Lin S.D. Water and Wastewater Calculations Manual

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(5.87)

Removal of noncarbonate hardness with soda ash and lime

(5.88)

(5.89)

Recarbonation for pH control (pH 艑 8.5)

(5.90)

Recarbonation for removal of excess lime and pH control (pH 艑 9.5)

(5.91)

(5.92)

Based on the above equations, the stoichiometric requirement for

lime and soda ash expressed in equivalents per unit volume are as fol-

lows (Tchobanoglous and Schroeder, 1985):

(5.93)

(5.94)

Approximately 1 eq/m

of lime in excess of the stoichiometric require-

ment must be added to bring the pH to above 11 to ensure Mg(OH)

com-

plete precipitation. After the removal of precipitates, recarbonation is

needed to bring pH down to a range of 9.2 to 9.7.

The treatment processes for water softening may be different depend-

ing on the degree of hardness and the types and amount of chemical

added. They may be single stage lime, excess lime, single stage lime-

soda ash, and excess lime-soda ash processes.

Coldwell—Lawrence diagrams are based on equilibrium principles for

solving water softening. The use of diagrams is an alternative to the sto-

ichiometric method. It solves simultaneous equilibria equations and

estimates the chemical dosages of lime-soda ash softening. The inter-

ested reader is referred to the American Water Works Association (1978)

publication: Corrosion Control by Deposition of CaCO

Films, and to

Beneﬁeld and Morgan (1990).

Example 1: Water has the following composition: calcium ⫽ 82 mg/L,

magnesium ⫽ 33 mg/L, sodium ⫽ 14 mg/L, bicarbonate ⫽ 280 mg/L, sul-

fate ⫽ 82 mg/L, and chloride ⫽ 36 mg/L. Determine carbonate hardness,

noncarbonate hardness, and total hardness, all in terms of mg/L of CaCO

Soda ash required seq/m

d 5 Ca

1 Mg

2 alkalinity

Lime required seq/m

d 5 CO

1 HCO

1 Mg

1 excess

MgsOHd

1 CO

MgCO

1 H

CasOHd

1 CO

CaCO

T 1 H

1 CO

1 H

2HCO

1 c

2Cl

d 1 CasOHd

MgsOHd

T 1 Ca

1 c

2Cl

1 c

2Cl

d 1 Na

CaCO

T 1 2Na

1 c

2Cl

1 2HCO

1 2CasOHd

2CaCO

T 1 MgsOHd

T 1 2H

Public Water Supply 405

406 Chapter 5

solution:

Step 1. Convert all concentration to mg/L of CaCO

using the following

formula:

The species concentration in milliequivalents per liter (meq/L) is computed

by the following equation

The species concentration expressed as mg/L of CaCO

is calculated from

Step 2. Construct a table for ions in mg/L as CaCO

Concentration

Molecular Equivalent

Ion species weight weight mg/L meq/L mg/L as CaCO

2⫹

40 20.0 82 4.0 200

2⫹

24.3 12.2 33 2.7 135

⫹

23 23.0 14 0.6 30

Total: 7.3 365

61 61 280 4.6 230

–

35.5 35.5 36 1.0 50

96.1 48 82 1.7 85

Total: 7.3 365

Step 3. Construct an equivalent bar diagram for the cationic and anionic

species of the water

The diagram shows the relative proportions of the chemical species important

to the water softening process. Cations are placed above anions on the graph.

The calcium equivalent should be placed ﬁrst on the cationic scale and be fol-

lowed by magnesium and other divalent species and then by the monovalent

species sodium equivalent. The bicarbonate equivalent should be placed ﬁrst

on the anionic scale and immediately be followed by the chloride equivalent

and then by the sulfate equivalent.

HCO

mg/L as CaCO

5 meq/L of species 3 50

smg/L of speciesd 3 50

equivalent weight of species

meq/L 5

mg/L

equivalent weight

100

5 50 for CaCO

Public Water Supply 407

Step 4. Compute the hardness distribution

Total hardness ⫽ 200 ⫹ 135 ⫽ 335 (mg/L as CaCO

)

Alkalinity (bicarbonate) ⫽ 230 mg/L as CaCO

Carbonate hardness ⫽ alkalinity

⫽ 230 mg/L as CaCO

Noncarbonate hardness ⫽ 365 – 230 ⫽ 165 (mg/L as CaCO

)

or ⫽ Na

⫹

⫹ Cl

–

⫹

Example 2: (single-stage lime softening): Raw water has the following com-

position: alkalinity ⫽ 248 mg/L as CaCO

, pH ⫽ 7.0, ␣

⫽ 0.77 (at T ⫽ 10°C),

calcium ⫽ 88 mg/L, magnesium ⫽ 4 mg/L. Determine the necessary amount

of lime to soften the water, if the ﬁnal hardness desired is 40 mg/L as CaCO

Also estimate the hardness of the treated water.

solution:

Step 1. Calculate bicarbonate concentration

At pH ⫽ 7.0, assuming all alkalinity is in the carbonate form

Step 2. Compute total carbonate species concentration C

(Snoeyink and

Jenkins, 1980)

Step 3. Estimate the carbonate acid concentration

Rearranging, and

] ⫽ (6.44 ⫺ 4.96) ⫻ 10

–3

mol/L

⫽ 1.48 ⫻ 10

⫺3

mol/L

⫽ 1.48 ⫻ 10

⫺3

mol/L ⫻ 1000 ⫻ 62 mg/mol

⫽ 92 mg/L

or ⫽ 148 mg/L as CaCO

(92 ⫻ 50/32)

[CO

] 5 0

5 [ H

] 1 [ HCO

] 1 [CO

]

5 [ HCO

]/a

5 4.96 3 10

/0.77

5 6.44 3 10

mol/L

HCO

5 248

1 g

1000 mg

1 mole

61 g

61 eq wt of HCO

50 eq wt of alkalinity

5 4.96 3 10

mol/L

Alkalinity 5 [HCO

] 1 [CO

] 1 [OH

] 1 [H

]

Step 4. Construct a bar diagram for the raw water converted concentration

of Ca and Mg as CaCO

Ca ⫽ 88 ⫻ 100/40 ⫽ 220 mg/L as CaCO

Mg ⫽ 4 ⫻ 100/24.3 ⫽ 16 mg/L as CaCO

408 Chapter 5

Step 5. Find hardness distribution

Calcium carbonate hardness ⫽ 220 mg/L

Magnesium carbonate hardness ⫽ 16 mg/L

Total hardness ⫽ 220 ⫹ 16 ⫽ 236 (mg/L)

Step 6. Estimate the lime dose needed

Since the ﬁnal hardness desired is 40 mg/L as CaCO

, magnesium hardness

removal would not be required. The amount of lime needed (x) would be equal

to carbonic acid concentration plus calcium carbonate hardness:

x ⫽ 148 ⫹ 220

⫽ 368 mg/L as CaCO

⫽ 272 mg/L as Ca(OH)

⫽ 206 mg/L as CaO

The purity of lime is 70%. The total amount of lime needed is

206/0.70 ⫽ 294 mg/L as CaO

Step 7. Estimate the hardness of treated water

The magnesium hardness level of 16 mg/L as CaCO

remains in the softened

water theoretically. The limit of calcium achievable is 30 to 50 mg/L of CaCO

and would remain in the water unless using 5% to 10% in excess of lime. Hardness

levels less than 50 mg/L as CaCO

are seldom achieved in plant operation.

Example 3: (excess lime softening): Similar to Example 2, except for concen-

trations of calcium and magnesium: pH ⫽ 7.0, ␣

⫽ 0.77 (at T ⫽ 10°C). Alkalinity,

calcium, and magnesium concentrations are 248, 158, and 56 mg/ L as CaCO

respectively. Determine the amount of lime needed to soften the water.

5 368 3

100

mg/L as CaO

5 368 mg/L as CaCO

74 as CasOHd

100 as CaCO

solution:

Step 1. Estimate H

as Example 2

⫽ 148 mg/L as CaCO

Step 2. Construct a bar diagram for the raw water

Public Water Supply 409

Step 3. Find hardness distribution

Calcium carbonate hardness ⫽ 158 mg/L

Magnesium carbonate hardness ⫽ 66 mg/L

Total carbonate hardness ⫽ 158 ⫹ 66 ⫽ 224 (mg/L)

Comment: Sufﬁcient lime (in excess) must be dosed to convert all bicarbon-

ate alkalinity to carbonate alkalinity and to precipitate magnesium as mag-

nesium hydroxide (needs 1 eq/L excess lime).

Step 4. Estimate lime required (x) is the sum for carbonic acid, total alka-

linity, magnesium hardness, and excess lime (say 60 mg/L as CaCO

) to raise

pH ⫽ 11.0

x ⫽ (148 ⫹ 248 ⫹ 66 ⫹ 60) mg/L as CaCO

⫽ 522 mg/L as CaCO

⫽ 522 ⫻ 74/100 mg/L as Ca(OH)

⫽ 386 mg/L as Ca(OH)

or ⫽ 522 ⫻ 0.56 mg/L as CaO

⫽ 292 mg/L as CaO

Example 4: (single stage lime-soda ash softening): A raw water has the fol-

lowing analysis: pH ⫽ 7.01, T ⫽ 10°C, alkalinity ⫽ 248 mg/L, Ca ⫽ 288 mg/L,

Mg ⫽ 12 mg/L, all as CaCO

. Determine amounts of lime and soda ash

required to soften the water.

solution:

Step 1. As in previous example, construct a bar diagram

Step 2. Find the hardness distribution

Total hardness ⫽ 288 ⫹ 12 ⫽ 300 (mg/L as CaCO

)

Calcium carbonate hardness, CCH ⫽ 248 mg/L CaCO

Magnesium carbonate hardness ⫽ 0

Calcium noncarbonate hardness, CNH ⫽ 288 – 248 ⫽ 40 (mg/L as CaCO

)

Magnesium noncarbonate hardness, MNH ⫽ 12 mg/L

Step 3. Determine lime and soda ash requirements for the straight lime-soda

ash process, refer to Eq. (5.85) and Eq. (5.86)

Lime dosage ⫽ H

⫹ CCH ⫽ (148 ⫹ 248) mg/L as CaCO

⫽ 396 mg/L as CaCO

or ⫽ 396 ⫻ 0.74 mg/L as Ca(OH)

⫽ 293 mg/L as Ca(OH)

and soda ash dosage ⫽ CNH (Refer to Eq. (6.88))

⫽ 40 mg/L as CaCO

⫽ (40 ⫻ 106/100) mg/L as Na

⫽ 42.4 mg/L as Na

Example 5: (excess lime-soda ash process): Raw water has the following

analysis: pH ⫽ 7.0, T ⫽ 10°C, alkalinity, calcium, and magnesium are 248,

288, and 77 mg/L as CaCO

, respectively. Estimate the lime and soda ash

dosage required to soften the water.

solution:

Step 1. Construct a bar diagram for the raw water. Some characteristics are

the same as the previous example.

410 Chapter 5

Step 2. Deﬁne hardness distribution

Total hardness ⫽ 288 ⫹ 77 ⫽ 365 (mg/L as CaCO

)

Calcium carbonate hardness, CCH ⫽ 248 mg/L as CaCO

Magnesium carbonate hardness, MCH ⫽ 0

Calcium noncarbonate hardness, CNH ⫽ 288 – 248 ⫽ 40 (mg/L)

Magnesium noncarbonate hardness, MNH ⫽ 77 mg/L

Step 3. Estimate the lime and soda ash requirements by the excess lime-soda

ash process

Lime dosage ⫽ carb. acid ⫹ CCH ⫹ 2(MCH) ⫹ MNH ⫹ excess lime

⫽ (148 ⫹ 248 ⫹ 2(0) ⫹ 77 ⫹ 60) mg/L as CaCO

⫽ 533 mg/L as CaCO

or ⫽ 533 ⫻ 74/100

⫽ 394 mg/L as Ca(OH)

and soda ash dosage for excess lime-soda ash (Y ) is

Y ⫽ CNH ⫹ MNH

⫽ (40 ⫹ 77) mg/L as CaCO

⫽ 117 mg/L as CaCO

or ⫽ 87 mg/L as Ca(OH)

12.2 Pellet softening

Pellet softening has been used for softening in the Netherlands for many

years. Pellet softening reactors have been installed at a number of loca-

tions in North America. The world’s largest pellet softening plant,

450,000 m

/d (119 MGD) of the design capacity, was installed in 2004

at the Cheng-Ching Lake Advanced Water Puriﬁcation Plant in

Kaohsiung, Taiwan. The pellet softening process reactors consist of

square (or rectangular) or inverted conical tanks where calcium crys-

tallizes on a suspended bed of ﬁne sand.

Advantages of the pellet softening reactor are its small size and low

installation cost. Residuals consist of small pellets that dewater read-

ily, minimizing residuals volume. The pellet can be used for steel man-

ufacture. However, pellet reactors should not be considered for systems

high in magnesium content because magnesium hydroxide is not

affected and may foul in the reactor.

Pellet softening is not proved and is not widely accepted as a treat-

ment system in the United States. Pilot testing is advisable. Design

should be carefully coordinated with the equipment manufacturer. Pellet

softening processes should be designed cautiously.

Design and operation considerations. The pellet softening process is used

for removal of only calcium carbonate (CaCO

) hardness. The process

is based on the crystallization of calcium carbonate on seeded sand

(0.2 to 0.63 mm in size, ﬁxed-bed height ⫽ 1.2 to 1.5 m) media. The chem-

ical reaction is described as below:

(5.94a)Ca

1 HCO

1 NasOHd

1 CaCO

T 1 H

Public Water Supply 411

Flocculated-settled water or raw water and caustic soda (NaOH) are

injected (pumped) into the pressure chamber of pellet reactor through

a nozzle system. Water muzzles should be used to ensure a proper dis-

tribution of the water across the surface of the reactor.

The reactor is ﬁlled with a bed of sand material (automatically seeded)

that is ﬂuidized by the water ﬂow. The precipitated CaCO

will form a

ﬁxed layer ﬁrst on the surface of the seeded sand grain and later on the

created pellet surface itself. The pH value and the magnesium hardness

will not inﬂuence the process.

The NaOH is mixed intensively with the water to avoid locally high

supersaturation, which would lead to spontaneous nucleation of CaCO

instead of crystal growth on the sand. The chemical feed installation

(NaOH dosing pumps) is controlled by the digital control system accord-

ing to the calculated NaOH dosage, which is a function of the amount

of calcium hardness to be removed.

Due to the growth of CaCO

on the sand, the size of the individual pel-

lets will grow. This causes the increase in the ﬂuidized bed height (at

least height ⫽ 10 m at 100 m/h ﬂow). To balance the height of the ﬂu-

idized bed, pellets must be discharged from the reactor; also, a speciﬁc

amount of new sand must be supplied to the pellet bed. The sizes of the

pellets can be controlled by the equilibrium of pellet extraction and

sand supply.

A small amount of supersaturated CaCO

may be carried in the out-

ﬂow of the reactor. Sulfuric acid is dosed at the outﬂow of the reactor

for the pH (7.5 to 7.9) adjustment. After softening in the pellet reactors,

the softened water and the bypass raw water may be blended and then

ﬂow by gravity to the rapid sand ﬁlters.

A pellet-reactor design should comply with the following criteria:

■

The water and NaOH in the pellet reactor should be properly dis-

tributed to avoid short-circuiting and to obtain plug-ﬂow conditions

in the pellet reactor.

■

The water and NaOH should be mixed intensively in the presence of

seed grains with a high speciﬁc surface area to achieve immediate

crystallization.

■

The turbulence in the reactor should be sufﬁciently high to prevent

scaling of inlet nozzles and the reactor wall, and low enough to reduce

pellet erosion.

Sizing for reactors. The design overﬂow rate is between 80 and 100 m/h

⋅ h). The height of the reactor is generally about 8 m. Thus, the

total area of the reactors can be easily determined with the softening

water ﬂow divided by the overﬂow rate.

412 Chapter 5

Example: Determine the size of pellet reactor for a plant ﬂow of 45,400 m

or 12 MGD.

solution:

Step 1. Convert the ﬂow unit

Q ⫽ 45,400 m

/d ⫽ 45400 m

/d ⫼ 24 h/d

⫽ 1892 m

Step 2. Determine the total area, A, for the reactors, using 80 m

⋅ h

A ⫽ Q/overﬂow rate

⫽ 1892 m

/h ⫼ 80 m

· h

⫽ 23.66 m

Using 2 square softening reactors, for each reactor would have an area

of 11.83 m

The length, L, is for a side of the square reactor, then

⫽ 11.83 m

L ⫽ 3.44 m

Step 3. The height of a reactor is usually 8 m; thus

The size of each of the 2 reactors is 3.44 m ⫻ 3.44 m ⫻ 8.00 m.

Caustic soda demand. For calculation purposes, the purity of caustic

soda is used as 100%. The estimation of NaOH demand for the total raw

water ﬂow rate is calculated as follows:

NaOH demand, mg/L ⫽ (C

– C

) 40/100 ⫹ excess

⫽ 0.4 (C

– C

) ⫹ 20 (5.94b)

where C

⫽ inﬂuent hardness, mg/L

⫽ efﬂuent hardness, mg/L

40 ⫽ molecular weight of NaOH as g/mol

100 ⫽ molecular weight of CaCO

as g/mol

20 ⫽ 0.5 mol/ NaOH, is the correction factor (f ) for CO

neutralization and softening efﬁciency.

40 mg/L of NaOH are required for the neutralization of

44 mg/L.

Softening efﬁciency is greatly reduced by too large pellet diameter, insuf-

ﬁcient sand seeding, and high operation velocity in the reactor. The efﬁ-

Public Water Supply 413

ciency (E) of the NaOH dosage (demand) without considering the NaOH

demand for CO

can be computed as:

E ⫽ 100% ⫺ (NaOH dosage ⫺ 0.4(C

⫺ C

))% (5.94c)

Example 1: Estimate the NaOH demand for pellet softening of the entire

raw water ﬂow rate and softening efﬁciency without considering the NaOH

demand for CO

. The calcium hardness in inﬂuent and efﬂuent are 250 and

80 mg/L as CaCO

, respectively.

solution:

Step 1. Estimation of NaOH demand by using Eq. (5.94b)

NaOH demand, mg/L ⫽ 0.4(C

– C

) ⫹ 20

⫽ 0.4(250 – 80) ⫹ 20

⫽ 88

Step 2. Calculate softening efﬁciency, E, using Eq. (5.94c)

E ⫽ 100% – (NaOH dosage – 0.4(C

– C

))%

⫽ 100% – (88 – 0.4 (250 – 80))%

⫽ 100% – 20% (⫽ 100% – correction factor, f, 20%)

⫽ 80%

If the softened water is blended with ﬂocculated /settled water at the soft-

ening reactor bypass and is blended additionally at postozonation with

ﬂocculated and ﬁltered water, both blended waters shall increase the total

hardness. Therefore, the water at softening must be softened further to

allow ﬁnal treated water hardness within the desired concentration. The

NaOH dosage for the blended water can be calculated as:

Dosage ⫽ NaOH demand ⫻ Q

/(Q

– Q

) (5.94d)

where Dosage ⫽ NaOH dosage for the blended water, mg/L

NaOH demand ⫽ calculated by using Eq. (5.94b), mg/L

⫽ ﬂow rate to the softening reactor

⫽ ﬂow rate softening bypass

⫽ ﬂow rate from ﬁltration

Example 2: Estimate the NaOH dosage for the blended water. Given: Q

, Q

and Q

as 1890, 105, and 95 m

/h, respectively. The NaOH demand is 88 mg/L.

solution: Using Eq. (5.94d),

Dosage ⫽ NaOH demand ⫻ Q

/ (Q

– Q

)

⫽ 88 mg/L ⫻ 1890 / (1890 – 105 – 95)

⫽ 98 mg/L

414 Chapter 5