Water and Wastewater Engineering
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6-6 WATER AND WASTEWATER ENGINEERING
• They have a high charge density.
• They are insoluble in the neutral pH range.
The inorganic chemicals commonly used in the United States are listed in Table 6-1 . They
are classified as hydrolyzable metal cations. In the United States, the predominant water treat-
ment coagulant is aluminum sulfate or “alu
m.” It is sold in a hydrated form as Al
2
(SO
4
)
3
· x H
2
O
(where x is usually 14), because it is the least expensive coagulant (MWH, 2005).
Polyelectrolytes such as polydiallyldimethyl ammonium chloride (poly-DADMAC) and epi-
chlorohydrin dimethylamine (epi-DMA) are the typic al organic coagulants used in water treat-
ment in the United
States (MWH, 2005). Their chemical formulae are summarized in Table 6-2 .
They are water soluble and cationic.
Physics of Coagulation
There are four mechanisms employed to destabilize natural water suspensions:
• Compression of the electric double layer,
• Adsorption and charge neutralization,
• Adsorption and interparticle bridging, and
• Enmeshment in a precipitate.
Although these mechanisms are d iscussed separately
, in practice several mechanisms are
employed simultaneously.
Surface of particle A
Surface of particle B
Repulsion curve no.1
Interaction energy
Repulsive
forces
Attractive
forces
Interaction energy
Attractive
forces
Repulsive
forces
0
0
Repulsion curve no.2
Net energy curve no.1
Net energy curve no.2
Van der Waals attraction
Distance between particles
FIGURE 6-4
Attractive and repulsive forces that result when two particles are brought together. Repul-
sion curve no. 1 and net energy curve no. 1 result when no coagulant is present. Coagulant
reduces the repulsion to curve no. 2.
COAGULATION AND FLOCCULATION 6-7
TABLE 6-1
Frequently used inorganic coagulants
Coagulant Chemical formula
Molecular weight,
g/mole Remarks
Aluminum sulfate Al
2
(SO
4
)
3
· 14H
2
O 594 Hg contamination may
be of concern
Sodium aluminate Na
2
Al
2
O
4
164 Provides alkalinity and
pH control
Aluminum chloride AlCl
3
133.5 Used in blends with
polymers
Polyaluminum chloride
Al
w
(OH)
x
(Cl)
y
(SO
4
)
z
Variable “PACl” used when
Hg contamination is a
concern
Polyaluminum sulfate
Al
w
(OH)
x
(Cl)
y
(SO
4
)
z
Variable “PAS” used when Hg
contamination is a
concern
Polyiron chloride
Fe
w
(OH)
x
(Cl)
y
(SO
4
)
z
Variable
Ferric chloride FeCl
3
162.5
Ferric sulfate Fe
2
(SO
4
)
3
400
TABLE 6-2
Frequently used cationic organic coagulants
CH
3
Epichlorohydrin
dimethylamine
(epi-DMA)
Coagulant
N
CH
3
OH
CH
CH
2
Cl
Polydiallyl dimethyl
ammonium
chloride
(poly-DADMAC)
Chemical formula
CH
2
CH
CH
3
CH
3
N
Cl
x
x
CH
2
N
Cl
CH
2
CH CH
CH
3
y
CH
3
CH
2
CH
2
CH CH
2
6-8 WATER AND WASTEWATER ENGINEERING
*Ionic strength is calculated as
I 1/2 C
i
Z
i
2
where I ionic strength, mole/L; C
i
concentration of species i, mole/L, and Z
i
number of replaceable hydrogen atoms or
their equivalent (for oxidation-reduction, Z
i
is equal to the change in valence).
60 mg/L
NaCl
600 mg/L
NaCl
6,000 mg/L
NaCl
0
20
40
60
80
100
0.010.020.0 30.0 40.0 50.0
Potential, mV
Distance, nm
FIGURE 6-5a
Effect of solution concentration on double layer.
Z 1
Z 2
Z 3
0
20
40
60
80
100
0.010.020.0 30.0 40.0 50.0
Distance, nm
Potential, mV
FIGURE 6-5b
Effect of charge on double layer. “Z” is the charge.
Compression of the Double Layer. If the electric double layer is compressed, the repulsive
force is reduced and particles will come together as a result of Brownian motion and remain
attached due to van der Waals forces of attraction. Both the ionic strength and the charge of coun-
terions are important in the compression of the double la
yer.
The DLVO mod el postulates that the van der Waals forces extend out into solution about
1 nm. If the double layer can be reduced to less than this , a rapidly flocculating suspension is
formed. As shown in Figure 6-5 a, increasing the ionic strength of the solution compresse
s the
double layer. Although this method is effective, the ionic s trength * i s much greater than would
be acceptable for potable water.
COAGULATION AND FLOCCULATION 6-9
A s shown in Figure 6-5 b, the charge of the counterions has a strong effect. In 1900, Hardy
summarized a series of experiments with various coagulants in what is known as the Schulze-Hardy
rule. They reported that for monovalent counterions, flocculation occu rred at a concentration
range of 25 to 15 millimoles/L; for divalent ions the range was 0.
5 to 2 millimoles/L; for triva-
lent ions the range was 0.01 to 0.1 millimoles /L (Schulze, 1882, 1883; Hardy, 1900a, 1900b).
For example, the ratio of Na
:Ca
:Al
to achieve a given residual turbidity would be as
shown in Figure 6-6 (O’Melia, 1972). According to the DLVO model, the ratios are 1:1/2
6
:1/3
6
.
Because coagulants are not “indifferent,” they will undergo many interactions in addition to elec-
trostatic attraction and repulsion. If, for example, phosphate is present, substantially more triva-
lent coagulant will be required because the coagulant will react with the phosphate. If multivalent
ions comprise the fixe
d layer next to the negatively charged particle, the double layer will be re-
duced significantly and the critical coagulation concentration will be much lower than predicted
by the Schultz-Hardy rule.
Adsorption and Charge Neutralization. Hydrolyzed metal salts, prehydrolyzed metal salts, and
cationic polymer
s have a positive charge. They destabilize particles through charge neutralization.
Adsorption and Interparticle Bridging. Schematically, polymer chains such as poly-
DADMAC and epi-DMA adsorb on particle surfaces at one or more sites along the polymer
chain. The adsorption is a result of (1) coulombic, charge-charge interactions, (2) dipole interac
-
tion, (3) hydrogen bonding, and (4) van der Waals forces of attraction (Hunter, 2001). Other sites
on the polymer chain extend into solution and adsorb on surfaces of other particles, thus creating
a “bridge” between the particles. This bridge results in a larger particle that settles more quickly
and forms a more dens
e sludge.
Enmeshment in a Precipitate. With doses exceeding saturation for the metal hydroxide, alumi-
num and iron salts form insoluble precipitates and particulate matter is entrapped in the precipitate.
This type of destabilization has been described as sweep coagulation (Packham, 1965; Stumm
Al
Dose of coagulant, mg/L
Residual turbidity, %
Ca
Na
0
10 100 1,000 10,000
10
20
30
40
50
60
70
80
90
100
FIGURE 6-6
Schematic coagulation curves illustrating DLVO theoretical relation-
ship between charge and dose to achieve a given turbidity reduction.
6-10 WATER AND WASTEWATER ENGINEERING
and O’Melia, 1968). In water treatment applications the mechanism is hypothesized to be nucle-
ation of the precipitate on a particle surface followed by growth of an amorphous precipitate that
entraps other particles.
CHEMISTRY OF COAGULATION
The chemistry of coagulation is extremely complex. The following discussion is limited to the
basic chem istry. Because metal coagulants hydrolyze to form acid products that affect pH that
in turn affects the solubility of the coagulant, it is
useful to begin with a review of a few basic
concepts that will help explain the interaction of coagulants and pH.
Buffer Solutions. A solution that resists large changes in pH when an acid or base is added or
when the solution is diluted is called a buffer solution. A solution containing a weak acid and
its salt is an e
xample of a buffer. Atmospheric carbon dioxide (CO
2
) produces a natural buffer
through the following reactions:
CO g CO H O H CO H HCO H CO
33
2
22223
2()
(6-2)
where H
2
CO
3
carbonic acid
HCO
3
bicarbonate ion
CO
3
2
carbonate ion
This is perhaps the most important buffer system in water and wastewater treatment.
It will be referred to several times in this and subsequent chapters as the carbonate buffer
system.
As depicted in Equation 6-2 , the CO
2
in solution is in equilibrium with atmospheric CO
2
(g).
Any change in the system components to the right of CO
2
causes the CO
2
either to be released
from solution or to dissolve.
One can examine the character of the buffer system in resisting a change in pH by assuming
the addition of an acid or a base and applying the law of mass action (Le Chatelier’s principle).
For example, if an acid is added to the system, it unbalances it by inc
reasing the hydrogen ion
concentration. Therefore, the carbonate combines with it to form bicarbonate. Bicarbonate reacts
to form more carbonic acid, which in turn dissociates to CO
2
and water. The excess CO
2
can be
released to the atmosphere in a thermodynamically open system. Alternatively, the addition of a
base consumes hydrogen ions, and the system moves to the right with the CO
2
being replenished
from the atmosphere. When CO
2
i s bubbled into the system or is removed by passing an inert
gas such as nitrogen through the liquid (a process called stripping ), the pH will change more dra-
matically because the atmosphere is no longer available as a source or sink for CO
2
. Figure 6-7
summarizes the four general responses of the carbonate buffer s ystem. The first two cases are
common in natural settings when the reactions proceed over a relatively long period of time. In a
water treatment plant, the reactions can be altered more quickly than the CO
2
can be replenished
from the atmosphere. The second two cases are not common in natural settings. They are used in
water treatment plants to adjust the pH.
In natural waters in equilibrium with atmospheric CO
2
, the amount of CO
2
in solution is
quite small in comparison to the HCO
3
in solution. The presence of Ca
2
in the form of lime-
stone rock or other naturally occurring sources of calcium results in the formation of calcium
COAGULATION AND FLOCCULATION 6-11
Case I
Acid is added to carbonate buffer system
a
Reaction shifts to the left as
HCO
2 3
*
is formed when H
and HCO
3
combine
b
CO
2
is released to the atmosphere
pH is lowered slightly because of the availability of free H
(amount depends on
buffering capacity)
Case II
Base is added to carbonate buffer system
Reaction shifts to the right
CO
2
from the atmosphere dissolves into solution
pH is raised slightly because H
combines with OH
(amount depends on
buffering capacity)
Case III
CO
2
is bubbled into carbonate buffer system
Reaction s hifts to the right because
HCO
2 3
*
is formed when CO
2
and H
2
O
combine
CO
2
dissolves into solution
pH is lowered
Case IV
Carbonate buffer system is stripped of CO
2
Reaction shifts to the left to form more
HCO
2 3
*
to replace that removed by
stripping
CO
2
is removed from solution
pH is raised
a
Refer to Equation 6-2.
b
The asterisk
*
in the H
2
CO
3
is used to signify the sum of CO
2
and H
2
CO
3
in solution.
FIGURE 6-7
Behavior of the carbonate buffer system with the addition of acids and bases or the addition and removal
of CO
2
. (Source: Davis and Cornwell, 2008.)
carbonate (CaCO
3
), which is very insoluble. As a consequence, it precipitates from solution. The
reaction of Ca
2
with CO
3
2
to form a precipitate is one of the fundamental reactions used to
soften water.
Alkalinity. Alkalinity is defined as the sum of all titratable bases down to about pH 4.5. It is
found by experimentally determining how much acid it takes to lower the pH of water to 4.5. In
6-12 WATER AND WASTEWATER ENGINEERING
most waters the only significant contributions to alkalinity are the carbonate species and any free
H
or OH
. The total H
that can be taken up by a water containing primarily carbonate species is
Alkalinity OH H
[][][][]HCO CO
3
2
3
2
(6-3)
where [] refers to concentrations in moles/L. In most natural water situations (pH 6 to 8), the
OH
and H
are negligible, such that
Alkalinity
[][]HCO CO
33
2
2
(6-4)
Note that [
CO
3
2
] is multiplied by two because it can accept two protons. The pertinent acid/base
reactions are
HCO H HCO p at C
32 3 1
6 35 25
K
a
.
(6-5)
HHCO H CO p at
3
2
3 2
10 33
K
a
.C25
(6-6)
From the p K values, some useful relationships can be found. The more important ones are as
follows:
1 . Below pH of 4.5, essentially all of the carbonate species are present as H
2
CO
3
, and the
alkalinity is negative (due to the H
).
2 . At a pH of 8.3 most of the carbonate species are present as
HCO
3
and the alkalinity
equals HCO
3
.
3 . Above a pH of 12.3, essentially all of the carbonate species are present as [
CO
3
2
] and the
alkalinity equals [CO
3
2
] [OH
]. The [OH
] may not be insignificant at this pH.
Figure 6-8 schematically shows the change of species described above as the pH is lowered
by the addition of acid to a water containing alkalinity. Note that the pH starts at above 12.3
and as acid is added the pH drops slowly as the first acid (H
) addition is consumed by free
hydroxide (OH
), preventing a significant pH drop, and then the acid is consumed by carbonate
(
CO
3
2
) being converted to bicarbonate (
HCO
3
). At about pH 8.3 the carbonate is essentially all
converted to bicarbonate, at which point there is another somewhat flat area where the acid is
consumed by converting bicarbonate to carbonic acid.
From Equation 6-4 and the discussion of buffer solutions, it can be seen that alkalinity serves
as a measure of buffering capa
city. The greater the alkalinity, the greater the buffering capacity.
We differentiate between alkaline water and water having high alkalinity. Alkaline water has a
pH greater than 7, while a water with high alkalinity has a high buffering capacity. An alkaline
water may or may not have a high buffering capacity. Likewise, a water with a high alkalinity
may or may not have a high pH.
B y convention, alkalinity is not expressed in molarity units as shown in the above equations,
but rather in mg/L a
s CaCO
3
. In order to convert species to mg/L as CaCO
3
, multiply mg/L as the
species by the ratio of the equivalent weight of CaCO
3
to the species equivalent weight:
mg/L as CaCO mg/L as the species
EW
E
CaCO
3
3
()
WW
species
⎛
⎝
⎜
⎞
⎠
⎟
(6-7)
COAGULATION AND FLOCCULATION 6-13
The alkalinity is then found by adding all the carbonate species and the hydroxide, and then
subtracting the hydrogen ions. When using the units “mg/L as CaCO
3
,” the terms are added
directly. The multiple of two for
CO
3
2
has already been accounted for in the conversion.
Example 6-1. A water contains 100.0 mg/L
CO
3
2
and 75.0 mg/L
HCO
3
at a pH of 10. Calcu-
late the alkalinity exactly at 25 C. Approximate the alkalinity by ignoring [OH
] and [H
].
Solution. First, convert
CO
3
2
,
HCO
3
, OH
, and H
to mg/L as CaCO
3
.
The equivalent weights are
CO MW EW
HCO MW EW
H
3
2
3
:,,
:,,
60 2 30
61 1 61
n
n
:,,
:,,
MW EW
OH MW EW
11 1
17 1 17
n
n
From the pH of 10, [H
] 10
10
moles/L and the mg/L of the species is
mg/L of speciesmoles/L GMW mg/g()()( )10
3
()()()10 1 10 10
10 3 7
moles/L g/mole mg/g mgg/L of H
The OH
concentration is determined from the ionization of water, that is
K
w
[][]OH H
mL acid
Hydroxide
Carbonate
Point of inflection
Point of inflection
14
13
12
11
10
pH
9
8
7
6
5
4
3
2
1
0
OH
–
H
H
2
OCO
3
2–
H
HCO
3
–
HCO
3
–
H
H
2
CO
3
FIGURE 6-8
Titration curve for a hydroxide-carbonate mixture. (Source: Sawyer, McCarty, and
Parkin, 1994.)
6-14 WATER AND WASTEWATER ENGINEERING
where K
w
10
14
(p K
w
14):
[]OH moles/L
10
10
10
14
10
4
and
mg/L moles/L g/mole mg/g
()()()10 17 10 1
4 3
.77
Now, the mg/L as CaCO
3
is found by using Equation 6-7 and taking the equivalent weight of
CaCO
3
to be 50:
CO
3
2
100 0
50
60
167.
⎛
⎝
⎞
⎠
HCO
3
75 0
50
61
61.
⎛
⎝
⎞
⎠
H
10
50
1
5 10
76
⎛
⎝
⎞
⎠
OH
17
50
17
5 0..
⎛
⎝
⎞
⎠
The exact alkalinity (in mg/L) is found by
Alkalinity mg/L CaC
61 167 5 0 5 10 233
6
.( ) OO
3
It is approximated by 61 167 228 mg/L as CaCO
3
. This is a 2.2% error.
Aluminum. A l uminum can be purchased as either dry or liquid alum [Al
2
(SO
4
)
3
· 14H
2
O].
Commercial alum has an average molecular weight of 594. Liquid alum is sold as approxi-
mately 48.8 percent alum (8.3 percent Al
2
O
3
) and 51.2 percent water. If it is sold as a more
concentrated solution, there can be problems with crystallization of the alum during shipment
and storage. A 48.8 percent alum solution has a crystallization point of 1 5.6 C. A 50.7 percent
alum solution will crystallize at 18.3 C. The alternative is to purchas
e dry alum. However, dry
alum costs about 50 percent more than an equivalent amount of liquid alum so that only users of
very small amounts of alum purchase it in this form.
When alum is added to a water containing alkalinity, the following reaction occurs:
Al SO H O HCO Al OH H O s
3243 2 3 2
14 6 2 3() () ()
68
3
22
CO H O
SO
4
2
(6-8)
such that each mole of alum added uses six moles of alkalinity and produces six moles of carbon
dioxide. The above reaction shifts the carbonate equilibrium and decreases the pH. However, as
long as sufficient alkalinity is present and CO
2
(g) is allowed to evolve, the pH is not drastically
COAGULATION AND FLOCCULATION 6-15
reduced and is generally not an operational problem. When sufficient alkalinity is not present to
neutralize the sulfuric acid production, the pH may be greatly reduced:
Al SO H O Al OH H O s HSO
243 2 3 224
14 2 33() () () 2
2
HO
(6-9)
If the sec ond reaction occurs , lime or sodium carbonate may be added to neutralize the acid
formed because the precipitate will dissolve.
E xample 6-2 illustrates the destruction of alkalinity.
Example 6-2. Estimate the amount of alkalinity (in mg/L) consumed from
the addition of 100
mg/L of alum.
Solution:
a . Using Equation 6-8 , note that 6 moles of
HCO
3
are consumed for each mole of alum
added.
b. Calculate the moles/L of alum added.
100 100
594
mg/L of alum
GMW of alu m
mg/L
g/
(
mmole mg/g
moles/L
)( )10
168 10
3
4
.
c. Calculate the moles/L of
HCO
3
consumed.
6 1 68 10 1 01 10
4 3
()..
moles/L moles/L
d. Convert to mg/L
()(
)
101 10
3
.
moles/L
GMW of HCO
3
()()1 01 10 61 6 16 10
3 2
..
moles/L g/mole g/LLor mg/L as HCO
3
61 6.
Comment. A rule of thumb used to estimate the amount of the alkalinity consumed by alum is
that 1 mg/L of alum destroys 0.5 mg/L of alkalinity as CaCO
3
.
An important aspect of coagulation is that the aluminum ion does not really exis t as Al
3
,
and that the final product is more complex than Al(OH)
3
. When the alum is added to the water,
it immediately dissociates, resulting in the release of an aluminum ion surrounded by six water
molecules. The aluminum ion starts reacting with the water, forming large Al · OH · H
2
O com-
plexes. Some have suggested that [Al
8
(OH)
20
· 28H
2
O]
4
i s the product that actually coagulates.
Regardless of the actual species produced, the complex is a very large precipitate that removes
many of the colloids by enmeshment as it falls through the water.
Iron. Iron can be purchased as either the sulfate salt (Fe
2
(SO4)
3
· x H
2
O) or the chloride salt
(FeCl
3
· x H
2
O). It is available in various forms, and the individual supplier should be consulted for