**2. Experimental Section**

## *2.1. Solution Preparation*

The pure calco-carbonic water (PCCW) was obtained by the dissolution of reagent grade calcium carbonate solid in distilled water under CO2 bubbling, as follows:

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

The initial pH value was fixed at 5.9, which corresponds to a supersaturation coefficient equal to 0.25 (calculated using Equation (2)) to maintain the solution undersaturated.

The degree of supersaturation (Ω) with respect to calcite, the most CaCO3 stable form, is defined as follows:

$$\Omega\_{\rm CaCO\_3} = \frac{[\rm Ca^{2+}] \cdot [\rm CO\_3^{2-}] \cdot \gamma\_{\rm Ca^{2+}} \cdot \gamma\_{\rm CO\_3^{2-}}}{K\_s(\rmcalcite)} \tag{2}$$

where [*i*], *γ<sup>i</sup>* and *Ks* (calcite) are the ions' concentrations, the activity coefficients and the solubility product of calcite, respectively.

All the additives used were introduced to the PCCW before the precipitation test. Studied foreign salts (MgCl2, Na2SO4, and MgSO4) quantities were calculated according to the solution ionic strengths (IS) of about 0.012 (IS0), 0.024 (IS1) and 0.036 mol L−<sup>1</sup>

(IS2). The antiscalants used were organic sodium salt of polyacrylate (C3H3NaO2)n and inorganic sodium tripolyphosphate (Na5P3O10), thereafter called, respectively, RPI and STPP. The corresponding quantities used are small and do not affect the ionic strength and the resistivity.

### *2.2. Fast Controlled Precipitation Set Up*

The experimental set up of the fast controlled precipitation (FCP) method was presented in Figure 1. Thermostatic water bath was used to maintain the temperature of the FCP test at 30 ◦C. A 0.5 L volume of pure calco-carbonic water (PCCW) was filled in a polytetrafluoroethylene (PTFE) cell and was stirred at 800 rpm. The solution pH and resistivity values were constantly measured each 5 min, using a pH meter (Hanna HI 110, Hanna Instruments, Woonsocket, RI, USA) and a conductivity meter (Meter Lab CDM210, Radiometer Analytical's, Villeurbanne, France). The measuring electrode positions in the round bottom cell were well controlled. The calcium ion concentration was measured using EDTA complexometric titration.

**Figure 1.** Fast controlled precipitation experimental set up.

In the FCP vessel, CaCO3 can precipitate on the cell wall and in the bulk solution. After the completion of the experiment, homogeneously formed precipitate mb can be recuperated by filtration using cellulose nitrate membrane with 0.45 μm porosity. The amount of Ca2+ residual in the solution was measured, and then the total precipitated calcium carbonate mt was calculated. The heterogeneous mass mw deposited on the cell wall can be deduced (mw = mt − mb), and its rate is calculated as follows:

$$\%\_{\text{hete}} = \frac{\text{m}\_{\text{W}}}{\text{m}\_{\text{t}}} \times 100 \tag{3}$$

Figure 2 represents a model of an FCP test reporting the evolution of pH and resistivity as a function of time of PCCW throughout the crystallization procedure. The figure emphasizes the limit between three different zones of precipitation. During zone 1, the resistivity is roughly constant and pH values increase up to reach the prenucleation pH "pHprenuc" at tprenuc. In zone 2, the pH continues rising up with a small change in the resistivity variation speed before precipitation time "tprec". The medium is considered to be supersaturated, and calcium carbonate precipitation is thermodynamically possible. In zone 3, the slope of the resistivity temporal evolution diverges significantly, which highlights the precipitation beginning. After attaining the precipitation threshold at "pHprec", the pH decreases considerably. Therefore, the precipitation is rapid and followed by a crystal growth stage.

**Figure 2.** Temporal evolution of pH and resistivity curves of a PCCW 400 mg L−<sup>1</sup> at 30 ◦C, 800 rpm.

The reproducibility of the experimental measurements was verified for three FCP tests using 400 mg L−<sup>1</sup> of PCCW, as seen in Figure 3.

**Figure 3.** Reproducibility of the temporal evolution of pH and resistivity curves for three FCP tests at 30 ◦C, 800 rpm and PCCW 400 mg L<sup>−</sup>1.

#### *2.3. X-ray Diffraction Method for Solid Precipitate Characterization*

The X-ray Diffraction (XRD) method is a very efficient and universal tool for determining the structure of crystals. At the end of each FCP test, the precipitate was recuperated by solution filtration through cellulose nitrate membrane with 0.45 μm porosity. The collected samples were dried at ambient conditions before XRD analysis. The analyses were performed using a diffractometer Philips X'PERT PRO (PANalytical, Philips, Amsterdam, The Netherlands) in step-scanning mode using Cu Kα (1.54 Å) radiation. The XRD patterns were chronicled in the angular range 2θ = 10–60◦, with a slight step size of 2θ = 0.017◦ and a fixed count time of 4 s. The software 'X-Pert HighScore Plus' was used to determine the XRD reflection positions. The XRD patterns of the formed precipitates were compared to the joint committee on powder diffraction standards data.

#### **3. Results and Discussion**

#### *3.1. Effect of Initial Calcium Carbonate Concentration*

The calcium carbonate concentrations vary in natural waters in a range of 100 to 600 mg L<sup>−</sup>1. Examples include geothermal water (100 mg L−1), tap water (200 to 400 mg L<sup>−</sup>1), and saline water (600 mg L<sup>−</sup>1) [37]. Therefore, three solutions with different dissolved CaCO3 content levels (200, 400, 600 mg L−1) were prepared to study the effect of initial calcium carbonate amount on the nucleation threshold. Figure 4 reports the temporal evolution of pH and ΔResistivity curves during the FCP tests by varying the initial concentration of calcium carbonate. The main results are presented in Table 1.

**Figure 4.** pH and ΔResistivity vs. time curves by varying the initial amount of calcium carbonate.

**Table 1.** FCP tests results by varying the initial amount of calcium carbonate.


As seen in Figure 4, the prenucleation (tprenuc) and the precipitation (tprec) time decrease as the CaCO3 amount increases. Indeed, tprenuc and tprec are roughly divided by two and by five, respectively, as the initial concentration increases from 200 to 600 mg L−<sup>1</sup> (Table 1). Ben Amor et al. [38] proved that the precipitation time was delayed from 90 to 7 min after increasing the water hardness from 20 to 50 ◦F by using a CO2 degasification test. Additionally, Fathi et al. [39] found that the increase in Ca(HCO3)2 content initially dissolved from 30 to 50 ◦F accelerates the nucleation time from 20 to 7 min.

Thus, the nucleation step (Δt=tprec − tprenuc) is shorter as the initial calcium carbonate concentration increases. According to Table 1, this nucleation phase lasts 120 min for 200 mg L−<sup>1</sup> and only 20 min for 600 mg L−1. This can be explained by the fact that the medium saturation state is affected by the initial concentration. According to Raffaella et al. [8], the lifetime of a cluster, before the growth phase, becomes longer when the concentration decreases as a result of the reduction in collision frequency. Indeed, the variation in the solution concentration modifies the frequency of collisions between the different species present (ions, ions pairs, and clusters). Thus, the maximum size that a germ can reach varies according to the different equilibriums between the association and dissociation processes.

From a thermodynamic point of view, the prenucleation threshold is attained at low Ω values less than two despite the difference in time to reach it (8 min for 600 mg L−<sup>1</sup> and 18 min for 200 mg L−1). However, at the precipitation threshold, the supersaturation coefficients increase from 24 to 51 and the time decreases from 138 to 28 min as the initial concentration of calcium carbonate increases from 200 mg L−<sup>1</sup> to 600 mg L<sup>−</sup>1, respectively.

Table 1 also reveals that the initial concentration of calcium carbonate [CaCO3]i influences the heterogeneous precipitation rate (%hete) of CaCO3. Indeed, %hete decreases from 56 to 34% as [CaCO3]i increases from 200 to 600 mg L−1. This is in agreement with Fathi et al. [39], who found that the heterogeneous precipitation rate, which was around 90% for 30 and 40 ◦F CaCO3 solutions, reached 63% for 50 ◦F solution. The same observation can be made for Ben Amor et al. [38], who proved that when the water hardness increases from 20 to 50 ◦F, the %hete decreases from 98 to 73%. Consequently, the adhesion of tartar on the cell walls is favored for low levels of calcium carbonate initially dissolved, and therefore for low nucleation thresholds. This can be due to the slow aggregation of ion pairs and clusters in low concentrated solutions, so the pre-nucleus remain at a small size for a longer time. Thus, it is more likely that they reach the surface and cling before they become large enough to not adhere to the cell wall.

## *3.2. Effect of Foreign Salts*

#### 3.2.1. Influence on the Nucleation Threshold

The most abundant salts found in natural waters are MgCl2, Na2SO4 and MgSO4. Their effect on the nucleation process of CaCO3 will be investigated. The results of FCP tests obtained in PCCW-MgCl2, PCCW-Na2SO4 and PCCW-MgSO4 solutions are compared to the results of PCCW solution. The pH and resistivity time curves are represented in Figures 5 and 6.

As shown in Table 2, the prenucleation time tprenuc varies from 12 to 60 min as a function of the solution composition. During this time, the resistivity remains invariable, corresponding to the prenucleation threshold frontier. As expected, the increase of Mg2+ and SO4 <sup>2</sup><sup>−</sup> ions concentrations highly delays the nucleation time for both ionic strengths (Table 2). Any precipitation time obtained in the presence of foreign ions was more than the 46 min precipitation time of CaCO3 in a PCCW solution. The MgSO4 ion greatly delayed the precipitation of CaCO3 compared to Mg2+ and SO4 <sup>2</sup><sup>−</sup> ions. Indeed, tprec increased from 46 to 214 min when MgSO4 concentration increased from 0 (IS0) to 828 (IS2) mg L<sup>−</sup>1. As to Mg2+ and SO4 <sup>2</sup>−, they increased the precipitation time from 46 min (PCCW) to only 102 and 64 min, respectively. Moreover, the ion pairs' formation (tprenuc) and aggregation (tprec) times were remarkably affected by the addition of each foreign ion. Indeed, the duration of the stable nuclei formation (Δt=tprec − tprenuc) was extended after the addition of these

ions to a PCCW solution. At the same ionic strength (IS2), magnesium had more of an influence on the formation of CaCO3 stable nuclei than sulfate since Δt was equivalent to 74 and 40 min for Mg2+ and SO4 <sup>2</sup><sup>−</sup> ions, respectively.

**Figure 5.** pH and ΔResistivity vs. time curves as a function of the added salt for IS0 and IS1.

**Figure 6.** pH and ΔResistivity vs. time curves as a function of the added salt for IS0 and IS2.


**Table 2.** FCP tests results by varying the added salt amount.

Furthermore, Table 2 shows that the supersaturation coefficient values of the prenucleation threshold Ωprenuc were very low and varied from 1 to 9. By contrast, the precipitation threshold was reached at high Ωprec, especially after adding Na2SO4 to the PCCW solution. In fact, at the same ionic strength IS1, SO4 <sup>2</sup><sup>−</sup> ion created a large supersaturation coefficient, which reached up to 1.55 times higher than the PCCW test (reference), while Mg2+ ion created a small supersaturation coefficient, which was 0.9 times lesser than that of PCCW. By combining these two ions to obtain MgSO4, Ωprec went down to 0.7 times less than that of PCCW. Consequently, sulfate ion had more of an impact on the pH of prenucleation and precipitation. As for magnesium ion, it influenced the nucleation time. Thus, the presence of magnesium and sulfate ions affected the nucleation and growth in different ways. Indeed, according to Waly et al. [40], two mechanisms can occur in the presence of magnesium and sulfate ions individually or together. The first mechanism involved is complexation, affecting the activity coefficients of calcium and carbonate ions by decreasing the total present ions for precipitation. The second implicated mechanism is inhibition, where the formed nuclei are inhibited from growing more by blocking the active growth sites. Therefore, both ions can attach to the recently formed calcium carbonate nuclei, causing a decrease in the nuclei growth rate due to the reduction in the available sites for growth by the blockage of the growth steps [41]. The growth can be suppressed entirely if the presence of foreign ions is dominant compared to the presence of calcium and carbonate ions [42].

#### 3.2.2. Influence on the Surface Scaling

The effect of foreign ions on CaCO3 formation has been investigated systematically in this paper, including aspects of kinetics, thermodynamics and behaviors. However, their influence on scale surface deposition has not yet been studied. For this, the total precipitation rate and the heterogeneous precipitation percentage are calculated using the weight method [38] in the absence and presence of foreign ions. As illustrated by Table 2, the total precipitation rate τprec decreases as the ionic strength increases. Indeed, τprec decreases for IS1 by 5% for magnesium, 18% for sulfate and 9% for the two combined ions (MgSO4) compared to the PCCW solution test. Moreover, τprec is practically invariant by increasing the ionic strength for each salt. Furthermore, in the presence of magnesium or sulfate ions or combined magnesium sulfate ions, more than 70% of the CaCO3 precipitates are formed on the different surfaces in contact with water (cell-wall and probes) for both ionic strengths, whereas this heterogeneous percentage does not exceed 45% for pure calco-carbonic water. Subsequently, the introduction of one of these two ions, or both at once, leads to an increase in the precipitation on the walls for both ionic strengths studied. At the macroscopic scale, it would seem that both magnesium and sulfate ions, although presenting opposite charges, have the same effect on the orientation of CaCO3 precipitation to the heterogeneous precipitation, regardless of their modes of action in solution. However, in the study of Chen et al. [43], it was proved that Mg2+ ions apparently inhibit both CaCO3 bulk precipitation, regarded as a homogenous process, and CaCO3 surface deposition, regarded as a heterogeneous process. It is known that Mg will bond with water and form a

complex at room temperature. This complex prohibits the nucleation and growth of calcite structure carbonate [44].
