Page 298 - Water and wastewater engineering

LIME–SODA SOFTENING 7-15

Five reactions that are employed in recarbonation are discussed below. In each case, the
chemical that is added to the water is printed in bold type. The notation (s) designates the solid
form and indicates that the compound has been removed from the water. The following reactions
are presented sequentially, although in reality they occur simultaneously.
1. Recarbonation after selective calcium removal.
After selective calcium removal, the water will be supersaturated with calcium carbon-
ate and the pH will be between 10.0 and 10.6. The addition of CO 2 lowers the pH to
between 8.5 and 9.0 and converts the carbonate ions to bicarbonate ions.
2 2 2
Ca CO 3 CO 2 H O Ca 2HCO 3 (7-26)
2
2. Recarbonation after the excess lime process.
After calcium and magnesium removal with excess lime, the pH will be above 11.0. Suf-
ficient CO 2 is added to convert the excess hydroxyl ions to carbonate ions and then to
convert the carbonate ions to bicarbonate. This will occur in the pH range of 10.0 to 10.5.
2

Ca 2 OH CO 2 CaCO s () HO (7-27)
3
2

2
2
Mg 2OH CO 2 Mg CO 3 2 H O (7-28)
2
Additional CO 2 is added to lower the pH to about 8.4 to 8.6.
H O Ca 2 (7-29)
3
CaCO (s) CO 2 2 2HCO 3
2

2
2
Mg CO 3 CO 2 H O Mg 2HCO 3 (7-30)
2
7-4 CHEMICAL DOSAGES BASED ON STOICHIOMETRY
The estimation of the chemical dosage is used to design the chemical storage silos, chemical feed
systems, and sludge disposal facilities. In the following examples, it is assumed that the reactions
go to completion, that the lime and soda ash are pure (100 percent of the chemical), and that the
extra lime added to drive the reaction is removed by recarbonation.
Estimating CO Concentration
2
CO 2 is of importance in two instances in softening. In the first instance, it consumes lime that other-
2 2
wise could be used to remove Ca and Mg . In the second instance, CO 2 is used to neutralize the
high pH of the effluent from the softening process. These reactions are an application of the concepts
of the carbonate buffer system discussed in Chapter 6.
The approximate concentration * of CO 2 may be estimated using the equilibrium expressions

for the dissociation of water and carbonic acid with the definition of alkalinity (Equation 6-3).
The pH and alkalinity of the water must be determined to make the estimate. The equilibrium
expressions for carbonic acid are
[H ][HCO 3 ]
K a1 p a 6 35 at 25 C (7-31)
K 1 .
[HCO 3 ]
2
*A more accurate estimation technique is described by Benefield and Morgan (1999).