Page 373 - Water and wastewater engineering

9-12 WATER AND WASTEWATER ENGINEERING

Limiting Salt. The precipitation of salts as a result of concentrating the salt to its solubility
limit is, in its simplest expression, a function of the permeate recovery rate (AWWA, 1999):
n
⎡ p ⎤ ⎡ q ⎤ m
K ⎢ A ⎥ ⎢ B ⎥ (9-13)
sp
⎣ ⎢ 1 r ⎦ ⎥ ⎣ ⎢ 1 r ⎦ ⎥
where K sp solubility product
A p cation of salt, moles/L
q
B anion of salt, moles/L
n, m number of moles
r permeate recovery ratio (also called “recovery rate”), decimal fraction
This expression is simplified because it does not account for activity coefficients. These, in turn,
cannot be calculated until recovery is determined. Furthermore, carbonate and phosphate con-
centrations are dependent on pH. Equation 9-13 will be used for illustrative purposes here but, in
actual design, computer programs supplied by manufacturers are used to perform the calculation.
Permeate recoveries can be improved by pretreating with acid and polymeric antiscalants.
The estimation of the limiting salt and the improvement in recovery by pretreatment with acid is
illustrated in the next two examples.

Example 9-1. Estimate the recovery rate for a groundwater with the following characteristics:
2
Ca 95.2 mg/L
CO 2 078 mg/L
.
3
Alkalinity 310 mg/L as CaCO 3
pH 7.65
Solution:
9
a. From Appendix A, K sp 4.95 10 .
b. Convert the concentrations to moles/L.
95 2 mg/L 3 2
.
2 38 10 moles/L offCa
.
3
40 10 mg/mole
078 mg/L 5 2
.
1 3 . 10 moles/L of CO 3
3
60 10 mg/mole
c. Solve Equation 9-13 for r.
⎡ 2 38 10 3 moles/L ⎤⎡ 1 3 10 5 moles/L ⎤
.
.
0
495 10 9 ⎢ ⎥⎢ ⎥
.
⎣ ⎢ 1 r ⎦ ⎥⎢ ⎣ 1 r ⎦ ⎥
.
( 1 r) 2 3 09 10 8 625
.

495 10 9
.
1 2 5 .r
r 1 5 .