Water and Wastewater Engineering
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LIME–SODA SOFTENING 7-37
From Table 7-5 at a temperature of 10 C and a TDS of 320 mg/L, the correction factor
is 2.56 and the LSI is
LSI pH pH
s
995316 2 77 2 56995 849. ... ..()1146.
As expected, this water is unstable and CaCO
3
will precipitate.
b. To achieve stability, the pH must be lowered to pH
s
. Using the second dissociation of
carbonic acid ( Equation 7-32 ), solve for the ratio [
CO
3
2
]/[
HCO
3
] with [H
] pH
s
in
moles/L:
K
a2
[][ ]
[]
HCO
HCO
3
2
3
[]
[][]
CO
HCO H
3
2
3
K
a2
Correcting K
a 2
for temperature using Equation 7-34 ,
K
K
a
a
2
6 498 2909 39002379
2
6 498 2
10
10
...
.
/T T
990939283 002379 283
11
3 05 10
..
.
/
()
[]
[]
CO
HCO
3
2
3
3 05 10
10
0 0094
11
849
.
.
.
and
[] [ ]CO HCO
3
2
3
0 0094.
The total alkalinity will not change. Only the form of alkalinity will change. The total
alkalinity is 0.50 10
3
equiv/L of
CO
3
2
1.20 10
3
equiv/L of
HCO
3
. In moles/L
these are
()()0 5010 30
60
3
. CO
3
2
equiv/L of g/equiv
gg/mole
moles/L
equiv/L
2 5010
120 10
4
3
.
.
oof g/equiv
g/mole
m
HCO
.
3
)( )61
61
120 10
3
ooles/L
Thus
[][HCO]2.5010moles /L 1.20 10
CO
3
2
3
4 3
mmoles
1.45 10 moles /L
3
This provides two simultaneous equations. Solving for [
HCO
3
],
0 0094 1 45 10
3
.HCOHCO.
33
moles/L[][]
7-38 WATER AND WASTEWATER ENGINEERING
and
[HCO ]
.
.
.
3
145 10
1 0094
144 10
3
3
moles/L
mooles/L
and
[]. . .CO
3
2
moles/L
0 0094 1 44 10 1 35 10
3
()
5
moles/L
c. The dose of CO
2
is estimated assuming that CO
2
H
2
CO
3
. The reaction is
CO
3
2
HCO
3
HCO
2 3
2
Because one mole of CO
2
produces two moles of
HCO
3
, the d ose of CO
2
to c onvert
carbonate to bicarbonate is
1 35 10
2
44 10 0
5
3
.
.
moles/L
mg/mole
⎛
⎝
⎜
⎞
⎠
⎟
()330
2
mg/L of CO
The total concentration of bicarbonate after the conversion is
1 35 10 1 44 10 1 45 10
53
.. .
moles/L moles/L
3
moles/L
Comments:
1. The small addition of CO
2
i s the result of blending the raw water with the treated water. The
raw water CO
2
converted the hydroxyl ion to carbonate. Otherwise, the high pH required to
remove the magnesium (>11.3) would have resulted in a higher CO
2
requirement.
2. The fact that the water is “stable” does not mean that it is noncorrosive.
3. To estimate the concentrations from split treatment, assume Ca
2
30 mg/L as CaCO
3
and Mg
2
10 mg/L as CaCO
3
in the d ischarge from first stage of softening because
the water has been softened to the prac tical solubility limits. Associated with this as-
sumption are the related quantities of CO
2
and OH
, that is CO
2
30 mg/L as CaCO
3
and OH
10 mg/L as CaCO
3
.
The recarbonation basin should provide (GLUMRB, 2003):
• A detention time of 20 minutes.
• Two compartments with a diffuser depth not less than 2.5 m.
• One compartment (the mixing compartment) should have a detention time 3 minutes.
The practice of on-site generation of CO
2
i s discouraged. Bulk pressurized or liquified CO
2
is commonly available and often used because it eliminates operation and maintenance problems
associated with on-site generation by combustion.
Approximately 50 to 75 percent of the applied CO
2
goes into solution. The room housing the
recarbonation basin must be ventilated to prevent the accumulation of the 25 to 50 percent of the
LIME–SODA SOFTENING 7-39
CO
2
that is not dissolved. Exposure to a 5 percent CO
2
concentration over a prolonged period
may cause unconsciousness.
Visit the text website at www.mhprofessional.com/wwe for supplementary materials
and a gallery of photos.
7-9 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 . Define hardness in terms of the chemical constituents that cause it and in terms of the
results as seen by the users of hard water.
2. Using diagrams and chemical reactions, explain how water becomes hard.
3. Given the total hardness
and alkalinity, calculate the carbonate hardness and noncar-
bonate hardness.
4. Explain the significance of alkalinity in lime-soda softening.
5. State the proper pH for removal of Ca
2
and Mg
2
and explain how the reactions
“ensure” the proper pH.
6. Explain why the solubility relationships do not fully explain the pH required to achieve
satisfactory precipitation of Ca
2
and Mg
2
.
7. Explain to a client why lime-soda softening cannot produce a water completely free of
hardness.
8. Explain to a client why a magnesium concentration of 40 mg/L as CaCO
3
is a design
objective for lime-soda softening.
9. Describe to a client under what circumstances CO
2
in raw water is to be removed by
precipitation or by stripping.
10. Given a water analysis, select an appropriate lime-soda softening process, that is,
selective calcium removal, excess lime softening, or split treatment.
11. Explain the purpose of recarbonation.
12. Explain why the softening process may be of benefit in removing constit
uents of
concern other than calcium and magnesium.
W ith the use of this text, you should be able to do the following:
13. Estimate the CO
2
concentration of a water given the pH, alkalinity, and water temperature.
14. Estimate the amount of lime and soda ash required to soften water of a stated composition.
15. Calculate the fraction of the “split” for a lime-soda softening system.
16. Draw bar graphs to describe a water during different stages of softening.
7-40 WATER AND WASTEWATER ENGINEERING
17. Show, by writing the chemical reactions, how caustic soda may be used instead of lime
in softening.
18. Design an upflow solids contact basin from a manufacturer’s data given the design
flow rate.
19. Design a recarbonation system for lime/soda softening given the flow rate and treated
water composition.
7-10 PROBLEMS
7-1. Using Equations 6-3, 7-31 , 7-32 , and the equilibrium constant expression for the ion-
ization of water, derive two equations that allow calculation of the bicarbonate and
carbonate alkalinities in mg/L as CaCO
3
from measurements of the total alkalinity
( A ) and the pH.
Answers (in mg/L as CaCO
3
):
HCO
H
H
3
50 000
50 000
,
,
ab
ab
A
K
W
[]
[]
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭⎭
⎪
=
1
2
2
2
2
ab
ab
K
K
[]
[]
()
H
CO
H
HCO
3
2
3
where A total alkalinity, mg/L as CaCO
3
K
2
second dissociation constant of carbonic acid
4.68 10
11
at 25 C
K
W
ionization constant of water
1 10
14
at 25 C
HCO
3
bicarbonate alkalinity in mg/L as CaCO
3
CO
3
2
carbonate alkalinity in mg/L as CaCO
3
7-2. If a water has a carbonate alkalinity of 120.00 mg/L as the ion and a pH of 10.30,
what is the bicarbonate alkalinity in mg/L as the ion?
7-3. Calculate the bicarbonate and carbonate alkalinities, in mg/L as CaCO
3
, of a water
having a total alkalinity of 233.0 mg/L as CaCO
3
and a pH of 10.47.
7-4. What is the pH of a water that contains 120 mg/L of bicarbonate ion and 15mg/L of
carbonate ion?
7-5. Calculate the bicarbonate and carbonate alkalinities, in mg/L as CaCO
3
, of the
water described in the following mineral analysis for a water sample taken from
Well No. 1 at the Eastwood Manor Subdivision near McHenry, Illinois (Woller and
Sanderson, 1976a).
LIME–SODA SOFTENING 7-41
Well No. 1, Lab No. 02694, November 9, 1971
Iron 0.2 Silica (SiO
2
) 20.0
Manganese 0.0 Fluoride0.35
Ammonium 0.5 Boron 0.1
Sodium 4.7 Nitrate 0.0
Potassium 0.9 Chloride4.5
Calcium 67.2 Sulfate 29.0
Magnesium 40.0 Alkalinity 284.0 as CaCO
3
Barium 0.5 pH 7.6 units
NOTE: All reported as “mg/L as the ion” unless stated otherwise.
7-6. Determine the total, carbonate, and noncarbonate hardness in mg/L as CaCO
3
and in
meq/L for the water analysis in Problem 7-5 using the predominant polyvalent cations.
7-7. Calculate the total, carbonate, and noncarbonate hardness for the water analysis in
Problem 7-5 in mg/L as CaCO
3
using all of the polyvalent cations. What is the
percent error in using only the predominant cations as in Problem 7-6?
7-8. The following mineral analysis was reported for a water sample taken from Well No. 1
at Magnolia, Illinois (Woller and Sanderson, 1976b). Determine the total, carbonate and
noncarbonate hardness in mg/L as CaCO
3
and in meq/L using the predominant polyva-
lent cation definition of hardness.
Well No. 1, Lab No. B109535, April 23, 1973
Iron 0.42 Zinc 0.01
Manganese 0.04 Silica (SiO
2
) 20.0
Ammonium 11.0 Fluoride0.3
Sodium 78.0 Boron 0.3
Potassium 2.6 Nitrate 0.0
Calcium 78.0 Chloride 9.0
Magnesium 32.0 Sulfate 0.0
Barium 0.5 Alkalinity 494.0 as CaCO
3
Copper 0.01 pH 7.7 units
NOTE: All reported as “mg/L as the ion” unless stated otherwise.
7-9. The following mineral analysis was reported for Michigan State University well water
(MDEQ, 1979). Determine the total, carbonate, and noncarbonate hardness in mg/L as
CaCO
3
and in meq/L using the predominant polyvalent cation definition of hardness.
Michigan State University Well Water
(continued)
Fluoride 1.1 Silica (SiO
2
) 3.4
Chloride 4.0 Bicarbonate 318.0 mg/L as CaCO
3
Nitrate 0.0 Sulfate 52.0
Sodium 14.0 Iron 0.5
7-42 WATER AND WASTEWATER ENGINEERING
7-10. An analysis of bottled water from the Kool Artesian Water Bottling Company is
listed below. Determine the total, carbonate, and noncarbonate hardness in mg/L as
CaCO
3
and in meq/L using the predominant polyvalent cation definition of hardness.
( Hint: use the solution to Problem 7-1 to find the bicarbonate concentration.)
Kool Artesian Water
Calcium 37.0 Silica 11.5
Magnesium 18.1 Sulfate 5.0
Sodium 2.1 Potassium 1.6
Fluoride 0.1 Zinc 0.02
Alkalinity 285.0 mg/L as CaCO
3
pH 7.6 units
NOTE: All units are mg/L as the ion unless stated otherwise
7-11. Prepare a bar chart of the Lake Michigan water analysis shown below. Because all of
the constituents were not analyzed, an ion balance is not achieved.
Constituent Expressed as
Milligrams
per liter
Total hardness CaCO
3
143.0
Calcium Ca
2
38.4
Magnesium Mg
2
11.4
Total iron Fe 0.10
Sodium Na
5.8
Total alkalinity CaCO
3
119
Bicarbonate alkalinity CaCO
3
115
ChlorideCl
14.0
Sulfate
S
O
4
2
26.0
Silica SiO
2
1.2
Total dissolved solids 180.0
Turbidity NTU
3.70
a
pH Units
8.4
a
Lake Michigan at Grand Rapids, MI Intake
a
Not in mg/L.
7-12. Using K
sp
, show why calcium is removed as a carbonate rather than a hydroxide in
lime-soda softening.
NOTE: All units are mg/L as the ion unless stated otherwise
Potassium 1.6 Manganese 0.07
Calcium 96.8 Zinc 0.27
Magnesium 30.4 Barium 0.2
Michigan State University Well Water (continued)
LIME–SODA SOFTENING 7-43
7-13. Using K
sp
, show why magnesium is removed as a hydroxide rather than a carbonate
in lime-soda softening.
7-14. Estimate the CO
2
concentration in mg/L as CO
2
and in mg/L as CaCO
3
for the water
analysis presented in Problem 7-5. Assume the water temperature was 4.4 C.
7-15. Estimate the CO
2
concentration in mg/L as CO
2
and in mg/L as CaCO
3
for the water
analysis presented in Problem 7-8. Assume the water temperature was 6 C.
7-16. If the pH of the MSU water (Problem 7-9) was 8.0 and the water temperature was
5 C, what is the estimated CO
2
concentration in mg/L as CO
2
and as mg/L as CaCO
3
?
7-17. Estimate the CO
2
concentration in mg/L as CO
2
and in mg/L as CaCO
3
for the water
analysis presented in Problem 7-11. Assume the water temperature was 10 C. For the
estimate of the CO
2
concentration, ignore the carbonate alkalinity.
7-18. Determine the lime and soda ash dose, in mg/L as CaCO
3
, to soften the following
water to a final hardness of 90.0 mg/L as CaCO
3
. If the price of lime, purchased as
CaO, is $61.70 per megagram (Mg), and the price of soda ash, purchased as Na
2
CO
3
,
is $172.50 per Mg, what is the annual chemical cost of treating 0.050 m
3
/ s of this
water? Assume the lime is 90% pure and the soda ash is 97% pure. The ion concen-
trations reported below are all mg/L as CaCO
3
.
C a
2
1 37.0
Mg
HCO
CO
3
2
2
40 0
197 0
90
.
.
.
7-19. What amount of lime and/or soda ash, in mg/L as CaCO
3
, is required to soften the
Village of Lime Ridge’s water to less than 120 mg/L hardness as CaCO
3
?
Compound Concentration, mg/L as CaCO
3
CO
2
4.6
Ca
2
257.9
Mg
2
22.2
248.0
32.1
HCO
3
SO
4
2
7-20. Determine the lime and soda ash dose, in mg/L as CaO and Na
2
CO
3
, to soften the
following water to a final hardness of less than 130 mg/L as CaCO
3
. The ion concen-
trations reported below are all mg/L as CaCO
3
. Assume the lime is 90% pure and the
soda ash is 97% pure.
C a
2
210.0
Mg
2
23.0
HCO
3
165.0
CO
2
5.0
7-44 WATER AND WASTEWATER ENGINEERING
7-21. Determine the lime and soda ash dose, in mg/L as CaO and Na
2
CO
3
, to soften the Thames
River water to a final hardness of less than 125 mg/L as CaCO
3
. Assume that all the alka-
linity is bicarbonate and that the lime is 90% pure and the soda ash is 97% pure.
Constituent Expressed as
Milligrams
per liter
Total hardness CaCO
3
260.0
Calcium hardness CaCO
3
235.0
Magnesium hardness CaCO
3
25.0
Total iron Fe 1.8
Copper Cu
2
0.05
Chromium Cr
6
0.01
Total alkalinity CaCO
3
130.0
ChlorideCl
52.0
Phosphate (total) 1.0
Silica SiO
2
14.0
Suspended solids 43.0
Total solids 495.0
pH units 7.5
Temperature C 10.0
Thames River, London
7-22. Determine the lime and soda ash dose, in mg/L as CaCO
3
to soften the following
water to a final hardness of less than 120.0 mg/L as CaCO
3
. If the price of lime, pur-
chased as CaO, is $61.70 per megagram (Mg), and the price of soda ash, purchased
as Na
2
CO
3
, is $172.50 per Mg, what is the annual chemical cost of treating 1.35 m
3
/ s
of this water? Assume the lime is 87% pure and the soda ash is 97% pure. The ion
concentrations reported below are all mg/L as CaCO
3
.
C a
2
293.0
Mg
2
55.0
HCO
3
301.0
CO
2
5.0
7-23. Determine the lime and soda ash dose, in mg/L as CaCO
3
, to soften the following
water to a final hardness of less than 90.0 mg/L as CaCO
3
. If the price of lime, pur-
chased as CaO, is $61.70 per megagram (Mg), and the price of soda ash, purchased
as Na
2
CO
3
, is $172.50 per Mg. What is the annual chemical cost of treating 0.050
m3/s of this water? Assume the lime is 90% pure and the soda ash is 97% pure. The
ion concentrations reported below are all mg/L as CaCO
3
.
C a
2
137.0
Mg
2
60.0
HCO
3
197.0
CO
2
9.0
PO
4
3
LIME–SODA SOFTENING 7-45
7-24. Determine the lime and soda ash dose, in mg/L as CaCO
3
, to soften the Kool Artesian
( Problem 7-10 ) water to a final hardness of 115 mg/L as CaCO
3
. Assume the water
temperature as pumped from the ground is 10 C. If the price of lime, purchased as
CaO, is $100 per megagram (Mg), and the price of soda ash, purchased as Na
2
CO
3
i s
$200 per Mg, what is the annual chemical cost of treating 0.500 m
3
/ s of this water?
Assume all the alkalinity is bicarbonate, lime is 88% pure, and soda ash is
98% pure.
7-25. Determine the lime and soda ash dose, in mg/L as CaCO
3
, to soften the Village of
Galena’s water to a final hardness of 130.0 mg/L as CaCO
3
. Assume the water
temperature as pumped from the ground is 8.5 C. If the price of lime, purchased as
CaO, is $100 per megagram (Mg), and the price of soda ash, purchased as Na
2
CO
3
is
$200 per Mg, what is the annual chemical cost of treating 0.500 m
3
/ s of this water?
Assume lime is 93% pure and soda ash is 95% pure.
Constituent Expressed as
Milligrams
per liter
Calcium Ca
2
177.8
Magnesium Mg
2
16.2
Total iron Fe 0.20
Lead
a
Pb
2
20
a
Sodium Na
4.9
Carbonate alkalinity CaCO
3
0.0
Bicarbonate alkalinity CaCO
3
276.6
ChlorideCl
0.0
Sulfate 276.0
Silica SiO
2
1.2
Total dissolved solids 667
pH units 8.2
Temperature C8.5
Village of Galena
a
Parts per billion.
7-26. Rework Problem 7-21 using caustic soda instead of lime. Soften the water to the
lowest hardness that can be achieved with caustic alone. Assume the caustic is 100%
pure, CO
2
concentration 9.96 mg/L, and that an excess of 40 mg/L of caustic will
be added.
7-27. Design an upflow solids contact basin for a softening plant treating groundwater. The
plant has a maximum day design flow rate of 50,000 m
3
/ d and average winter de-
mand of 25,000 m
3
/ d. Verify that the design satisfactorily meets the GLUMRB guid-
ance for flocculation and mixing period, detention time, upflow rate (overflow rate),
and weir loading. Use Table 7-4 to select the upflow clarifier(s).
7-28. Design an upflow solids contact basin for a softening plant treating groundwater. The
plant has a maximum day
design flow rate of 10,000 m
3
/ d and average winter demand
SO
4
2
7-46 WATER AND WASTEWATER ENGINEERING
of 5,000 m
3
/ d. The primary softening clarifier is to be followed by a secondary clari-
fier that is to be used as settling tank for coagulation of the unsettled precipitate from
the first tank. Verify that the design satisfactorily meets the GLUMRB guidance for
side water depth, flocculation and mixing period, detention time,
upflow rate (over-
flow rate), and weir loading. Use Table 7-4 to select the upflow clarifier(s).
7-29. Estimate the dose of CO
2
in mg/L to stabilize the water from split treatment soften-
ing. The estimated constituents and parameters of interest in the blended water are
listed in the table below.
7-30. Estimate the dose of CO
2
in mg/L to stabilize the water from split treatment soften-
ing. The estimated constituents and parameters of interest in the blended water are
listed in the table below.
7-11 DISCUSSION QUESTIONS
7-1. Is the Lime Ridge water (Problem 7-19) a likely candidate for air stripping to remove
CO
2
before lime-soda softening? Explain why or why not.
7-2. Explain why many lime-soda softening utilities have raised their target hardness from
between 75 and 120 mg/L as CaCO
3
to a target hardness between 120 and 150 mg/L
as CaCO
3
.
7-3. A water that contains only carbonate hardness can be softened with NaOH alone.
True or false?
Constituent
or parameter
Concentration,
mg/L as CaCO
3
or units as shown
Ca
2
63.0
Mg
2
35.0
84.7
128.4
pH 10.1 units
TDS 240 mg/L
Temperature 4C
CO
3
2
HCO
3
Constituent
or parameter
Concentration,
mg/L as CaCO
3
or units as shown
Ca
2
53.65
Mg
2
40.0
25.2
53.2
pH 9.89 units
TDS 560 mg/L
Temperature 12C
CO
3
2
HCO
3