Page 347 - Corrosion Engineering Principles and Practice

318 C h a p t e r 8 C o r r o s i o n b y W a t e r 319

8.8 Ion-Association Model
The saturation indices discussed previously can be calculated based upon
total analytical values for all possible reactants. Ions in water, however, do
not tend to exist totally as free ions [21]. Calcium, for example, may be
paired with sulfate, bicarbonate, carbonate, phosphate, and other species.
Bound ions are not readily available for scale formation and such binding,
or reduced availability of the reactants, decreases the effective ion-activity
product. Saturation indices such as the LSI are based upon total analytical
values rather than free species primarily because of the intense calculation
requirements for determining the distribution of species in water.
Speciation breakdown of all species in a given water requires numerous
computer iterations to achieve the following [22]:

• The verification of electroneutrality via a cation-anion balance,
and balancing with an appropriate ion (e.g., sodium or potassium
for cation-deficient waters; sulfate, chloride, or nitrate for anion-
deficient waters).
• Estimating ionic strength; calculating and correcting activity
coefficients and dissociation constants for temperature;
correcting alkalinity for noncarbonate alkalinity.
• Iterative calculation of the distribution of species in the water
from dissociation constants. A partial listing of possible ion
pairs is given in Table 8.16.
• Verification of mass balance and adjustment of ion concentrations
to agree with analytical values.
• Repeating the process until the desired resolution is achieved.
• Calculation of saturation levels based upon free concentrations
of ions estimated using the ion-association model (ion pairing).

The ion-association model has been used by major water treatment
companies since the early 1970s. When indices are used to establish
operating limits such as maximum concentration ratio or maximum
pH, the differences between indices calculated using ion pairing can
have some serious economic significance. For example, experience on
a system with high-TDS water may be translated to a system operating
with a lower-TDS water. The high indices found acceptable in the
high-TDS water may be unrealistic when translated to a water where
ion pairing is less significant in reducing the apparent driving force
for scale formation. Table 8.17 summarizes the impact of TDS upon
LSI when it is calculated using total analytical values for calcium and
alkalinity, and when it is calculated using the free calcium and
carbonate concentrations determined with an ion-association model.
Indices based upon ion-association models provide a common
denominator for comparing results between systems. For example,
calcite saturation level calculated using free calcium and carbonate