**3. System CaCO3-H2O-CO2**

Scaling is a complex phenomenon that takes a long time to manifest itself in industrial or domestic facilities. Several techniques, such as mechanical stirring [29], aeration [30], electrochemical precipitation [31], magnetic water treatment [32] have been used in laboratories to assess the effectiveness of chemical or physical treatment, and the influence of certain parameters on scale formation over time. However, the most interesting method used for CaCO3 precipitation is the CO2 repelling method [16, 17, 33] where the CO2 containing solution is air bubbled which increases the solution pH and provokes the CaCO3 precipitation (**Figure 3**). Indeed, this method is an accelerated simulation of the natural scaling phenomenon

**Figure 2.** *XRD diagrams of vaterite, calcite and aragonite.*

#### **Figure 3.**

*Schematic illustration of the CO2 repelling method used for CaCO3 precipitation. A cylindrical cell containing a diffuser at the bottom and covered with a lid. The lid contains different openings, one of which allows samples to be removed to determine the calcium amount left in the solution and another opening allows CO2 repelling from the solution while the air is bubbling. The flow of the injected air was controlled by an air flow meter, and the temperature of the solution was controlled by a thermostat with circulating water. An electrode is used to record the pH.*

in which the precipitation of CaCO3 takes place, in a short experiment time that do not exceed 90 min, following the removal of the dissolved CO2 by the atmospheric air, according to the following reaction [16, 17]:

$$\text{Ca}^{2+} + 2\text{HCO}\_3^- \rightarrow \text{CaCO}\_3 + \text{CO}\_2 + \text{H}\_2\text{O} \tag{1}$$

The saturation index (SI) is a measure of the deviation of the system from equilibrium. When SI < 0, the solution is undersaturated and no crystallization occurs. When SI = 0, the solution is in equilibrium, and when SI > 0, the solution is supersaturated, and crystallization could occur spontaneously. For CaCO3, SI is given by the following equation:

$$SI = \log \Omega \tag{2}$$

where <sup>Ω</sup> <sup>¼</sup> *IAP Ksp* <sup>¼</sup> *Ca*2<sup>þ</sup> ð Þ *CO*2� ð Þ <sup>3</sup> *Ksp* is the supersaturation ratio of the solution with respect to CaCO3 and IAP and Ksp represent respectively, the ionic activity product and the thermodynamic solubility product of CaCO3. The solubility products of the different polymorphs of CaCO3, given in **Table 1**, were determined by the temperature dependent equations given by Plummer and Busenberg [27] and Brecevic and Kralj [4]. *Ca*<sup>2</sup><sup>þ</sup> � � <sup>¼</sup> *<sup>γ</sup>Ca*2<sup>þ</sup> *Ca*<sup>2</sup><sup>þ</sup> � � and *CO*<sup>2</sup>� 3 � � <sup>¼</sup> *<sup>γ</sup>CO*2� <sup>3</sup> *CO*<sup>2</sup>� 3 � � are the activities of the ions Ca2+ and CO3 <sup>2</sup>�, respectively. The activity coefficients *<sup>γ</sup>Ca*2<sup>þ</sup> and *<sup>γ</sup>CO*2� <sup>3</sup> are calculated using the extended Debye-Huckel equation:

$$\log \gamma\_i = -\frac{AZ\_i^2 \sqrt{I}}{1 + Ba\_i \sqrt{I}} + b\_i \sqrt{I} \tag{3}$$

*Effect of Operating Parameters and Foreign Ions on the Crystal Growth of Calcium Carbonate… DOI: http://dx.doi.org/10.5772/intechopen.94121*


**Table 1.**

*Logarithmic solubility products of the various polymorphs of calcium carbonate CaCO3 as a function of temperature.*

where A, B are constants defined by Harmer [34], ai and bi are ion-specific parameters assigned by Truesdell and Jones [35], Zi is the valence of the i-species and I is the ionic strength:

$$I = \frac{1}{2} \sum\_{i} Z\_i^2 c\_i \tag{4}$$

where ci is the concentration of the i-species.

In the carbonation process, the CO2 gas firstly dissolves into water to form the carbonic acid H2CO3 which transforms into *HCO*� <sup>3</sup> , *CO*<sup>2</sup>� <sup>3</sup> and *H*<sup>þ</sup> according to the following equations:

$$\text{CO}\_2(\text{g}) \longleftrightarrow \text{CO}\_2(\text{l}q), \quad \text{P}\_{\text{CO}\_2} = \text{K}\_H(\text{CO}\_2) \tag{5}$$

$$\text{CO}\_2(lq) + H\_2O \leftrightarrow H\_2\text{CO}\_3\tag{6}$$

$$H\_2\text{CO}\_3 \leftrightarrow H\text{CO}\_3^- + H^+, \quad \frac{\left(H\text{CO}\_3^-\right)(H^+)}{(\text{CO}\_2)} = 10^{-K\_1} \tag{7}$$

$$\mathrm{HCO}\_{3}^{-}\leftrightarrow\mathrm{CO}\_{3}^{2-} + H^{+}, \quad \frac{\left(\mathrm{CO}\_{3}^{2-}\right)(H^{+})}{\left(\mathrm{HCO}\_{3}^{-}\right)} = \mathbf{10}^{-K\_{2}}\tag{8}$$

where KH, K1 and K2 are the Henry's law coefficient, first and second dissociation constants of carbonic acid (given in **Table 2** [36]), respectively and (*HCO*� <sup>3</sup> ), (*H*þ) and (CO2) are the activities of the ions *HCO*� <sup>3</sup> , *H*<sup>þ</sup> and CO2, respectively.

The electric neutrality of the calco-carbonic solution gives:

$$2\left[\text{Ca}^{2+}\right] + \left[\text{H}^{+}\right] = \left[\text{OH}^{-}\right] + \left[\text{HCO}\_{3}^{-}\right] + 2\left[\text{CO}\_{3}^{2-}\right] \tag{9}$$

and

$$\chi\left(\text{CO}\_3^{2-}\right) = \chi\_{\text{CO}\_3^{2-}}\left[\text{CO}\_3^{2-}\right] = \frac{1}{2}\chi\_{\text{CO}\_3^{2-}}\left(2\left[\text{Ca}^{2+}\right] + \left[\text{H}^+\right] - \left[\text{OH}^-\right] - \left[\text{HCO}\_3^-\right]\right) \tag{10}$$

From Eq. (8), the activity of *CO*<sup>2</sup>� <sup>3</sup> is determined by:

$$\left(\mathrm{CO}\_{3}^{2-}\right) = \left(\mathrm{HCO}\_{3}^{-}\right)\mathbf{10}^{pH-K\_{2}} = \chi\_{\mathrm{HCO}\_{3}^{-}}\left[\mathrm{HCO}\_{3}^{-}\right]\mathbf{10}^{pH-K\_{2}}\tag{11}$$

where *γCO*2� <sup>3</sup> and *γHCO*� <sup>3</sup> are the activities coefficients of the ions *CO*<sup>2</sup>� <sup>3</sup> and *HCO*� 3 , respectively. It is worth to note that the concentration of *HCO*� <sup>3</sup> ions can be assumed to be equal to the total alkali concentration (TAC) for pH in the range


#### **Table 2.**

*Henry's law coefficient (KH), and first and second dissociation constants (K1, K2) of carbonic acid for different temperatures (values are taken from Ref. [36]).*

6–8.8. Indeed, *CO*<sup>2</sup>� 3 and *OH*� ½ � are small in this pH range [37] and in a first approximation:

$$\text{TAC} = \left[\text{HCO}\_3^-\right] + 2\left[\text{CO}\_3^{2-}\right] + \left[\text{OH}^-\right] \approx \left[\text{HCO}\_3^-\right] \tag{12}$$
