Calcium Carbonate Precipitation Potential
[CCPP]

Saturation index (SI) is only a qualitative indicator of calcium carbonate precipitation, because it does not indicate extent of precipitation can occur at SI positive values of it. Using mathematical calculations aqueous carbonate solutions can calculate the potential amount of calcium carbonate precipitation, namely the equivalent of calcium carbonate supersaturation.
The calcium carbonate precipitation was accompanied by a decrease in pH , reduction of hardness as 1 mole (and 2 equivalents) of total alkalinity , for each mole of calcium carbonate precipitate. The potential for calcium carbonate precipitation increases with saturation index and intensity of the buffering effect of water. The intensity buffer is a function of pH and total alkalinity.
Because the intensity of buffer decreases with increasing pH , CCPP also decreases with increasing pH. With pH, alkalinity and calcium hardness constant CCPP decreases with increasing total dissolved salts ( TDS or Total Dissolved Salt ).

Theory of equilibrium.
The dissociation of carbonic acid (CO2, or H2O.H2CO3) produces hydrogen and bicarbonate ions:

H2CO3 >>> H+ + HCO3- (1)

then bicarbonates and hydrogen carbonate ions:

HCO3- >>> H+ + CO32- (2)

In particular, calcium carbonate gives:

CaCO3 >>> Ca2+ + CO32- (3)
• (1) [ H+]+ [HCO3- ] / [H2CO3] = K1 (in equilibrium)
K'1 = K1 . 10e
• (2) [ H+]+ [CO32-] / [HCO3-] = K2 (in equilibrium)
K'2 = K2 . 102e
• (3) [ Ca2+ ]+ [CO32-] / [CaCO3] = Ks (in equilibrium)
K's = Ks . 10es

K1, K2 and Ks are constants for a given temperature and ionic strength (ionic strength is a function of concentration and valence of ions present in solution), terms in bracket represent the molar concentrations and e represent ionic activity coefficients.
The K'1, K'2 and K's constants involved in these relationships are usually expressed by negative powers of 10. To simplify their cologarithmes are used : pK'1, pK'2 and pK's.
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NOTE:
The e term can be expressed as ionic strength function of solution considered m by equation:

e = m / (1+1,4m)

so we have with Ks, es = 4m(1+3,9m)

The ionic strength isdefined by relationship:

m = 1/2S cnvn² (Lewis and Randall, 1921)

wherein cn represents concentration of n ion with vn valence present in solution, this concentration is expressed in moles per liter.

pK1 and pK2 are function of temperature T (as °C) were given by Larson and Buswell. We have:

• pK1 = 6.583 - 12.3 TP + 163.5 TP2 - 646 TP3
• pK2 = 10.627 - 15.04 TP + 135.3 TP2 - 328 TP3
• pKS = 8.022 + 14 TP - 61 TP2 + 444 TP3

(with TP = water temperature as °C/1000).
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Thus, solubility of calcium carbonate increases with decreasing pH due to reactions:

CO32– + H+ <<<>>> HCO3-
H+ + HCO3- <<<>>> H2CO3

While solubility of calcium carbonate increases as the pH decreases, solubility product remains unchanged. The higher the pH drop over the concentration of calcium carbonate decreases. Therefore, in order to maintain conditions of saturation, calcium concentration must be rised.

Oversaturation of calcium carbonate.
The oversaturated solutions of calcium carbonate can be obtained from saturated or subsaturated solutions when calcium hardness, pH and alkalinity increase.
The degree of saturation of calcium carbonate (S) is given by ratio of actual ion activity product and product of constant thermodynamic solubility at infinite dilution (Ks):

S = [Ca2+][CO32–]/cKs

Values 1 <= S <1 respectively represent oversaturation or undersaturation.

Precipitation of calcium carbonate.
Excess calcium carbonate will be precipitated as following:

Ca2+ + CO32– >>> CaCO3

therefore bicarbonate ions will be dissociated to reconstruct carbonate ions:

HCO3- >>> H+ + CO32-

result of these reactions will be:

Ca2+ + HCO3 >>> CaCO3 + H+

and hydrogen ions H+ released in above reaction can react with alkalinity (French TAC), ie, bicarbonate ion HCO3-and reforming carbon dioxide:

xH+ + xHCO3- >>> xH2CO3

The overall reaction is as follows:

Ca2+ + (1+x)HCO3- >>> CaCO3 + xH2CO3

The relative degrees of neutralization bicarbonates pH dependent (e.g., first fractional ionization of carbonic acid) and respective levels of alkalinity and bicarbonates.
With pH less than 9, reaction of hydrogen ions with hydroxyl ions OH- present is negligible. Precipitation of calcium carbonate, thus, constitutes not only a decrease in calcium hardness and alkalinity, but also pH.
Note that hardness and two mole equivalents of alkalinity (10 °F) is consumed for each mole of precipitated calcium carbonate CaCO3.

Calculation of Calcium Carbonate Precipitation Potential.
CCPP will be calculated as follows for water with considered calcocarbonic parameters, in particular, water TAC = TAC1 and water at equilibrium = TACeq,
with TAC as ° F.

CCPP (mg CaCO3/L) = 10[TAC1 - TACeq]

So we will proceed by iterative calculation:

• for aggressive water: neutralizing water with CaCO3 to equilibrium saturation (pH = pHs) and thus obtain alkalinity (TAC) at equilibrium (saturation index, SI = -0.1 <= IS <= 0.1).
• for scale-forming water: TAC iterative reduction of water (decrements value = 0.1) until saturation equilibrium (pH = pHs) and thus obtain alkalinity (TAC) at equilibrium (IS = -0.1 <= IS <= 0.1).

Notes:
To CaCO3 equivalents alkalinities, we would have: CCPP (mg CaCO3 / L) = 50.045[TAC1-TACeq].
To aggressive water, CCPP value is negative and equal to amount of calcium carbonate dissolvable potentially, and to scale-fooling water, it will be positive and equal to amount precipitable potentially.

Note: for waters at equilibrium CCPP = 0. 