Environmental Engineering Reference
In-Depth Information
Hence, as
k
L
increases, so does the rate of mass transfer.
In addition, for Case II,
k
G
is the limiting rate and hence
K
L
≈
k
g
. For Case III,
k
L
is the limiting rate and
K
L
≈
k
L
.
3.9
Remember
Mass balances can be written for both the total mass in a system and a specific component
of the system.
Equilibrium processes are limited by the degree of separation in a single contact, so
cascades of contact stages are used to achieve a higher degree of separation.
The minimum number of equilibrium stages is a theoretical concept based upon infinite
flows within a cascade and no feed or product streams.
Equilibrium analysis of separation processes can be performed both graphically and
numerically by the use of operating lines (obtained from mass balances) and equilibrium
lines.
Mass transfer (rate) analysis of a process is characterized by an overall mass transfer
coefficient (OMTC), which is a global term that includes system contributions to mass
transfer resistance.
3.10
Questions
3.1 Define a microscopic and macroscopic balance.
3.2 State the basis for an equilibrium- and rate-limited process.
3.3 Describe
the
assumptions
about
solute-sorbent
interactions
for
the
following
isotherms:
Langmuir-single component
Langmuir-competitive
Freundlich.
3.11
Problems
3.1
Use liquid-phase rather than gas-phase compositions and derive the equation below.
For this case, the flows are in a direction opposite to those in Figure 3.6.
ln
[1
mV
)]
x
N
+
1
−
x
1
/
x
1
−
x
1
+
mV
)
−
(
L
/
(
L
/
N
=
.
ln (
mV
/
L
)
3.2
Derive an equation for
J
A
analogous to Equation (3.83) in terms of liquid-phase
concentrations.
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