Page 407 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

362 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

backwash a filter. The weir crest must be higher enough than In other words, a high backwash rate for a short duration
the top of the media to fluidize the media to the extent yields the same result as a moderate backwash rate for a
required. Flow from the other filters must exceed the back- longer duration; the volume of backwash water is key. For
wash flow as the weir must continue to overflow during the the data shown, a backwash volume of greater than about
2
3
backwash. Such a system has the advantage of simplicity, that 6.0 m =m showed no improvement in water quality of the
is, no pumps and no elevated storage, but the filter box must be backwash water, leveling off at about 0.21 mg iron=Lat
2
3
deeper to provide for the higher tailwater elevation. Kawamura volumes 6.0 m =m . The coefficients k and (vt=d), the inter-
(1999, p. 79) recommends that at least four and preferably six cept and slope, respectively of Equation 12.45 should be
filters should feed into the intermediate backwash reservoir. determined by pilot plant for the situation at hand.
12.4.4.3 Backwash Volume
Example 12.7 Storage Volume for Backwash
For an hydraulic backwash, the rate and duration are key
Water
questions. Amirtharajah (1985) derived the relation
Given
vt

(12:45) Suppose a filter bed is 4267 6.096 m (14 20 ft) plan area
ln C ¼ ln k
d 2
and that the backwash HLR is 1.018 m=min (25 gpm=ft ).
where Required
Storage volume for 30 min backwash.
C is the concentration of particles in backwash water
3
(kg=m ) Solution
3
k is the coefficient (kg=m )
v is the superficial velocity of backwash, that is, Q(back- V(backwash) ¼ HLR(backwash) A(filter) Dt(backwash)
wash)=A(filter bed) (m=s) ¼ 1:018m=min (4:267m 6:096m) 30 min
3
t is the elapsed time since start of backwash(s) ¼ 795m (210,000gal)
d is the representative diameter of collectors, that is, media
grains (m) If cubic, the size is about 9.3 9.3 9.3 m (30.5 30.5
30.5 ft)
Figure 12.31 shows the relationship for experimental data If cylindrical, the size is about 10 m high, 10 m
(data not shown) with r ¼ 0.93 for 16 runs with expanded bed diameter.
porosities ranging from 0.55 to 0.78 (Amirtharajah, 1985). Comments 2
For a given grain diameter, d, the exponent is the volume of If HLR(filtration) ¼ 0.122 m=min (3.0 gpm=ft ), the run
backwash water per unit area of filter bed and is the product duration is 20 h, the water production during a filter run is
vt, that is, the backwash superficial velocity time elapsed time.
V(production) ¼ HLR(filtration) A(filter) Dt(filter-run)
¼ 0:122 m= min (4:267 m 6:096 m) (20 60 min )
3
¼ 3,808 m (1,008,000 gal)
2
Backwash water volume (gal/ft )
0 40 80 120 160 200 240 If the backwash volume used in a normal backwash is
1000 about 400 m , the percentage of water production used
3
Expanded porosities: 0.55 < e < 0.78
for backwash is about 400=3808 ¼ 0.105, or 10%.
Backwash water quality (mg iron/L) 10 y = 476 e (–1.3781/2.303)x Given
100
Example 12.8 Volume of Backwash Water
(–1.3781x)
= 476 10
Figure 12.31 represents a backwash water quality versus
backwash volume relationship for a contemplated plant
with 4.27 m 6.10 m (14 ft 20 ft) filters. The two filters
occupy a ‘‘bay’’ with common gullet for backwash water
1
and water from the coagulated water flume enters the bay
to serve both filters simultaneously.
0.21
Required
0.1 Estimate the backwash storage volume required.
0 2 4 6 8 10
3
2
Backwash water volume (m /m ) Solution
1. Service Need The backwash water volume must be
FIGURE 12.31 Backwash water quality as function of backwash sufficient to serve both filters in one bay in a sequen-
water volume. (From Amirtharajah, A., Water Res. (J. Int. Water tial backwash, that is, one filter and then the other
Qual. Assoc.), 19(5), 587, 1985.) backwashed.