Page 526 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Adsorption 481

Example 15.5 Sizing a Packed-Bed Reactor in effluent adsorbate concentration. Then, when the leading
from Isotherm part of the wave front reaches the end of the column, the
adsorbate concentration increases rapidly until it equals the
Given influent concentration (i.e., the breakthrough curve develops).
Benzene, a ‘‘priority pollutant’’ is to be removed from a Zogorski and Faust (1978, pp. 753–776) discuss the length
groundwater to be used for drinking water. Q ¼ 3785 of the mass-transfer zone, i.e., L wf , and its velocity, v wf ,as
3
m =day (1.0 mgd) and C 0 (benzene) ¼ 2.5 mg=L.
basic parameters characterizing column behavior. They give
Required the methodology for determining both L wf and v wf : (1) pilot
Determine the area and length of a reactor for 30 days of scale experiments are conducted in which several columns of
operation.
different lengths are set up; (2) for each column, ‘‘break-
Solution through times’’ are plotted against ‘‘bed depth’’; (3) the
1. Freundlich isotherm coefficients. slope of the plot is the reciprocal of v wf and the intercept is
L wf . They determined v wf and L wf for different GAC particle
From Table 15.3, for Filtrasorb 300, K(benzene) ¼
1.0 and 1=n(benzene) ¼ 1.60. sizes, adsorbent species, influent concentrations, and HLR
2. Calculate X(C 0 ), from Freundlich isotherm relation. values (described in the next section).

Mullins et al. (1980, p. 278) obtained 0.0061 v wf
1=n
X* ¼ KC 0
0.012 m=day (0.02 v wf 0.04 ft=day) and 0.2 L wf
¼ 1.0 (2.5 mg=L) ^1.60 0.3 m for three GACs adsorbing chloroform in Louisville tap
2
¼ 4.3 mg benzene=g carbon water at HLR 10.2 m=h (4.2 gpm=ft ). For a 1.0 m-long
¼ 0.0043 kg=m 3 GAC column they found that a column could be operated
6–12 weeks before breakthrough, i.e., 1.0 m=v wf . They noted
3. Assume HLR ¼ 12.2 m=h ¼ 0.0034 m=s (5.0 that the small diameter adsorbent particles have steeper wave
2
gal=min=ft ) fronts, i.e., a smaller length mass-transfer zone than larger
4. Assume constants, particles. This is due to the faster diffusion per unit of GAC
mass for the smaller particles.
r(GAC) 1.40 g=mL
P ¼ 0.40 15.2.4.2 Empirical Data for L wf and v wf
Table 15.4 gives L wf and v wf as determined for different
5. Calculate v wf from Equation 15.48, experimental conditions (from Zogorski and Faust, 1978,
p. 762). The effects of media size, adsorbate species, C 0 ,
HLR C 0 and HLR are shown. The data show that one might expect
(15:48)
v wf
X*(C 0 ) r (1 P) 0.11 L wf 0.49 m and 0.02 v wf 2.2 m=day for a wide
3
¼ (0.0034 m=s) (0.0025 kg=m )=[(0.0043 kg range of operating conditions. These ranges may serve as
3
B=kg C) (1400 kg=m ) (1 0.35)] default values for preliminary designs.
¼ 2.17 10 6 m=s
15.2.4.3 Theoretical Results for L wf and v wf
¼ 0.19 m=day
The results of Table 15.5 were generated by a Fortran model
Then, assume L wf 1.0 m and calculate L(reactor) that solved Equation 15.24 by finite difference, i.e., using
by Equation 15.50, with v wf by Equation 15.48. Equation 15.39, for conditions stated (see headings and foot-
notes). The important points are the following: (1) both L wf
L(reactor) v wf t þ L wf ) (15:50) and v wf are proportional to C 0 ; (2) both L wf and v wf are
¼ 0.19 m=day 365 day þ 1.0 m proportional to HLR; (3) the effects of HLR and C 0 on L wf
¼ 6.6 m and v wf were as expected, as seen by Equation 15.48; (4) the
values of L wf and v wf are in the same order of magnitude as
Discussion seen in Table 15.4 (which may be fortuitous).
The method of Equation 15.48 provides a more expedient
means to estimate the wave-front velocity (as compared to
a pilot plant). 15.2.5 PROBLEMS
The first limitation of the foregoing theory is that competition
15.2.4.1.3 Past Studies is likely if two or more adsorbates are present. A second is
Several literature sources refer to the ‘‘wave front’’ concept in that bacterial growths are probable and cause deviations in the
terms of v wf and L wf , e.g., USEPA (1971, pp. 4–9), Zogorski velocity of wave fronts and the shapes of breakthrough curves
and Faust (1978, pp. 753–776), Mullins et al. (1980, pp. 273– for any given adsorbate.
307). These corroborate what has been described in previous
sections, e.g., Section 15.2.4.1. For example, according to 15.2.5.1 Competition between Adsorbents
USEPA (1971), as the carbon becomes saturated, the zone For a given adsorbent, different adsorbates have different
of adsorption moves downward with only a gradual increase affinities to adsorb, as reflected in the isotherm coefficients,