Crystallization of CaCO₃ in Aqueous Solutions with Extremely High Concentrations of NaCl

Abstract

The effect of NaCl at extremely high concentrations from 3.5 to 14 wt. % on the crystallization of CaCO₃ was investigated in depth. The static test experiment verified that the Ca²⁺ retention efficiency (η) of NaCl on CaCO₃ scale increased from 31.06% (3.5 wt. %) to 41.56% (14 wt. %). Based on the calculation of supersaturation rations, the high concentration of NaCl could reduce the activity coefficients of [Ca²⁺] and [CO₃²⁻], thus reducing the actual concentration of CaCO₃. The CaCO₃ deposition rate constants (k) showed that NaCl slowed down the rate of CaCO₃ crystallization. The X–ray diffraction (XRD) testing disclosed that the growth of (1 0 4) and (1 1 0) faces from calcite was impeded, while the formation of (1 1 1) face from aragonite was induced by the increasing concentration of NaCl. The inductively coupled plasma optical emission spectrometry (ICP–OES) results indicated that Na⁺ could be doped into CaCO₃, leading to the one–dimensional crystal growth. It was further proved that NaCl heightens the efficiency of the typical phosphate inhibitors (2–phosphonobutane–1,2,4–tricarboxylic acid (PBTCA) and 1–hydroxyethane–1,1–diphosphonic acid (HEDP)) on prohibiting the scale of CaCO₃.

1. Introduction

Seawater is widely used in the reverse osmosis desalination plants [1,2,3,4,5,6], multi-stage-flash desalination process [7], circulating cooling water systems, and other water treatment systems [8]. In these processes, seawater is inevitably concentrated by two to four times. In particular, the NaCl concentration can reach the level of 3.5–14 wt.% [9,10]. As the excessive inspissation of the saline water, scaling would occur when the ionic activity product of precipitation was larger than its solubility product [11,12,13]. The disaster was occurring as scaling shortens the lifespan of membranes, reducing their overall efficiency of the heat transfer tubes and increasing the maintenance and operational costs as well [14,15].

Despite this, the superiorities of increasing the concentration factor of the system was particularly significant in sealed circulating cooling water systems, such as reducing the amount of make–up water, declining sewage discharge, and even achieving zero emission [16,17]. Moreover, the salt stress could inhibit the growth of bacteria in the tubes [18]. Actually, Na⁺ and Cl⁻ are the main components and CaCO₃ was the major scale type in concentrated seawater [19]. Earlier, Choi et al. and Sheikholeslami et al. discovered that NaCl at high concentrations (3.5–5.2 wt.%) delayed the crystallization of CaSO₄ [20,21]. It is of great importance if the CaCO₃ scaling could be delayed when seawater is concentrated by 2–4 times. Therefore, a better understanding about the crystallization of CaCO₃ in the extremely high salinity brines was rather urgent. However, until now, only Visscher et al. critically evaluate the CaCO₃ solubility data at extreme concentrations of NaCl [22] In addition, no one had studied the scale inhibition effect of characteristic inhibitor in NaCl solution with such high concentrations.

Herein, the effect of NaCl solution (3.5 wt.%–14 wt.%) on CaCO₃ crystallization and the combined effect of NaCl and typical phosphate scaling inhibitors (2–phosphonobutane–1,2,4–tricarboxylic acid (PBTCA) and 1–hydroxyethane–1,1–diphosphonic acid (HEDP)) were evaluated for the first time. The static test showed that the Ca²⁺ retention efficiency (η) was raised with the NaCl concentration increase. The prompt addition test and the calculation of the deposition rate constants proved that high salinity prolonged the CaCO₃ crystallization. The X–ray diffraction (XRD) test clearly showed that NaCl mainly prohibited the growth of (1 0 4) and (1 1 0) facets of calcite and induced the formation of (1 1 1) facets of aragonite. The inductively coupled plasma optical emission spectrometry (ICP–OES) tests indicated that Na⁺ could be doped into CaCO₃, inducing crystallization of CaCO₃ to one–dimensional forms. The quantum calculation and morphology analysis verified that Na⁺ could not only enhance the chelate effect between the selected inhibitor and Ca²⁺, but also accelerate the lattice distortion of CaCO₃ combining with the inhibitor. Thereby, the η values of HEDP and PBTCA in NaCl solution improved enormously, and they were as high as 83.50% and 92.16%, respectively, under the optimal conditions.

2. Experimental Section

2.1. Materials and Instruments

NaCl and CaCl₂ were purchased from Xilong Chemical Co., Ltd. (Guangdong, China). NaHCO₃ and Na₂CO₃ were obtained from Lingfeng Chemical Reagent Co., Ltd. (Shanghai, China). HEDP (50 wt.%) and PBTCA (50 wt.%) were got from Taihe Water Treatment Co., Ltd. (Shandong, China). All reagents used in the experiments were of analytical grade, and they were applied without further purification. The ultrapure water with 18.2 MΩ cm (Hitech, Medium–E400, Shanghai, China) was used thorough the experiment.

The precipitated solids were characterized by X–ray diffraction (XRD) analysis after three times of rinsing with ultrapure water and air drying at 40 °C. The XRD patterns were recorded on a Bruker D8 Advanced X–ray powder diffraction diffractometer (Bruker AXS, Karlsruhe, Germany). The scanning electron microscopy (SEM) analysis was performed on a FEI 400FEG (FEI, Hillsboro, Oregon, USA) device. The Nitrogen Adsorption (BET method) was carried out with a Gemini VII2390 (Micromeritics, Norcross, GA, USA) instrument. The inductively coupled plasma optical emission spectrometry (ICP–OES) was performed on a Varian 720–ES (Varian Medical Systems, Palo Alto, California, USA) spectrometer.

2.2. Static Test Experiment

The evaluation of the inhibition effect against CaCO₃ deposits under static conditions was carried out according to Chinese National Standard (GB/T16632–2008) [23].The testing solution containing 0.006 mol/L Ca²⁺ and 0.012 mol/L HCO₃⁻ was prepared in a 250 mL volumetric flask, and, then the different concentrations of NaCl (3.5 wt.%–14 wt.%) were added into the parallel testing solutions. The pH level of the solutions was adjusted to 9.0 with 0.01 mol/L Na₂B₄O₇ buffer solution. Then, the specimens were maintained at 80 °C for 10 h in thermostat water bath. After cooling to room temperature, these supersaturated solutions were filtered and then dried in vacuum at 50 °C for 12 h. The concentration of Ca²⁺ was titrated by an Ethylenediaminetetraacetic acid (EDTA) standard solution. The Ca²⁺ retention efficiency was determined by the formula [24]:

$$\eta \%=\frac{C_{\mathrm{final}}-C_{\mathrm{blank}}}{C_{\mathrm{initial}}-C_{\mathrm{blank}}}\times 100,$$

(1)

where C_final and C_blank represented the Ca²⁺ in the filtrate with and without inhibitors, respectively. C_initial was the initial concentration of Ca²⁺.

2.3. The Precipitation of CaCO₃ by Prompt Addition

The testing was performed as follows [25]. First, 25 mL of 0.04 mol/L CaCl₂ solution and 200 mL of NaCl (3.5 wt.%–14 wt.%) were prepared in advance. Then, the mixture was introduced into a three–necked glass reactor which was equipped with a calcium ion selective electrode and pH electrode. The reactor was placed in a constant temperature thermostatic water bath at 25 °C with continuous stirring. Before the addition of carbonate, the initial pH value of each solution was adjusted to 6.4 using 0.01 mol/L HCl. In the following stage, 25 mL of 0.04 mol/L Na₂CO₃ was added rapidly into the vessel. The pH values and the calcium ion concentrations were measured continuously.

2.4. Molecular Dynamics (MD) Simulation

The MD simulation was used to simulate the interaction between calcite surface and molecules. The space group of calcites is R 3(–) C, and its lattice parameters are a = b = 4.99 Å, c = 17.06 Å, α = β = 90°, and γ = 120° [26]. The interaction model was built with the Visualizer module. It would be cleaved with a surface along the 1 0 4 and 1 1 0 planes, setting the depth as 12.14 Å and 9.98 Å. Build the 2D surface into a super cell, adding a vacuum slab (about 30 Å) on the calcite to build a 3D cell for avoiding the influence of other periodic atoms. Then, the energy minimized inhibitor molecule and water molecules could be placed onto a proper position of the surface, ensuring the whole molecule to be inside the vacuum slab. The dimension of the super cell containing the crystal and inhibitor were 32.38 Å × 24.95 Å × 18.90 Å for 1 0 4 plane and 32.38 Å × 31.88 Å × 19.03 Å for 1 1 0 plane. The super cells with periodic boundary conditions were treated as a 3D periodic system for the dynamics simulation, and the same calcite 3D layer was used for all the inhibitor molecules [18]. The crystal grew along with rigid sequence and orientation, to prevent any surface displacements during the simulation. The atoms in the calcite crystal were frozen during simulation, and only the additive molecules could vibrate freely [27]. The equilibration and subsequent simulations were conducted in the canonical (NVT) ensemble. The system temperature was maintained at 298 K using the Andersen thermostat with an integration time step of 1.0 fs [28]. The time step was 1 fs, MD simulation ran for 10 ns: 1 ns for equilibration stage and then 9 ns for production stage. The trajectory was recorded every 1 ps. The interaction energy (E_interaction) between the surface and additive molecules could be calculated as follows:

$$E_{\mathrm{interaction}}=E_{\mathrm{total}}-E_{\mathrm{surf}+\mathrm{water}}-E_{\mathrm{add}+\mathrm{water}}+E_{\mathrm{water}},$$

(2)

where E_total was the total energy of the optimized surface–additive complex in the presence of water, E_surf+water was the energy of the calcite surface and water, E_add+water was the energy of the additive and water, and E_water was the total energy of water. The binding energy (E_binding) reflected the intermolecular interactions between adsorbent and crystal, which was defined as the inverse value of the interaction energy [29]:

$$E_{\mathrm{binding}}=-E_{\mathrm{interaction}}.$$

(3)

The quantum calculation was performed to get insight into the interaction between Ca²⁺ and scale inhibitors. The HEDP and PBTCA molecules were optimized by B3LYP–6–31G (d) method with Gaussian 09 software (Gaussian, Inc., Wallingford, CT, USA). The possible structures of Ca–ions and inhibitor molecules were also simulated by quantum calculation.

3. Results and Discussion

3.1. Supersaturation Ratio and the Ca²⁺ Retention Efficiency

The crystallization process of CaCO₃ included nucleation, crystal growth, agglomeration and recrystallization [30]. The crucial driving force for both nucleation and growth was the supersaturation level [31]. The degree of mineral supersaturation could be quantified by the supersaturation ratio (SR), which was the ratio of dissolved CaCO₃ ionic activity product (IAP) to the solubility product (K_sp), as shown in Equation (4) [32]:

$$\mathrm{SR}=\frac{\mathrm{IAP}}{K_{\mathrm{sp}}}=\frac{{\gamma }_{\mathrm{Ca}}\left[{\mathrm{Ca}}^{2+}\right]{\gamma }_{{\mathrm{CO}}_3}\left[{\mathrm{CO}}_3^{2-}\right]}{K_{\mathrm{sp}}},$$

(4)

where [Ca²⁺] and [CO₃²⁻] were the concentrations of calcium and carbonate ions, respectively, and γ_Ca and γ_CO3 were the activity coefficients of [Ca²⁺] and [CO₃²⁻], respectively. The ionic strength of NaCl solution in this study was 0.72–3.75 mol/kg and, thus, γ_Ca and γ_CO3 could be calculated by the Pitzer model, which was applicable to ionic strength from 0.01 to 6 mol/kg [33].

For SR > 1, there was a thermodynamic potential for precipitation of CaCO₃, and the solution was supersaturated with respect to this salt [34]. As shown in

Table 1. Activity coefficients of [Ca²⁺] and [CO₃²⁻], supersaturation ratio and the Ca²⁺ retention efficiency of NaCl, 2–phosphonobutane–1,2,4–tricarboxylic acid (PBTCA) and 1–hydroxyethane–1,1–diphosphonic acid (HEDP) in different salinities.

NaCl (wt.%)	0	3.5	7	10.5	14
γCa (×10−2)	80 ± 3%	9 ± 1%	5 ± 3%	2 ± 6%	2 ± 7%
γCO3 (×10−2) SR	80 ± 2% 292 ± 9%	10 ± 3% 20 ± 8%	8 ± 1% 11 ± 9%	5 ± 1% 5 ± 4%	3 ± 8% 4 ± 9%
ηNaCl	–	31 ± 6%	35 ± 7%	38 ± 4%	41 ± 6%
η4 μM HEDP	19 ± 7%	48 ± 1%	54 ± 1%	58 ± 1%	60 ± 6%
η8 μM HEDP	30 ± 3%	62 ± 2%	67 ± 7%	68 ± 1%	70 ± 4%
η16 μM HEDP	48 ± 1%	73 ± 8%	78 ± 6%	81 ± 1%	83 ± 1%
η4 μM PBTCA	27 ± 8%	56 ± 1%	61 ± 1%	65 ± 6%	70 ± 4%
η8 μM PBTCA	42 ± 5%	73 ± 8%	77 ± 9%	80 ± 6%	82 ± 3%
η16 μM PBTCA	52 ± 7%	84 ± 7%	88 ± 8%	90 ± 8%	92 ± 6%

, the values of γ_Ca and γ_CO3 decreased with the salinity increase, and it showed that the effective concentration and ion interaction of Ca²⁺ and CO₃²⁻ in the system decreased correspondingly. SR of CaCO₃ was larger than 1 and it decreased dramatically with the salinity increase, which indicated that CaCO₃ has less thermodynamic potential to precipitate in high salinity than in pure water. Simultaneously, the effect of concentration of NaCl on CaCO₃ crystallization was studied by a static test. The results of η (seen in Table 1) increased with the promotion of the NaCl concentration, which demonstrated that an extremely high concentration of NaCl could hinder the crystallization of CaCO₃.

3.2. pH Measurement

As shown in Equation (5), calcium carbonate precipitation reaction was pH–dependent [25]. From the curves of pH versus time, as presented in Figure 1a, it is found that the pH values skyrocketed due to CO₃²⁻ being hydrolyzed to OH⁻, then a sharp drop existed at the first stage, proving the beginning of the CaCO₃ precipitation, and then they became flat as time went on and finally stabilized. The maximal pH value, equivalent to the amount of required supersaturation degree that triggers CaCO₃ precipitation, was known as critical pH (pH_c), and, when the precipitation reaction reached equilibrium, the pH value was the saturation pH (pH_s) [32,33,34,35]:

$$C{a}^{2+}+HC{O}_3^{-}+H_{2}O\leftrightarrow CaC{O}_3+H_3{O}^{+}.$$

(5)

In Figure 1a, it is shown that, without NaCl, pH_c achieved the value of 9.71 and decreased sharply. The pH_c values increased more and the drops of pH were less abrupt when NaCl was added. It was possible to deduce that, in the presence of NaCl, the system needs to be kept at a higher supersaturated condition to trigger CaCO₃ precipitation. The result supported the calculation of SR. From

Table 2. Values of pH_c, pH_s and induction time tested by pH measurement, and the surface areas of crystals measured by the Nitrogen Adsorption (BET method) testing in different salinities.

NaCl(wt.%)	0	3.5	7	10.5	14
pHc	9 ± 1%	9 ± 2%	9 ± 6%	10 ± 2%	10 ± 1%
pHs Induction time (s)	8 ± 6% 25 ± 2%	9 ± 1% 79 ± 8%	9 ± 5% 118 ± 2%	9 ± 8% 160 ± 8%	9 ± 2% 189 ± 6%
s (m2/10 g)	1 ± 6%	4 ± 4%	4 ± 6%	7 ± 2%	8 ± 5%

, the pH_s values increased with the addition of NaCl, indicating a less carbonate consumption, which indicated the lesser precipitation of CaCO₃. The induction time, the period between the formation of supersaturated condition and nucleation onset, became longer accompanying the supplement of NaCl, as shown in Figure 1b. This delay occurred because the nuclei of CaCO₃ were unstable in supersaturated conditions due to the competition between the interfacial energy of the crystal surface and the mutative Gibbs energy on the addition of NaCl in solution [36]. Correspondingly, the decrease of free calcium ions in solutions became slower (seen in Figure 1b) with the NaCl concentration increase, which meant that the binding of Ca²⁺ to CO₃²⁻ was hindered.

3.3. Reaction Kinetics of CaCO₃ Crystal

The kinetic rates and order of reaction for CaCO₃ precipitation at various salinities were analyzed using the following kinetics equations [37,38,39]:

$${\left(C_{\mathrm{t}}-C_{\mathrm{eq}}\right)}^{-1}-{\left(C_0-C_{\mathrm{eq}}\right)}^{-1}=kst.$$

(6)

In this equation, c_t (mol/L) was the concentration of Ca²⁺ in solution at time t, c_eq (mol/L) was the concentration of Ca²⁺ at equilibrium, c₀ (mol/L) was the initial concentration of Ca²⁺, k was the rate constant, and s (m²/g) was the surface area of crystal measured by BET tests (seen in Table 2).

Set (c_t – c_eq)⁻¹ = T, (c₀ – c_eq)⁻¹ = T₀, Equation (7) was obtained as follows:

$$T-T_0=kst.$$

(7)

The linear plots of T − T₀ vs. st are shown in Figure 2. Commonly, the slopes of these curves reflected the crystal growth rates. The fastest crystallization rate constant of CaCO₃ was achieved when NaCl was absent in the solution. The k value decreased continuously when NaCl concentration increased from 3.5 to 14 wt. %, which also demonstrated that CaCO₃ crystallization became more difficult to occur.

3.4. XRD and SEM Characterization for CaCO₃ Crystals

The effect of NaCl on the crystallization of CaCO₃ was studied by a XRD test. The XRD patterns of CaCO₃ crystals formed in the solution with different concentrations of NaCl are given in Figure 3A. Curve a in Figure 3A showed that the diffraction peaks at 23.0°, 29.4°, 36.1°, 39.4°, 43.1°, 47.5°, and 48.4° were ascribed to 0 1 2, 1 0 4, 1 1 0, 1 1 3, 2 0 2, 0 2 4 and 1 1 6 characteristic planes of calcite, respectively [40]. In the presence of NaCl (from 3.5 wt.% to 14 wt.%), the new diffraction peaks at 26.2°, 27.2°, 33.1°, 36.2°, 37.8°, 38.4°, 42.8°, 45.9°, 50.2°, and 52.5° appeared clearly, which corresponded to 1 1 1, 0 2 1, 0 1 2, 2 0 0, 1 1 2, 1 3 0, 1 2 2, 2 2 1, 1 3 2 and 1 1 3 planes of aragonite, respectively. The 1 0 4 and 1 1 0 planes of calcite declined obviously. In addition, the polymorphic fraction of aragonite in CaCO₃ could be evaluated using the following equation in the absence of vaterite [41]:

$$X_{\mathrm{A}}=\frac{3.9I_{\mathrm{A}}}{I_{\mathrm{C}}+3.9I_{\mathrm{A}}}$$

(8)

$$X_{\mathrm{C}}=1-X_{\mathrm{A}}$$

(9)

where X_A and X_C were the calculated fractions of aragonite and calcite, respectively. I_A and I_C were the integrated intensities of aragonite 1 1 1 and calcite 1 0 4, respectively.

It could be seen in

Table 3. Fractions of calcite’s and aragonite’s phases in the CaCO₃ crystals.

NaCl (wt%)	0	3.5	7	10.5	14
Calcite (%)	100	58 ± 7%	39 ± 3%	38 ± 3%	37 ± 7%
Aragonite (%)	0	41 ± 2%	60 ± 7%	61 ± 6%	62 ± 2%

that the calcite fraction decreased distinctly and the aragonite fraction increased significantly on increasing the NaCl concentration. It was well known that calcite is the most stable form, while aragonite is unstable modification of CaCO₃ [42,43]. Thus, NaCl could induce lattice distortion of CaCO₃, which postponed the scaling of CaCO₃ in the solution. For comparison, the XRD test was also performed with the same addition of KCl (3.5–14 wt.%). As shown in Figure 3B, the formed CaCO₃ scales exhibited the same crystal configuration after adding various amounts of KCl. These results demonstrated that Na⁺ could cause aragonite formation indeed.

The XRD results (Figure 3C,D) displayed that, when 8 μM HEDP or 4 μM PBTCA are added to the system, the characteristic peak of vaterite appeared, but 1 0 4 and 1 1 0 peaks of calcite changed indistinctively. When 4 μM HEDP or PBTCA with NaCl are added to the solution, the intensity of 1 0 4 peak decreased significantly and 1 1 0 peak disappeared. In addition, the 1 1 0 peak of calcite was hardly changed in only NaCl solution or only inhibitor solution, but this peak disappeared for complex solutions. Therefore, it could be verified that NaCl accelerated the lattice distortion of CaCO₃ in combination with HEDP or PBTCA.

In order to reveal the effect of NaCl on the crystal morphology and growth orientation, SEM observations were carried out, as shown in Figure 4. It was found that, in the absence of NaCl, the morphology of CaCO₃ was regular rhombohedrons and glossy calcite particles, while, in NaCl solution (3.5 wt.%–14 wt.%), the CaCO₃ particles grew in one direction and formed the rod–shaped grains, which could be identified as aragonite phase [44]. With the addition of NaCl, the crystal size became larger because NaCl decreased the supersaturation with respect to CaCO₃ [36]. The ICP–OES measurements were used to further investigate the elemental composition of CaCO₃. The Na⁺ concentrations (mg/L) in the crystallization products prepared in NaCl (3.5 wt. %–14 wt. %) were 1.01, 1.19, 2.33, 3.10, respectively. It was revealed that Na⁺ could be doped into the crystal lattice due to the similar ionic radius of Ca²⁺ (1.00 Å) and Na⁺ (1.02 Å) [45], and, therefore, Na⁺ could substitute Ca²⁺ site in the lattice and induce the crystal growth of CaCO₃. Moreover, it may induce the transition of the most stable calcite to aragonite [46,47,48,49]. The SEM results also showed that, when HEDP or PBTCA are added in the NaCl solution (Figure 4B,C), the crystals were gathered by many smooth ellipsoidal particles, and, with the NaCl concentration increase, they eventually form spheres. Overall, it could be concluded that inhibitors accelerate the crystal transformation of CaCO₃ from calcite to vaterite with the stimulation role of NaCl.

3.5. MD Simulation

The MD simulations were performed to model the interaction between scaling inhibitors and CaCO₃ at a micro level. The calcite (1 0 4) and (1 1 0) faces were chosen for the simulation study since HEDP and PBTCA mainly hindered the growth of the (1 0 4) and (1 1 0) faces detected by XRD tests. The initial configurations of inhibitor molecules in NaCl solution on the calcite surface and the MD simulation results are shown in Figure 5. After the end of the program work, the inhibitor molecules moved to right above the calcite surface by overcoming the steric effect and their configurations were changed by a chelating effect. The E_binding values of HEDP or PBTCA with NaCl (seen in

Table 4. The binding energy (kcal/mol) of two inhibitors in NaCl on the calcite (1 0 4) and (1 1 0) surfaces.

Surface	NaCl (wt.%)	Ebinding of HEDP in NaCl	Ebinding of PBTCA in NaCl
(1 0 4)	0	22 ± 3%	26 ± 1%
	3.5	48 ± 6%	64 ± 7%
	7	60 ± 3%	83 ± 9%
	10.5	93 ± 1%	103 ± 2%
	14	123 ± 2%	137 ± 7%
	0	64 ± 7%	74 ± 2%
(1 1 0)	3.5	140 ± 6%	146 ± 1%
	7	158 ± 5%	147 ± 2%
	10.5	192 ± 4%	173 ± 5%
	14	216 ± 9%	184 ± 1%

) were greater than those in water solution, which indicated that both HEDP and PBTCA were more thermodynamically favorable to adsorb on calcite surfaces in high salinity brines.

3.6. The Effect of Inhibitors in NaCl Solutions with Different Concentrations for the Crystallization of CaCO₃

The HEDP and PBTCA molecules were optimized by B3LYP–6–31G (d) method and the optimal configurations are shown in Figure 6. It was directly seen that the distance between O (label 7) and O (label 19) of HEDP was 0.4007 nm, which is close to the distance (0.4048 nm) of neatest calcium ions on the calcite surfaces (1 1 0) and (1 0 4) [24]. The length from O (label 21) to O (label 26) and O (label 7) to O (label 9) of PBTCA were 0.5093 nm and 0.4820 nm, respectively, which were close to the distance (0.4990 nm) of nearest calcium ions on the surface of calcite (1 0 4) [24], indicating that the O atoms in HEDP or PBTCA could adsorb on Ca²⁺ and match the lattice of calcite [50]. The quantum calculation method was also used to investigate the possible structure of Ca²⁺ and inhibitor molecules. The results, as shown in Figure 6, indicated that a HEDP molecule could chelate with one Ca²⁺ ion by two phosphonate groups, while PBTCA chelated with two Ca²⁺ ions by forming chemical bonds with one phosphonate group and two carboxylic acid groups. Moreover, Zhang et al. obtained the binding energies of 19.46 and 18.75 kcal/mol for Ca²⁺ with phosphonic acid group and carboxylic acid group [51], respectively, from the theoretical DFT calculations, which implied the chelation of between HEDP, PBTCA, and Ca²⁺. It could be concluded that HEDP and PBTCA showed the inhibition effect on the deposition of CaCO₃, which was related to their chelate ability with Ca²⁺ and the capability of inducing the CaCO₃ lattice transformation from calcite to vaterite (Figure 3C,D) [52,53,54,55].

The inhibition effect of two inhibitors on CaCO₃ scale at different concentrations of NaCl (3.5 wt. %–14 wt. %) by static test is given in Table 1. The inhibition efficiencies of HEDP and PBTCA in all NaCl solutions were about twice that of the corresponding η in water. Under the optimal conditions, η of HEDP or PBTCA could reach to 83.50% and 92.16% when the concentration of NaCl was 14 wt. %. It was proved that NaCl heightens the efficiency of PBTCA and HEDP on prohibiting the scale of CaCO₃.

4. Conclusions

In summary, the delay effect of NaCl solution with extremely high concentration on the crystallization of CaCO₃ was investigated. The SR and k calculations showed that a high concentration of NaCl reduced the thermodynamic and kinetic potential of CaCO₃ crystallization. The XRD test revealed that a high concentration of NaCl impeded the growth of (1 0 4) and (1 1 0) faces of calcite while inducing the formation of the (1 1 1) face of aragonite. The ICP–OES test verified that Na⁺ could be doped into CaCO₃, resulting in the growth of crystals towards one–dimensional and forming the elongated pseudo-hexagonal crystals. It was further testified that NaCl increased the efficiency of the phosphate inhibitors on prohibiting the scale of CaCO₃. Both HEDP and PBTCA could chelate with Ca²⁺ and induced the lattice distortion of CaCO₃. At the same time, NaCl enhanced the binding energy of HEDP or PBTCA absorbed on CaCO₃ and accelerated the lattice distortion.