Water and Wastewater Engineering
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LIME–SODA SOFTENING 7-47
7-12 REFERENCES
AWWA (1978) Corrosion Control by Deposition of CaCO
3
Films, American Water Works Association,
Denver.
Benefield, L. D., J. F. Judkins, and B. L. Weand (1982) Process Chemistry for Water and Wastewater
Treatment, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 267–306, 418–419, 460.
Benefield, L. D. and J. M. Morgan (1999) “Chemical Precipitation,” in R. D. Letterman (ed.) Water
Quality and Treatment, 5th ed., American Water Works Association, McGraw-Hill, New York,
pp. 9.1–9.91.
Davis, M. L. and D. A. Cornwell (2008) Introduction to Environmental Engineering, McGraw-Hill,
New York, pp. 236–259.
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. 35–38, 66–80.
Horsley, M. B., D. B. Elder, and L. L. Harms (2005) “Lime Softening,” in E. E Baruth (ed.), Water
Treatment Plant Design, McGraw-Hill, New York, pp. 11.1–11.20.
Kawamura, S. (2000) Integrated Design and Operation of Water Treatment Facilities, 2nd ed, John Wiley &
Sons, New York, pp. 74–139.
Langelier, W. F. (1936) “The Analytical Control of Anticorrosion Water Treatment,” Journal of American
Water Works Association, vol. 28, p. 1,500.
MDEQ (1979) Annual Data Summary, Michigan Department of Public Health, Lansing, MI.
Merrill, D. T. (1978) “Chemical Conditioning for Water Softening and Corrosion Control,” in R. L. Sanks
(ed.) Water Treatment Plant Design, Ann Arbor Science, Ann Arbor, Michigan, pp. 497–565.
MWH (2005) Water Treatment: Principles and Design, John Wiley & Sons, Hoboken, New Jersey,
pp. 957, 1371, 1403, 1431, 1445, 1472, 1564.
Rossum, J. R. and D. T. Merrill (1983) “An Evaluation of the Calcium Carbonate Saturation Indexes,”
Journal of the American Water Works Association, vol. 69, no. 2, p. 95.
Sawyer, C. N., P. L. McCarty, and G. F. Parkin (2003) Chemistry for Environmental Engineering and
Science, McGraw-Hill, Boston, pp. 179, 564.
S chock, M. R. (1999) “Internal Corrosion and Deposition Control,” in R. D. Letterman (ed.) Water
Quality and Treatment, 5th ed., American Water Works Association, McGraw-Hill, New York,
pp.17.1–17.109.
Sorg, T. J., O. T. Love, Jr. and G. Logsdon (1977) Manual of Treatment Techniques for Meeting the
Interim Primary Drinking Water Regulations, U.S. Environmental Protection Agency Report
600/8.77.005, MERL, Cincinnati, Ohio.
Woller, D. M. and E. W. Sanderson (1976a) Public Water Supplies in McHenry County, Illinois State
Water Survey, Publication No. 60–19, Urbana, IL.
Woller, D. M. and E. W. Sanderson (1976b) Public Water Supplies in Putnam County, Illinois State
Water Survey, Publication No. 60–15, Urbana, IL.
8-1
8-6 CHAPTER REVIEW
8-7 PROBLEMS
8-8 DISCUSSION QUESTION
8-9 REFERENCES
ION EXCHANGE
8-1 INTRODUCTION
8-2 FUNDAMENTAL CONCEPTS OF ION
EXCHANGE
8-3 PROCESS OPERATION
8-4 ION EXCHANGE PRACTICE
8-5 OPERATION AND MAINTENANCE
8
CHAPTER
8-2 WATER AND WASTEWATER ENGINEERING
8-1 INTRODUCTION
Ion exchange * i s a reversible reaction in which a charged ion in solution is exchanged for a simi-
larly charged ion electrostatically attached to an immobile solid particle. The largest application of
ion exchange in water treatment is for softening, where calcium, magnesium and other polyvalent
cations are exchanged for
sodium (Clifford, 1999). It is used both in individual homes [called
point-of-entry (POE) or point of use (POU)] and in municipal systems. Ion exchange is also used
to remove specific contaminants such as arsenic, barium, nitrate, and radium.
In common pra
ctice the raw water is passed through a bed of resin. The resin is the made by
polymerization of organic compounds into a porous matrix. Commercially available resins are
selected for the bed. Typically, in water softening, sodium is exchanged for cations in solution.
When the bed become
s saturated with the exchanged ion, it is shut down and regenerated by
passing a concentrated solution of sodium back through the bed.
Because of its large application in softening water, the focus of this chapter is on this
application.
8-2 FUNDAMENTAL CONCEPTS OF ION EXCHANGE
Ion Exchange Resins and Reactions
Ion Exchange Resins. The most common polymeric resin matrix is a cross-linked polystyrene
to which charged functional groups are attached by covalent bonding. Divinylbenzene (DVB)
is used as a cross-linking agent with the styrene. A higher DVB cross-linkage provides a more
stable resin but will result in slower ion ex change kinetics. The co
mmon functional groups are
in four categories: strongly acidic (for example, sulfonate, SO
3
); weakly acidic (for example,
carboxylate, COO
); strongly basic (for example, quaternary amine, N
(CH
3
)
3
), and weakly
basic (for example, tertiary amine, N(CH
3
)
2
).
Figure 8-1 is a schematic representation of a resin bead and two typical functional groups.
Cation exchange resins contain mobile positive ions, such as hydrogen (H
) or sodium (Na
) ,
that are attached to immobile functional acid groups, such as sulfonic (SO
3
) and carboxylic
(COO
) groups. The functional groups are fixed to the resin matrix or backbone. These are the
cation ion exchange sites. The number of sites is finite, and when they all have been exchanged
the ion exchange resin will no longer soften the water.
Strong Cation Exchange Reactions. The word “strong” in strong cation exchange does not
refer to the physical strength of the resin but rather to the Arrhenius theory of electrolyte strength
in which the functional group of the resin is dissociated completely in its ionic form at any pH.
Equation 8-1 represents the exchange of sodium for calcium in the form of carbonate hardness
and Equation 8-2 represents the exchange of sodium for noncarbonate hardness
Ca(HCO
3
)
2
2{ źSO
3
ź
Na
á
} { źRSO
3
}
2
Ca
2á
2NaHCO
3
(8-1)
CaCl
2
2{ źSO
3
ź
Na
á
} { źSO
3
}
2
Ca
2á
2NaCl
(8-2)
*Often noted in the literature as IX.
ION EXCHANGE 8-3
where denotes the resin and the bold font represents the solid resin phase. Magnesium
and other polyvalent ions are removed by similar reactions. The sulfonic group provides a
strong reactive site and the exchange resin readily removes all polyvalent cations. The reac-
tions are reversible.
Weak Cation Exchange Reactions. The weak cation exchange re
sins can remove carbonate
hardness as shown in Equation 8-3 , but they cannot remove noncarbonate hardness.
Ca(HCO
3
)
2
2{ źCOOH} { źCOO}
2
Ca2H
2
CO
3
(8-3)
The weak cation exchange resins are regenerated with a strong acid (HCl or H
2
SO
4
).
Ion Exchange Kinetics
The rate of ion exchange depends on the rates of the various transport mechanisms carrying the
ion to be removed to the resin as well as the exchange reaction rate itself. The mechanisms are as
follows (Reynolds and Richards, 1996): (1) movement of the ions from the bulk solution to the
film or boundary layer surrounding the exchange soli
d, (2) diffusion of the ions through the film
to the solid surface, (3) diffusion of the ions inward through the pores of the solid to the exchange
Polymer
chain
Fixed coion
Mobile counter ion
Crosslinking
0.15 – 1.2 mm
SO
3
Na
SO
3
Na
SO
3
Na
SO
3
Na
(a)
(b)
N
Cl
CH
3
CH
3
CH
3
N
CH
3
CH
3
CH
3
Cl
N
Cl
CH
3
CH
3
CH
3
FIGURE 8-1
S chematic of organic cation-exchange bead ( a ). The bead is shown as a polystyrene polymer cross-linked with divinyl benzene
with fixed coions (minus charge) balanced by mobile positively charged counterions (positive charge). ( b ) strong cation ex-
change resin on left (Na
form) and strong-base on right (Cl
form).
8-4 WATER AND WASTEWATER ENGINEERING
sites, (4) exchange of the ions by reaction, (5) diffusion of the exchanged ions outward through
the pores to the solid surface, (6) diffusion of the exchanged ions through the boundary layer, and
(7) movement of the exchanged ions into the bulk solution.
For a column of resin, the exchange reac
tions begin to saturate the upper levels before the
lower levels. The progress of this satu ration through the column results in a “wave” of satu-
ration as shown in Figure 8-2a . If samples are taken at the bottom of the column, a curve of
increasing concentration is detected as shown in Figure 8-2b . This curve is called the break-
through curve.
At some point in time the effluent concentration exceeds the design criteria,
for example at concentration C
c
in Figure 8-2b . The column is then taken out of service and
regenerated.
C
0
C
a
C
a
C
b
C
c
C
d
Breakpoint
0
(
1
)
(a)
(b)
(
2
)(
3
)(
4
)
(
1
)(
2
)(
3
)(
4
)
Breakthrough
curve
C
b
C
c
Effluent
concentration
Volume of effluent
Concentration of gas in effluent
C
0
C
0
C
0
C
0
Inlet
concentration
C
d
Exchange
zone
Exchange
zone
FIGURE 8-2
Ion exchange wave ( a ) and breakthrough ( b ). ( Source: Treybal, 1968.)
ION EXCHANGE 8-5
Properties of Ion Exchange Resins
Exchange Capacity. One of the major considerations in selecting an ion exchange resin is the
quantity of counterions that can be exchanged onto the resin. This quantity is called the exchange
capacity of the resin. The total capacity is dependent on the quantity of functional groups on a resin
bead. The exchange capacity m
ay be reported as milliequivalents per gram of dry resin (meq/g) or
as milliequivalents per milliliter of wet resin (meq/mL). The typical dry-weight capacity of a strong
acid cation exchange resin falls in the range of 3.6 to 5.5 meq/g. Typical wet-volume capacity is
1.8 to 2.0 meq CaCO
3
/ mL.
Selectivity. Ion exchange resins have a variable preference or affinity for the ions in solution.
This preference or affinity is called selectivity. Q uantitatively, for a binary exchange, selectivity
may be expressed as a selectivity coefficient ( K
j
i
). For the generalized cation reaction
n[] [ ]RA RB
n
++
++
Bn nA
n
(8-4)
the equilibrium expression is
K
B
A
n
nn
A
=
+
+
[]{ }
{}[ ]
RB
RA
n++
B
(8-5)
where K
B
A
apparent equilibrium constant or selectivity coefficient for cation (or
anion) A exchanging with ion B onto resin
[A
] aqueous-phase concentration of presaturant ion, eq/L
[B
n
] aqueous-phase concentration of counterion, eq/L
{ RA }, { RB
n
} activities of resin-phase presaturant ion and counterion, respectively
n valence of the exchanging ion
A similar expression can be written for anions. Although the activity terms are a function of
ionic strength, c oncentrations are used in practice because they are measured more eas
ily than
activities. Thus, Equation 8-5 is conveniently expressed as
K
Cq
Cq
j
i
j
n
i
i j
n
()
()
(8-6)
where K
j
i
equilibrium
constant for cation (or anion) i exchanging with ion j
C
j
aqueous phase concentration of presaturant ion j, meq/L
q
i
resin phase concentration of counterion i, meq/L
C
i
aqueous phase concentration of counterion i, meq/L
q
j
resin phase concentration of presaturant ion j, meq/L
n valence of the exchanging ion
8-6 WATER AND WASTEWATER ENGINEERING
For the cation exchange of calcium and sodium expressed in Equation 8-2 , the equilibrium constant
would be expressed as
K
Cq
Cq
Na
Ca
()
()
Na Ca
Ca Na
2
2
(8-7)
The greater the selectivity coefficient ( K ), the greater is the preference for the ion by the
exchange resin. Commercial exchange resins used in water treatment tend to prefer (1) ions of
higher valence, (2) ions with smaller solvated volume, (3) ions with greater ability to polarize,
(4) ions that react strongly with the exchange sites on the resin, and (5) ions that do not form
com
plexes (Helfferich, 1962).
For process design evaluation, separation factors are used rather than selectivity coefficients.
The binary separation factor is a measure of the preference of one ion for another ion. It may be
expressed as
j
i
i j
i j
YX
XY
(8-8)
where
j
i
separation factor
Y
i
resin phase equivalent fraction of counterions
X
j
equivalent fraction of presaturant ion in aqueous phase
X
i
equivalent fraction of counterion in aqueous phase
Y
j
resin phase equivalent fraction of presaturant ion
The equivalent fraction in the aqueous phase is calculated as
X
C
C
i
i
T
(8-9)
and
X
C
C
j
j
T
(8-10)
where C
T
total aqueous ion concentration
C
i
aqueous phase concentration of counter ion, eq/L
C
j
aqueous phase concentration of presaturant ion, eq/L
Similarly, for resin phase
Y
q
q
i
i
T
(8-11)
ION EXCHANGE 8-7
and
Y
q
q
j
j
T
(8-12)
where q
T
total exchange capacity of resin, eq/L.
Because a binary system involves only the presaturant ion and one other ion to be exchanged,
CCC
T i j
(8-13)
and
qqq
T i j
(8-14)
Separation factors for commercially available strong acid cation exchange resins are given
in Table 8-1 .
A combination of Equations 8-7 and 8-8 yields
Na
Ca
Ca
Na
Na
Na
K
qY
CX
T
T
⎛
⎝
⎜
⎞
⎠
⎟
(8-15)
The implication of this equation is that, with q
T
constant, divalent/monovalent exchange
depends inversely on solution concentration and directly on the distribution ratio Y
Na
/ X
Na
between the resin and the water. The higher the solution concentration C
T
, the lower the
divalent/monovalent separation factor; that is, the selectivity tends to reverse in favor of the
monovalent ion as ionic strength (that is, a function of C ) increases. This is the theoretical
basis for regeneration of the cation exchange resin by the application of a high concentration
of sodium.
Rearrangement of Equation 8-8 with appropriate substitution of terms yields an expression
that allows
the calculation of the resin phase concentration of the counterion of interest if the
binary separation factor and total resin capacity are known.
q
Cq
CC
i
i T
i j i
j
(8-16)
where a
i
j
1/
j
i
.
The use of this expression in estimating the maximum volume of water that can be treated by
a given resin is illustrated in Example 8-1 .
8-8 WATER AND WASTEWATER ENGINEERING
TABLE 8-1
Separation factors of ions for resins
a
Strong acid cation resins
b
Strong base anion resins
c
Cation, i
i/
Na
Anion, i
i/
Cl
d
Ra
2
13.0
UO CO
2 3
3
4
()
3200
Ba
2
5.8
ClO
4
e
150
Pb
2
5.0
CrO
4
2
100
Sr
2
4.8
SeO
4
2
17
Cu
2
2.6
SO
4
2
9.1
Ca
2
1.9
HAsO
4
2
4.5
Zn
2
1.8
HSO
4
4.1
Fe
2
1.7
NO
3
3.2
Mg
2
1.67 Br
2.3
K
1.67
SeO
3
2
1.3
Mn
2
1.6
HSO
3
1.2
1.3
NO
2
1.1
Na
1.0 Cl
1.0
H
0.67
BrO
3
0.9
HCO
3
0.27
CH
3
COO
0.14
F
0.07
a
Above values are approximate separation factors for 0.005–0.010 N solution (TDS 250–
500 mg/L as CaCO
3
).
b
SAC resin is polystyrene divinylbenzene matrix with sulfonate functional groups.
c
SBA resin is polystyrene divinylbenzene matrix with N
(CH
3
)
3
functional groups (i.e., a
Type 1 resin).
d
Separation factors are approximate and are based on various literature sources and on
experiments performed at the University of Houston.
e
ClO
4
/Cl
separation factor is for polystyrene SBA resins; on polyacrylic SBA resins, the
ClO
4
/Cl
separation factor is approximately 5.0.
( Source: Clifford, 1999.)
NH
4
ION EXCHANGE 8-9
Example 8-1. Estimate the maximum volume of water per liter of resin that can be treated by
a strong acid exchange resin in the sodium form if the resin has total capacity of 2.0 eq/L, the
calcium concentration is 1.4 meq/L, and the sodium concentration is 2.6 meq/L. Assume no other
cations are in the solution.
Solution:
a . Calculate the separation factor for sodium over calcium using the separation factor from
Table 8-1 .
j
i
j
i
a
19
1119053
.
..
j
i
//
b. The maximum useful capacity of the resin for calcium is
q
Cq
CC
T
Ca
Ca
Ca Na
i
j
()( )(14 20 1000
2
..,meq Ca /L eq/L of resin mmeq/eq
meq Ca /L meq Na /L
)
(( ) ( )(14 26 0
2
..
..
,,
53
1 008 1 000
2
)
or meq Ca /L of resin
c. The maximum volume of water that can be treated per volume of resin per cycle is
q
C
Ca
Ca
meq Ca /L of resin
meq C
1 000
14
2
,
.
aa /L of water
or L of water/L
2
714 29 710
.ofresin
V
Comments:
1 . This is the maximum amount of Ca
2
that can be removed assuming 100% efficiency
of transfer, 100% regeneration efficiency, and that sufficient contact time has been
provided to achieve equilibrium. This seldom happens in actual practice because, as
noted in Figure 8-2 , complete breakthrough would have to occur to completely
saturate
the bed.
2. For multicomponent systems such as a hard water containing several polyvalent cations,
Equation 8-16 must be expanded to take into account the concentrations and separation
factors for each of the components. MWH (2005) provides an extensive discussion on the
method.
Resin Particle Size. Particle size has two effects on the ion exchange process. The rate of
ion exchange decreases with increasing particle size. In contrast, the headloss through the bed
increases as the bead size decreases. Because excessive pressure drops through the bed have the