Page 156 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

130 5 Principles for Gas Separation

L d
t x ¼ ð5:14Þ
V az
where L is the length/height of the column and d is the width of the adsorption
wave (see Fig. 5.2). This is also called the breakthrough time. The lifetime of an
adsorbent column bed before the breakthrough point can be estimated using this
equation, when regeneration or replacement of adsorbent column is necessary in
order to maintain an effective adsorption process.
Although d can determined by the analysis of gas-solid mass transfer, no single
model applies to all gas-solid systems. The exact wave width depends on the packing
density, the activated carbon properties and incoming adsorbate concentration. There
have been several models developed. One widely used model for breakthrough time t x
is the modified Wheeler equation [8, 14], which is for single adsorbate.

M eq q Q C 0
b
t x ¼ W ln 1 ð5:15Þ
QC 0 K x C x
where t x ¼ break through time (s), M eq ¼ adsorption capacity (kg/kg), C 0 ¼ inlet
3
concentration (kg/m ), W ¼ weight of the adsorbent (kg), q ¼ bulk density of the
b
3
3
packed adsorbent (kg/m ), Q ¼ gas phase volumetric flow rate (m /s), K x ¼ mass
3
transfer rate coefficient (1/s), C x ¼ exit concentration (kg/m ). This exit concen-
tration is determined based on local emission standards or air quality requirement.
Note that the last term is related to the breakthrough efficiency, which is the
column adsorption efficiency when breakthrough occurs.
C x
g ¼ 1 ð5:16Þ
x
C 0
Then the breakthrough time Eq. (5.15) can be described in terms of breakthrough
efficiency as

M eq q Q g x
b
t x ¼ W ln ð5:17Þ
QC 0 K x 1 g
x
Example 5.3: Adsorption column breakthrough time
Continuing from Example 5.2 above, we obtained M eq ¼ 0:128 kg VOC/kg ACð Þ,
5 3 3 3
C 0 ¼ 1:53 10 ðkg VOC/m Þ, Q ¼ 0:1m =sð Þ, q ¼ 400 kg AC/m . Now, the
b
1
mass transfer coefficient of the adsorbent is K x ¼ 20 s . The cross-sectional area of
2
the bed is given as 0.1 m . The designed adsorption efficiency is g ¼ 0.9. That is,
x
the breakthrough occurs when the outlet n-butanol concentration reaches 10 % of
the inlet concentration. Determine the length of the bed if it is to be replaced every
2 months (assuming 60 days).
Solution
First we convert the unit of breakthrough time from months to seconds.