Water and Wastewater Engineering
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6-56 WATER AND WASTEWATER ENGINEERING
4.2m
2.5m
w
w
D
One paddle wheel
w0.14 m
Profile
15 m
0.8 m0.8 m
0.4 m
Plan
Baffle Baffle
0.4 m
0.4
0.4 m
4.2 m
5.0 m
Flow
Flow
3 Cross-flow
paddle wheels
on each shaft
0.4 m
10.3 m
1.0 m1.0 m
2.5 m
2.5 m
2.5 m
0.4 m
4.2 m 4.2 m 4.2 m
FIGURE P-6-23
(Source: Peavy et al., 1985.)
6-22. Design the first compartment of a cross-flow paddle flocculator for the city of None-
such by determining the basin dimensions, the paddle configuration, the power
requirement, motor power, and rotational speeds for the following parameters:
D e sign flow rate 36 10
3
m
3
/ d
t 23 min
Three flocculator compartments with G 40, 30, 20 s
1
COAGULATION AND FLOCCULATION 6-57
For each compartment L W
Water temperature 10 C
A ssume the design recommendations in Table 6-7 apply
To complete the design, provide a dimensioned sketch of the basin and wheels.
Hint: for a first trial assume a wheel diameter of 3.5 m.
6-23.
Design the first compartment of a cross-flow paddle flocculator for the city of Some-
such by determining the basin dimensions, the paddle configuration, the power re-
quirement, motor power, and rotational speeds for the following parameters:
D e sign flow rate 28.8 10
3
m
3
/ d
t 25 min
Three flocculator compartments with G 50, 40, 20 s
1
For each compartment L W
Water temperature 5 C
A ssume the design recommendations in Table 6-7 apply
To complete the design, provide a dimensioned sketch of the basin and wheels.
Hint: for a first trial assume a wheel diameter of 3.0 m.
6-11 DISCUSSION QUESTIONS
6-1. The zeta potential of colloids measured in water from Lake Michigan would be
greater than, less than, or the same as the zeta potential for the same colloidal
dispersion measured in a water from the Atlantic ocean. Select the correct
phrase.
6-2. In Jar Test II in Example 6-3 the pH was held constant while the alum dose was
varied. Explain why the s
ettled turbidity varies from a high of 14 to a low of 4.5 and
then rises again to 13.
6-3. Which type of rapid mix (in-line blender or back mix reactor) would be selected for
the jar test data shown below.
Jar No 1 2 3 4 5
Coagulant dose, mg/L 0 5 20 50250
Final turbidity, (NTU) 8.35 8.26 7.92 7.51 6.49
Coagulant was Ferric Chloride
6-58 WATER AND WASTEWATER ENGINEERING
6 -12 REFERENCES
A mirtharajah, A. (1978) “Design of Raid Mix Units,” in R. L. Sanks (ed.) Water Treatment Plant Design
for the Practicing Engineer, Ann Arbor Science, Ann Arbor, MI, pp. 131–147.
A mirtharajah, A. and K. M. Mills (1982) “Rapid-Mix Design for Mechanisms of Alum Coagulation,
Journal of American Water Works Association, vol. 74, no. 4, pp. 210–216.
Base, C. F. and R. E. Mesmer (1976) The Hydrolysis of Cations, Wiley-Interscience, New York.
Bayer, T., K. Himmler, and V. Hessel (2003) “Don’t Be Baffled by Static Mixers,” Chemical
Engineering, May, pp. 50–57.
Birkner, F. and J. Morgan (1968) “Polymer Flocculation Kinetics of Dilute Colloidal Suspensions,”
Journal of American Water Works Association, vol. 60, no. 2, pp. 175–191.
Camp, T. R. and P. C. Stein (1943) “Velocity Gradients and Hydraulic Work in Fluid Motion,” Journal of
Hydraulics Division, American Society of Civil Engineers, vol. 102, pp. 559–568.
Davis, M. L. and D. A. Cornwell (2008) Introduction to Environmental Engineering, McGraw-Hill,
Boston, Massachusetts, p. 205.
Derjaguin, B. V. and L. D. Landau (1941) “Theory of Stability of Strongly Charged Lyophobic Soles and
Coalesance of Strongly Charged Particles in Solutions of Electrolytes, Acta Physicochim. URSS,
vol. 14, pp. 733–762.
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. 34.
Hahn, H. H. and W. Stumm (1968) “Kinetics of Coagulation with Hydrolyzed Al(III),” Journal of
Colloidal Interface Science, vol. 28, no. 1, pp. 457–467.
Hardy, W. B. (1900a) Proceedings of the Royal Society of London, vol. 66, p. 110.
Hardy, W. B. (1990b) Z. physik Chem., vol. 33, p. 385.
Harris, H. S. , W. F. Kaufm
an, and R. B. Krone (1966) “Orthokinetic Flocculation in Water Purification,”
Journal of Environmental Engineering Division, ASCE, vol. 92, pp. 95–111.
H udson, H. E. (1981) Water Clarification Processes, Practical Design and Evaluation, Van Nostrand
Reinhold, New York, pp. 115–117.
H unter, R. J. (2001) Foundations of Colloid Science, vols. 1 and 2, Oxford University Press, Oxford,
United Kingdom.
H unter, R. J. and P. S. Liss (1979) “The Surface Charge of Suspended Particles in Estuarine and Coastal
Waters,” Nature, vol. 282, p. 823.
Johnson, P. N. and A. Amirtharajah (1983) “Ferric Chloride and Alum as Single and Dual Coagulants,”
Journal of American Water Works Association, vol. 75, pp. 232–239.
Kawamura, S. (2000) Integrated Design and Operation of Water Treatment Facilities, 2nd ed. John Wiley
& Sons, New York, pp. 74–139.
Kolmogorov, A. (1941) “Dissipation Energy in Locally Isotropic Turbulence,” Dokl. Akad. Nauk. SSSR,
vol. 32, pp. 19–21.
Kruyt, H. R. (1952) Colloid Science, Elsevier, New York.
Langelier, W. F. (1921) “Coagulation of Water with Alum by Prolonged Agitation,” Engineering News
Record, vol. 86, pp. 924–928.
Letterman, R. D., J. E. Quon and R. S. Gemmell (1973) “Influence of Rapid-Mix Parameters on
Flocculation,” Journal of American Water Works Associ
ation, vol. 65, pp. 716–722.
MWH (2005) Water Treatment: Principles and Design, John Wiley & Sons, Hoboken, New Jersy,
pp. 658, 674–675, 686, 743, 750.
Niehof, R. A. and G. I. Loeb (1972) “The Surface Charge of Particulate Matter in Sea Water,” Limnology
Oceanography, vol. 17, p. 7.
O’Melia, C. R. (1972) “Coagulation and Flocculation,” in W. J. Weber, Jr. (ed.), Physicochemical
Processes for Water Quality Control, Wiley-Interscience, New York, pp. 68–69.
COAGULATION AND FLOCCULATION 6-59
Packham, R. F. (1965) “Some Studies of the Coagulation of Dispersed Clays with Hydrolyzing Salts,”
Journal of Colloid Science, vol. 20, pp. 81–92.
Peavy, H. S., D. R. Rowe, and G. Tchobanoglous (1985) Environmental Engineering, McGraw-Hill, New
York, pp. 147–151.
Reynolds, T. D. and P. A. Richards (1996) Unit Operations and Processes in Environmental Engineering,
PWS Publishing Company, Boston, pp. 181, 197, 268.
R ushton, J. H. (1952) “Mixing of Liquids in Chemical Processing,” Industrial & Engineering Chemistry,
vol. 44, no. 12, p. 2, 931.
Sawyer, C. N., P. L. McCarty and G. F. Parkin (1994) Chemistry for Environmental Engineering,
4th edition, McGraw-Hill, Inc., New York, p. 473.
S chulze, H. (1882) J. Prakt. Chem., vol 25, p. 431.
S chulze, H. (1883) J. Prakt. Chem., vol 27, p. 320.
S moluchowski, M. (1917) “Verrsuch einer mathe
matischen Theorie der Koagulationskinetic Kolloider
Losunger,” Zeit. Phys. Chemie, vol. 92, pp. 129–168.
Stumm, W. and C. R. O’Melia (1968) “Stoichiometry of Coagulation” Journal of American Water Works
Association, vol. 60, pp. 514–539.
Stumm, W. and J. J. Morgan (1970) Aquatic Chemistry, John Wiley & Sons, New York.
Verway, E. J. W. and J. T. G. Overbeek (1948) Theory of the Stability of Lyophobic Colloids, Elsevier,
Amsterdam.
Willis, J. F. (2005
) “Clarification,” in E. E. Baruth (ed.), Water Treatment Plant Design, A merican
Water Works Association and American Society of Civil Engineers, McGraw-Hill, New York,
pp. 7-24–7-25.
7-1
CHAPTER
7
LIME–SODA SOFTENING
7-1 HARDNESS
7-2 LIME-SODA SOFTENING
7-3 SOFTENING PROCESSES
7-4 CHEMICAL DOSAGES BASED
ON STOICHIOMETRY
7-5 CONCURRENT REMOVAL OF OTHER
CONSTITUENTS
7 -6 PROCESS CONFIGURATIONS
AND DESIGN CRITERIA
7-7 OPERATION AND MAINTENANCE
7-8 STABILIZATION
7-9 CHAPTER REVIEW
7-10 PROBLEMS
7-11 DISCUSSION QUESTIONS
7 -12 REFERENCES
7-2 WATER AND WASTEWATER ENGINEERING
Hardness range
(mg/L as CaCO3)Description Comment
0–50Extremely soft
50–100 Very soft
100–150 Soft to moderately hard Acceptable to most users
150–300 Hard
300 Very hard
TABLE 7-1
Hard water classification
7 -1 HARDNESS
The term hardness i s used to characterize a water that does not lather well, causes a scum in the
bath tub, and leaves hard, white, crusty deposits (scale) on coffee pots, tea kettles, and hot water
heaters. The failure to lather well and the formation of scum on bath tubs is the result of the reac-
tions of calcium and magne
sium with the soap. For example:
Ca soap Ca soap s
2
2
() ()()
(7-1)
where (s) a solid precipitate
A s a result of this complexation reaction, soap cannot interact with the dirt on clothing, and
the calcium-soap complex itself forms undesirable precipitates.
Hardness i s defined as the sum of all poly valent cations (in consistent
units). The common
units of expression are mg/L as CaCO
3
or milliequivalents per liter (meq/L). Qualitative terms
used to describe hardness are listed in Table 7-1 . The distribution of hard waters in the United
States is shown in Figure 7-1 .
Although all polyvalent cations contribute to hardness, the predominant contributors are cal-
cium and magnesium. With the exc
eption of a few other important polyvalent cations and natural
organic matter ( NOM), the focus of this discussion will be on calcium and magnesium.
Hardness in natural waters comes from the dissolution of minerals from geologic formations
that contain calcium and magnesium. Two co
mmon minerals are calcite (CaCO
3
) and dolomite
[CaMg(CO
3
)
2
]. The natural process by which water becomes hard is shown schematically in
Figure 7-2 . As rainwater enters the topsoil, the respiration of microorganisms increases the CO
2
content of the water. As shown in Equation 6-2, the CO
2
reacts with the water to form H
2
CO
3
. Cal-
cite and dolomite react with the carbonic acid to form calcium bicarbonate [Ca(HCO
3
)
2
] and mag-
nesium bicarbonate [Mg(HCO
3
)
2
]. While CaCO
3
and CaMg(CO
3
)
2
are not very soluble in water,
the bicarbonates are quite soluble. Calcium chloride (CaCl
2
), gypsum (CaSO
4
), magnesium chloride
(MgCl
2
), and magnesium sulfate (MgSO
4
) may also go into solution to contribute to the hardness.
Because calcium and magnesium predominate, the convention in performing softening
calculations is to define the total hardness (TH) of a water as the sum of these elements
TH Ca Mg
22
(7-2)
The concentrations of each element are in consistent units (mg/L as CaCO
3
or meq/L). Two
components of total hardness are: (1) that associated with the HCO
3
anion (called carbonate
hardness and abbreviated CH) and (2) that associated with other anions (called noncarbonate
hardness and abbreviated NCH). Total hardness, then, may also be defined as
TH CH NCH
(7-3)
LIME–SODA SOFTENING 7-3
Carbonate hardness is d efined as the amount of hardness equal to the total hardness or the total
alkalinity, whichever is less. Carbonate hardness is often called temporary hardness because
boiling the water removes it. Heating drives the CO
2
o ut of solution and the pH increases as
shown in Equation 6-2 and Figure 6-7. The resulting reaction is
Ca 2HCO CaCO s CO g H O
3
2
3 22
() ()
(7-4)
Extremely soft
Very soft
Soft to moderately hard
Hard
Very hard
FIGURE 7-1
General distribution of hard water in untreated municipal water supplies.
Rain
Subsoil
Topsoil
Bacterial action
CO
2
Limestone
CaCO
3
(s) H
2
CO
3
Ca(HCO
3
)
2
CO
2
H
2
O
H
2
CO
3
MgCO
3
(s) H
2
CO
3
Mg(HCO
2
)
2
FIGURE 7-2
Natural process by which water is made hard. (Source: Davis and Cornwell,
2008.)
7-4 WATER AND WASTEWATER ENGINEERING
Noncarbonate hardness is defined as the total hardness in excess of the alkalinity. If the alkalin-
ity is equal to or greater than the total hardness, then there is no noncarbonate hardness. Noncarbon-
ate hardness is called permanent hardness because it is not removed when water is heated.
Bar charts of water composition are useful in understanding the proce
ss of softening. By
convention, the bar chart is constructed with cations in the upper bar and anions in the lower bar.
In the upper bar, calcium is placed first and magnesium second. Other cations follow without any
specified order. The lower bar is constructed with bicarbonate placed first. Other anions follow
without any specified order. Construction of a bar chart is illustrated in Example 7-1.
Example 7-1. Given the following analysis of a groundwater, construct a bar chart of the con-
stituents, expressed as CaCO
3
.
Ion mg/L as ion
EW CaCO
3
/EW ion
a
mg/L as CaCO
3
Ca
2
103 2.50258
Mg
2
5.5 4.12 23
Na
16 2.18 35
HCO
3
255 0.82 209
SO
4
2
49 1.04
51
Cl
37 1.41 52
a
Equivalent weight of CaCO
3
/equivalent weight of ion.
Solution. The concentrations of the ions have been converted to CaCO
3
equivalents. The
results are plotted in Figure 7-3 .
The cations total 316 mg/L as CaCO
3
, of which 281 mg/L as CaCO
3
is hardness. The anions
total 312 mg/L as CaCO
3
, of which the carbonate hard ness is 209 mg/L as CaCO
3
. There is a
HCO
3
–
Carbonate hardness
Total hardness
Cations
Anions
0 100
Ion concentration, mg/L as CaCO
3
200
209
260
312
316
281
258
300 400
Noncarbonate
hardness
HCO
3
–
SO
4
2–
Cl
–
Ca
++
Mg
++
Na
+
FIGURE 7-3
Bar graph of groundwater constituents. (Source: Davis and Cornwell, 2008.)
LIME–SODA SOFTENING 7-5
discrepancy between the cation and anion totals bec ause there are other ions that were not ana-
lyzed. If a complete analysis were conducted, and no analytical error occurred, the equivalents of
cations would equal exactly the equivalents of anions. Typically, a complete analysis may vary
5
% because of analytical errors.
The relationships between total hardness, carbonate hardness, and noncarbonate hardness
are illustrated in Figure 7-4 . In Figure 7-4a , the total hardness is 250 mg/L as CaCO
3
,
the carbonate hardness is equal to the alkalinity
HCO
3
200 mg/L as CaCO
3
), and the
noncarbonate hardness is equal to the difference between the total hardness and the carbonate
hardness (NCH TH CH 2 50 200 50 mg/L as CaCO
3
). In Figure 7-4b , the total
hardness is again 250 mg/L as CaCO
3
. However, because the alkalinity
HCO
3
is greater than
the total hardness, and because the carbonate hardness cannot be greater than the total hard-
ness (see Equation 7-3 ), the carbonate hardness is equal to the total hardness, that is, 250
mg/L as CaCO
3
.
With the carbonate hardness equal to the total hardness, then all of the hardness is carbonate
hardness and there is no noncarbonate hardness. Note that in both cases it may be assum ed that
the pH is less than 8.3 because
HCO
3
is the only form of alkalinity present.
Example 7-2. A water has an alkalinity of 200 mg/L as CaCO
3
. The Ca
2
concentration is
160 mg/L as the ion, and the Mg
2
concentration is 40 mg/L as the ion. The pH is 8.1. Find the
total, carbonate, and noncarbonate hardness.
Solution. The molecular weights of calcium and magnesium are 40 and 24, respectively.
Because each has a valence of 2
, the corresponding equivalent weights are 20 and 12. Using
Equation 6-7 to convert mg/L as the ion to mg/L as CaCO
3
and adding the two ions as shown
in Equation 7-2 , the total hardness is
TH mg/L
mg/meq
m
g
/me
q
mg/L160
50
20
40
⎛
⎝
⎜
⎞
⎠
⎟
550
12
567
3
mg/meq
m
g
/me
q
mg/L as CaCO
⎛
⎝
⎜
⎞
⎠
⎟
where 50 is the equivalent weight of CaCO
3
.
By definition, the carbonate hardness is the lesser of the total hardness or the alkalinity.
Because, in this case, the alkalinity is less than the total hardness, the carbonate hardness (CH) is
equal to 200 mg/L as CaCO
3
. The noncarbonate hardness is equal to the difference
NCH TH CH mg/L as CaCO 567 200 367
3
Note that concentrations of Ca
2
and Mg
2
can only be added and subtracted if they are in
equivalent units, for example, moles/L or milliequivalents/L or mg/L as CaCO
3
.
The removal of ions that cause hardness is called softening. The majority of treatment
systems that employ softening are those using a groundwater source. There are, however,
a number of surface water sources with a groundwater component that is hard that employ
softening as part of their treatment process. Softening can be a
ccomplished by the lime-sod a
process, ion exchange, nanofiltration, or reverse osmosis. Lime-soda softing is discussed in
this chapter. The other methods are discussed in chapters 8 and 9.
7-6 WATER AND WASTEWATER ENGINEERING
Total hardness (TH)
Carbonate hardness (CH)
Ca
2
Mg
2
Na
0
0
250275
275
(b)
Ca
2
Mg
2
Cl
Total hardness (TH)
Carbonate hardness (CH)
0
0
250
250200
(a)
Noncarbonate
hardness (NCH)
HCO
3
HCO
3
FIGURE 7-4
Relationships between total hardness, carbonate hardness, and noncarbonate
hardness. (Source: Davis and Cornwell, 2008.)
7-2 LIME-SODA SOFTENING
Objectives
Prior to the mid-twentieth century, the primary purpose of lime-soda softening by mu nicipal
water treatment systems was to satisfy domestic consumer desire to reduce the aesthetic and
economic impact of soap precipitation. The importance of this objective ha
s been reduced by the
introduction of synthetic detergents and home water softeners. Other benefits of lime-soda soft-
ening systems have been shown to be quite substantial. These include removal of heavy metals,
NOM, turbidity, and pathogens as well as improving the water quality that reduces costs
for
distribution system corrosion, boiler and cooling water feed, and home water heater systems.
The concurrent removal of arsenic, chromium, iron, lead, manganese, and mercury provides an
additional benefit to the removal of hardness and, in some cases, may be the overriding reason for
s
election of the technology (Kawamura, 2000).
Lime-Soda Softening Chemistry
Solubility Product. Because all solids are soluble to some degree, there is an equilibrium
between the ions in solution and the solid. This equilibrium can be expressed as
A B aA bB
ab
ba
()s
(7-5)
where (s) solid precipitate.