Page 340 - Water and wastewater engineering

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 .

i
19.
j
i
a1/ j i 1 1 9./ 0 53.
j
b. The maximum useful capacity of the resin for calcium is

Cq T
Ca
q
Ca j
C Ca C
Na i
m
.
.
,
(14 meq Ca 2 /L )(20 eq/L of resin )(1 000 meq/eq)

((14 . meq Ca 2 /L) (26 . meq Na /L)(0..53)
, 1 008 or , 1 000 meq Ca 2 /L of resin
c. The maximum volume of water that can be treated per volume of resin per cycle is
2
,
q Ca 1 000 meq Ca /L of resin
V 2
a
.
C Ca 14 meq Ca /L of water
714 29 or 710 L of water/L of resin
.
Comments:
2
1. This is the maximum amount of Ca 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