It was important to establish the scaling mechanism to slow down scaling, which is one of the important problems faced by saline wastewater treatment with falling film evaporators. In this paper, the phase equilibrium data of ternary system NaCl-CaCl2-H2O at 303.15–373.15 K were measured, and the prediction of the flow characteristics and scaling tendency of salt-containing wastewater in the evaporation tube was investigated by numerical simulation based on the phase equilibrium results. The results showed that the mesostable phase diagram of the ternary system was of simple type, and w(NaCl) and w(CaCl2) showed regular variation with temperature when w(NaCl) in the system was 15–28%. Moreover, the components of the four saline wastewaters (10% NaCl + 9, 10, 11, 12% CaCl2) with less salt content had a faster heating and a faster rate of evaporation of the liquid film in the evaporation tube. Based on the solubility in the experiments and simulations, it was concluded that NaCl crystals were precipitated at tube lengths of 718 mm, 942 mm, 966 mm, and 1,000 mm for four salt concentrations in the evaporation process by comparison, and the reliability of the predicted loci was also demonstrated by a falling film evaporation experimental setup.

  • Creatively predict scaling site based on phase equilibrium and fluid simulation.

  • Systematic study of multi-temperature phase equilibrium data for ternary systems.

  • Fine analysis of the flow characteristics of the brine in the evaporation tube.

Graphical Abstract

Graphical Abstract
Graphical Abstract

The resource utilization of high-salt wastewater could help alleviate water shortages and solve water environment problems (Badiuzzaman et al. 2017; Xu et al. 2018). In recent years, high-salt wastewater from the coal chemical industry has received widespread attention (Fang et al. 2018; Hou et al. 2019). The demand for water and the high volume of high-salt wastewater produced by the coal chemical industry seriously restricted the development of the industry (Lefebvre & Moletta 2006; Cui et al. 2017). Coal chemical wastewater was divided into high saline wastewater and organic wastewater, and its high saline wastewater salt components were mainly Na+, K+, Ca2+, Mg2+, Cl, , and , which form salts with high solubility, that are difficult to treat, polluting, and have high economic gain from reuse (Zhao & Liu 2016). Usually, most of the coal chemical wastewater was treated by a zero discharge process, and after membrane concentration, inorganic ions (Na+, Ca2+, Cl, etc.) were separated from the brine by evaporation technology (Son et al. 2021). Among the more mature evaporation technologies, multiple effect distillation (MED) and mechanical vapor recompression (MVR) were processing technologies with falling film evaporator as the core, and their excellent evaporation characteristics gave them an indispensable position in the field of desalination (Kouhikamali et al. 2014). However, high-salt wastewater may have caused equipment scaling in the evaporation process, which not only affected the heat transfer performance of the equipment but also caused a waste of resources (Zhao et al. 2019; Lu et al. 2020). Thus, it was necessary to study the problem of equipment salt scaling in coal chemical high-salt wastewater salt extraction technology to achieve more efficient recycling of inorganic salts.

In the coal chemical treatment process, the common types of scaling in evaporation tubes were particle scaling and crystallization scaling (Epstein 1979). Among them, particle scaling has been extensively studied by numerical simulation for scale formation mechanism (Najibi et al. 1997; Pääkkönen et al. 2012; Song et al. 2019), while precipitation crystalline scaling of some typical aqueous salt systems (formed by inorganic ions such as Na+, Ca2+, Cl) in coal chemical wastewater and prediction of scaling sites has not been studied enough. The formation conditions of crystallization scaling in the evaporation process depended on the supersaturation of the solution in the flow state (Belmiloudi 2011). Therefore, it was important to master the phase equilibrium relationship of the solution and the characteristics of the solution flow in the tube for the judgment of the critical conditions of the crystallization point. Many researchers had reported on the saturation of the solution and the flow characteristics under actual working conditions. Assarsson (1953) analyzed the sodium salt system at a certain temperature using phase diagrams and obtained data on the solubility of the sodium salt in different systems. With the in-depth study of the phase equilibria, Yang et al. (2010, 2011) specifically studied the solid–liquid phase equilibria of the ternary system NaCl-CaCl2-H2O at 323.15 K and 348.15 K. It was found that there were large differences in the content of the components in the system at different temperatures, and the co-saturation point was shifted. Rathgeber et al. (2019) enriched the phase equilibrium data of brines by studying the solubility phase diagram of the NaCl-CaCl2-H2O system in the undersaturated range. Lu et al. (2017) studied the solubility of sodium salt systems in multiple temperature ranges and found that the solubility of NaSO4 in coal chemical wastewater was greater in low-temperature environments than in pure water. The study of phase equilibrium in the multi-temperature range of the NaCl-CaCl2-H2O ternary system, which was typical for the coal chemical industry, had not been reported in the literature, which limited the universality of phase equilibrium data research results.

In addition, the influencing factors for fouling in different operating conditions of the evaporation process should not be neglected, which were mainly reflected in the working fluid characteristics and operating parameters (Zhao & Chen 2013). Gourdon et al. (2010) studied the evaporation process of aqueous NaCO3 and Na2SO4 solutions in a vertical falling film evaporation tube and analyzed the fouling behavior of different working fluids, and the results showed that the crystal mass distribution depended on the composition of the solution. Izadi et al. (2011) studied fouling experiments on heat exchanger tubes with different seawater samples and confirmed that the difference in fouling behavior was influenced by the different compositions of the working fluid. Lv et al. (2020) studied the fouling behavior of Na2SO4 and mixed salts in heat exchanger tubes and analyzed the effect on fouling thermal resistance at different operating parameters. The results showed that the fouling thermal resistance was determined by the variation of Na2SO4 content and solubility. Therefore, for saline wastewater with a complex multi-salt system, the increasing salt concentration in the evaporation process might cause equipment blockage and lead to dangerous accidents (K. Li et al. 2018; D. Li et al. 2018). And the phase equilibrium speculation of fouling sites in the evaporation process was a very important way to guide the solution to the scaling problem, and it was necessary to study it to tackle the problem of salt fouling prevention.

Combining the characteristics of multi-salt phase equilibrium and evaporation system, the phase equilibrium of the ternary system NaCl-CaCl2-H2O at 303.15–373.15 K was studied in this paper, taking the saline wastewater of the coal chemical industry as an example. Meanwhile, the flow characteristics of saline wastewater in a falling film evaporation tube were simulated using a multiphase flow volume of fluid (VOF) model for the prediction of tube scaling trends and verified by an experimental setup. The experimental results and simulation data provided a basis for the prevention of salt scaling problems and the purification of NaCl and CaCl2 from high-salt wastewater in the coal chemical industry.

Apparatus and reagents

The reagents used in the experiment, NaCl and CaCl2, were all from Tianjin Kemiou Chemical Reagent Co., Ltd, with purity and purity: mass fraction ≥99.0%, and both were analytical pure reagents. The water used for sample preparation and experimental process analysis was deionized water, with a pH of about 6.6 and conductivity <1 × 10−5 s · m−1. The CO2 was removed by boiling before use.

The instruments used in the experiment were an electronic balance (AL104, Mettler-Toledo Company, accuracy 1.0 × 10−4 g); ultra-pure water machine (UPT-II-20T, Sichuan Youpu Ultra-pure Technology Co., Ltd); precision constant temperature air blowing drying oven (DHG-9053J, Shanghai Sanfa Scientific Instrument Co., Ltd); digital density meter (JL3002LD, Guangzhou Techland Materials Technology Co., Ltd, accuracy 2.0 × 10−4 g · cm−3); constant temperature water bath oscillator (THZ-82, Changzhou Zhibo Instrument Manufacturing Co., Ltd, accuracy ±0.1 °C); and X-ray powder diffractometer (XRD, D8 Advance, Bruck, Germany).

Experimental methods

The salt components of high-salt wastewater of the coal chemical industry were mainly Na+, K+, Ca2+, Mg2+, Cl, , and , among which the cations were Na+, Ca2+, and the anions were mainly Cl. Therefore, in this paper, the isothermal solution equilibrium method was used to study the solubility data of the ternary system NaCl-CaCl2-H2O (Bian et al. 2018; K. Li et al. 2018; D. Li et al. 2018). According to the common saturation point of the ternary system, experimental points were selected to calculate its composition, and the samples were accurately weighed and put into glass bottles, deionized water was added, sealed, and placed in a constant temperature water bath oscillator in the temperature range of 303.15–373.15 K (in the vibration state). Whereafter, the supernatant was removed periodically, weighed and recorded, and then chemically analyzed until the equilibrium standard was reached when the content of each chemical component remained constant. The equilibrated liquid phase and wet slag were chemically analyzed and the density of the liquid phase was determined using a digital densitometer, while the equilibrated solid phase was identified by an XRD.

Analytical method

The Cl ion concentration was measured by titration with a standard solution of silver nitrate under near-neutral conditions with an indicator of potassium chromate (Sheykhi & Moore 2012) with a relative error ≤± 0.3%. In the presence of ammonia buffer solution and chromium black T indicator, Ca2+ concentration was measured by EDTA standard solution (Deng & Li 2008) with a relative error ≤± 0.4%. According to the electric neutrality of electrolyte solution, the concentration of Na+ ions was calculated by the subtraction method (Yang et al. 2015). Balance determination was carried out for each group of samples three times, and the results were averaged to ensure the accuracy of the determination results.

Numerical simulation

  • (1)

    Mathematical models of flow and heat transfer

There were three types of multiphase flow models in numerical simulation, including the VOF model (Liu et al. 2020), mixture model (González-Teruel et al. 2020), and Eulerian model (Dolejší & Svärd 2020). Among them, the VOF model was a surface tracing method under a fixed Eulerian grid, where different fluid components were traced by solving the same momentum set equation for the volume fraction of each fluid phase (Yang et al. 2008). The VOF model was suitable for multiple flow processes (e.g., stratified flow) that required one or more interfluent fluid interfaces, and the evaporation process of falling film in a vertical tube belonged to the category of the stratified free-surface flow of gas–liquid two-phase, so the VOF model was used to simulate the formation of falling film in a vertical tube.

The VOF model defined the volume fraction of the fluid phase α such that the sum of the volume fractions αb of the different phases in each control volume was 1:
formula
(1)
In this paper, n = 2, b was the liquid phase (L) or gas phase (G), and the sum of the two gas volume fractions was 1. The viscosity μ and density ρ of each control body could be derived from the following equations:
formula
(2)
formula
(3)
Then the continuity equation (Yang et al. 2008) for the volume fraction of each phase was as follows:
formula
(4)
where ρ was the density of the fluid, t and were the time and velocity vectors, respectively. The mass source term was . In the cold film formation process (no phase change) was zero. However, in the evaporative down film process (where the mass transfer occurred between the gas and liquid), the mass transfer was the mass source term .
Using the same velocity field for both gas-liquid phases in each control body, the momentum equation (Pu et al. 2019) was as follows:
formula
(5)
where p, μ, and T were the pressure, viscosity, and temperature, respectively. Here, and F were the gravitational acceleration and volume force source terms, respectively.
The temperature field variables in the gas-liquid phase in the control body were given by the energy equation (Liu et al. 2020):
formula
(6)
Here, E, keff, and Q were the energy, effective heat transfer coefficient, and fluid source terms, respectively.
According to the characteristics of the high-flow descending film in the tube, the RNG k-ɛ model was chosen as the turbulence model in this paper (Victor & Steven 1986). The turbulent viscosity μt was influenced by the turbulent energy K and turbulent dissipation rate ɛ.
formula
(7)
where the turbulent energy equation K was as follows:
formula
(8)
where αk, μeff, and Gk were the turbulent Prandtl number, effective viscosity, and turbulent kinetic energy generated by laminar velocity, respectively. Here Gb, ε, and YM were the turbulent kinetic energy, turbulent kinetic energy dissipation rate, and waves generated by transition diffusion incompressible turbulence, respectively.
The turbulent dissipation rate equation ε was:
formula
(9)
where , and were constants, and R was a user-defined parameter.
The convective heat transfer coefficient of the liquid film can be obtained from Newton's cooling equation as follows:
formula
(10)
where Tw, Tm, and qw were the wall temperature, the average liquid film temperature, and the heat flow density, respectively.
The equation for heat flow density was as follows:
formula
(11)

Here, QL was the heat flow rate.

  • (2)

    Physical model construction and determination of boundary conditions

The falling film evaporation tube was modeled by 3D modeling software, and its structural parameters are shown in Table 1.

  • (3)

    Problem assumptions and solution settings

Table 1

Model structure parameter

ParameterValue (mm)
The length of the falling film evaporation tube 1,000 
The internal diameter of the falling film evaporation tube 40 
The internal diameter of the distributor 30 
The height of the liquid distributor 23 
The wall thickness of the falling film evaporation tube 
The gap between distributor and tube wall 1.5 
ParameterValue (mm)
The length of the falling film evaporation tube 1,000 
The internal diameter of the falling film evaporation tube 40 
The internal diameter of the distributor 30 
The height of the liquid distributor 23 
The wall thickness of the falling film evaporation tube 
The gap between distributor and tube wall 1.5 

In this study, the model was simplified with the following main assumptions: the pressure applied to the cross-section inside the evaporation tube was uniform; the effect of vapor on the falling film inside the tube can be neglected; the thermodynamic equilibrium was maintained inside the evaporation tube; and the mixture of NaCl and CaCl2 was an incompressible Newtonian fluid. In addition, the solution settings for the numerical simulation are shown in Table 2.

  • (4)

    Independence detection

Table 2

Boundary conditions and solver parameters

Boundary conditions/solver parametersSetting
Inlet Velocity inlet 
Outlet Outflow 
The evaporation model UDF 
Multiphase flow model VOF 
Turbulent flow model RNG k-ɛ 
Pressure–velocity coupling SIMPLE 
Discretization scheme of pressure PRESTO! 
Discretization scheme of volume fraction and momentum QUICK 
Boundary conditions/solver parametersSetting
Inlet Velocity inlet 
Outlet Outflow 
The evaporation model UDF 
Multiphase flow model VOF 
Turbulent flow model RNG k-ɛ 
Pressure–velocity coupling SIMPLE 
Discretization scheme of pressure PRESTO! 
Discretization scheme of volume fraction and momentum QUICK 

The physical model of the evaporation tube was drawn according to the structural parameters of the model in Table 1, and the physical model was meshed as shown in Figure 1. To reduce the error of numerical simulation, this paper simulated the models with the number of networks of 99,584, 260,162, 319,875, 427,855, 596,554, 896,951, and 1,630,536, and compared the film thickness distribution at 500 mm in the axial direction. From Figure 2, it could be obtained that the difference in liquid film thickness was small when the number of networks exceeded 590,000. To save computing time, 596,554 grids were selected at this time.
Figure 1

Physical model and meshing diagram.

Figure 1

Physical model and meshing diagram.

Close modal
Figure 2

Film thickness distribution of different mesh numbers.

Figure 2

Film thickness distribution of different mesh numbers.

Close modal

Study on phase equilibrium of the NaCl-CaCl2-H2O ternary system

Solubility data had been reported for binary systems (NaCl-H2O, CaCl2-H2O) at different temperatures. As shown in Table 3, the solubility data of the experimental data in this paper and the binary system in the literature are listed, and the experimental methods and data in this paper were found to be reliable by comparison.

Table 3

Mass fraction solubility (w) of saturated solutions in pure water at different temperatures, p = 0.1 MPa

NoT/KNaCl-H2O
CaCl2-H2O
ReferenceThis workReferenceThis work
S/(wt%)S/(wt%)
303.15 26.50 Chawong et al. (2017)  26.53 – – 
313.15 26.77 Li et al. (2011)  26.88 – – 
323.15 26.90 Ge et al. (2020)  26.95 56.34 Yang et al. (2010)  56.35 
NoT/KNaCl-H2O
CaCl2-H2O
ReferenceThis workReferenceThis work
S/(wt%)S/(wt%)
303.15 26.50 Chawong et al. (2017)  26.53 – – 
313.15 26.77 Li et al. (2011)  26.88 – – 
323.15 26.90 Ge et al. (2020)  26.95 56.34 Yang et al. (2010)  56.35 

The equilibrium liquid phase composition, wet slag composition, physical and chemical properties density, and equilibrium solid phase composition for the ternary system NaCl-CaCl2-H2O at temperatures 303.15–373.15 K are listed in Table 4.

Table 4

Solid–liquid equilibrium composition and physicochemical properties of the NaCl-CaCl2-H2O ternary system (T = (303.15 to 373.15) K, p = 0.1 MPaa)

T/KNo.Liquid phase, 100w
Wet residue, 100w
DensityEquilibrium solid phased
100w1b100w2100w1100w2ρ g/cm−3
303.15 26.53 NDc ND 1.1917 NC 
23.76 4.26 70.56 70.56 1.2082 NC 
21.23 6.92 64.6 64.6 1.2120 NC 
15.23 13.26 58.77 58.77 1.2215 NC 
11.78 18.22 53.08 53.08 1.2390 NC 
5.89 25.64 46.16 46.16 1.2598 NC 
3.73 28.67 43 43 1.2694 NC 
2.22 34.2 38.82 38.82 1.3114 NC 
1.53 37.2 33.37 33.37 1.3356 NC 
10 0.68 43.71 14.01 14.01 1.3655 NC 
11 0.3 48.6 13.73 49.11 1.4450 NC + CC6 
12 49.9 ND ND 1.4557 CC6 
313.15 26.88 ND ND 1.1882 NC 
23.57 5.10 74.51 1.74 1.2088 NC 
21.16 7.74 69.67 2.95 1.2126 NC 
14.85 14.1 65.29 5.86 1.2199 NC 
12.32 18.37 59.08 8.67 1.2389 NC 
5.78 26.08 52.3 13.48 1.2570 NC 
3.88 28.37 47.78 15.57 1.2632 NC 
3.23 32.29 43.15 18.84 1.3004 NC 
2.59 36.24 35.31 24.39 1.3199 NC 
10 1.82 41.37 23.51 32.08 1.3730 NC 
11 1.00 52.53 17.39 54.93 1.4869 NC + CC4 
12 53.69 ND ND 1.4892 CC4 
323.15 27.01 ND ND 1.1850 NC 
23.4 6.12 84.14 1.27 1.2120 NC 
21.05 9.11 72.88 3.14 1.2219 NC 
15.94 13.92 69.03 5.18 1.2270 NC 
11.94 19.99 63.17 8.55 1.2522 NC 
5.54 27.03 57.18 12.15 1.2668 NC 
3.40 33.68 50.74 17.25 1.3130 NC 
2.33 37.66 37.8 23.95 1.3446 NC 
1.85 42.09 25.59 31.99 1.3850 NC 
10 1.25 48.81 21.29 38.77 1.4520 NC 
11 1.05 54.51 8.49 58.99 1.5132 NC + CC2 
12 56.35 ND ND 1.5240 CC2 
333.15 27.21 ND ND 1.1817 NC 
23.15 6.53 73.69 2.21 1.2105 NC 
20.55 9.96 71.69 3.53 1.2221 NC 
15.64 14.51 62.07 6.48 1.2253 NC 
11.81 20.97 57.04 10.27 1.2567 NC 
8.48 24.25 52.28 12.54 1.2610 NC 
4.85 28.41 45.42 16.24 1.2715 NC 
3.15 38.78 38.6 24.75 1.3642 NC 
2.16 45.93 31.28 32.3 1.4339 NC 
10 1.08 51.41 28.81 36.91 1.4866 NC 
11 0.64 54.37 10.20 58.66 1.5170 NC + CC2 
12 57.80 ND ND 1.5522 CC2 
343.15 27.35 ND ND 1.1781 NC 
23.25 6.95 83.58 1.27 1.2120 NC 
20.45 10.65 80.47 3.14 1.2263 NC 
15.5 15.02 77.65 5.18 1.2295 NC 
12.3 20.99 70.11 8.55 1.2609 NC 
7.87 24.37 62.48 12.15 1.2584 NC 
4.92 30.07 41.21 17.25 1.2922 NC 
3.05 40.73 29.19 23.95 1.3912 NC 
2.27 50.3 27.63 31.99 1.4973 NC 
10 1.05 57.06 16.66 48.05 1.5681 NC 
11 0.30 57.76 12.28 62.08 1.5690 NC + CC2 
12 58.69 ND ND 1.5785 CC2 
353.15 27.75 ND ND 1.1750 NC 
23.09 7.74 79.39 2.11 1.2149 NC 
20.3 11.39 74.92 3.53 1.2284 NC 
15.44 15.46 69.42 5.62 1.2302 NC 
12.73 21.29 62.83 9.25 1.2690 NC 
7.56 25.39 57.3 11.76 1.2689 NC 
4.85 31.09 36.31 20.88 1.3070 NC 
2.82 42.03 21.72 34.13 1.4135 NC 
2.01 52.06 16.91 43.98 1.5290 NC 
10 1.23 56.89 29.83 40.44 1.5855 NC 
11 0.28 58.01 10.36 63.44 1.5907 NC + CC2 
12 59.50 ND ND 1.6068 CC2 
363.15 27.92 ND ND 1.1717 NC 
23.16 7.78 77.09 2.42 1.2130 NC 
20.26 12.15 67.99 4.86 1.2348 NC 
15.35 15.98 61.39 7.29 1.2340 NC 
12.09 21.41 56.37 10.68 1.2642 NC 
7.97 25.31 51.88 13.29 1.2715 NC 
5.46 30.76 42.92 18.62 1.3113 NC 
2.97 43.26 31.3 30.53 1.4359 NC 
1.95 53.16 26.46 39.85 1.5538 NC 
10 1.06 57.1 21.46 45.41 1.5989 NC 
11 0.25 58.5 12.98 60.39 1.6102 NC + CC2 
12 60.4 ND ND 1.6338 CC2 
373.15 28.15 ND ND 1.1686 NC 
23.37 8.13 74.55 7.12 1.2149 NC 
20.31 12.59 61.87 13.35 1.2383 NC 
15.3 16.47 52.21 21.8 1.2368 NC 
12.51 21.59 37.51 34.95 1.2705 NC 
7.56 26.01 29.82 41.41 1.2772 NC 
4.95 33.1 15.7 61.7 1.3360 NC 
3.09 44.28 85.18 1.64 1.4565 NC 
1.82 54.82 82.84 2.74 1.5870 NC 
10 0.95 58.29 81.15 3.66 1.6271 NC 
11 0.20 60.05 8.49 58.8 1.6440 NC + CC2 
12 61.30 ND ND 1.6608 CC2 
T/KNo.Liquid phase, 100w
Wet residue, 100w
DensityEquilibrium solid phased
100w1b100w2100w1100w2ρ g/cm−3
303.15 26.53 NDc ND 1.1917 NC 
23.76 4.26 70.56 70.56 1.2082 NC 
21.23 6.92 64.6 64.6 1.2120 NC 
15.23 13.26 58.77 58.77 1.2215 NC 
11.78 18.22 53.08 53.08 1.2390 NC 
5.89 25.64 46.16 46.16 1.2598 NC 
3.73 28.67 43 43 1.2694 NC 
2.22 34.2 38.82 38.82 1.3114 NC 
1.53 37.2 33.37 33.37 1.3356 NC 
10 0.68 43.71 14.01 14.01 1.3655 NC 
11 0.3 48.6 13.73 49.11 1.4450 NC + CC6 
12 49.9 ND ND 1.4557 CC6 
313.15 26.88 ND ND 1.1882 NC 
23.57 5.10 74.51 1.74 1.2088 NC 
21.16 7.74 69.67 2.95 1.2126 NC 
14.85 14.1 65.29 5.86 1.2199 NC 
12.32 18.37 59.08 8.67 1.2389 NC 
5.78 26.08 52.3 13.48 1.2570 NC 
3.88 28.37 47.78 15.57 1.2632 NC 
3.23 32.29 43.15 18.84 1.3004 NC 
2.59 36.24 35.31 24.39 1.3199 NC 
10 1.82 41.37 23.51 32.08 1.3730 NC 
11 1.00 52.53 17.39 54.93 1.4869 NC + CC4 
12 53.69 ND ND 1.4892 CC4 
323.15 27.01 ND ND 1.1850 NC 
23.4 6.12 84.14 1.27 1.2120 NC 
21.05 9.11 72.88 3.14 1.2219 NC 
15.94 13.92 69.03 5.18 1.2270 NC 
11.94 19.99 63.17 8.55 1.2522 NC 
5.54 27.03 57.18 12.15 1.2668 NC 
3.40 33.68 50.74 17.25 1.3130 NC 
2.33 37.66 37.8 23.95 1.3446 NC 
1.85 42.09 25.59 31.99 1.3850 NC 
10 1.25 48.81 21.29 38.77 1.4520 NC 
11 1.05 54.51 8.49 58.99 1.5132 NC + CC2 
12 56.35 ND ND 1.5240 CC2 
333.15 27.21 ND ND 1.1817 NC 
23.15 6.53 73.69 2.21 1.2105 NC 
20.55 9.96 71.69 3.53 1.2221 NC 
15.64 14.51 62.07 6.48 1.2253 NC 
11.81 20.97 57.04 10.27 1.2567 NC 
8.48 24.25 52.28 12.54 1.2610 NC 
4.85 28.41 45.42 16.24 1.2715 NC 
3.15 38.78 38.6 24.75 1.3642 NC 
2.16 45.93 31.28 32.3 1.4339 NC 
10 1.08 51.41 28.81 36.91 1.4866 NC 
11 0.64 54.37 10.20 58.66 1.5170 NC + CC2 
12 57.80 ND ND 1.5522 CC2 
343.15 27.35 ND ND 1.1781 NC 
23.25 6.95 83.58 1.27 1.2120 NC 
20.45 10.65 80.47 3.14 1.2263 NC 
15.5 15.02 77.65 5.18 1.2295 NC 
12.3 20.99 70.11 8.55 1.2609 NC 
7.87 24.37 62.48 12.15 1.2584 NC 
4.92 30.07 41.21 17.25 1.2922 NC 
3.05 40.73 29.19 23.95 1.3912 NC 
2.27 50.3 27.63 31.99 1.4973 NC 
10 1.05 57.06 16.66 48.05 1.5681 NC 
11 0.30 57.76 12.28 62.08 1.5690 NC + CC2 
12 58.69 ND ND 1.5785 CC2 
353.15 27.75 ND ND 1.1750 NC 
23.09 7.74 79.39 2.11 1.2149 NC 
20.3 11.39 74.92 3.53 1.2284 NC 
15.44 15.46 69.42 5.62 1.2302 NC 
12.73 21.29 62.83 9.25 1.2690 NC 
7.56 25.39 57.3 11.76 1.2689 NC 
4.85 31.09 36.31 20.88 1.3070 NC 
2.82 42.03 21.72 34.13 1.4135 NC 
2.01 52.06 16.91 43.98 1.5290 NC 
10 1.23 56.89 29.83 40.44 1.5855 NC 
11 0.28 58.01 10.36 63.44 1.5907 NC + CC2 
12 59.50 ND ND 1.6068 CC2 
363.15 27.92 ND ND 1.1717 NC 
23.16 7.78 77.09 2.42 1.2130 NC 
20.26 12.15 67.99 4.86 1.2348 NC 
15.35 15.98 61.39 7.29 1.2340 NC 
12.09 21.41 56.37 10.68 1.2642 NC 
7.97 25.31 51.88 13.29 1.2715 NC 
5.46 30.76 42.92 18.62 1.3113 NC 
2.97 43.26 31.3 30.53 1.4359 NC 
1.95 53.16 26.46 39.85 1.5538 NC 
10 1.06 57.1 21.46 45.41 1.5989 NC 
11 0.25 58.5 12.98 60.39 1.6102 NC + CC2 
12 60.4 ND ND 1.6338 CC2 
373.15 28.15 ND ND 1.1686 NC 
23.37 8.13 74.55 7.12 1.2149 NC 
20.31 12.59 61.87 13.35 1.2383 NC 
15.3 16.47 52.21 21.8 1.2368 NC 
12.51 21.59 37.51 34.95 1.2705 NC 
7.56 26.01 29.82 41.41 1.2772 NC 
4.95 33.1 15.7 61.7 1.3360 NC 
3.09 44.28 85.18 1.64 1.4565 NC 
1.82 54.82 82.84 2.74 1.5870 NC 
10 0.95 58.29 81.15 3.66 1.6271 NC 
11 0.20 60.05 8.49 58.8 1.6440 NC + CC2 
12 61.30 ND ND 1.6608 CC2 

aStandard uncertainties, u: u(w1) = 0.002, u(w2) = 0.004, u(T) = 0.1 K and u(P) = 10 kPa.

bw1, NaCl mass fraction; w2, CaCl2 mass fraction.

cND, not determined.

dNC: NaCl; CC2: CaCl2·2H2O; CC4: CaCl2· 4H2O; CC6: CaCl2·6H2O.

Based on the solid–liquid equilibrium data in Table 4, the equilibrium data of this ternary system at different temperatures were plotted, as shown in Figure 3.
Figure 3

Equilibrium data diagram of NaCl-CaCl2-H2O ternary system at T = (303.15 − 373.15) K. (a) Equilibrium phase diagram of the NaCl-CaCl2-H2O ternary system. (b) Equilibrium data of the ternary system.

Figure 3

Equilibrium data diagram of NaCl-CaCl2-H2O ternary system at T = (303.15 − 373.15) K. (a) Equilibrium phase diagram of the NaCl-CaCl2-H2O ternary system. (b) Equilibrium data of the ternary system.

Close modal

Figure 3(a) and (b) show the equilibrium phase diagram and equilibrium data of the NaCl-CaCl2-H2O ternary system at temperatures of 303.15–373.15 K, respectively. Combining Figure 3(a) and (b), it can be seen that w(NaCl) gradually decreased as w(CaCl2) increased in the equilibrium system. This was because the dissolution of CaCl2 in saturated NaCl solution led to an increase in the concentration of Cl, which was influenced by the homoionic effect and shifted the dissolution equilibrium of NaCl, resulting in a gradual decrease in w(NaCl).

The solubilities of NaCl and CaCl2 increased slightly with the increase in temperature and the solubility curves shifted. And at w(NaCl) = 15–28%, w(NaCl) and w(CaCl2) showed regular changes with temperature (see Figure 3(b)). This was mainly because of two positive soluble salts containing the same anion, when the content of one salt was relatively low, the effect of temperature on dissolution was greater than the effect of the same ion.

Figure 4 shows a schematic diagram of the ternary system NaCl–CaCl2-H2O. Points A and C represent the binary co-saturation points of NaCl-H2O and CaCl2-H2O, respectively. And point B is the co-saturation point of the NaCl-CaCl2-H2O ternary system (the XRD pattern is shown in Figure 5). Meanwhile, the phase diagram consists of one co-saturation point, two dissolution curves, one unsaturated region, and three crystallization regions. AB and BC are the solubility univariate curves of NaCl and CaCl2. In addition, Zone I is the unsaturated zone of NaCl and CaCl2, where no crystallization occurs. Zones II, III, and IV are the crystallization zones of CaCl2·nH2O(n = 2,4,6), NaCl + CaCl2·nH2O(n = 2,4,6), and NaCl, respectively. Among them, the crystalline region of NaCl is larger than that of CaCl2, indicating that NaCl had a better crystallization ability than CaCl2 in this system.
Figure 4

Schematic diagram of the NaCl-CaCl2-H2O ternary system.

Figure 4

Schematic diagram of the NaCl-CaCl2-H2O ternary system.

Close modal
Figure 5

X-ray diffraction patterns of co-saturation points.

Figure 5

X-ray diffraction patterns of co-saturation points.

Close modal
As can be seen from Figure 6, the density of the system at the same temperature decreased rapidly with the increase of w(NaCl), and then tended to level off. This was because the density of the equilibrium system was mainly influenced by the content of CaCl2; with the increase of w(NaCl), w(CaCl2) decreased correspondingly, and the density of the system decreased rapidly. Compared with the other components, the density of saturated NaCl solution at T = 373.15 K was the smallest at 1.1686 g·cm−3, while the density of saturated CaCl2 solution at T = 373.15 K was the largest at 1.6608 g·cm−3, which indicated that the density of the system at different temperatures was mainly affected by temperature, but the density of saturated NaCl solution didn't change significantly at different temperatures.
Figure 6

Density diagram of NaCl-CaCl2-H2O ternary system at different temperatures.

Figure 6

Density diagram of NaCl-CaCl2-H2O ternary system at different temperatures.

Close modal

Numerical simulation analysis of the flow characteristics of the ternary system NaCl-CaCl2-H2O in the evaporation tube

Based on the specific parameters of physical properties of brine (Sharqawy et al. 2011), the physical parameters (density, specific heat, thermal conductivity and viscosity) of four saline wastewaters (10% NaCl + 9, 10, 11 and 12% CaCl2) at different temperatures were fitted in this paper, as shown in Table 5, where x was the temperature and y was the value of physical parameters at different temperatures. The physical properties of the four saline wastewaters were imported into Fluent software and the solver parameters (see Table 2) were set for the numerical simulation of the evaporation process.

Table 5

Equations for fitting physical properties parameters of saline wastewater with different components

Physical Parameter SystemDensity ρ g/cm−3Specific heat Cp J/(Kg·K)Thermal conductivity λ W/(m·K)Viscosity μ (Pa·s)
10% NaCl + 9%CaCl2 y = −2305.41091 + 41.44078x − 0.18894x2 + 0.000382233x3–0.00000029274x4 y = 3629.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 9.24264 − 0.10747x + 0.000481945x2 − 0.000000946721x3 + 0.000000000690216x4 y = 0.00185/(1 + 0.01664*(x − 273.15) + 0.000774987*(x − 273.15)*(x − 273.15)) 
10% NaCl + 10%CaCl2 y = 1945.24704 − 11.39017x + 0.05731x2 − 0.000127232x3 + 0.000000101645x4 y = 4302.46344 − 14.21445x + 0.08166x2 − 0.000183988x3 + 0.000000152972x4 y = 0.00557 − 0.00441x + 0.0000522921x2 − 0.000000153605x3 + 0.000000000143415x4 y = 0.00237/(1 + 0.04582*(x − 273.15) + 0.000256838*(x − 273.15)*(x − 273.15)) 
10% NaCl + 11%CaCl2 y = −7075.9821 + 100.98704x − 0.46569x2 + 0.000951034x3 − 0.000000729282x4 y = 3589.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 3.65433 − 0.0411x + 0.000187112x2 − 0.000000365954x3 + 0.000000000262311x4 y = 0.00241/(1 + 0.04014*(x − 273.15) + 0.000142605*(x − 273.15)*(x − 273.15)) 
10% NaCl + 12%CaCl2 y = −162.41315 + 14.83451x − 0.06402x2 + 0.000121263x3 − 0.0000000884544x4 y = 3574.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 2.43073 − 0.02547x + 0.0001125x2 − 0.000000208281x3 + 0.000000000137839x4 y = 0.00263/(1 + 0.04605*(x − 273.15) + 0.00000678246*(x − 273.15)*(x − 273.15)) 
Physical Parameter SystemDensity ρ g/cm−3Specific heat Cp J/(Kg·K)Thermal conductivity λ W/(m·K)Viscosity μ (Pa·s)
10% NaCl + 9%CaCl2 y = −2305.41091 + 41.44078x − 0.18894x2 + 0.000382233x3–0.00000029274x4 y = 3629.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 9.24264 − 0.10747x + 0.000481945x2 − 0.000000946721x3 + 0.000000000690216x4 y = 0.00185/(1 + 0.01664*(x − 273.15) + 0.000774987*(x − 273.15)*(x − 273.15)) 
10% NaCl + 10%CaCl2 y = 1945.24704 − 11.39017x + 0.05731x2 − 0.000127232x3 + 0.000000101645x4 y = 4302.46344 − 14.21445x + 0.08166x2 − 0.000183988x3 + 0.000000152972x4 y = 0.00557 − 0.00441x + 0.0000522921x2 − 0.000000153605x3 + 0.000000000143415x4 y = 0.00237/(1 + 0.04582*(x − 273.15) + 0.000256838*(x − 273.15)*(x − 273.15)) 
10% NaCl + 11%CaCl2 y = −7075.9821 + 100.98704x − 0.46569x2 + 0.000951034x3 − 0.000000729282x4 y = 3589.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 3.65433 − 0.0411x + 0.000187112x2 − 0.000000365954x3 + 0.000000000262311x4 y = 0.00241/(1 + 0.04014*(x − 273.15) + 0.000142605*(x − 273.15)*(x − 273.15)) 
10% NaCl + 12%CaCl2 y = −162.41315 + 14.83451x − 0.06402x2 + 0.000121263x3 − 0.0000000884544x4 y = 3574.44689 − 5.54014x + 0.04136x2 − 0.000101021x3 + 0.0000000891147x4 y = 2.43073 − 0.02547x + 0.0001125x2 − 0.000000208281x3 + 0.000000000137839x4 y = 0.00263/(1 + 0.04605*(x − 273.15) + 0.00000678246*(x − 273.15)*(x − 273.15)) 

Simulation of flow characteristics of saline wastewater and prediction of scaling tendency

In this paper, the flow and scaling trends of the four saline wastewaters (10% NaCl + 9, 10, 11, 12% CaCl2) in evaporation tubes were calculated. Firstly, numerical simulations were performed for the saline wastewater at an inlet temperature of T0 = 303.15 K, a wall temperature of TW = 380.15 K, and an inlet velocity of V0 = 0.1365 m/s. However, the temperature variation of the saline wastewater inside the tube directly affected the evaporation rate of the liquid film. The temperature distribution of the liquid film for different components in the evaporation tube is shown in Figure 7.
Figure 7

Liquid film temperature graph in the evaporation tube. (a) Axial temperature distribution of liquid film inside the tube. (b) Liquid film temperature distribution of saline wastewater (10% NaCl + 9% CaCl2) at 2 mm from the wall.

Figure 7

Liquid film temperature graph in the evaporation tube. (a) Axial temperature distribution of liquid film inside the tube. (b) Liquid film temperature distribution of saline wastewater (10% NaCl + 9% CaCl2) at 2 mm from the wall.

Close modal

Figure 7(a) depicts the distribution of the liquid film temperature along the tube length for the four saline wastewaters at a tube wall heating temperature of 380.15 K.

It can be seen that the axial temperature of the saline wastewater in the tube first increased rapidly and then tends to stabilize, which was because the temperature difference between the liquid film and the heating wall of the tube at the entrance was large, resulting in a large heat transfer rate and a rapid increase in the liquid film temperature. When the temperature difference between the liquid film and the heating wall of the tube decreased, the heat transfer rate became smaller and the growth rate became slower. In contrast, the highest temperature at the outlet of different components was 377 K and the lowest temperature was 370 K. The main reason was that the lower the salt content of the wastewater, the higher its thermal conductivity, and the faster the temperature in the evaporation tube will rise.

Figure 7(b) shows the temperature diagram of the liquid film at 2 mm from the wall for the saline wastewater (10% NaCl + 9% CaCl2). It can be seen that the temperature of this component at the inlet containing saline wastewater near the wall increased rapidly, which indicated that the liquid film near the wall was the main region in the heat transfer process. In addition, in the area containing the presence of vapor in the evaporation tube (0.5–2 mm radial range), the temperature changes didn't differ much.

Figure 8(a) shows the volume fraction of liquid along the tube length for the four saline wastewaters, and Figure 8(b) shows the volume fraction cloud of liquid along the tube length for the 10% NaCl + 9% CaCl2 fraction. Combining Figures 8(a) and (b), it can be seen that the volume fraction of the liquid decreased sharply after the saline wastewater enters the evaporation tube. This was due to the large temperature difference between the liquid and the heating wall. Subsequently, the volume fraction of the liquid showed a relatively stable state during its downward flow due to the influence of heat transfer from the wall and the presence of steam. And then, in the range of tube length of 600–1,000 mm, the liquid film temperature reached about 373.15 K, and the liquid evaporation rate was accelerated, leading to a rapid decrease in the liquid volume fraction. In addition, the liquid volume fraction of saline wastewater 10% NaCl + 9% CaCl2 at the outlet was the smallest, with a minimum value of 0.39.
Figure 8

Volume fraction distribution of liquid in the evaporation tube. (a) The liquid volume fraction of different components in the tube. (b) Cloud plot of liquid volume fraction of saline wastewater (10% NaCl + 9% CaCl2) along the length of the tube.

Figure 8

Volume fraction distribution of liquid in the evaporation tube. (a) The liquid volume fraction of different components in the tube. (b) Cloud plot of liquid volume fraction of saline wastewater (10% NaCl + 9% CaCl2) along the length of the tube.

Close modal
Figure 9(a) and (b) shows the variation of w(NaCl) and w(CaCl2) with the tube length in the four saline wastewaters. The w(NaCl) and w(CaCl2) of the four saline wastewaters increased with increasing tube length, with w0(NaCl) = 10%, w0(CaCl2) = 9%, 10, 11, and 12% at the inlet. In comparison, the salt-containing wastewater (10% NaCl + 9% CaCl2) should have a relative w(CaCl2) of 13.11 and 15.06% at tube lengths of 100 and 600 mm, exceeding the w(CaCl2) of the other components. This was because the lower the salt content of the component, its high thermal conductivity, and liquid film evaporation rate, the mass fraction of each substance in the component increased rapidly.
Figure 9

Variation of w(NaCl) and w(CaCl2) with tube length in different components of the evaporation tube. (a) Mass fraction of NaCl in saline wastewater. (b) Mass fraction of CaCl2 in saline wastewater.

Figure 9

Variation of w(NaCl) and w(CaCl2) with tube length in different components of the evaporation tube. (a) Mass fraction of NaCl in saline wastewater. (b) Mass fraction of CaCl2 in saline wastewater.

Close modal
Based on the equilibrium data of the NaCl-CaCl2-H2O ternary system (Figure 3) and the simulation of the flow characteristics of the salt-containing wastewater (Figure 9), the solubility of w(NaCl) and w(CaCl2) in the experiment and simulation were compared, and the scaling trends of the four salt-containing wastewaters in the evaporation tube were obtained as shown in Figure 10.
Figure 10

The scaling trend of saline wastewater in the evaporation tube.

Figure 10

The scaling trend of saline wastewater in the evaporation tube.

Close modal

According to the results in Figure 10, the salt-containing wastewater (10% NaCl + 9, 10, 11, 12% CaCl2) evaporated continuously during the evaporation process leading to the increase in salt concentration, and, finally, the salt-containing wastewater precipitated NaCl crystals at 718 mm, 942 mm, 966 mm and 1,000 mm in the tube, respectively. Among them, at the crystallization points A, B, C, and D, w(NaCl) was 16%, and the corresponding w(CaCl2) was greater than the phase equilibrium data of the system when the salt-containing wastewater reached the crystallization conditions and the crystallization ability of NaCl was better than CaCl2, and thus NaCl crystallized and precipitated. For the wastewater with lower salt content, its thermal conductivity was higher, the liquid volume fraction decreased faster, and crystallization occurred earlier in the evaporation tube compared to other components.

Experimental validation of salt-containing wastewater scaling sites

To study the flow characteristics in the evaporation tube of salt-containing wastewater and to verify the accuracy of the fouling sites in the numerical simulation, a falling film evaporation experimental setup was built, as shown in Figure 11.
Figure 11

Schematic of falling film evaporation test system. 1-Liquid storage tank; 2-Preheat electric wire; 3-Pump; 4-Valve; 5-Flowmeter; 6-Adjustment tank; 7-Adjustment tank electric heating wire; 8-Vertical tube reservoir; 9-Vertical tube electric heating wire; 10-Vertical falling film evaporation tube;11- Insulation layer; 12-Entry thermocouple;13-Experimental section thermocouple; 14-Export thermocouple; 15-Thermometer; 16-Simple condenser tube;17-Measurement position.

Figure 11

Schematic of falling film evaporation test system. 1-Liquid storage tank; 2-Preheat electric wire; 3-Pump; 4-Valve; 5-Flowmeter; 6-Adjustment tank; 7-Adjustment tank electric heating wire; 8-Vertical tube reservoir; 9-Vertical tube electric heating wire; 10-Vertical falling film evaporation tube;11- Insulation layer; 12-Entry thermocouple;13-Experimental section thermocouple; 14-Export thermocouple; 15-Thermometer; 16-Simple condenser tube;17-Measurement position.

Close modal

The experimental process was to transport the salt wastewater of a certain concentration in the storage tank through the pipe to the storage tank at the top of the tube by the pump, and the salt wastewater was evenly distributed on the inner wall of the tube through the liquid distributor downward under the action of gravity. Among them, the descending film evaporation tube was a custom-made device (made of flexible steel pieces), which could be disassembled at a specific location to measure the scaling rate, the outer wall of the tube was wound with electric heating wire for heating (the heating section was 1,000 mm), the heat insulation layer was used outside the electric heating wire for heat insulation treatment, and the temperature was measured by a thermocouple. To ensure the accuracy of the experimental data and empty the air inside the tube, the descending film evaporation device was operated continuously and then verified experimentally.

When the device was in stable operation for 1 h, the fouling rate at tube lengths of 690 mm, 718 mm, 942 mm, 966 mm, and 1,000 mm was measured in this experiment (scaling rate = mass difference/(area·time)), and the data were integrated as shown in Figure 12, from which it can be seen that the fouling rates at the simulated predicted loci are all greater than 0, thus proving the reliability of the predicted fouling loci.
Figure 12

Scaling rate at predicted points in the evaporation tube.

Figure 12

Scaling rate at predicted points in the evaporation tube.

Close modal

In this paper, the solid–liquid phase equilibrium of the NaCl-CaCl2-H2O ternary system at different temperatures (303.15–373.15 K) by the isothermal dissolution method and the falling film flow of four saline wastewaters in the falling film evaporation tube were simulated by the VOF model. The conclusions are as follows.

  • (a)

    Based on the phase equilibrium data, the phase diagram and schematic diagram of the system at multiple temperatures (T = (303.15–373.15 K)) were determined, and the results showed that the mesostable phase diagram of the system was simple and showed a regular variation of w(NaCl) and w(CaCl2) with temperature when w(NaCl) was 15–28%. The phase diagram of the multi-temperature brine system in this paper provided a detailed equilibrium relationship of solubility, which was important for solving the challenges of salt recovery and the prevention of salt scaling in coal chemical wastewater.

  • (b)

    Based on the phase equilibrium data, the flow characteristics of four salt-containing wastewaters (10% NaCl + 9, 10, 11, 12% CaCl2) were simulated, and the risk of precipitation of NaCl crystals for the four salt concentrations during evaporation was obtained at tube lengths of 718 mm, 942 mm, 966 mm, and 1,000 mm, respectively, and verified by a falling film evaporation experimental setup, which proved the reliability of the predicted points. The combination of phase equilibrium and numerical simulation provided a novel method for the accurate determination of scaling sites and trends.

This study was financially supported by the scientific research fund project of the National Natural Science Foundation of China (Grant No.52070123), Natural Science Foundation of Shandong Province (Grant No.ZR2020ME224), Key Scientific and Technological Innovation Project in Shandong Province (Grant No.2019JZZY020808), and Project of Shandong Province Higher Educational Young Innovative Talent Introduction and Cultivation Team [Wastewater treatment and resource innovation team].

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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