Environmental Engineering Reference
In-Depth Information
bulk phase value) to the concentration difference across the layer:
N
A
=
k
(
C
A
,
1
−
,
C
A
,
2
)
(2.4)
where
N
A
=
mass flux of
A
across the fluid layer
k
=
mass transfer coefficient
C
A
=
concentration of component
A
.
In choosing between these two models, one needs to consider the specific process.
The use of mass transfer coefficients represents a lumped, more global view of the many
process parameters that contribute to the rate of transfer of a species from one phase to
another, while diffusion coefficients are part of a more detailed model. The first gives a
macroscopic view, while the latter gives a more microscopic view of a specific part of
a process. For this reason, the second flux equation is a more engineering representation
of a system. In addition, most separation processes involve complicated flow patterns,
limiting the use of Fick's Law. A description of correlations to estimate values of
k
for
various systems is contained in Appendix B.
2.6
Countercurrent operation
The analysis of equilibrium-stage operations is normally performed on the basis of counter-
current flow between two phases. Because most separation processes, whether described
in terms of equilibrium or mass transfer rates, operate in this flow scheme, it is useful to
compare countercurrent to cocurrent flow. Figure 2.2 illustrates cocurrent and counter-
current operation. Assuming mass transfer across a barrier between the two fluid phases,
generic concentration profiles can be drawn for each case (Figure 2.3).
A few points become obvious. First, in each case, the concentration difference across
the barrier changes with axial position
x
. So, the flux (or rate) will change with position.
Second, for cocurrent flow, the concentration difference (driving force for mass transfer)
becomes very small as the flow moves axially away from the entrance (
x
0). So, the
separation becomes less efficient as the barrier becomes longer in the axial direction.
For countercurrent operation, the driving force is maintained at a larger value along the
=
C
A
,i
C
A,
o
C
A
,i
C
A
,o
C
A
,2
C
A
,4
C
A
,1
C
A
,3
Cocurrent
Countercurrent
x
x
Figure 2.2
Cocurrent vs countercurrent operation.
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