Standard Methods for Examination of Water & Wastewater_15 pptx

Ion Exchange

This chapter discusses the unit process of ion exchange, including topics such as
ion exchange reactions, unit operations of ion exchange, sodium and hydrogen
cycles, regeneration, and design of ion exchangers. Some of these topics have already
been discussed in the various sections of the unit operations in Part II and will only
be incorporated into this chapter by reference.

16.1 ION EXCHANGE REACTIONS

Ion exchange

is the displacement of one ion by another. The displaced ion is originally
a part of an insoluble material, and the displacing ion is originally in solution. At the
completion of the process, the two ions are in reversed places: the displaced ion
moves into solution and the displacing ion becomes a part of the insoluble material.
Two types of ion exchange materials are used: the cation exchange material and
the anion exchange material. The

cation exchange material

exchanges cations, while
the

anion exchange material

exchanges anions. The insoluble part of the exchange
material is called the

host

. If

R

−

n



represents the host part and

C

+

m

the exchangeable
cation, the cation exchange material may be represented by (

R

−

n

)

r

(

C

+

m

)

rn

/

m

, where

r

is the number of active sites in the insoluble material,

rn

/

m

is the number of charged
exchangeable particles attached to the host material,

−

n

is the charge of the host,
and

+

m

is the charge of the exchangeable cation. On the other hand, if

R

+

o

represents
the host part of the anion exchange material and

A

−

p

its exchangeable anion, the
exchange material may be represented by (

R

+

o

)

r

(

A

−

p

)

ro

/

p

, where the subscripts and
superscripts are similarly defined as those for the cation exchange material. Letting
be the displacing cation from solution, the cation exchange reaction is
(16.1)
Also, letting be the displacing anion from solution, the anion exchange reaction
may be represented by
(16.2)
As shown by the previous equations, ion exchange reactions are governed by
equilibrium. For this reason, effluents from ion exchange processes never yield pure
water.
16
C
s
+q
R
−n
()
r
C
+m
()
rn/m
rn
q

C
s
+q
+  R
−n

()
r
C
s
+q
()
rn/q
rn
m

C
+m
+
A
s
−t
R
+o
()
r
A
−p
()
ro/ p
ro
t

A
s
−t

+  R
+o
()
r
A
s
−t
()
ro/t
ro
p

A
−p
+

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720

Table 16.1 shows the

displacement series

for ion exchange materials. When an
ion species high in the table is in solution, it can displace ion species in the insoluble
material below it in the table and, thus, be removed from solution. As noted in this
table, to remove any cation in solution, the displaceable cation must be the proton
H

+

; and to remove any anion, the displaceable anion must be the hydroxyl ion OH

−

.
Originally, natural and synthetic alumino silicates, called

zeolites

, were the
only ones used as exchange materials. Presently, they have been largely replaced
by synthetic resins.

Synthetic resins

are insoluble polymers to which are added,
by certain chemical reactions, acidic and basic groups called

functional groups

.
These groups are capable of performing reversible exchange reactions with ions in
solution. The total number of these groups determines the

exchange capacity

of the

exchange material, while the type of functional group determines ion selectivity.
When the exchange capacity of the exchange material is exhausted, the exchanger
may be regenerated by the reverse reactions above. The principles of regeneration
are discussed in the section on “Sodium, Hydrogen Cycle, and Regeneration.”

16.2 UNIT OPERATIONS OF ION EXCHANGE

Figure 16.1 shows the schematics of the unit operations of ion exchange. Figure 16.1a
shows a cation exchanger and Figure 16.1b shows an anion exchanger. In both units,
the influent is introduced at the top of the vessel. The bed of ion exchanger materials
would be inside the vessels, where, as the water to be treated passes through, exchange

TABLE 16.1
Displacement Series
for Ion Exchange

La

3

+

Y

3

+


Ba

2

+

Pb

2

+

Sr

2

+

Ca

2

+

Ni

2

+

I

−

Cd

2

+

Br

−

Cu

2

+

Cl

−

Zn

2

+

F

−

Mg

2

+

OH

−

Ag

+

—
Cs

+

—
Rb

+

—
K

+

—
—
Na

+

—
Li

+

—
H

+

—
SO
4
2−
CrO
4
2−
NO
3
−
AsO
4

−3
PO
4
−3
MoO
4
−2
NH
4
+

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721

of ions takes place. This exchange of ions is the chemical reaction of the unit process
of ion exchange; the mere physical passing through of the water with the attendant
head loss and pumping consideration is the unit operation of ion exchange. The unit
operations of head losses are similar to those of granular filtration discussed in Part
II. The unit operation of pumping was also discussed in Part II. After ion exchange,
product waters are withdrawn at the respective bottoms of the vessels.

16.3 SODIUM, HYDROGEN CYCLE, AND REGENERATION

As shown in Table 16.1, sodium, lithium, and hydrogen are the logical choices
for the exchangeable ions. In practice, however, sodium and hydrogen are the
ions of choice. The cation exchange resin using sodium may be represented by
(

R

−

n

)

r

(Na

+

)

rn

. Its exchange reaction with Ca

+2

and similar cations is shown below:
(16.3)
As shown, Ca

+2

has become embedded in the resin, thus removed from solution,
and Na

+

has become solubilized. Similar reactions may be formulated for the rest
of the ions in Table 16.1.
As soon as the resin is exhausted, it may be regenerated. As shown in Equation
(16.3), by the

Law of Mass Action

, the reaction may be driven to the left by increasing
the concentration of the sodium ion on the right. In practice, this is what is actually
done. The resin is regenerated by using a concentration of NaCl of about 5 to 10%,
thus, driving the reaction to the left. Operations where regeneration is done using
NaCl is said to run on the

sodium cycle

. Regeneration may also be made using acids,

FIGURE 16.1

Unit operations of ion exchange.
Cation exchanger Anion exchanger
Cation waste stream
Regenerant
Backwash waste
(Rinsing waste)
Regenerant
waste stream

(cation salts)
Regenerant
Backwash waste
(Rinsing waste)
NaCI (sodium cycle)
or
HCI; H
2
SO
4
(acid cycle)
NaOH
or
NH
4
OH
Anionic waste
Backwash
(and rinsing)
Sodium salts (sodium cycle)
or
Acids (hydrogen cycle)
Regenerant
waste
Backwash
(and rinsing)
(a) Cation exchanger (b) Anion exchanger
R
−n
()

r
Na
+
()
rn
rn
2

Ca
+2
+  R
−n
()
r
Ca
+2
()
rn/2
rnNa
+
+

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722

such as H
2
SO

4
. When regeneration is through the use of acids, the cycle is called
the hydrogen cycle (from the proton or hydrogen ion content of acids).
Table 16.2 shows approximate exchange capacities and regeneration require-
ments for ion exchangers. As shown, the values have great ranges. Thus, in practice,
one must have to perform an actual experiment or obtain data from the manufacturer
for a particular ion exchanger to determine the exchange capacity and regeneration
requirement. The capacity of an ion exchanger in terms of volume of influent treated
varies with the nature and concentration of ions in solution. This is much the same
as the characteristics of activated carbon. Hence, the experimental procedure is
practically the same as that of activated carbon.
Tables 16.3 and 16.4 show some additional properties of exchangers. The acidic
exchangers are cationic exchangers. They are called acidic because their exchange
sites are negatively charged to which the H
+
ion can attach, hence, acidic. The strongly
acidic cation exchangers readily remove cations from solutions, while the weakly
acidic exchangers will remove ions such as calcium and magnesium but have limited
ability to remove sodium and potassium, which are way down the table in the dis-
placement series. The basic exchangers, on the other hand, are anionic. They have
positively charged exchange sites to which the hydroxyl ion can attach and other
basic species such the quaternary and amine groups. The strongly basic exchanger
can readily remove all anions. The weakly basic ones remove mainly the anions of
strong acids such as , Cl
−
, and .
16.4 PRODUCTION OF “PURE WATER”
Theoretically, it would seem possible to produce pure water by combining the cation
exchanger operating on the hydrogen cycle and the anion exchanger operating on
the OH cycle. This is shown in the following discussions. Let Equation (16.1) be

written specifically for the hydrogen cycle. The resulting equation is
(16.4)
TABLE 16.2
General Properties of Ion Exchangers
Exchanger, cycle
Exchange Capacity,
Regenerant
Regenerant Requirement,
Cation exchangers:
Natural zeolite, Na 175–350 NaCl 3–6
Synthetic zeolite, Na 350–700 NaCl 2–3
Resin, Na 350–1760 NaCl 1.8–3.6
Resin, H 350–1760 H
2
SO
4
2–4
Anion exchanger:
Resin, OH 700–1050 NaOH 5–8
geq
m
3

geq
m
3

SO
4
2−

NO
3
−
R
−n
()
r
H
+
()
rn
rn
q

C
s
+q
 R
−n
()
r
C
s
+q
()
rn/q
rnH
+
++
TX249_frame_C16.fm Page 722 Friday, June 14, 2002 4:47 PM

© 2003 by A. P. Sincero and G. A. Sincero
From this equation, the number of reference species is rn/q(q), based on the
cation in solution; and the equivalent mass of species is

TABLE 16.3
Some Additional Properties of Cation Exchangers
Material
Exchange Capacity,
, Average
Packed Density,
, Average
Particle Shape
Strongly Acidic:
Sulfonated polystyrene:
Homogeneous resin:
1% cross-linked 5.4 750 Spherical
2% cross-linked 5.5 720 Spherical
4% cross-linked 5.2 800 Spherical
5–6% cross-linked 5.0 810 Spherical
8–10% cross-linked 4.9 855 Spherical
12% cross-linked 5.1 840 Spherical
14% cross-linked 4.6 940 Spherical
16% cross-linked 4.9 860 Spherical
20% cross-linked 3.9 840 Spherical
Macroporous 4.8 790 Spherical
Sulfonated phenolic resins 2.4 800 Granular
Resins from phenol methylene
sulfuric acid
2.9 730 Granular
Sulfonated coal 1.6 430 Granular

Weakly Acidic:
Acrylic or meta acrylic:
Homogeneous resin:
5% cross-linked 10.0 720 Spherical
10% cross-linked 6.5 750 Spherical
Macroporous 8.0 745 Spherical
Phenolic and related
condensation products
2.5 720 Granular
Polystyrene phosphonic acid 6.6 735 Granular
Polystyrene iminodiacetate 2.9 735 Spherical
Inorganic materials:
Greensand 0.14 1280 Granular
Aluminum silicate 1.4 800 Granular
Celluloses:
Phosphonic, low capacity 1.0 — Fiber
Phosphonic, high capacity 7.0 — Granular
Methyl carboxylic 0.7 — Fiber
dry meq
gm

kg
m
3

C
s
+q
rn
q

C
s
+q
rn
q

q()

C
s
+q
q

=
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© 2003 by A. P. Sincero and G. A. Sincero
Letting the molar concentration of be gmol/L, the corresponding con-
centration in geq/L is

Note: From , the units of q is equivalents per mole.
Therefore, the total concentration in gram equivalents per liter of removable cations
in solution, [CatT]
eq
, is the sum of all the cations. Let there be a total of i cations.
Thus,
(16.5)
As [CatT]
eq
of cations is removed from solution, a corresponding number of equiv-

alent concentrations of anions pair with the H
+
ions displaced from the cation bed.
TABLE 16.4
Some Additional Properties of Anion Exchangers
Material
Exchange Capacity,
, Average
Packed Density,
, Average
Particle
Shape
Strongly Basic:
Polystyrene matrix:
Trimethyl benzene ammonium:
1% cross-linked 3.2 700 Spherical
2% cross-linked 3.5 700 Spherical
4% cross-linked 4.0 670 Spherical
8% cross-linked 3.5 720 Spherical
Dimethyl hydroxyethyl benzyl ammonium
1–4% cross-linked 3.2 705 Spherical
6% cross-linked 3.1 705 Spherical
8% cross-linked 3.4 705 Spherical
10–12% cross-linked 3.0 705 Spherical
Condensation products with pyridium
quaternary amine
4.0 800 Spherical
Weakly Basic:
Aminopolystyrene 5.6 690 Spherical
Mixed aliphatic amine and quaternary

ammonium
3.7 900 Granular
Epoxy polyamine 8.5 740 Spherical
dry meq
gm

kg
m
3

C
s
+q
C
s
+q
[]
C
s
+q
[]C
s
+q
C
s
+q
q


qC

s
+q
[]=
qC
s
+q
[]
CatT[]
eq
q
i
C
s
i
+q
i
[]
i=1
i=m
∑
=
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© 2003 by A. P. Sincero and G. A. Sincero
Let [AnionT]
eq
and [HT ]
eq
be the total anions and the hydrogen ions displaced,
respectively. Since the number of equivalents of one substance in a reaction is equal
to the number of equivalents of all the other substances participating in the reaction,

(16.6)
Let the [AnionT ]
eq
from the effluent of the cation exchanger be introduced into
an anion exchanger. For the anion exchanger operating under the OH cycle, the total
equivalents of OH
−
released from the anion bed is equal to that of the anions,
[AnionT]
eq
, removed from solution. Let [OHT ]
eq
be this total OH
−
. Since [AnionT ]
eq
is equal to [HT]
eq
, [OHT ]
eq
must be equal to [HT ]
eq
. This means that all the acids
produced in the cation exchanger are neutralized in the anion exchanger, and all
ions in the water have been removed by using the combination of cation exchanger
followed by anion exchanger.
On the surface, the combination of cation exchanger and anion exchanger would
mean that pure water is produced. As shown in Equations (16.1) and (16.2), however,
the unit process of ion exchange is governed by equilibrium constants. The values
of these constants depend upon how tightly the removed ions from solution are

bound to the bed exchanger sites. In general, however, by the nature of equilibrium
constants, the concentrations of the affected solutes in solution are extremely small.
Practically, then, we may say that “pure water” has been produced.
By analogy with Equation (16.5),
(16.7)
As with q
i
, the units of t
i
are equivalents per mole.
Example 16.1 A wastewater contains the following ions: = 120 mg/L,
Cu
2+
= 30 mg/L, Zn
2+
= 15 mg/L, and . Calculate the total equiv-
alents of cations and anions, assuming the volume of the wastewater is 450 m
3
.
Solution:
Total equivalents of cations = 2.395(450) = 1077.75 Ans
Total equivalents of cations = 2.069(450) = 931.05 Ans
Ions (mg/L) Equiv. Mass Cations (meq/L) Anions (meq/L)

58
a
— 2.069
b
31.75 0.945 —
32.7 0.469 —

29.35 0.681 —
∑ = 2.395 ∑ = 2.069
Note: The ions are not balanced, meaning error in analysis.
a
Equiv. mass .
b
120/58 = 2.069
AnionT[]
eq
HT[]
eq
CatT[]
eq
==
AnionT[]
eq
t
i
A
s
i
−t
i
[]
i=1
i=m
∑
=
CrO
4

2−
Ni
2+
20 mg/L=
CrO
4
2−
120=
Cu
2+
30=
Zn
2+
15=
Ni
2+
20=
CrO
4
2−
52 4 16()+[]/258==
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© 2003 by A. P. Sincero and G. A. Sincero
16.5 ACTIVE OR EXCHANGE ZONE
Figure 16.2 is the same figure illustrated in a previous chapter under carbon adsorp-
tion. The length of the active zone was derived in that chapter and is reproduced next.
(16.8)
where
δ
= length of active zone

= total volume of water or wastewater treated at complete exhaustion of
bed
= volume treated at breakthrough
[C
o
] = influent concentration to
δ

= total volume treated at time t
n+1

= total volume treated at time t
n

[C
n+1
] = concentration of solute at effluent of
δ
at time t
n+1

[C
n
] = concentration of solute at effluent of
δ
at time t
n

A
s

= surficial area of exchanger bed
FIGURE 16.2 Active zones at various times during adsorption and the breakthrough curve.
δ
2
V
x
V
b
–()C
o
[]∑
V
n+1
V
n
–()
C
n+1
[]C
n
[]+
2



–



A

s
ρ
p

X
M



ult

=
V
x
V
b
V
n+1
V
n
C
C C C
C
C
V V
V
L
Clean water
TX249_frame_C16.fm Page 726 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero

ρ
p
= pack density of ion exchange material
(X/M)
ult
= ultimate exchange capacity of the bed or simply, the exchange capacity
of the bed.
It should be emphasized that to use the equation [C
o
], [C
n+1
], and [C
n
] should
be the total concentration of ions. For example, if the influent is composed of the
ions Ca
2+
= 50 mg/L, Mg
2+
= 60 mg/L, and Zn
2+
= 2 mg/L, then [C
o
]
meq
in meq/L is
50/(Ca/2) + 60/(Mg/2) + 2/(Zn/2).
Example 16.2 A breakthrough experiment is conducted for a wastewater pro-
ducing the results below. Determine the length
δ

of the active zone. The diameter
of the column used is 2.5 cm, and the packed density of the bed is 750 kg/m
3
. [C
o
]
is equal to 2.2 meq/L. (X/M)
ult
= 6.5 meq/g.
Solution:
C, meq/L , L
0.06 1.0
0.08 1.20
0.09 1.30
0.10 1.40
0.20 1.48
0.46 1.58
1.30 1.70
1.80 1.85
2.10 2.00
C, meq/L , L ()
0.06 1.0 0.20 0.07 0.014
0.08 1.20 0.10 0.085 0.0085
0.09 1.30 0.10 0.095 0.0095
0.10 1.40 0.08 0.15 0.012
0.20 1.48 0.10 0.33 0.033
0.46 1.58 0.12 0.88 0.1056
1.30 1.70 0.15 1.55 0.2325
1.80 1.85 0.15 1.95 0.2925
2.10 2.00 ∑ = 0.7076

V
δ
2
V
x
V
b
–()C
o
[]∑
V
n+1
V
n
–()
C
n+1
[]C
n
[]+
2



–



A
s

ρ
p
X
M



ult

=
V V
n+1
V
n
–
C
n +1
[]C
n
[]+
2



(
V
n+1
V
n
– )

C
n++
++
1
[]C
n
[]+
2



A
s
π
0.025()
2
4

0.00049 m
2
==
TX249_frame_C16.fm Page 727 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
Therefore,
16.6 DESIGN OF ION EXCHANGERS
Generally, designs of ion exchangers should include the following: quantity of
exchange materials and regenerants; dimension of the bed (volume of bed); interval
of bed regeneration, backwash, and rinse water requirements. The amount of exchange
materials determines the dimension of the bed. The interval of regeneration may be
arbitrarily set from which the quantity of exchange bed material may be calculated.

Regeneration, backwash, and rinse waters may pose pollution problems.
16.6.1 QUANTITY OF EXCHANGE MATERIALS
Before discussing quantities of exchange materials, a method of expressing exchange
capacity in terms of calcium carbonate is addressed. This method of expressing
capacity is very troublesome, and it should not have been adopted; nonetheless, it
is used and we must know it. As shown in Tables 16.2, 16.3, and 16.4, equivalents,
among other units, are used to express exchange capacities. This is appropriate
because reactants react in equivalent amounts; but to express this in terms of calcium
carbonate is a bit unusual. As addressed in previous chapters, however, arbitrarily
adopt CaCO
3
/2 = 50 as the equivalent mass of calcium carbonate. From this, the
exchange capacity, expressed in equivalents, may be obtained by dividing the
exchange capacity expressed in calcium carbonate by 50.
Let us first derive the formula for the exchange materials for the cation bed. The
amount of exchange bed materials required can be determined by calculating first
the amount of displacing ions in solution to be removed. Let the exchange capacity
of the bed be (X/M )
ult
meq/g of bed. The equivalents of ion displaced from the bed
is equal to the equivalents of displacing ion in solution; therefore, the mass of bed
material CatTBedMass in kilograms is
(16.9)
Q is the m
3
/d of flow and t
int
is the interval of regeneration in hours. In concept, the
interval of regeneration may be arbitrarily set. A value of 8 hours is not unreasonable.
The factor (1000/24) is used so that the unit of CatTBedMass will be in kilograms.

δ
221–()2.2[]0.7076–{}
0.00049()750()1000()6.5()

0.0012 m 1.2 mm===
CatTBedMass
CatT[]
eq
()Q()t
int
()
X
M




ult


1000
24



=

∑
i=m
i=1

q
i
C
s
i
+q
i
[]()Q()t
int
()
X
M




ult


1000
24



=
TX249_frame_C16.fm Page 728 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
By analogy, the mass of bed material for the anion exchanger, AnionTBedMass,
in kilograms is
(16.10)

Using the packed density of bed material
ρ
p
kg/m
3
, the volume of bed can be
calculated. Let CatTBedVol and AnionTBedVol be the respective volumes in m
3
. Thus,
(16.11)
(16.12)
A very important property of exchanger beds is percentage of swell. This actually
determines the final size of the tank into which the material is to be put when the
unit is put into operation. Thus, we use the parameter swell, which is the fraction
of swelling of the bed. Values of this parameter vary over a wide range from zero
for zeolites (greensand) to 1.0 for polystyrene iminodiacetate. Thus, an experiment
should be performed on any given exchanger to determine percent swell or the
manufacturer should be consulted.
Example 16.3 Using a bed exchanger, 75 m
3
of water per day is to be treated
for hardness removal between regenerations having intervals of 8 h. The raw water
contains 400 mg/L of hardness as CaCO
3
. The exchanger is a resin of exchange
capacity of 1412.8 geq/m
3
. Assume that the packed density of the resin is 720 kg/m
3
.

Calculate the mass of exchanger material to be used and the resulting volume when
the exchanger is put into operation.
Solution: Assume cation exchanger:
AnionTBedMass
Anion[]
eq
()Q()t
int
()
X
M



ult


1000
24



=

∑
i=m
i=1
t
i
A

s
i
−t
i
[]()Q()t
int
()
X
M



ult


1000
24



=
CatTBedVol
∑
i=1
i=m
q
i
C
s
i

+q
i
[]()Q()t
int
()
X
M



ult

ρ
p

1 swell+()
1000
24



=

∑
i=m
i=1
q
i
C
s

i
+q
i
[]()Q()t
int
()1 swell+()
ρ
p
X
M



ult


1000
24



=
AnionTBedVol
∑
i=m
i=1
t
i
A
s

i
−t
i
[]()Q()t
int
()1 swell+()
ρ
p
X
M




ult


1000
24



=
CatTBedMass
∑
i=m
i=1
q
i
C

s
i
+q
i
[]()Q()t
int
()
X
M




ult


1000
24



=
TX249_frame_C16.fm Page 729 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
Also, assume that all of the cations are removed.
Therefore,
Assume swell = 0.8
16.6.2 QUANTITY OF REGENERANT
Let CatRegenerant in kilogram equivalents be the quantity of regenerant required
and R be the regenerant requirement in equivalents per equivalent of solute removed.

The concentration of removable cations in gram equivalents per liter is [CatT]
eq
=
; therefore,
(16.13)
This equation represents the regenerant required between intervals of regeneration.
The kilograms of regenerant depend upon the regenerant used. For example, if the
regenerant is common table salt, then CatRegenerant should be multiplied by NaCl
to obtain the kilograms of the salt.
By analogy with cation exchangers, the kilogram equivalents of regenerant,
AnionRegenerant, used to regenerate anion exchangers is
(16.14)
i=1
i=m
∑
q
i
C
s
i
+q
i
[]
400
50

8 meq/L 0.004 geq/L== =
X
M




ult
1412.8
geq
m
3

1412.8
1000() meq
720 1000() g

1.96
meq
g

== =
CatTBedMass
0.004 75()8()
1.96


1000
24



51.02 kg Ans==
CatTBedVol

∑
i=m
i=1
q
i
C
s
i
+q
i
[]()Q()t
int
()1 swell+()
ρ
p
X
M



ult


1000
24



=
CatTBedVol

51.02
720

1 0.8+()0.13 m
3
Ans==
∑
i=m
i=1
q
i
C
s
i
+q
i
[]
CatRegenerant
i=1
i=m
∑
q
i
C
s
i
+q
i
[]R()Q()t
int

()
1
24



=
AnionRegenerant
i=1
i=m
∑
t
i
A
s
i
+t
i
[]R()Q()t
int
()
1
24



=
TX249_frame_C16.fm Page 730 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
Example 16.4 Using a bed exchanger, 75 m

3
of water per day is to be treated
for hardness removal between regenerations having intervals of 8 hours. The raw
water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
. The exchanger is a resin of
exchange capacity of 1412.8 geq/m
3
. Assume that the packed density of the resin is
720 kg/m
3
. Calculate the kilograms of sodium chloride regenerant required assuming
R = 2 and that all of the cations were removed.
Solution:
Therefore,
16.6.3 WASTEWATER PRODUCTION
In the operation of ion exchangers wastewaters are produced. These come from the
solvent water used to dissolve the regenerant and the backwash and rinse requirements.
To illustrate the method for the production of wastewater from the solvent water, let us
use an example calculation. In the sodium cycle, the concentration of NaCl is about 5
to 10% for an average of 7.5%. This means that, for example, if the quantity of
regenerant required is 0.26 kg, the volume of wastewater produced from regeneration
can be calculated as follows: the total mass of regenerant solution is 0.26/0.075 =
3.47 kilograms; the corresponding volume is 3.47/1000 = 0.0035 m
3
. For an interval
of regeneration of 8 h and assuming a rate of flow for the water treated of 75 m
3

/d, the
volume of water treated is 75/24(8) = 25 m
3
. Thus, the wastewater produced is 0.0035/25
(100) = 0.014% by volume.
The other wastewater produced as a result of regeneration is the backwash and
rinse waters. As soon as the bed is exhausted, it must be backwashed to remove
debris accumulated during the service cycle. In addition, after regeneration, the bed
should be rinsed to remove any residual regenerant. Backwash and rinse water
requirements should be determined by experiment on an actual exchanger bed to be
used in design.
CatRegenerant
i=1
i=m
∑
q
i
C
s
i
+q
i
[]R()Q()t
int
()
1
24




=
i=1
i=m
∑
q
i
C
s
i
+q
i
[]
80
40.1/2()1000()

15
24.3/2()1000()

+ 5.22 10
−3
()
geq
L

==
5.22 10
−3
()
keq
m

3

=
CatRegenerant 5.22 10
−3
()2()75()8()
1
24



=
0.26 kg per interval of regeneration Ans=
TX249_frame_C16.fm Page 731 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
The quantity of backwash and rinse requirement is best expressed as a function
of bed volume. Let CatBackwashRinseVol be the m
3
of backwash and rinse waters
required for the cation exchanger and BackwashRinseV be the corresponding m
3
of
backwash and rinse waters per cubic meter of bed. For the cation exchanger, the
volume of bed was previously derived as
with the swelling not being considered. Thus,
(16.15)
By analogy, the corresponding equation for the anion exchanger is
(16.16)
AnionBackwashRinseVol is the m
3

of backwash and rinse waters required for the anion
exchanger. An example backwash and rinse waters requirement is 18 m
3
/m
3
of bed
volume.
Example 16.5 Using a bed exchanger, 75 m
3
of water per day is to be treated
for hardness removal between regenerations having intervals of 8 hours. The raw
water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
. The exchanger is a resin of
exchange capacity of 1412.8 geq/m
3
. Assume that the packed density of the resin is
720 kg/m
3
. Calculate the total volume of rinse and backwash requirement if the
backwash and rinse per unit volume of bed is 18 m
3
/m
3
.
Solution:
CatBedVol
∑

i=m
i=1
q
i
C
s
i
+q
i
[]()Q()t
int
()
ρ
p
X
M



ult

1000
24



m
3
=
CatBackwashRinseVol

∑
i=m
i=1
q
i
C
s
i
+q
i
[]()Q()t
int
()BackwashRinseV()
ρ
p
X
M



ult

1000
24



=
AnionBackwashRinseVol
∑

i=m
i=1
t
i
A
s
i
+t
i
[]()Q()t
int
()BackwashRinseV()
ρ
p
X
M



ult


1000
24



=
CatBackwashRinseVol
∑

i=m
i=1
q
i
C
s
i
+q
i
[]()Q()t
int
()BackwashRinseV()
ρ
p
X
M



ult


1000
24



=
i=1
i=m

∑
q
i
C
s
i
+q
i
[]



5.22 10
−3
()
keq
m
3

=
X
M




ult
1412.8
geq
m

3

1412.8
1000() meq
720 1000() g

1.96
meq
g

== =
TX249_frame_C16.fm Page 732 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
Therefore,
16.7 HEAD LOSSES IN ION EXCHANGERS
During ion exchange, the water or wastewater is allowed to flow through the bed.
In order for this to happen, head loss allowances must be provided between influent
and effluent. Ion exchanger media are actually granular, so head loss calculations
are the same as those in granular filters. In addition, the mechanics of backwashing
are also exactly the same as in granular filters. Rinsing may be done in downflow
mode or in upflow mode. If it is done in a downflow mode, then it is the same as
regular filtration. If rinsing is done in an upflow mode, then the mechanics are the
same as backwashing. Rinsing in an upflow mode is more effective as more intimate
contact between bed grains and regenerant are facilitated by the grains being sus-
pended and agitated by the upward flow of the regenerant solution. Granular head
loss calculation formulas were already derived in a previous chapter on filtration
and will not be repeated here. Example calculations were also presented in that
chapter, which should be consulted for a review of the material.
GLOSSARY
Active zone—A segment of exchanger bed engaged in exchanging ions.

Anion exchange bed material—Exchanges anions in solution for the anions in
the bed.
Cation exchange bed material—Exchanges cations in solution for the cations
in the bed.
Displacement series—A table of ions indicating that ions at the top of the table
can displace ions below them in the table.
Exchange capacity—The ultimate quantity of ions that an ion exchanger can
remove from solution.
Hydrogen cycle—A mode of operation of anion exchangers in which regener-
ation is done using acid.
Ion exchange—The displacement of one ion by another.
Sodium cycle—A mode of operation of cation exchangers in which regeneration
is done using NaCl.
Synthetic resins—Insoluble polymers to which are added, by certain chemical
reactions, acidic and basic groups called functional groups.
Zeolites—Natural and synthetic alumino silicates.
SYMBOLS
A
−p
Represents the exchangeable anion in the anion exchanger
[Anion]
eq
Gram equivalents per liter of total displacing anion in
solution
CatBackwashRinseVol
5.22 10
−3
()75()8()18()
720 1.96()

1000
24



1.66 m
3
Ans==
TX249_frame_C16.fm Page 733 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
CatBackwashRinseVol Cubic meters of backwash and rinse waters required for
the anion exchanger
AnionTBedMass Kilograms of anion bed material
AnionTBedVol Cubic meters of bed volume
AnionRegenerant Kilogram equivalents of regenerant required for anion
exchangers
A
s
Surficial area of exchanger bed
Displacing anion in solution
Gram moles per liter of ith displacing anion in solution
C
+m
Represents the exchangeable cation in the cation exchanger
[C
n
] Concentration of solute at effluent of
δ
at time t
n

[C
n+1
] Concentration of solute at effluent of
δ
at time t
n+1
[C
o
] Influent concentration to
δ

Gram moles per liter of ith displacing cation in solution
[CatT]
eq
Gram equivalents per liter of total removable cations in
solution
BackwashRinseV Cubic meters of backwash and rinse waters required for
the cation or anion exchanger per cubic meter of bed
CatBackwashRinseVol Cubic meters of backwash and rinse waters required for
the cation exchanger
CatTBedMass Kilograms of cation exchange material
CatTBedVol Cubic meters of bed volume
CatRegenerant Kilogram equivalents of regenerant required for cation
exchangers
Displacing cation in solution
[HT]
eq
Equivalent concentration of displaced hydrogen ion from
anion exchanger
+m Charge of the exchangeable cation in the cation exchanger,

equivalents per mole
−n Charge of the cation exchanger host, equivalents per mole
+o Charge of the anion exchanger host, equivalents per mole
−p Charge of the exchangeable anion in the anion exchanger,
equivalents per mole
+q Charge of displacing cation in solution, equivalents per mole
q
i
Charge of the ith displacing cation in solution, equiv-
alents per mole
Q Cubic meters of flow per day
r Number of active sites in the insoluble cation or anion
host material
R Regenerant requirement in equivalents per equivalent of
solute removed
swell Fraction swelling of bed material
t Charge of displacing anion in solution, equivalents per mole
t
i
Charge of ith displacing anion in solution, equivalents
per mole
t
int
Time interval of regeneration, hours
A
s
−t
A
s
i

−t
i
[]
C
s
i
+q
i
[]
C
s
+q
TX249_frame_C16.fm Page 734 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
R
−n
Represents the host part of a cation exchanger
Representation of anion exchanger material
Representation of cation exchanger material
R
+o
Represents the host part of an anion exchanger
Volume treated at breakthrough
Total volume treated at time t
n
Total volume treated at time t
n+1
Total volume of water or wastewater treated at complete
exhaustion of bed
(X/M)

ult
Ultimate exchange capacity of the bed or simply, the
exchange capacity of the bed. For ion exchangers, (X/M)
ult
has the units of milligram equivalents of solute exchanged
per gram of exchanger material
δ
Length of active zone
ρ
p
Pack density of ion exchange material, kilograms per
cubic meter
PROBLEMS
16.1 A wastewater contains the following ions: = 120 mg/L, Cu
2+
=
30 mg/L, Zn
2+
= 15 mg/L, and . Calculate the total gmols
of cations and anions, assuming the volume of the wastewater is 450 m
3
.
16.2 A breakthrough experiment is conducted for a wastewater producing the
results in the following table. Determine the packed density of the bed if
δ
= 0.0012 m. The diameter of the column used is 2.5 cm. [C
o
] is equal
to 2.20 meq/L. (X/M)
ult

= 6.5 meq/g.
16.3 Using a bed exchanger, a volume of water is treated for hardness removal
between regenerations having intervals of 8 h. The raw water contains
400 mg/L of hardness as CaCO
3
. The exchanger is a resin of exchange
capacity of 1412.8 geq/m
3
. Assume that the packed density of the resin
is 720 kg/m
3
. The mass of exchanger material is 51.02 kg and its volume
is 0.13 m
3
at a swell of 0.8. Calculate the volume of water treated.
C (meq/L) (L)
0.06 1.0
0.08 1.20
0.09 1.30
0.10 1.40
0.20 1.48
0.46 1.58
1.30 1.70
1.80 1.85
2.10 2.00
(R
+o
)
r
(A

−p
)
ro/ p
(R
−n
)
r
(C
+m
)
rn/m
V
b
V
n
V
n+1
V
x
CrO
4
2−
Ni
2+
20 mg/L=
V
x
TX249_frame_C16.fm Page 735 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
16.4 Using a bed exchanger, a volume of water is treated for hardness removal.

The raw water contains 400 mg/L of hardness as CaCO
3
. The exchanger
is a resin of exchange capacity of 1412.8 geq/m
3
. Assume that the packed
density of the resin is 720 kg/m
3
. The mass of exchanger material is
51.02 kg and its volume is 0.072 m
3
. Calculate the volume of water treated
if regeneration is to take place every 8 h.
16.5 Using a bed exchanger, a volume of water is treated for hardness removal.
The raw water contains 400 mg/L of hardness as CaCO
3
. Assume that the
packed density of the resin is 720 kg/m
3
. The mass of exchanger material
is 51.02 kg and its volume is 0.13 m
3
at a swell of 0.8. Calculate the
exchange capacity if the volume of water treated is 75 m
3
/d and if regen-
eration is to take place every 8 h.
16.6 Using a bed exchanger, a volume of water is treated for hardness removal.
The raw water contains 400 mg/L of hardness as CaCO
3

. Assume that the
packed density of the resin is 720 kg/m
3
. The mass of exchanger material
is 51.02 kg and its volume is 0.13 m
3
at a swell of 0.8. The exchange capacity
is 1412.8 geq/m
3
and the volume of water treated is 75 m
3
/d. Determine
the interval of regeneration.
16.7 Using a bed exchanger, 75 m
3
of water per day is to be treated for hardness
removal between regenerations having intervals of 8 h. The raw water
contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
. The exchanger is a resin
of exchange capacity of 1412.8 geq/m
3
. Assume that the packed density
of the resin is 720 kg/m
3
. The kilograms of sodium chloride regenerant
required is 0.26. Calculate R assuming that all of the cations were
removed.

16.8 Using a bed exchanger, a volume of water is to be treated for hardness
removal between regenerations having intervals of 8 h. The raw water
contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
. The exchanger is a resin
of exchange capacity of 1412.8 geq/m
3
. Assume that the packed density
of the resin is 720 kg/m
3
. The kilograms of sodium chloride regenerant
required is 0.26. Calculate the volume of water treated assuming R = 2
and that all of the cations were removed.
16.9 Using a bed exchanger, 75 m
3
of water per day is treated for hardness
removal. The raw water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
.
The exchanger is a resin of exchange capacity of 1412.8 geq/m
3
. Assume
that the packed density of the resin is 720 kg/m
3
. The kilograms of sodium
chloride regenerant required is 0.26. Calculate the interval of regeneration

assuming R = 2 and that all of the cations were removed.
16.10 Using a bed exchanger, a volume of water is to be treated for hardness
removal between regenerations having intervals of 8 hours. The raw water
contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
. The exchanger is a resin
of exchange capacity of 1412.8 geq/m
3
. Assume that the packed density
of the resin is 720 kg/m
3
. The total volume of the rinse and backwash
requirement is 1.66 m
3
. If the backwash and rinse per unit volume of the
bed is 18 m
3
/m
3
, calculate the volume of water treated.
TX249_frame_C16.fm Page 736 Friday, June 14, 2002 4:47 PM
© 2003 by A. P. Sincero and G. A. Sincero
16.11 Using a bed exchanger, 75 m
3
of water per day is to be treated for hardness
removal. The raw water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg

2+
.
The exchanger is a resin of exchange capacity of 1412.8 geq/m
3
. Assume
that the packed density of the resin is 720 kg/m
3
. The total volume of the
rinse and backwash requirement is 1.66 m
3
. If the backwash and rinse per
unit volume of the bed is 18 m
3
/m
3
, calculate the interval of regeneration.
16.12 Using a bed exchanger, 75 m
3
of water per day is to be treated for
hardness removal. The raw water contains 80 mg/L of Ca
2+
and 15 mg/L
of Mg
2+
. The exchanger is a resin of exchange capacity of 1412.8 geq/m
3
.
Assume that the packed density of the resin is 720 kg/m
3
. The total

volume of the rinse and backwash requirement is 1.66 cubic meters and
the interval of regeneration is 8 h. Calculate the backwash and rinse per
unit volume of the bed.
16.13 Using a bed exchanger, 75 m
3
of water per day is to be treated for hardness
removal. The raw water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+
.
The exchanger is a resin of exchange capacity of 1412.8 geq/m
3
. The total
volume of the rinse and backwash requirement is 1.66 m
3
, the interval of
regeneration is 8 h, and the backwash and rinse per unit volume of the
bed is 18 m
3
/m
3
. Calculate the packed density of the bed.
16.14 Using a bed exchanger, 75 m
3
of water per day is to be treated for hardness
removal. The raw water contains 80 mg/L of Ca
2+
and 15 mg/L of Mg
2+

.
The total volume of the rinse and backwash requirement 1.66 m
3
, the
interval of regeneration is 8 h, and the backwash and rinse per unit volume
of the bed is 18 m
3
/m
3
. The packed density of the bed is 720 kg/m
3
.
Calculate the exchange capacity of the bed.
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