Page 156 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Sedimentation 111

0.0007 0.0015
y = 0.0015965 – 0.0006482x R = 0.99215
y = 0.00039955*e^(–0.5724x) R = 0.9996 25
0.0006 0.12

20
0.0005 0.10 0.0010

0.0004 0.08 15
v i (m/s) v i (ft/min) j(settling) (kg/s/m 2 ) j(settling) = X · v i j(settling) (lb/s/ft 2 )
i
0.0003 0.06 10

0.0002 0.04 0.0005
5
0.0001 0.02

0.0000 0.00 0.0000 0
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
3
3
(a) X (kg/m ) (b) X (kg/m )
i
i
0.0015 0.0015
25
25

20 j(total)
20
0.0010 0.0010
j(bulk) (kg/s/m 2 ) j(bulk)=X · v i 15 j(bulk) (lb/s/ft 2 ) j(total) (kg/s/m 2 ) j(settling) 15 j(total) (lb/s/ft 2 )

i
0.0005 10 0.0005 10

j(bulk)=X ·v
5 i i 5

0.0000 0 0.0000 0
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
3
3
(c) X (kg/m ) (d) X (kg/m )
i
i
FIGURE 6.17 Solids flux in final clarifier for wastewater treatment: (a) initial settling velocity v, X i , (b) solids flux density by settling,
(c) interface fall due to bulk flow, and (d) total flux density by settling and bulk. (Adapted from Dick, R.I., J. Sanit. Eng. Div., ASCE,96
(SA2), 423, April 1970.)
the level in the sludge blanket where the associated X i occurs plots. The foregoing is an introduction to principles involved
is the ‘‘bottleneck.’’ Thus, a design requirement is that in taking into account the ‘‘solids flux theory.’’ Techniques for
A(plan) j(limit) J(solids)=j(limit). If A(plan) < A(plan) j(limit) , evaluating the effects of R=Q and solids loading on X and X r
have been given by Keinath (1985, 1990) and Hermanowicz
the excess solids will leave the clarifier, i.e., J(excess) ¼
[J(solids)=A(plan) J(solids)=A(plan) j(limit) ] A(plan). (1998).
6.6.2.6 Example of Limiting Flux Density Using Plots
Example 6.6 illustrates how to apply the foregoing ideas in Example 6.6 Sludge Thickening
terms of numerical data. Table CD6.5 incorporates the equa- (Adapted from Dick, 1970)
tions that generate plots similar to those of Figure 6.17; in
addition, it also computes the revised values of X and X r . Given
A new operating value of R may be tried as a revised input, Activated sludge system with Q ¼ 0.044 m =s (1.0 mgd),
3
for which a new value of j(limit) is obtained for the linked X ¼ 2000 mg=L, X r ¼ 6000 mg=L.