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340 4. Adsorption and Ion Exchange

where V f is the effluent volume until the first appearance of the solute in the exit stream,
V br the effluent volume until breakpoint, and V tot the effluent volume until the exit solute
concentration is equal to its inlet concentration.
The dependence of q o on residence time has been noticed and modeled elsewhere, in the
case of zinc and acid dyes adsorption by bone char and acti respecti ated carbon, v o v ely (K
et al ., 2002). The following equations were successfully applied:

q d o,be o,ma x q 1e x p res t (4.212)

p
x
q d o,be x o,ma q 1e res t 0.5 (4.213)
where q o,bed and q o,max are the bed maximum capacity and the real maximum capacity
(measured in batch reactor systems), t res the residence time, and a system-specific con-
stant. It is obvious that if the residence time is infinite, the bed maximum capacity is equal
,
xpected,
to the real maximum capacity which is theoretically e as noted else where
v
(Inglezakis and Grigoropoulou, 2003). These equations hae been also tested in Pb 2
adsorption by clinoptilolite (zeolite) and shoactory results (Inglezakis, 2002b). wed satisf
In conclusion, the maximum adsorption capacity should be measured in fixed-bed experi-
fusion coefficients should ments under dynamic conditions, and if models are applicable, dif
be also determined in fed-bed apparatus. Due to the fact that the equilibrium isotherms ix
require extended data series and thus are time-consuming experiments, the latter are quite dif-
ficult to be conducted in fixed-bed reactors and from this point of view, it is more practical to
evaluated equilibrium isotherms in batch reactor systems. Then, it is known that when apply-
ing fixed-bed models using an equilibrium isotherm obtained in batch-type experiments, the
equilibrium discrepancy (if it exists) can be compensated by a different estimate for the solid
diffusion coefficient (Inglezakis and Grigoropoulu, 2003; Weber and Wang, 1987).

Example 9
Wastewater containing 100 ppm Pb 2 and minor amounts of other ions has to be treated
able e (20°C). The maximum alloxit concentration is 10 ppm. The aailable adsorbent is w v
a zeolite of particle size 2 mm (
0.8), particle density 2 g/cm 3 , and bulk density 1
S
g/cm 3 . Suppose that solid diffusion is the controlling mechanism. Solid diffusion is meas-
ured and found to be about 10 –9 cm 2 /s. Furthermore, the system obeys the f a orable v
Langmuir isotherm with La 0.1. The MEL is q max 200 mg/g. ailable amount of v The a
the zeolite is 100 kg.
(a) Propose an optimum design for this operation by using an LDF model.
(b) Compare the LDF model with Helfw operation and s model for upflo ferich’ Q rel 5
BV/h.

Solution
Model analysis : The simple LDF model for solid diffusion control will be used, namely
eq. (4.141). For the specified system with La = 0.1, the N ( T – 1) versus ( C / C ) is sho wn
s 0
in Figure 4.34.