Page 333 - Adsorption, Ion Exchange & Catalysis- 2007, Elsevier - Copy

Else_AIEC-INGLE_cH004.qxd 7/1/2006 6:54 PM Page 329
4.2 Design of Adsorption and Ion-Exchange Processes 329

“Diffusion-type” models are two-parameter models, inolving v k or D s and La , while
f
BDST models are one-parameter models, inolving only v , as q max is an experi-
.
mentally deried parameterThe determination of La requires the whole experimental
v
equilibrium curve, and in case of sigmoidal or other non-Langmiur or Freundlich-type
w
isotherms, these models are unusable. From this point of vie BDST models are more
,
easily applied in adsorption operations, at least as a first approximation.
Example 8
Cheng et al . (2004) studied the adsorption of toluene (VOC) in a fixed bed of activated car-
bon fibers at 298 °C and 1 atm. The inlet concentration of toluene was 17.36 mg/m 3 and
vish isotherm with ys the Dubinin–Radusk the carrier gas was air T e . oluene obe k 1.101
10 –9 mol 2 /J 2 and q o 57.73 kg/m 3 . The following data are gi en. v
Toluene : af icient inity coef f f 1 (approximate v molar polarizability alue), P e 3.11
10 4 cm 3 /mol, density 0.8669 kg/m 3 , MB 92.14 g/mol and saturated v apor pressure
at the gien temperature = 0.375 v 10 4 . Pa
Carbon fs iber : particle radius r 13 10 –3 mm, particle density 87 kg/m 3 .
p
Bed : diameter D 6 mm, height H 8 mm, mass of solid phase 15 mg and inter-
stitial v elocity u 17 m/s.
According to the experimental data, the first appearance of toluene in the exit stream is
at about 50 min, while after 100 min the exit concentration is 10% of the inlet one.
Calculate the time needed for the same breakpoint concentration using the Wheeler–Jonas
W aluation of equation and ood and Stampfer equation for the e v k . v
Moreover, examine the Wheeler–Jonas equation for the specified experimental condi-
tions. On the basis of the results, predict the breakpoint time for lower interstitial v eloci-
ties down to 1 m/s.

Solution
In the absence of more experimental data and for the purposes of the present e we xample,
assume that the first appearance of toluene just after 50 min corresponds to an exit con-
centration of 0.01%, which is practically close to zero. This value will be used as the
breakpoint concentration in the follo wing calculations.
The Dubinin–Radushkvich isotherm is (eq. (4.19)) e

 A   2 
q e q o exp  k   
     

where from eq. (4.18),

P  s 
A RT ln  P   