Environmental Engineering Reference
In-Depth Information
Table 7.6
Data from pilot column
breakthrough test, Example 7.2.
Effluent solute
Volume of water
concentration,
treated,
V
(L)
C
(mg/L)
1500
0.3
1750
2.4
1900
7.9
2200
65.5
2400
143.0
2500
170.1
2600
185.6
2800
197.0
3000
199.4
3200
199.9
3300
200.0
7.10.2 Kinetic approach
If the design fluid volumetric flowrate (
Q
) is sufficiently low that equilibrium is rapid
in comparison, the Equation (7.17) below is a good approximation of the concentration
profile for the breakthrough curve as a function of fluid volume (
V
) put through the column
[11]. A Langmuir isotherm is assumed where
k
1
is the adsorption rate constant for this
isotherm. When
q
0
M
C
0
V
, the effluent solute concentration is approximately zero.
For
q
0
M
C
0
V
, the effluent solute concentration is
C
. See for yourself why this makes
sense physically.
C
C
0
=
1
exp
k
1
C
0
V
)
,
(7.17)
1
+
Q
(
q
0
M
−
where
C
=
effluent solute concentration
C
0
=
influent solute concentration
k
1
=
rate constant
q
0
=
maximum solid-phase concentration of the sorbed solute
(g
/
gorlb
/
lb)
M
=
mass of the adsorbent
V
=
throughput volume
Q
=
fluid volumetric flowrate.
This equation can be rewritten as:
ln
C
0
1
k
1
q
0
M
Q
k
1
C
0
V
Q
C
−
=
−
,
(7.18)
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