Page 390 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Rapid Filtration 345

Log C/C
Q o
0 C/C o 1.0 0.01 0.1 1.0
0 0
t 0

Saturated zone at t n 2.3 λ
Z(sat) Z(sat) t 0

Filter
Z (cm) Inflection Z (cm) Inflection
media
Point
point
t n 2.3 λ

t n

(a) (b) 100 (c) 100

FIGURE 12.18 Iwasaki’s kinetic equation illustrated. (a) Column. (b) C(Z) t plots, arithmetic scale. (c) C(Z) t plots, semi-log scale.

depth of the filter bed, for example, ln cycles per filtration velocity. Values range 0.2 l o 20
meter. Note that this discussion belabors the point a ln-cycles=m (or 0.087 l o =2.3 8.7 log-cycles=m);
bit, especially to one adept in basic mathematics. for reference, Appendix C.3.3 reviews the natural-ln
3. Filter coefficient: For reference, the magnitudes of to common-log conversion. To summarize, the
the clean-bed filter coefficient, l o , from several steeper the log(C=C o ) versus Z curve, the higher the
value of l o =2.3 and the more effective the filtration
sources are compiled in Table 12.2. As seen, l o
varies with the kinds of particles entering the filter process. The trends of l o =2.3 with particle size, and
bed, the kind and size of filter media, and the filtration velocity are seen in the polystyrene data,

TABLE 12.2
Filter Coefficients as Affected by Variables
Particles Filter Medium
v
Size Size l o
1
2
Source a Material (mm) Material (mm) (mm=s) (gpm=ft ) (m )
Maroudas Polystyrene-angular 65 Glass 2.00 6.30 7.64 2.6
spheres 25.00 30.34 0.7
88.50 107.39 0.2
90 25.00 30.34 1.2
100.00 121.34 0.4
125 22.80 27.67 2.1
83.50 101.32 1.3
Ives Algae 5 Sand 0.54 1.40 1.70 14.0
0.70 1.40 1.70 14.7
Eliassen Ferric hydroxide 6–20 Sand 0.46 1.40 1.70 20.0
Fox=Cleasby Ferric hydroxide 4–25 Sand 0.70 2.70 3.28 10.0
1.40 1.70 0.6
Khan b Aluminum hydroxide 633 Anthracite d 10 ¼ 1.10 4.12 5.00 4.8
597 UC ¼ 1.6 4.12 5.00 4.1
399 4.12 5.00 3.4
Source: Adapted from Herzig, J.P. et al., Ind. Eng. Chem., 62(5), 22, 1970.
a
Sources, except for Khan, are listed by Herzig et al. (1970).
b
Khan (1993).