Water and Wastewater Engineering
Подождите немного. Документ загружается.
10-40 WATER AND WASTEWATER ENGINEERING
10-7 PROBLEMS
10-1. Calculate the diameter of a discrete particle whose terminal settling velocity is 1.044
cm/s. The particle density is 2.65 g/cm
3
and the water temperature is 12 C. Assume
Stokes’ law applies and that the density of water is 1,000 kg/m
3
.
10-2. You have been asked to evaluate the ability of a horizontal flow gravity grit chamber
to remove particles having a diameter of 1.71 10
4
m. The depth of the grit cham-
ber is 1.0 m. The detention time of the liquid in the grit chamber is 60 s. The particle
density is 1.83 g/cm
3
. The water temperature is 12 C. Assume the density of water is
1,000 kg/m
3
.
10-3. If the settling velocity of a particle is 0.70 cm/s and the overflow rate of a hori-
zontal flow clarifier is 0.80 cm/s, what percent of the particles are retained in the
clarifier?
10-4. If the settling velocity of a particle is 2.80 mm/s and the overflow rate of an up-
flow clarifier is 0.560 cm/s, what percent of the particles are retained in the
clarifier?
10-5. If the settling velocity of a particle i
s 0.30 cm/s and the overflow rate of a horizon-
tal flow clarifier is 0.25 cm/s, what percent of the particles are retained in the
clarifier?
10-6. If the flow rate of the original plant in Problem 10-3 is increased from 0.150 m
3
/ s to
0.200 m
3
/ s, what percent removal of particles would be expected?
10-7. If the flow rate of the original plant in Problem 10-4 is doubled, what percent re-
moval of particles would be expected?
10-8. If the flow rate of the original plant in Problem 10-5 is doubled, what percent re-
moval of particles would be expected?
10-9. If a 1.0-m
3
/ s flow water treatment plant uses 10 sedimentation basins with an over-
flow rate of 15 m
3
/ d · m
2
, what should be the surface area (m
2
) of each tank?
10-10. Assuming a conservative value for an overflow rate, determine the surface area
(in m
2
) of each of two sedimentation tanks that together must handle a flow of
0.05162 m
3
/ s of lime softening floc.
10-11. Repeat Problem 10-10 for an alum or iron floc.
10-12. Two sedimentation tanks operate in parallel. The combined flow to the two tanks is
0.1000 m
3
/ s. The depth of each tank is 2.00 m and each has a detention time of 4.00 h.
What is the surface area of each tank, and what is the overflow rate of each tank in
m
3
/ d · m
2
?
10-13. Determine the detention time and overflow rate for a settling tank that will reduce the
influent suspended solids concentration from 33.0 mg/L to 15.0 mg/L. The following
batch settling column data are available. The data given are percent removals at the
sample times and depths shown.
SEDIMENTATION 10-41
Depths,
a
Time, min 0.5 1.5 2.53.5 4.5
10 50 32201815
20 75 45353025
40 85 65 48 43 40
55 90 75 60 5046
85 95 87 75 65 60
95 95 88 80 70 63
a
Depths from top of column, column depth 4.5 m.
10-14. The following test data were gathered to design a settling tank. The initial suspended
solids concentration for the test was 20.0 mg/L. Determine the detention time and
overflow rate that will yield 60% removal of suspended solids. The data given are
suspended solids concentrations in mg/L.
Time, min
Depth,
a
m
10 20 35 507085
0.5 14.0 10.0 7.0 6.2 5.0 4.0
1.0 15.0 13.0 10.6 8.2 7.0 6.0
1.5 15.4 14.2 12.0 10.0 7.8 7.0
2.0 16.0 14.6 12.6 11.0 9.0 8.0
2.5 17.0 15.0 13.0 11.4 10.0 8.8
a
Depths from top of column, column depth 2.5 m.
10-15. The following test data were gathered to design a settling tank. The initial turbidity
for the test was 33.0 NTU. Determine the detention time and overflow rate that will
yield 88% removal of suspended solids. The data given are suspended solids concen-
trations in NTU.
Time, min
Depth,
a
m
30 60 90 120
1.0 5.6 2.0
2.0 11.2 5.9 2.6
3.5 14.5 9.9 6.6 3.0
a
Depths from top of column, column depth 4.0 m.
10-16. Design a horizontal flow rectangular sedimentation basin for a maxim um day
design flow rate of 25,000 m
3
/ d. Assume an overflow rate of 40 m
3
/ d · m
2
and
10-42 WATER AND WASTEWATER ENGINEERING
a water temperature of 12 C. Provide the following in your summary of the de-
sign:
Q
design
N umber of tanks
W i dth of each tank
Length of each tank
S i de water depth
Depth of sludge zone
L:D
v
f
R e ynolds number
N umber of launders
L a under length
Weir loading
T ype of sludge collector
10-17. Design a horizontal flow rectangular sedimentation basin for a maximum day design
flow rate of 15,000 m
3
/ d. Assume an overflow rate of 50 m
3
/ d · m
2
and a water tem-
perature of 15 C. Provide the following in your summary of the design:
Q
design
N umber of tanks
W i dth of each tank
Length of each tank
S i de water depth
Depth of sludge zone
L:D
v
f
R e ynolds number
N umber of launders
L a under length
Weir loading
T ype of sludge collector
10-18. Design a horizontal flow rectangular sedimentation basin using high-rate settlers for
a maximum day design flow rate of 25,000 m
3
/ d. Assume a water temperature of
12 C, that the angle of the settler tubes is 60 , and that they have a hydraulic diameter
of 0.05 m. Also assume the floc has excellent settling characteristics. Provide the fol-
lowing in your summary of the design:
Q
design
N umber of tanks
SEDIMENTATION 10-43
W i dth of each tank
Length of settler
Length of each tank
S i de water depth
Depth of sludge zone
v
approach
v
fc
R e ynolds number
Froude number
N umber of launders
L a under length
Weir loading
T ype of sludge collector
10-19. Design a horizontal flow rectangular sedimentation basin using high-rate settlers for
a maximum day design flow rate of 15,000 m
3
/ d. Assume a water temperature of
15 C, that the angle of the settler tubes is 60 , and that they have a hydraulic diameter
of 0.05 m. Also assume the floc has excellent settling characteristics. Provide the fol-
lowing in your summary of the design:
Q
design
N umber of tanks
W i dth of each tank
Length of settler
Length of each tank
S i de water depth
Depth of sludge zone
v
approach
v
fc
R e ynolds number
Froude number
N umber of launders
L a under length
Weir loading
T ype of sludge collector
10-8 DISCUSSION QUESTIONS
10-1. Use a scale drawing to sketch a vector diagram of a horizontal-flow sedimentation
tank that shows how 25 percent of the particles with a settling velocity one-quarter
that of the overflow rate will be removed.
10-44 WATER AND WASTEWATER ENGINEERING
10-2. Use a scale drawing to sketch a vector diagram that shows a plate settler with one
plate located at half the depth of the tank will remove 100 percent of the particles that
enter with a settling velocity equal to one-half that of the overflow rate.
10-3. Describe design remedies for the following problems in a settling tank: jetting of the
influent, density currents from cooler or warmer water, waves on the settling basin.
10-4. What design alternative i
s available to increase the Froude number of a horizontal-
flow rectangular sedimentation basin?
10-9 REFERENCES
AWWA (1990) Water Treatment Plant Design, 2nd ed., American Water Works Association, Denver,
Columbus, McGraw-Hill, New York, pp. 116, 125.
Camp, T. R. (1936) “A Study of the Rational Design of Settling Tanks,” Sewage Works Journal, vol. 8,
no. 9, pp 742–758.
Camp, T. R. (1946) “Sedimentation and the Design of Settling Tanks,” Transactions of the American
Society of Civil Engineers, vol. 111, p. 895.
Davis, M. L. and D. A. Cornwell (2008) Introduction to Envi ronmental Engineering, M cGraw-Hill,
New York, pp. 269, 281.
E ckenfel
der, W. W. (1980) Industrial Water Pollution Control, McGraw-Hill, New York, 1989, p. 61.
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, pp. 34–35.
Kawamura, S. (2000) Integrated Design and Operation of Water Treatment Facilities, 2nd ed., John
Wiley & Sons, New York, pp. 139–189.
Metcalf and Eddy (2003) Wastewater Engineering: Treatment and Reuse, 4th ed
ition, McGraw-Hill,
Boston, MA, p. 379.
MWH (2005) Water Treatment: Principles and Design, John Wiley & Sons, Hoboken, New Jersey,
pp. 811–814, 824–829.
Newton, I. (1687) Philosophiae Naturalis Principia Mathematica.
Pierpont, J. W. and M. Alvarez (2005) “ Optimizing Ballasted Sedimentation for Organics-Laden Surface
Water,” Opflow, JUL, p. 15.
Reynolds, O. (1883) “An Experimental Investigation of the Circumstances Which Determine Whether
the Motion of Water Shall Be Dire
ct or Sinuous and the Laws of Resistance in Parallel Channels,”
Transactions of the Royal Society of London, vol. 174.
Stokes, G. G. (1845) Transactions of the Cambridge Philosophical Society, vol. 8, p. 287.
Walker, J. D. (1978) “Sedimentation,” in R. L. Sanks (ed.) Water Treatment Plant Design for the
Practicing Engineer, Ann Arbor Science, Ann Arbor, Michigan, pp. 149–182.
Willis, J. F. (2005) “Clarification,” in E. E. Baruth, (ed.), Water Treatment Plant Design, American Water
Works Association and American Society of Civil Engineers, McGraw-Hill, New york, p. 7.1–10-44.
Yao, K. M. (1970) “Theoretical Study of High-Rate Sedimentation,” Journal of Water Pollution Control
Federation, vol. 42, p. 218.
11-1
11-6 GRANULAR FILTRATION PRACTICE
11-7 OPERATION AND MAINTENANCE
11-8 CHAPTER REVIEW
11-9 PROBLEMS
11-10 DISCUSSION QUESTIONS
11-11 REFERENCES
GRANULAR FILTRATION
11-1 INTRODUCTION
11-2 AN OVERVIEW OF THE FILTRATION
PROCESS
11-3 FILTER MEDIA CHARACTERISTICS
11-4 GRANULAR FILTRATION THEORY
11-5 THEORY OF GRANULAR FILTER
HYDRAULICS
11
CHAPTER
11-2 WATER AND WASTEWATER ENGINEERING
11-1 INTRODUCTION
Settled water turbidity is generally in the range from 1 to 10 NTU with a typical value being
2 NTU. Because these levels of turbidity interfere with the subsequent disinfection processes,
the turbidity must be reduced. The Interim Enhanced Surface Water Treatment Rule (IESWTR)
promulgated by the U.S. Environmental Protection Agency (EPA) requ
ires that the treated water
turbidity level be 0.3 NTU in 95 percent of monthly measurements with no sample to exceed 1
NTU. In order to reduce the turbidity to this level, a filtration process is normally used. The most
common filtration process is granular filtration where the suspended or colloidal impurities
are
separated from water by passage through a porous medium. The medium is usually a bed of sand
or other media such as coal, activated carbon, or garnet. In the last two decades, filters composed
of membranes have been employed with increasing frequen
cy. Granular filtration process are the
subject of this chapter. Membrane processes are discussed in Chapter 12.
11-2 AN OVERVIEW OF THE FILTRATION PROCESS
A n umber of classification systems are used to desc ribe granular filters including media type,
filtration rate, washing technique, and filtration rate control. This discussion is limited to slow
sand, rapid sand, and high-rate filters with either multimedia or deep monomedium the focu
s
is on rapid sand and high-rate filters. Pressure filters (also called precoat filters) and automatic
backwash filters are not discussed. Discussion of these types of filters may be found in Cleasby
and Logsdon, 1999; Kawamura, 2000; MWH, 2005; Reynolds and Richards, 1996.
Granu
lar filters are called depth filters because the particulate matter in the water penetrates
into the filter as well as being caught on the surface. Figure 11-1 shows a cutaway drawing of a
Filter media
Graded gravel
Underdrain blocks
Outlet main
Wash water
outlet
Inlet
main
Gullet
Wash trough
Surface wash unit
FIGURE 11-1
T ypical gravity filter box. ( Source: F. B. Leopold Co.)
GRANULAR FILTRATION 11-3
conventional depth filter. The bottom of the filter consists of a support media and water collec-
tion system. The support media is designed to keep the filtration media (sand, coal, etc.) in the
filter and prevent it from leaving with the filtered water. Layers of graded gravel (large on bot-
tom, small on top) traditionally have been used for the support. The underdrain block
s collect the
filtered water. In newer designs, integrated media support (IMS
®
) that combines a synthetic layer
with a synthetic underdrain block is being used.
In a conventional filter, water containing the suspended matter is applied to the top of the
filter. The suspended matter is filtered from the water. As material accumulates in the interstices
of the granular medium, the headloss thro
ugh the filter increases. When either the headloss or the
effluent turbidity reaches a predetermined limit, filtration is terminated and the filter is cleaned.
Under ideal conditions, the time required for headloss to reach the preselected value (called the
terminal headloss ) corresponds to the time when the turbidity in the effl
uent reaches its pre-
selected value. In actual practice, one or the other will govern the cleaning cycle. The filter is
cleaned by backwashing; that is, clean water is pumped backwards through the filter.
A s illustrated in Figure 11-2 , the efficiency of particle removal varies during the filtration
cycle (called a filter run ). The ripening or maturat
ion stage occurs initially as the filter is put back
0
0
2.0
1.0
0.2
0.4
0.6
0.8
1.0
5
20
0
40 60 80 100
10 15
minutes
Filter ripening
Time of filter run
Terminal headloss
Headloss through filter
Clean bed headloss
Time of filter run, h
Effluent turbidity, NTU
Headloss, m
hours
Run terminated
20 2530 20 40 60 80 100
Run terminated
FIGURE 11-2
I dealized turbidity and headloss during a filter run. Note changes in time scale.
11-4 WATER AND WASTEWATER ENGINEERING
into service after cleaning. The peak occurs because of residual backwash water being flushed
from the media, and from particles in the influent water that are too small to be captured. As the
clean media captures particles, it becomes more efficient because the particles that are captured
beco
me part of the collector surface in the filter. Amirtharajah (1988) suggests that up to 90 per-
cent of the particles that pass through a well-operating filter do so during the ripening stage.
After ripening, the effluent turbidity is essentially constant and, under steady-state condi-
tions, can be maintained below 0.1 NTU. On the other hand, headloss continues to rise as
par-
ticles collect in the filter. At some point the number of particles that can be effectively captured
begins to decline and breakthrough occurs.
Nomenclature
There are several methods of classifying filters. One way is to classify them according to the type
of medium used, such as sand, coal (called anthracite ), dual media ( coal plus sand), or mixed
media ( coal, sand, and garnet). Another common way to cla
ssify the filters is by nominal filtra-
tion rate or hydraulic loading rate ( m
3
of water applied/d · m
2
of surface area, or m/d). A third
alternative is to classify the filters by the pretreatment level.
Based on the hydraulic rate, the filters are described as being slow sand filters, rapid sand
filters, or high-rate filters.
Slow sand filters were first introduced in the 1800s. The water is applied to the sand at a
loading rate of 3 to 8 m
3
/ d · m
2
. As the suspended or colloid al material is applied to the sand,
the particles begin to collect in the top 75 mm and to clog the pore spaces. As the pores become
clogged, water will no longer pass through the sand. At this point the top layer of sand is scraped
off, cleaned, and replaced. Although slow sand
filters require large areas of land and are labor
intensive, the structures are inexpensive in comparison to the other types, and they have a long
history of success.
In the late 1800s, health authorities began to understand that clean water was a major fac-
tor in preventing disease. The limitations of slow sand filters in meeting the need for filtration
systems
to serve large populations became readily apparent. Rapid sand filters were developed to
meet this need. These filters have graded (layered) sand in a bed. The sand grain size distribution
is selected to optimize the passage of water while minimizing the passage of particulate matter.
Rapid sand filters are cleaned in place by
backwashing. The wash water flow rate is such that
the sand bed is expanded and the filtered particles are removed from the bed. After backwashing,
the sand settles back into place. The largest particles settle first, resulting in a fine sand layer on
top and a coarse sand layer on the bottom. Rapid sand filters are the
most common type of filter
in service in water treatment plants today.
Traditionally, rapid sand filters have been designed to operate at a loading rate of 120 m
3
/
d · m
2
( 5 m/h). Filters now operate successfu lly at even higher loading rates through the use of
proper media selection and improved pretreatment.
In the wartime era of the early 1940s, dual media filters were developed. They are designed
to utilize more of the filter depth for particle removal. In a rapid sand filter, the finest sand is on
the top; hence, the sm
allest pore spaces are also on the top. Therefore, most of the particles will
clog in the top layer of the filter. In order to use more of the filter depth for particle removal, it is
necessary to have the large particles on top of the small particles. This is accomplished by placing
a layer of coarse coal on top of a layer of fine sand to form a dual-media filter. Coal has a lower
specific
gravity than sand, so, after backwash, it settles more slowly than the sand and ends up on
top. Some dual-media filters are operated up to loading rates of 480 m
3
/ d · m
2
(20 m/h).
GRANULAR FILTRATION 11-5
In the mid-1980s, deep-bed, monomedi a filters c ame into use. The filters are designed to
achieve higher loading rates while at the same time producing lower turbidity in the finished
water. They operate at loading rates up to 600 m
3
/ d · m
2
(25 m/h).
When pretreatment of the water is by coagulant addition, flocculation, and clarification, the
filter is classified as conventional filtration. If pretreatment consists of coagulation and floccula-
tion but not clarification, the filtration process is called direct filtration. The process is called
in-line or contact filtration when coagu
lant addition but only incidental flocculation is used. In
some processes, coagulation is followed by two filtration steps: a roughing filter followed by
another filter.
11-3 FILTER MEDIA CHARACTERISTICS
Grain Size
The grain size, or perhaps m ore correctly the grain size distribution, affects both the hydraulic
performance of the filtration process and the efficiency of particle removal.
The size distribution, or variation, of a sample of granular material is determined by passing
the sample through a series of standard sieves (
screens). One standard series is the U.S. Standard
Sieve Series. The U.S. Standard Sieve Series (Appendix B) is based on a sieve opening of 1 mm.
Sieves in the “fine series” stand successively in the ratio of (2)
0.25
to one another, the largest
opening in this series being 5.66 mm and the smallest 0.037 mm. All material that passes through
the smallest sieve opening in the series is caught in a pan that acts as the terminus of the series
(Fair and Geyer, 1954).
The grain size analysis begins by placing the sieve screens in ascending order with the
largest opening on top and the smallest opening on the bottom. A sand sample is placed on
the top sieve, and the stack is shaken for a prescribed amount of time. At the end of the shak-
ing period, the mass of material retained on each sieve is determined. The cumulative mass is
recorded and converted into percentage
s by mass equal to or less than the size of separation
of the overlying sieve. Then a cumulative frequency distribution is plotted. For many natural
granular materials, this curve approaches geometric normality. Logarithmic-probability paper,
therefore, results in an almost straight-line plot. This facilitates interpolation. The geometric
mean ( X
g
) and geometric standard deviation ( S
g
) are useful parameters of central tendency and
variation. Their magnitud es may be determined from the plot. The parameters most commonly
used, however, are the effective size, E, and the uniformity coefficient, U. The effective size is
the 10 percentile size, that is, the media grain diameter at which 10 percent of the m
edia by
weight is smaller, d
10
. The uniformity coefficient is the ratio of the diameter of media at which
60 percent by weight is smaller to the 10 percentile sizes, d
60
/ d
10
. Use of the 10 percentile was
suggested by Allen Hazen because he observed that resistance to the passage of water offered
by a bed of sand within which the grains are distributed homogeneously remains almost the
sam e, irrespective of size variation (up to a uniformity coefficient of about 5.0), provided that
the 10 percentile remains unchanged (Hazen, 1892). Use of the ratio of the 60 percentile to the
10 percentile as a measure of uniformity was suggested by Hazen because this ratio covered the
range in size of half the sand. * On the basis of logarithmic normality, the probability integral
*It would be logical to speak of this ratio as a coefficient of nonuniformity because the coefficient increases as the magnitude
of nonuniformity increases.