Calcium Carbonate
Precipitation Potential |

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
H_{2}O.H_{2}CO_{3}) produces hydrogen
and bicarbonate ions:

then bicarbonates and hydrogen carbonate ions:

In particular, calcium carbonate gives:

- (1) [ H
^{+}]+ [HCO_{3}^{- }] / [H_{2}CO_{3}] = K1 (in equilibrium)

K'1 = K1 . 10^{e} - (2) [ H
^{+}]+ [CO_{3}^{2}^{-}] / [HCO_{3}^{-}] = K2 (in equilibrium)

K'2 = K2 . 10^{2}^{e} - (3) [ Ca
^{2+ }]+ [CO_{3}^{2}^{-}] / [CaCO_{3}] = Ks (in equilibrium)

K's = Ks . 10^{e}^{s}

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:

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

The ionic strength isdefined by relationship:

wherein c_{n} represents concentration of n ion with
v_{n} 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 TP
^{2}- 646 TP^{3} - pK2 = 10.627 - 15.04 TP + 135.3 TP
^{2}- 328 TP^{3} - pKS = 8.022 + 14 TP - 61 TP
^{2}+ 444 TP^{3}

(with TP = water temperature as °C/1000).

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Thus, solubility of calcium carbonate increases with decreasing pH
due to reactions:

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):

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

**Precipitation of calcium carbonate.**

Excess calcium carbonate will be precipitated as following:

therefore bicarbonate ions will be dissociated to reconstruct carbonate ions:

result of these reactions will be:

and hydrogen ions H^{+ }released in above reaction can
react with alkalinity (French TAC), ie,
bicarbonate ion HCO^{3-}and reforming carbon dioxide:

The overall reaction is as follows:

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
CaCO_{3}.

**Calculation of Calcium Carbonate Precipitation Potential**.

CCPP will be calculated as follows for water with considered
calcocarbonic parameters, in particular, water TAC = TAC_{1}
and water at equilibrium = TACeq,

with TAC as ° F.

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[TAC_{1}-TAC_{eq}].

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.

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