.5)
This equation is derived in Middleman [1].
For countercurrent flow:
C
1
=
C
A
,
i
−
C
A
,
4
(2.6)
C
2
=
C
A
,
o
−
C
A
,
3
.
For cocurrent flow:
C
1
=
C
A
,
i
−
C
A
,
1
(2.7)
C
2
=
C
A
,
o
−
C
A
,
2
.
C
2
are the concentration differences at each end of the barrier. This analysis
will be used in the chapter on membranes (Chapter 9).
C
1
and
2.7
Productivity and selectivity
In the evaluation of a separation process, there are two primary considerations: productivity
and selectivity. The productivity, or throughput, of a process is the measure of the amount
of material which can be treated by this process in a given amount of time. This quantity
is usually specified by the feed flowrate to the process and/or the amount of a product
stream. The selectivity of the process is the measure of the effectiveness of the process
to separate the feed mixture. Selectivity is usually given by a separation factor (
α
ij
),
which is a ratio of compositions in the product streams for an equilibrium process or
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