Nucleation and crystallization studies of CaSO_{4}.2H_{2}O were carried out under simulated conditions of scale formation in the reverse osmosis desalination technique. Equal molar ratios of CaCl_{2} and NaSO_{4} aqueous solutions were mixed with saline solution of NaCl (40 g/L). Turbidity measurements were carried out for the mixed solutions at different time intervals to determine induction period for the crystal formation of gypsum at ambient temperature (25 °C). Induction period was measured under different high supersaturation ratios ranging from 4.47 to 6.71. Induction period decreases exponentially with increasing supersaturation ratios. Free energy barrier values, critical nucleus radius and nucleation rates were calculated with and without addition of antiscalant {(scale inhibitor) [sodium hexametaphosphate (NaPO_{3})_{6}, SHMP]} using crystallization equations that relate induction period with supersaturation ratios. The radius of critical nucleus increased by about 30% with SHMP addition compared with the baseline at all the studied supersaturation ratios. Most importantly, scanning electron microscope (SEM) photomicrographs show that, the shapes of crystals of the uninhibited solutions are needle-like and plate-like crystals at supersaturation ratios of 4.47 and 6.71, respectively. Addition of 4.0 mg/L SHMP antiscalant modify the shape of crystals to be similar to that at low supersaturation ratio.

## INTRODUCTION

Calcium sulfate dihydrate (gypsum) is the major compound that forms scale on reverse osmosis (RO) membranes, followed by calcium carbonate. These scales represent a major problem in desalination with RO membrane that decreases membrane efficiency (Abdel-Aal *et al.* 2015).

Inhibitors play an important role in retarding crystallization. They change the surface properties of the crystals, so, nucleation, growth, shape of crystals and agglomeration or dispersion behavior change (Nyvlt & Ulrich 1995). In addition, basic studies of gypsum nucleation and crystal growth under simulated conditions of production of phosphoric acid industrially using pure chemicals with and without additives like crystal modifiers, inhibitors and promoters were conducted by Abdel-Aal *et al.* (1998, 2004, 2007; Abdel-Aal 2004) and El-Shall *et al.* (2000, 2002, 2005). In addition, a new finding for CaSO_{4}.2H_{2}O nucleation and crystal growth in saline solution simulated to RO desalination with and without tri-sodium phosphate (TSP) inhibitor was studied (Abdel-Aal *et al.* 2016a, 2016b).

Several studies for the effectiveness of additives in retarding the crystallization of calcium sulfate dihydrate (CaSO_{4}.2H_{2}O) from supersaturated solutions have been investigated (Rolfe 1966, Solmon & Rolfe 1966, Flint 1969, Tlili *et al.* 2008, Amjad *et al.* 2014, Bystrianský *et al.* 2016).

A large number of RO scales control chemicals like ascorbic acid, ethylene diamine tetra acetic acid, TSP, sodium nitrate, sodium hexametaphosphate (SHMP) and commercial additives like STD-100, STD-101, FM-101 were studied (Rahman 2013). The advantages of using SHMP as antiscalant are that it is cheap and highly effective against calcium sulfate and calcium carbonate based scales. Also, it's considered as a good dispersant for iron corrosion products, so it can delay their precipitation and deposition for long time intervals (Cowan & Weintritt 1976). However, SHMP has some limitations like its short shelf life because it acts as food for microorganisms and the sludge-forming orthophosphate (Butt *et al.* 1995).

The aim of this work is to study the nucleation fundamentals of CaSO_{4}.2H_{2}O using a crystallization equation that relates induction times with supersaturation ratios in a synthetic saline solution of NaCl simulating the desalination process of RO with and without SHMP additive.

### Experimental studies

Pure chemicals with high analytical grade of CaCl_{2} (Merck, Germany), NaCl (ADWIC, Egypt), Na_{2}SO_{4} (Sigma-Aldrich) and SHMP (NaPO_{3})_{6} (NICE, India), with high analytical grade were used to prepare aqueous solutions with different concentrations.

Two aqueous solutions of CaCl_{2} and Na_{2}SO_{4} were prepared with equal molar ratios of 2.0 mol/L. A 40 g amount of NaCl salt was dissolved in 1.0 L of distilled water to prepare the saline solution. A stock solution with 1,000 mg/L of SHMP was prepared. The reaction was carried out by adding equal volumes of CaCl_{2} and Na_{2}SO_{4} to 40 g/L NaCl solution, and the net volume was 100 mL. Five calcium sulfate solutions of various supersaturation ratios were prepared by mixing both calcium chloride and sodium sulfate solutions to the saline medium of 40 g/L NaCl, as shown in Table 1. SHMP was added in the range from 2 to 10 mg/L.

CaCl_{2}, mL
. | Na_{2}SO_{4}, mL
. | Saline water, 40 g/L NaCl, mL . | Water or inhibitor solution, mL . | Supersaturation ratio (S)
. |
---|---|---|---|---|

4.0 | 4.0 | 85 | 7 | 4.47 |

4.5 | 4.5 | 85 | 6 | 5.03 |

5.0 | 5.0 | 85 | 5 | 5.59 |

5.5 | 5.5 | 85 | 4 | 6.15 |

6.0 | 6.0 | 85 | 3 | 6.71 |

CaCl_{2}, mL
. | Na_{2}SO_{4}, mL
. | Saline water, 40 g/L NaCl, mL . | Water or inhibitor solution, mL . | Supersaturation ratio (S)
. |
---|---|---|---|---|

4.0 | 4.0 | 85 | 7 | 4.47 |

4.5 | 4.5 | 85 | 6 | 5.03 |

5.0 | 5.0 | 85 | 5 | 5.59 |

5.5 | 5.5 | 85 | 4 | 6.15 |

6.0 | 6.0 | 85 | 3 | 6.71 |

All experiments were carried out at ambient temperature (25 °C). Samples of the reaction mixture were withdrawn at different time intervals to measure the turbidity (NTU) using a direct reading of digital turbidimeter (2100 NA, HACH, USA).

_{4}.2H

_{2}O scale crystals were prepared according to the following equation: The supersaturation ratio (

*S*) was calculated as follows (Tavare 1995): where

*S*: supersaturation ratio,

*c*: calcium sulfate dihydrate concentration, %,

*c**: calcium sulfate dihydrate (solute) solubility under the applied conditions = 0.31 g/100 ml of saline water (40 g/L NaCl) (Abdel-Aal

*et al.*2015).

## RESULTS AND DISCUSSION

### Determination of the induction period

*t*

_{ind}) is defined as the time elapsed between achievement of supersaturation ratio by addition of reactants and appearance of nuclei. In general,

*t*

_{ind}value was determined by turbidity monitoring of supersaturated solutions. Induction period was obtained by plotting the turbidity against time of crystallization. The obtained plots at different supersaturation ratios of baseline (without SHMP antiscalant addition) are shown in Figure 1. It can be concluded that turbidity increases slowly with time followed by a sharp rise after a critical time period, producing an inflection in the curve. The time that corresponds to this inflection is referred to as the induction period as explained in Figure 1 (at

*S*= 4.47,

*t*

_{ind}= 11 minutes).

### Effect of SHMP on the induction period

_{4}.2H

_{2}O crystallization at supersaturation ratio of 5.59 was studied. The results are given in Figure 2. Addition of SHMP inhibitor shifted the plots towards longer times compared with the baseline (without SHMP addition). In addition, the induction periods increased with increasing SHMP concentration. Effect of supersaturation ratio on induction period with and without constant SHMP concentrating additions were determined and are given in Table 2.

. | Induction period, min . | |
---|---|---|

Supersaturation ratio (S) . | Without SHMP . | With SHMP . |

4.47 | 11.0 | 569 |

5.03 | 6.5 | 192 |

5.59 | 5.5 | 84 |

6.15 | 3.5 | 43 |

6.71 | 1.5 | 8 |

. | Induction period, min . | |
---|---|---|

Supersaturation ratio (S) . | Without SHMP . | With SHMP . |

4.47 | 11.0 | 569 |

5.03 | 6.5 | 192 |

5.59 | 5.5 | 84 |

6.15 | 3.5 | 43 |

6.71 | 1.5 | 8 |

### Surface energy (γ) calculation

*S*) and induction periods (

*t*

_{ind}) are correlated using the following equation (He

*et al.*1994, Izmailov

*et al.*1999, Lancia

*et al.*1999): where

*A*is an empirical constant (dimensionless) and

*B*depends on the number of variables, and is given by: where β is a geometric (shape) factor of 16π/3 for the spherical nucleus, ƒ(θ) is a correction factor; when purely homogeneous nucleation takes place ƒ(θ) = 1 and when heterogeneous nucleation occurs ƒ(θ) = 0.01.

*V*

_{m}is the molar volume (74.69 cm

^{3}mol

^{−1}for gypsum),

*T*is the absolute temperature (K) and

*R*is the gas constant (J/mol K), γ is the surface energy (J/m

^{2}),

*N*

_{A}is the Avogadro's number (mol

^{−1}) (El-Shall

*et al.*2002).

*t*

_{ind}) versus 1/log

^{2}

*S*for high supersaturation ratios of 4.47 to 6.71 with and without 4.0 mg/L SHMP are presented in Figure 5.

The surface energies were calculated from the previous correlated equation of classic homogenous nucleation theory. From Figure 5, slope = *B*/*T*^{3}, where *T* = 273 K and by applying equation of *B* values, surface energies (γ) were calculated. The calculated values of surface energies are 1.44 × 10^{−6} and 1.85 × 10^{−6} J/m^{2} without and with SHMP, respectively. It is obvious that, surface energy increases with addition of SHMP inhibitor.

### Nucleation rate (J _{s}) calculation

*J*

_{s}is the nucleation rate and

*F*is a frequency constant and is known as the pre-exponential factor and has a theoretical value of 10

^{30}(nuclei/cm

^{3}s) (Lancia

*et al.*1999, El-Shall

*et al.*2002). From the calculated value of the surface energy of gypsum crystals (γ), the nucleation rate can be calculated. The results obtained from the calculation of the nucleation rates of CaSO

_{4}.2H

_{2}O crystals with and without SHMP at high supersaturation ratios ranged from 4.47 to 6.71 and are represented in Figure 6 and Table 3. An increase in the surface energy leads to a decrease in gypsum crystal nucleation rate (Myerson 1993).

. | Nucleation rate, nuclei/cm^{3}s (J_{s}) × 10^{28}. | Free energy change for formation of critical nucleus size ΔG_{cr} × 10^{−20}, J. | ||
---|---|---|---|---|

Supersaturation ratio (S)
. | Without SHMP . | With 4.0 mg/L SHMP . | Without SHMP . | With 4.0 mg/L SHMP . |

4.47 | 0.97 | 0.004 | 1.91 | 4.20 |

5.03 | 1.86 | 0.015 | 1.64 | 3.61 |

5.59 | 2.98 | 0.043 | 1.44 | 3.18 |

6.15 | 4.27 | 0.096 | 1.30 | 2.86 |

6.71 | 5.66 | 0.179 | 1.18 | 2.60 |

. | Nucleation rate, nuclei/cm^{3}s (J_{s}) × 10^{28}. | Free energy change for formation of critical nucleus size ΔG_{cr} × 10^{−20}, J. | ||
---|---|---|---|---|

Supersaturation ratio (S)
. | Without SHMP . | With 4.0 mg/L SHMP . | Without SHMP . | With 4.0 mg/L SHMP . |

4.47 | 0.97 | 0.004 | 1.91 | 4.20 |

5.03 | 1.86 | 0.015 | 1.64 | 3.61 |

5.59 | 2.98 | 0.043 | 1.44 | 3.18 |

6.15 | 4.27 | 0.096 | 1.30 | 2.86 |

6.71 | 5.66 | 0.179 | 1.18 | 2.60 |

It is obvious that, without SHMP addition, the nucleation rate is rapidly increased with increase of supersaturation ratios, while with SHMP addition, the nucleation rate is marginally increased with increase of supersaturation ratios. Moreover, SHMP addition decreases nucleation rate at all the studied supersaturation ratios compared with the baseline (without SHMP). Low nucleation rates can be achieved either by addition of scale inhibitor or decrease the supersaturation ratio. The nucleation rates at *S* = 5.03 are 0.015 × 10^{28} nuclei/cm^{3}s and 1.86 × 10^{28} nuclei/cm^{3}s with and without 4.0 mg/L SHMP addition, respectively.

### Free energy change (ΔG _{cr}) calculation

*G*

_{cr}) calculation for the formation of critical nucleus sizes are obtained from the following Arrhenius type equation (He

*et al.*1994, Abdel-Aal

*et al.*2015): where

*K*is Boltzmann constant and

*T*is the absolute temperature.

The results for the calculation of free energy changes (Δ*G*_{cr}) are given in Table 3. These results reveal that the free energy change for formation of critical nucleus size has increased with decreasing supersaturation ratio. In parallel, it is increased with addition of SHMP at all studied supersaturation ratios. So, addition of SHMP inhibitor changes the surrounding medium around the crystals to be less supersaturated.

### Critical nucleus radius (r ) calculation

*r*) is calculated from the following equation (He

*et al.*1994, Lancia

*et al.*1999):

*i*) in the critical nucleus is calculated from the following relation (Boomadevi

*et al.*2002): The results of calculation of the radius of the critical nucleus (

*r*) and the number of molecules in the critical nucleus (

*i*) at the studied supersaturation ratios with and without 4.0 mg/L of SHMP inhibitor are represented in Table 4 and Figure 7. These results show that, the radius of the critical nucleus is decreased with increasing supersaturation ratio.

. | Radius of critical nucleus, cm × 10^{−8}. | Number of molecules in the critical nucleus . | ||
---|---|---|---|---|

Supersaturation ratio (S)
. | Without SHMP . | With 4.0 mg/L SHMP . | Without SHMP . | With 4.0 mg/L SHMP . |

4.47 | 5.66 | 7.37 | 6 | 14 |

5.03 | 5.25 | 6.84 | 5 | 11 |

5.59 | 4.93 | 6.42 | 4 | 9 |

6.15 | 4.67 | 6.08 | 4 | 8 |

6.71 | 4.46 | 5.80 | 3 | 7 |

. | Radius of critical nucleus, cm × 10^{−8}. | Number of molecules in the critical nucleus . | ||
---|---|---|---|---|

Supersaturation ratio (S)
. | Without SHMP . | With 4.0 mg/L SHMP . | Without SHMP . | With 4.0 mg/L SHMP . |

4.47 | 5.66 | 7.37 | 6 | 14 |

5.03 | 5.25 | 6.84 | 5 | 11 |

5.59 | 4.93 | 6.42 | 4 | 9 |

6.15 | 4.67 | 6.08 | 4 | 8 |

6.71 | 4.46 | 5.80 | 3 | 7 |

The radius of the critical nucleus is increased with SHMP addition by about 30% compared with the baseline at the studied supersaturation ratios. SHMP additions result in increased induction time, decreased nucleation rate and decreased growth efficiency, resulting in an increase in the critical nucleus radius.

### SEM photomicrographs of CaSO_{4}.2H_{2}O crystals

_{4}.2H

_{2}O crystals produced at low supersaturation of 4.47 and high supersaturation of 6.71 with and without 4.0 mg/L of SHMP inhibitor are shown in Figure 8.

SEM photomicrographs show that, the shapes of crystals of the baseline (without inhibitor) are needle-like and plate-like crystals at supersaturation ratios of 4.47 and 6.71, respectively. Addition of 4.0 mg/L SHMP inhibitor converts the shape of the crystals to be similar to that at low supersaturation. So, at low supersaturation with inhibitor addition the crystals are needle-like with high aspect ratio (length to width) of about 12:1 compared to aspect ratio of about 9:1 for the baseline. On the other hand, at high supersaturation ratio, most of the plate-like crystals are modified to needle-like and tabular-like crystals with addition of the inhibitor.

Nucleation and crystallization of CaSO_{4}.2H_{2}O in saline water was studied with and without SHMP as inhibitor. The results reveal that decreasing the supersaturation ratio increases the induction time, which leads to decreasing nucleation and crystal growth. Addition of SHMP inhibitor increases the induction time. So, SHMP inhibitors achieve the same behavior as decreasing the supersaturation ratio. The mechanism of inhibition of crystallization of gypsum with this inhibitor is related to decreasing the supersaturation ratio in the localized areas around the growing crystals. This mechanism of either growth or inhibition crystallization of calcium sulfate or calcium oxalate with either promoter or inhibitor is confirmed in the previously published articles (Abdel-Aal *et al.* 2004, 2009, 2016a, 2016b).

## CONCLUSION

Nucleation and crystallization of CaSO_{4}.2H_{2}O in saline water was studied with and without SHMP as inhibitor. The results reveal that SHMP increases the induction periods at all the studied supersaturation ratios due to the decrease of the rate of nucleation. The induction periods increase with decrease of the supersaturation ratio and with addition of SHMP as well. The nucleation rates at a supersaturation ratio of 5.03 are 0.015 × 10^{28} nuclei/cm^{3}s and 1.86 × 10^{28} nuclei/cm^{3} s with and without SHMP addition, respectively. The radius of the critical nucleus is increased with SHMP addition by a percentage around 30% compared with the baseline at the studied supersaturation ratios.

The number of molecules required for formation of stable nucleus is calculated to be in the range 3–6 and 7–14 molecules without and with SHMP addition, respectively. The numbers of molecules required for formation of a stable nucleus are higher at lower supersaturation ratios and with SHMP additions. SEM photomicrographs show that the shapes of crystals of the baseline (without antiscalant) are needle-like and plate-like crystals at supersaturation ratios of 4.47 and 6.71, respectively. Addition of 4.0 mg/L SHMP antiscalant converts the shape of crystals to be similar to that at low supersaturation. So, at low supersaturation with antiscalant addition the crystals are needle-like with high aspect ratio (length to width) of about 12:1 compared to aspect ratio of about 9:1 for the baseline. On the other hand, at high supersaturation ratio, most plate-like crystals are modified to needle-like and tabular-like crystals with addition of the antiscalant.