Water and Wastewater Engineering
Подождите немного. Документ загружается.
11-46 WATER AND WASTEWATER ENGINEERING
Hints from the Field
Although the rise of turbidity during ripening of the filter results in only a small fraction of the
filter run average turbidity, the potential for breakthrough of a significant dose of pathogens war-
rants significant operational consideration. This takes the form of diversion of the filtrate, that
is, “filter-to-waste,” or, preferably, “filter-to-recycle” to the head end of the plant. The major
sources of suspended s
olids responsible for the rise in turbidity after the filter is put back on line
are the backwash water and the material released during interparticle c ollisions of the media on
the closure of the backwash valve (Amirtharajah and Wetstein, 1980). The latter effect can be
ameliorated approximately 20 percent by slow closure of the backwash valve (on the order of two
minute
s). The peak effluent turbidity during ripening may be in the range of three to seven times
that of the steady state operation. It may take 30 to 40 minutes of diversion of the filtered water
to waste before the steady state effluent turbidity is achieved. Real-time monitoring of turbidity
during the filter-to-waste operation provides an efficient means of achieving a s
afe effluent qual-
ity while minimizing the “wasting” of treated water.
Visit the text website at www.mhprofessional.com/wwe for supplementary materials
and a gallery of photos.
11-8 CHAPTER REVIEW
When you have completed studying this chapter, you should be able to do the following without
the aid of your textbooks or notes:
1 . Sketch and label a rapid granular filter identifying the following pertinent features:
inlet main, outlet main, wash water outlet, gullet, support media (graded gravel), graded
filter medium, and backwash troughs.
2. Define effective size and uniformity coefficient and explain their
use in designing a
rapid sand filter.
3. Compare the microscopic and macroscopic models of filtration with respect to explain-
ing the mechanisms of filtration and the ability to predict the time to turbidity break-
through and the time to reach the limiting headloss.
4. From a design point of view, explain the role of filtration rate, grain
size distribution,
and porosity in controlling headloss through a granular filter.
5. Explain the role of estimating the depth of the expanded bed in designing the rapid
granular filter.
6. Compare the advantages and disadvantages in selecting the type of filter, that is, sand,
dual media, or deep bed monomediu
m anthracite.
7. Qualitatively compare the effectiveness of bed expansion and surface wash in back-
washing a filter.
8. Explain why it is important to provide for “filter-to-waste” or “filter to recycle” in the
filter design.
GRANULAR FILTRATION 11-47
W ith the use of this text, you should be able to do the following:
9 . Perform a grain size analysis and determine the effective size and uniformity coef-
ficient.
10. Calculate the headloss through a clean stratified filter bed and determine if it is
excessive.
11. Calculate the depth of an expanded filter bed during backwash and lo
cate the backwash
trough elevation with respect to the top of the filter bed during filtration.
12. Calculate the number and size of filter beds given the maximum day flow rate and the
filtration rate.
13. Calculate the equivalent diameter for a filter media having a specific gravity different
from sand.
14. Design a backwash system including the layou
t for the placement of backwash troughs,
size of the troughs, trough elevation, and the volume of backwash tank.
15. Determine gullet dimensions (depth and width) given the length, backwash flow rate,
and wash water velocity in the effluent pipe.
16. Calculate the maximum headloss that can be achieved without creating a negative pres-
sure in the filter med
ia.
11-9 PROBLEMS
11-1. For a flow of 0.8 m
3
/ s, how many rapid sand filter boxes of dimensions 10 m 20 m
are needed for a hydraulic loading rate of 110 m
3
/ d · m
2
?
11-2. If a dual-media filter with a hydraulic loading rate of 300 m
3
/ d · m
2
were built instead
of the standard filter in Problem 11-1 , how many filter boxes would be required?
11-3. The water flow meter at the Troublesome Creek water plant is malfunctioning. The
plant superintendent tells you the four dual media filters (each 5.00 m 10.0 m) are
loaded at a velocity of 280 m/d. What is the flow rate through the filter
s in m
3
/ s?
11-4. A plant expansion is planned for Urbana. The new design flow rate is 1.0 m
3
/ s.
A deep bed monomedia filter with a design loading rate of 600 m
3
/ d · m
2
of filter
is to be used. If each filter box is limited to 50 m
2
of surface area, how many filter
boxes will be required? Check the design loading with one filter box out of service.
Propose an alternative design if the design loading rate is exceeded with one filter
box out of service.
11-5. The Orono Sand and Gravel Company has made a bid to supply sand for Eau Gaul-
lie’s new s
and filter. The request for bids stipulated that the sand have an effective
size in the range 0.35 to 0.55 mm and a uniformity coefficient in the range 1.3 to 1.7.
Orono supplied the following sieve analysis as evidence that their sand will meet the
specifications. Perform a grain size analysis (semilog plot) and determine whether or
not the sand m
eets the specifications. Use a spreadsheet program you have written to
plot the data and fit a curve.
11-48 WATER AND WASTEWATER ENGINEERING
U.S. Standard Sieve No. Mass percent retained
8 0.0
12 0.01
16 0.39
20 5.70
3025.90
40 44.00
50 20.20
70 3.70
100 0.10
Sand analysis
11-6. The Lexington Sand and Gravel Company has made a bid to supply sand for
Laramie’s new sand filter. The request for bids stipulated that the sand have an
effective size in the range 0.35 to 0.55 mm and a uniformity coefficient in the range
1.3 to 1.7. Lexington supplied the following sieve analysis (sample size
500.00 g)
as evidence that its sand will meet the specifications. Perform a grain size analysis
(log-log plot) and determine whether or not the sand meets the specifications. Use a
spreadsheet program you have written to plot the data and fit a curve.
U.S. Standard
Sieve No.
Mass
retained, g
12 0.00
16 2.00
20 65.50
30 272.50
40 151.0
50 8.925
70 0.075
Sand analysis
11-7. Rework Example 11-1 with the 70, 100, and 140 sieve fractions removed. Assume
the original sample contained 100 g.
11-8. The selection of an appropriate clean bed headloss equation is, in part, based on the
acceptable upper bound of the Reynolds number that is appropriate for the equation.
If the Rose equation (Equation 11-9) is suitable up to R of 6, determine the upper
filtration rate for san
d and anthracite beyond which it is not recommended. Use a
spreadsheet program you have written, plot the Reynolds number versus the filtration
rate for the following cases:
a . Sand
E
v
a
0 5
7 5 12 15 20
.
.; ; ; ;
mm
m/h m/h m/h m/h m/h
Water temperature C
25
15
GRANULAR FILTRATION 11-49
b. Anthracite coal
E
v
a
11
7 5 12 15 20
.
.; ; ; ;
mm
m/h m/h m/h m/h m/h
Water temperature
C
25
15
U se the following equation to calculate the Reynolds number.
R
()()() ()()
vd vd
aa
where density, kg/m
3
v
a
approach velocity
d effective diameter of media (E)
dynamic viscosity, Pa · s
kinematic viscosity, m
2
/ s
11-9. The Ergun equation for calculating clean bed headloss ( Table 11-2 ) has been pro-
posed for use in cases where larger media and higher filtration rates are used such
as deep bed monomedium filters. The first term in the Ergun equation accounts for
viscous forces. The sec
ond term accounts for inertial forces. Calculate the ratio of the
inertial term to the total headloss estimate for various filtration rates using a spread-
sheet you have written. Assume the following values:
k
v
228
0.50
1.14 10
3
Pa · s
L 1.5 m
999 kg/m
3
d 1.1 mm
g 9.81 m/s
2
k
i
4.4
Identify the filtration rate at which the inertial term accounts for half of the clean bed
headloss. See Trussell and Chang (1999) for more on k
v
and k
i.
11-10. The rapid sand filter being designed for Eau Gaullie has the characteristics and sieve
analysis shown below. Using the Rose equation, determine the headloss for the clean
filter bed in a stratified condition.
Depth 0.60 m
Filtration rate 120 m
3
/ d · m
2
Sand specific gravity 2.50
Shape factor 0.80
Stratified bed porosity 0.42
Water temperature 19 C
11-50 WATER AND WASTEWATER ENGINEERING
U.S. Standard
Sieve No.
Mass percent
retained
8–12 0.01
12–16 0.39
16–20 5.70
20–3025.90
30–40 44.00
40–50 20.20
50–70 3.70
70–100 0.10
Sand analysis
11-11. Determine the height of the expanded bed for the sand used in Problem 11-10 if the
backwash rate is 1,000 m/d.
11-12. The rapid sand filter being designed for Laramie has the characteristics shown below.
Using the Rose equation, determine the headloss for the clean filter bed in a stratified
condition.
Depth 0.75 m
Filtration rate 230 m
3
/ d · m
2
Sand specific gravity 2.80
Shape factor 0.80
Stratified bed porosity 0.50
Water temperature 5 C
Sand analysis
U.S. Standard
Sieve No.
Mass percent
retained
8–12 0.00
12–16 0.40
16–20 13.10
20–30 54.50
30–40 30.20
40–50 1.785
50–70 0.015
11-13. Determine the maximum backwash rate and the height of the expanded bed for the
sand used in Problem 11-12 .
11-14. As noted in Example 11-2 , the headloss was too high. Rework the example without
the 100–140 sieve fraction to see how much this would improve the headloss charac-
teristics. Assume that the fraction above
sieve size number 8 does not contribute to
the headloss and that recalculation of the percentages is not required.
GRANULAR FILTRATION 11-51
11-15. What effect does removing the 100–140 sieve fraction have on the depth of the ex-
panded bed in Example 11-3 ?
11-16. Determine the number of filter beds for Eau Gaullie ( Problem 11-10 ) if the maximum
day design flow rate is 3,800 m
3
/ d.
11-17. Determine the number of filter beds for Laramie ( Problem 11-12 ) if the maximum
day design flow rate is 55,000 m
3
/ d.
11-18. In the continuing design of Eau Gaullie’s rapid sand filter ( Problems 11-10 , 11-11 ,
and 11-16 ), determine the area of each filter cell and the plan dimensions of a filter
box. Assume a gullet width of 0.5 m.
11-19. In the continuing design of Laramie’s rapid sand filter ( Problems 11-12 , 11-13 and
11-17 ), determine the area of each filter c
ell and the plan dimens ions of a filter box.
Assume a gullet wid th of 0.8 m.
11-20. Design the backwash system for Eau Gaullie’s rapid sand filter. Use the filter dimen-
sions from Problem 11-18 . The backwash system includes the layout of the back-
wash troughs, backwash veloc
ity, flow rate of backwash water per trough, the trough
dimension (width and depth), trough elevation, volume of backwash tank, and eleva-
tion of the lowest water level in the backwash tank.
11-21. Design the backwash system for Laramie’s rapid sand filter. Use the filter dimen-
sions from Problem 11-19 . The backwash system includes the layo
ut of the back-
wash troughs, backwash velocity, flow rate of backwash water per trough, the trough
dimension (width and depth), trough elevation, volume of backwash tank, and eleva-
tion of the lowest water level in the backwash tank.
11-22. Determine the gullet dimensions for Eau Gaullie’s rapid sand filter. Use the filter di-
mensions from Problem 11-18 and
the backwash rate from Problem 11-20 . Assume a
250 mm diameter pipe from the gullet is to carry the wash water at a velocity of
0.9 m/s.
11-23. Determine the gullet dimensions for Laram ie’s rapid sand filter. Use the filter d i-
mensions from Problem 11-19 and the backwash rate from Problem 11-21 . Assume
a 700 mm d
iameter pipe from the gullet is to carry the wash water at a velocity of
1.2 m/s.
11-24. Determine the depth of the filter box for Eau Gaullie’s sand filter. Use the clean bed
headloss from Problem 11-10 and velocity headloss from Problem 11-22 . Assume
the minimum depth of water above the filter bed is 2.4 m, that the gravel is 0.25 m
d
eep, and that the depth of the underdrain is 0.25 m.
11-25. Determine the depth of the filter box for Laramie’s sand filter. Use the clean bed
headloss from Problem 11-12 and velocity headloss from Problem 11-23 . Assume
the minimum depth of water above the filter bed is 2.4 m and that an IMS drain that
is 30 cm d
eep is used.
11-26. Design the structural components * of a rapid sand filter for the village of Waffle. The
maximum day flow rate is 8,700 m
3
/ d. The design criteria and sand analysis are given
*These do not include the pipe gallery or control system.
11-52 WATER AND WASTEWATER ENGINEERING
below. Assume a 375 mm diameter pipe from the gullet is to carry the wash water at
a velocity of 1.2 m/s. Verify that the sand meets the GLUMRB recommendations for
E and U. A djust the grain size distribution if the sand does not meet the specification.
Depth 0.50 m
Filtration rate
150 m
3
/ d · m
2
Sand specific gravity 2.65
Shape factor 0.75
Stratified bed porosity 0.40
Water temperature 10 C
Trial backwash velocity 65 m/h
Trial gullet width 0.5 m
U n derdrain 30 cm deep filter block with 1 mm orifice
Gravel support 32 cm in 4 lay
ers
S urface wash revolving arms at GLUMRB recommended rate
The following is to be provided to complete this portion of the filter design:
Clean bed headloss
B a ckwash velocity
Depth of expanded bed
N umber of filter beds
Area of an individual filter bed
Plan dimensions
B a ckwash trough layout
M a ximum backwash water trough flow rate
B a ckwas
h trough dimensions
B a ckwash trough weir elevation above undisturbed bed
U.S. Standard
Sieve No.
Mass percent
retained
10–14 2.0
14–20 16.5
20–25 15.4
25–30 38.2
30–35 15.9
35–40 6.5
40–50 4.4
50–60 1.0
Sand analysis
NOTE: geometric mean diameter of successive sieves is d
g
( d
1
d
2
)
0.5
.
GRANULAR FILTRATION 11-53
G ullet dimensions
B a ckwash water volume
B a ckwash tank volume
M a ximum allowable filtration headloss
Depth of filter box
B a ckwash tank low water elevation
11-27. Design the structural components of a dual-media rapid filter for the city of Apple
Valley. The maximum day flow rate is 45,000 m
3
/ d. The design criteria and media
analyses are given below. Assume a 525 mm diameter pipe from the gullet is to carry
the wash water at a velocity of 1.5 m/s. Verify that the sand meets the GLUMRB
recommendations for E and U. Adjust the grain size distribution if the sand d
oes not
meet the specification. Also verify that largest grain size anthracite coal will have the
same approximate settling velocity as the finest sand grain size.
Filtration rate 15 m/h
Water temperature 12 C
B a ckwash 85 m/h
Trial gullet width 0.8 m
U n derdrain 30 cm deep fine sc
reen
Gravel support none required
S urface wash revolving arms at GLUMRB recommended rate
Air scour at GLUMRB recommended rate
Parameter Sand Anthracite coal
Depth 0.30 m 0.50 m
Sand specific gravity 2.65 1.60
Shape factor 0.75 0.75
Stratified bed porosity 0.47 0.60
Media characteristics
U.S. Standard
Sieve No.
Sand
mass percent
retained
Anthracite
coal mass percent
retained
4–7 9.9
7–8 13.0
8–10 28.0
10–12 20.0
12–14 13.3
14–16 8.62
Media analysis
(continued)
11-54 WATER AND WASTEWATER ENGINEERING
The following is to be provided to complete this portion of the filter design:
Clean bed headloss
B a ckwash velocity
Depth of expanded bed
N umber of filter beds
Area of an individual filter bed
Plan dimensions
B a ckwash trough layout
M a ximum backwash water trough flow rate
B a ckwas
h trough dimensions
B a ckwash trough weir elevation above undisturbed bed
G ullet dimensions
B a ckwash water volume
B a ckwash tank volume
M a ximum allowable filtration headloss
Depth of filter box
B a ckwash tank low water elevation
11-10 DISCUSSION QUESTIONS
11-1. Identify two design parameters that may be adjusted if the clean bed headloss in a
granular filter is too large.
11-2. Which of the following granular filtration systems should be chosen if the quality of
raw water is highly variable: (a) dual media, (b) monomedia?
U.S. Standard
Sieve No.
Sand
mass percent
retained
Anthracite
coal mass percent
retained
16–18 4.22
18–20 10.60 2.96
20–25 41.50
25–30 31.10
30–35 9.70
35–40 4.7
40–45 2.4
Media analysis (continued)
NOTE: geometric mean diameter of successive sieves is d
g
( d
1
d
2
)
0.5
.
GRANULAR FILTRATION 11-55
11-3. Explain what air binding is, and describe the design method for avoiding it.
11-4. Explain the purpose of “filter-to-waste.”
11-11 REFERENCES
A mirtharajah, A. (1978) “Design of Granular-Media Filter Units,” in R. L. Sanks (ed.), Water Treatment
Plant Design for the Practicing Engineer, Ann Arbor Science, Ann Arbor, Michigan, pp. 675–737.
A mirtharajah, A. and D. P. Wetstein (1980) “Initial Degradation of Effluent Quality During Filtration,”
Journal American Water Works Association, vol. 72, no. 9, pp. 518–524.
A mirtharajah, A. (1988) “Some Theoretical and Conceptual Views of Filtration,” Journal American
Water Works Association, vol. 80, no. 12, pp. 36–46.
AWWA (1996) ANSI/AWWA Standar
d No. B604-96, Standard for Granular Activated Carbon,
American Water Works Association, Denver, Colorado.
AWWA (2001) ANSI/AWWA Standard No. B100-01, Standard for Filtering Material, American Water
Works Association, Denver,Colorado.
AWWA (2002) Filter Maintenance and Operations Guidance Manual, AWWA and AWWA Research
Foundation, Denver,Colorado.
Baumann, E. R. (1978) in R. L. Sanks, ed., Water Treatment Plant Design for the Practicing Engineer,
Ann Arbor Science, Ann Arbor, Michigan, pp. 231–281.
Camp, T. R (1970) “Water Treatm
ent,” in V. Davis (ed.) Handbook of Applied Hydraulics, 3rd ed.,
McGraw-Hill, NewYork, p. 38–52.
Carmen, P. C. (1937) “Fluid Flow through Granular Beds,” Transactions of Institute of Chemical
Engineers, London, vol. 15, p. 150.
Castro, K., G. Logsdon, and S. R. Martin (2005) “High-Rate Granular Media Filtration,” in E. E. Baruth
(ed.), Water Treatment Plant Design, American Water Works Association and American Society of
Civil Engineers, McGraw-Hill, New York, p. 8.1–8.41.
Cleasby, J. L. (1972) “Filtration,” in W. J. Weber, Jr., (ed.) Physicochemical Processes for Water Quality
Control, Wiley-Interscience, NewYork, pp. 173–174.
Cleasby, J. L. and G. S. Logsdon (1999) “Granular Bed and Precoat Filtration, in R. D. Letterman (ed.)
Water Quality and Treatment, 5th ed., American Water Works Association, McGraw-Hill,
NewYork, pp. 8.1–8.99.
Cornwell, D. A. and R. G. Lee (1994) “Waste Stream Recycling: Its Effect on Water Quality,” Journal of
the Amer
ican Water Works Association, November, p. 50.
Cornwell, D. A. et al. (2001) Treatment Options for Giardia, Cryptosporidium and Other Contaminants
in Recycled Backwash Water, American Water Works Association Research Foundation, Denver,
Colorado.
Dharmarajah, A. H., and J. L. Cleasby (1986) “Predicting the Expansion Behavior of Filter Media,”
Journal of the American Water Works Association, December, pp. 66–76.
Ergun, S. (1952) “Fluid Flow Through Pa
cked Columns,” Chemical Engineering Progress, vol. 48,
no. 2, p. 89.
Fair, G. M. and J. C. Geyer (1954) “ Water Supply and Waste-Water Disposal, John Wiley & Sons, New
York, p. 678.
Fair, G. M. and L. P. Hatch (1933) “ Fundamental Factors Governing the streamline Flow of Water
Through Sand, ” Journal of American Water Works Association, vol. 25, no. 11, p. 1551.
Ferry, J. D. (1936) “Statistical Evaluation of Sieve Constants in Ultrafiltration,” Journal of General
Physiology,
vol. 20, pp. 95–104.
GLUMRB (2003) Recommended Standards for Water Works, Great Lakes–Upper Mississippi River
Board of State and Provincial Public Health and Environmental Managers, Health Education
Services, Albany, New York, p. 40–54.