Experimental Determination and Modeling of the Solubility of Sodium

Article pubs.acs.org/jced

Experimental Determination and Modeling of the Solubility of Sodium Chloride in Subcritical Water from (568 to 598) K and (10 to 25) MPa Xin Ding,† Yali Lei,‡,§ Zhenxing Shen,‡,§ Yunsong Yu,† Qiang Zhou,† Jinjia Wei,† and Tao Fang*,† †

School of Chemical Engineering and Technology, and ‡Department of Environmental Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China § Key Lab of Aerosol Chemistry & Physics, Institute of Earth Environment, Chinese Academy of Sciences, Xi’an 710061, China

ABSTRACT: The solubility of sodium chloride was investigated by using a continuous flow method over the temperature and pressure ranges of (568 to 598) K and (10 to 25) MPa, respectively. The results showed that the solubility of sodium chloride increased with increasing water density. In general, over the low-density ranges, the increase of solubility is not significant. Whereas, over the high-density ranges, the solubility greatly increases with density. The experimental solubility data were also correlated with seven empirical and semiempirical models (empirical, enthalpy, Cp-, Flory−Huggins, ionization, second-order polynomial, and third-order polynomial models). The correlated results indicated that the second-order polynomial model provided the best fit. The solubility data of sodium chloride in sub-, near-, and supercritical water from this work and literature were collected with a view to evaluating the correlative and predictive capability of these models over a wide range. The enthalpy model gave the best correlated and predicted result with respect to the solubilities in near- and supercritical water. In the whole region, the third-order polynomial model was proven the most suitable model. Moreover, the corrosion behavior of the apparatus was characterized using scanning electron microscopy/energy dispersive X-ray spectroscopy, X-ray diffraction, and X-ray photoelectron spectroscopy methods, and the possible corrosion mechanism is also briefly discussed. dioxide and other small molecules with SCWO treatment.8 Moreover, supercritical water is an ideal solvent that can be used in several processes, such as reactions,9,10 extraction,11 and biomass gasification.12,13 However, because of the changes of the solvation behavior of sub- and supercritical water in comparison to ambient conditions, the solubility of inorganic compounds in sub- and supercritical water are significantly reduced.14,15 This change results in serious deposition and corrosion problems in the SCWO system.16−19 The deposited inorganic salts can block feed and outlet lines and then decrease the flow rates and wastewater treatment efficiency.20−22 On the basis of experimental research results, the salts deposition and corrosion that occurs in the subcritical region is typically more severe than that in the supercritical region.23 Salt deposition

1. INTRODUCTION With the development of the industrial economy, energy and environmental issues have become important for the sustainable development of human society. Particularly, untreated coking wastewater discharged from the coal and oil industries causes serious harm to the environment.1 Therefore, it is necessary to treat coking wastewater before discharge into the environment.2,3 Supercritical water oxidation technology (SCWO), as a potential promising treatment technology, has received widespread attention over the past few decades.4−7 As shown in Figure 3, when the temperature and pressure of system is higher than the critical point of water (Tc = 647.30 K, Pc = 22.13 MPa), some special properties such as strong reactivity will appear. Therefore, supercritical water can be applied to treat a large amount of toxic stubborn wastes which are not efficiently handled by traditional methods. In general, the refractory toxic and organic substances contained in coking wastewater can be decomposed into nitrogen, hydrogen, carbon © 2017 American Chemical Society

Received: May 15, 2017 Accepted: August 18, 2017 Published: August 31, 2017 3374

DOI: 10.1021/acs.jced.7b00436 J. Chem. Eng. Data 2017, 62, 3374−3390

Journal of Chemical & Engineering Data

Article

fit the solubility data. In this work, seven models that are available in the literature were used to correlate the experimental solubility data. These models, namely, the empirical model, enthalpy model, Cp-model, Flory−Huggins model, ionization model, second-order polynomial model, and third-order polynomial model, are based on obtaining the correlations between the solubility (using molality as the unit) and system density.25,32,33 Thus, these models are referred to as density-based models. 2.1. Empirical Model. The empirical model is the simplest model among the solubility models for describing the solubility as a polynomial of one of the system parameters. In general, researchers assumed that the solubility of solid solutes is related to the pure solvent molar density ρ (mol·L−1). Therefore, the solubility of inorganic salts was interpreted by a polynomial of water density, as shown in the formula of eq 1. Then, eq 1 can be simplified to get eq 2. Although this model lacks any clear thermodynamic background, a correlation between the solubility and density can be obtained within the measured temperature and pressure ranges.34,35

and corrosion are considered to be the greatest obstacles for the industrial development of SCWO. To eliminate the serious problems that exist in SCWO systems, removing the inorganic salts from the water phase before the raw materials enter the main treatment sections is considered to be an efficient method.24 Therefore, a sound understanding of the solubility of inorganic salts under sub- and supercritical conditions is vital for applying this method with SCWO systems. Until now, several studies related to the solubility of sodium chloride which is considered as the major inorganic component in coking wastewater have been reported in literature. Leusbrock et al. measured the solubility of sodium chloride in supercritical water with the flow method.25 Armellini et al. also determined the solubility of sodium chloride in near- and supercritical water.15 The solubility of sodium chloride in high temperature and pressure water vapor was investigated by Higashi et al.26 Galobardes et al. determined the solubility of sodium chloride in high temperature steam.27 Unfortunately, among these studies, no reports concerning the solubility data could be available under low temperature subcritical water. As discussed above, the salt deposition and corrosion phenomena especially in subcritical region such as preheater, cool-down devices, feeding inlet tube, outlet tube, etc. are worthy of more attention than those in supercritical region. It is necessary to obtain abundant and comprehensive solubility data regarding salts in subcritical water for designing and optimizing SCWO industrial systems. This work utilized sodium chloride, as the target inorganic salt, to investigate its solubility in subcritical water. The investigated temperature and pressure ranges were (568 to 598) K and (10 to 25) MPa, which are consistent with the conditions of preheater and cool-down devices in SCWO systems.28 This study also enlarges the available solubility database of inorganic salts. The seven empirical and semiempirical models were applied to correlate the solubility data determined in this work and reported in literature. The optimal adjusted parameters and AARD value of models were calculated first using the available solubility data. Furthermore, the possible parallel hydrolysis of the cation was also verified by changes in pH value of the sample. The solubility data of sodium chloride reported in the literature were also collected to evaluate the correlations and predictions of solution models above and propose which model is most suitable to be applied in the correlation of whole region from sub- and near- to supercritical water. According to the existing research reports, the most severe corrosion of alloy and stainless steel has been found in subcritical water with the coexistence of oxygen and chloride.23,24,29−31 In this study, the corrosion behavior of the experimental apparatus has been characterized by several methods including scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDS), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) methods. On the basis of the literature survey, no studies have been reported on the corrosion behavior that occurs within such a flow-type measuring apparatus. The corrosion mechanism is also briefly discussed in this paper.

y = bρa

(1)

ln y = a ln ρ + k

(2)

In this model, y represents the salt solubility, ρ is the water density, and a and k in eq 2 are adjustable parameters. According to the studied results, the adjustable parameters in this model do not have actual physical meaning; namely, this model is considered as a purely empirical model. 2.2. Enthalpy Model. The enthalpy model is one of the most frequently used solubility models; it was derived from an dissolution equilibrium theory for a solid phase in water.15,36,37 Generally speaking, the dissolution equilibrium of inorganic salts in water can be described by the following expression (eq 3). Ks =

α AaBb·z H2O(f) α AaBb(s)αHz 2O(f)

(3)

Here, AaBb represents the salt solute, a and b are the numbers of anions and cations in the salt molecule, respectively. The numerator, AaBb·zH2O(f), represents the salt hydrate, z is the parameter that describes the number of water molecules in the salt hydrate, f and s represent the fluid and solid phase, respectively, and α represents the activity. Some assumptions have been made to simplify this equation. Under sub- and supercritical conditions, the dissolution of an inorganic salt in water can be assumed to be an ideal process, namely, no reactions or interactions occur in the electrolyte solution system. According to this, the activity of the solid solute can be regarded as 1; the activity of the salt hydrate can be replaced by its concentration, and the activity of water can be replaced by the density of the pure solvent.15,38 Therefore, eq 3 can be simplified to eq 4. Ks =

c AaBb·z H2O(f) 1·ρHz O

2 (f)

2. THEORETICAL EMPIRICAL AND SEMIEMPIRICAL MODEL In addition to the aspects of experimentally determining the solubility of sodium chloride in sub- and supercritical water, several solubility correlation models also have been applied to

(4)

The numerator CAaBb·zH2O(f) represents the concentration of the salt complex, and ρ is the density of pure water. The standard Arrhenius approach can be used to interpret the dissolution equilibrium constant Ks. 3375



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⎛ ΔGs ⎞ ⎟ K s = exp⎜ − ⎝ RT ⎠

solvent system are all applied to describe the solubility of the water−salt system. The variables H and S denote the water phase and solid phase, respectively. In this work, the heat of fusion and melting temperature of sodium chloride were obtained from the National Institute of Standards and Technology (NIST) online database. Other parameters in the model can be calculated using the following equations. The molar volume of pure water νH can be interpreted as follows:

(5)

The Gibbs enthalpy of solvation ΔGs (J ·mol−1) can be described using the heat ΔHs (J ·mol−1) and entropy ΔSs (J · mol−1·K−1) of solvation, as shown by eq 6. ΔGs = ΔHs − T ΔSs

(6)

By substituting eq 5 and eq 6 into eq 4, the enthalpy model can be obtained. c AaBb·z H2O(f) ⎛ ΔHs ΔSs ⎞ ⎟ = exp⎜ − + z ⎝ RT 1·ρH O R ⎠

νH =

(7)

2 (f)

⇔ln c AaBb·zH2O(f) = −

ΔHs ΔSs + + z ln ρH O 2 (f) RT R

δ H/(J·m−3)1/2 = 14110[1 + 1.145(1 − Tr1/2)]Tr1/4ρr (15)

(9)

The variables Tr and ρr represent the reduced temperature and ρ T density, where Tr = T and ρr = ρ . Tc and ρc denote the critical

where R is the ideal gas constant and T represents thermodynamic temperature (K). Equation 9 was used to correlate the solubility data in this study, where a, b, and c are adjustable parameters. 2.3. Cp-Model. The Cp-model is another commonly used solubility model that was derived from dissolution equilibrium theory. The difference between the enthalpy model and Cpmodel is that the derivation of the Cp-model requires another equation, which is used to interpret the Gibbs enthalpy of solvation ΔGs (J·mol−1) with the heat ΔHs (J·mol−1) and entropy ΔSs (J·mol−1·K−1) of solvation.39 ΔGs = ΔHs0 − T ΔSs0 +

=A −

∫ Δcp dT − T ∫

Δcp

B − CT ln T T

T

dT

c

δs =

νs

(16)

where Δμs is the cohesive energy of the solid salt. The molar volume of the inorganic salt can be obtained using the equation proposed by Shin et al.40 ln νs = −ln ρH + βs

(10)

(17)

Equations 13−17 were simultaneously calculated to correlate the solubility data in this work, where Δμs and βs are adjustable parameters. 2.5. Ionization Model. Mesmer et al. developed a purely empirical equation that was applied to describe the solubility of a solute during ionization in water, acid and base systems as a strong function of the logarithm of the pure solvent density, and provided the following expression.44

(12)

where a, b, c, and d are adjustable parameters. 2.4. Flory−Huggins Model. The Flory−Huggins model is a theoretical model based on the Flory−Huggins theory and regular solution theory and combined with more associating parameter terms.40,41 Therefore, this model should give more accurate results than other empirical and semiempirical models described above. The assumptions that inorganic salts are soluble in water but water is insoluble in inorganic salts and that supercritical water is as an expanded fluid were proposed for deriving this model. On the basis of the assumptions above, this model can be defined as follows: ⎞ Δhsm ⎛ T ν ln ys = ⎜ m − 1⎟ + s (δ H − δs)2 RT ⎝ Ts ⎠ RT νs ν −1+ − ln s νH νH

Δμs 27,43

(11)

b + c ln T + d ln ρ T

c

temperature and density, respectively. The solubility parameter δs for inorganic salt can be described as follows:

Substituting eq 5 and eq 11 into eq 4 gives the general expression of the Cp-model: ln y = a −

−1

where MH (mol·kg ) and ρH (mol·L ) are the molar mass and density of pure water, respectively. The solubility parameter of pure water δH can be calculated using the Hansen solubility parameters equation, which was proposed by Marcus et al.42

(8)

a b + + c ln ρ RT R

(14) −1

By replacing ΔHs, ΔSs, z, and CAaBb·zH2O(f) with a, b, c and y, respectively, the following equation is acquired: ln y = −

MH ρH

ln y = c1 +

⎛ c c d ⎞ c2 d + 32 + 43 + ⎜d1 + 2 + 32 ⎟ ln ρ ⎝ T T T T T ⎠ (18)

Equation 18 has been simplified into several different forms.15,45,46 Among them, the following equation has been proven to provide more accurate correlated results than the other forms:33 ln y = a + b/T + (c /T ) ln ρ

(19)

Equation 19 was used to correlate the solubility data in this work, where a, b, and c are adjustable parameters. 2.6. Second-Order Polynomial Model. In previous studies, an empirical relation called a second-order polynomial model was proposed by Khan et al. to describe the solubility of sodium sulfate in supercritical water.35 The correlation results were demonstrated to be in good agreement with measured solubility data. Thus, this model was used to fit and predict the

(13)

Tm s ,

In this model, the melting temperature molar heat of fusion Δhm s of inorganic salts and other properties of the pure 3376



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First, a 0.5 mol/L sodium chloride solution was prepared and placed into a salt solution vessel. The salt solution was pumped into the system with a metering pump (2PB00C series, Beijing Spacecrafts, Beijing, China) and then flown through a nonreturn valve, which was applied to avoid the liquid in the equilibrium cell from returning back to the inlet tube. The feed rates of the initial salt solution ranged from 2.5 to 5.0 mL/ min−1 because, in this range, the fluctuations of temperature were within an acceptable range. A back-pressure regulator (BPR, 26-1700 series, Tescom) was used to maintain a constant pressure within the whole system, and the pressure was controlled within ±0.1 MPa. The salt solution that flows through the BPR was finally collected into a residual liquid vessel. After the required pressure was reached, a temperature control device (AI-501 model, Xiamen Yudian Automation Technology Co., Ltd.) was used to heat the equilibrium cell and hold the temperature inside the cell within ±0.5 K. The temperature and pressure in the cell were measured via a calibrated standard platinum resistance thermocouple (JJG 833 series, Shenyang Zhongse thermometric instrument Material Co. Ltd.) and a calibrated pressure gauge (1008S series, Ashcroft), respectively. In the constant temperature process, the temperature of cell wall was relatively high but that of the middle part of the cell was relatively low. Therefore, a mechanical stirring device was applied to ensure that heat transfer inside the cell was even and the inner temperature remained uniform. Which ensures the solid phase could be sufficiently deposited from the liquid phase. The salt-laden water at the equilibrium state flew out from the outlet tube. Behind the tube, a filter (SS-4F-K4-0.5 model, Swagelok, pore size of 0.5 μm) was installed to prevent any particles including solid salt from escaping the cell with the flow rate. And then, the fluid was cooled to ambient temperature by a cooling tank (DL-1005 model, Shanghai Bilon Instruments Manufacturing Co. Ltd.). As a result of the serious corrosion effect of the subcritical water on metal, the fluid will be mixed with a large amount of metal particles which will block the ball valve and expansion valve to render the device ineffective. Therefore, another filter (SS-4F-K4-0.5 model, Swagelok, pore size of 0.5 μm) installed behind the cooling tank was applied to remove the metal particles impurity mixed in the effluent. Finally, the effluent was decompressed through an expansion valve and collected in a sampling bottle that was immersed in a coldwater bath at zero degrees. To ensure the reliability of the solubility data, the equilibrium state needed to be determined at the time of sampling. During the experiments, the conductivity of the salt-contained effluent was measured every 10 min from the outlet until two successive conductivity values were approximately consistent. Thus, it can be considered to reach the equilibrium state. The results indicated that the desired equilibrium state was reached within approximately 1 h. The effluent was sampled every 10 min, and each sampling time was 3−5 min. For comparison, the experimental solubility data of NaCl in water at the density ranges of 4.46−5.74 mol·L−1 are plotted in Figure 2, which are very close to the data at the similar density ranges reported by Leusbrock et al.25 and by Armellini et al.15 That is to say, our experimental results agreed well with the reported solubility data, indicating the accuracy and the validity of the employed method and the performance of the apparatus. Meanwhile, the solubility data of NaCl measured in this work and reported in the literature are listed in Table 2.

experimental data in this work. The general form of this model is shown below:35 ln y = aρ2 + bρ + c

(20)

Equation 20 was used to fit the solubility data in this work, where a, b, and c are adjustable parameters. 2.7. Third-Order Polynomial Model. Similar with a second-order polynomial model, Khan et al. also provided another empirical relationship between the solubility and a third-order polynomial of the pure water density. This model was also applied to correlate the concentration of the sodium carbonate in supercritical water in their work. The model form is provided as follows:35 ln y = aρ3 + bρ2 + cρ + d

(21)

Equation 21 was used to fit the solubility data in this work, where a, b, c, and d are adjustable parameters. As described above, among these models, some are thermodynamic-based models, such as the enthalpy and Cpmodels which are based on the proposed dissolution equilibrium theory of solid solute. The Flory−Huggins model is a strict theoretical model which is based on two traditional solution theories. These models have been successfully applied in correlating the solubilties of several inorganic salts in supercritical water with the range of data available.25,48,49,51 In contrast, other models are purely empirical models which do not have any thermodynamic theoretical background. In that case, the prediction of an empirical model over a wide range is less reliable than that of theoretical solubility model.

3. EXPERIMENTAL SECTION 3.1. Chemicals. Sodium chloride (sodium chloride, analytical purity, more than 99.5% mass fraction) was purchased from Tianjing Baishi Chemical Co. Ltd. Deionized water (18.3 MΩ, 5.2 μs/cm, analytical purity) was obtained from Xi’an Dongguan Chemical Co. Ltd. Further purification was not performed before these chemicals were used. The information on the chemical reagents used is listed in Table 1. Table 1. Chemical Reagents Used in This Work chemical reagent sodium chloride deionized water

source Tianjing Baishi Chemical Co. Ltd. Xi’an Dongguan Chemical Co. Ltd.

mass fraction purity

purification method

CASRN

≥99.7%

none

7647-14-5

≥99.7%

none

7732-18-5

3.2. Experimental Apparatus and Procedures. The solubility of sodium chloride in subcritical water was determined using a flow-type measuring apparatus. This apparatus was designed and produced based on the work of Higashi et al.26 and Leusbrock et al.25,48,49,51 The schematic diagram of the apparatus is shown in Figure 1. In the apparatus, a high temperature and pressure equilibrium cell was produced by Hastelloy C-276 to prevent severe corrosion to the cell body. The inner diameter, height, and available volume of the equilibrium cell are 40 mm, 100 mm, and 125 mL, respectively. Each part of the apparatus is connected via a 316 L stainless steel tube with a 3 mm outside diameter and 1 mm inner diameter. 3377



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Figure 1. Schematic diagram of solubility measurement apparatus: 1, salt solution vessel; 2, residual liquid vessel; 3, metering pump; 4, back pressure regulator; 5, nonreturn valve; 6, three-way valve; 7, thermocouple; 8, mechanical agitation; 9, temperature control device; 10, high temperature and pressure equilibria cell; 11, safety valve; 12, pressure gauge; 13, filter; 14, cooling; 15, ball valve; 16, expansion valve; 17, sampling bottle; 18, cold water bath.

from mass concentration (mg/L) to molality (mol/kg) in order to satisfy the correlation requirements of the solubility models. The pH values of the collected samples were measured using a standard pH electrode (Rex PHS-3C model, Shanghai INESA Scientific Instrument CO., Ltd.). 3.4. Corrosion Characterization Methods. The morphologies of the surfaces of the corrosion powders and the inner surfaces of the 316L SS tubes were analyzed using a JSM6390A scanning electron microscope (SEM). The components of the corrosion powders and oxide films on the inner surfaces of the 316L SS tubes were examined via energy diffraction spectra (EDS) using a JEOL JSM-6390A. The crystal structures and chemical compositions of the corrosion powder were identified using a SHIMADZU-6100 X-ray diffractometer (XRD) and Kratos AXIS ULtrabld X-ray photoelectron spectrometer (XPS), respectively.

4. RESULTS AND DISCUSSION 4.1. Experimental Solubility Results. The experimental solubility data of sodium chloride in subcritical water over the temperature range of (568 to 598) K and the pressure range of (10 to 25) MPa are listed in Table 3. The temperature and pressure ranges investigated in this work locate in dark blue region of phase diagram in Figure 3, namely the subcritical fluid region. Whereas, the phase diagram of pure water is greatly affected by NaCl solute. On the basis of the vapor pressure curve of aqueous solution of NaCl measured by Keevil et al.,47 the vapor pressure of NaCl solution increases with temperature in the range of 568−598 K. At the temperature of 600.3 K, the vapor pressure of NaCl solution is 7.85 MPa which is lower than the minimum experimental pressure value in this study. By comparing the temperature and pressure conditions investigated in this work and the vapor pressure of NaCl solution in the same temperature ranges, it can be concluded that the selected temperature and pressure region is located above the vapor pressure curve of NaCl solution. That is to say, the investigated system is in the homogeneous liquid state in the present experimental conditions. The density of pure water was

Figure 2. Comparisons between experimental solubility data of sodium chloride in water with the reported data in the literature: (blue ▲) experimental solubility data; (red ●) literature data from Higashi et al.; (■) literature data from Leusbrock et al.

3.3. Analytical and Solubility Measurement Methods. The solubility measurements of the solute were obtained using ionic chromatography (IC). Among them, the concentrations of the sodium cations in the collected samples were detected using a CS12A column (Dionex Co., Sunnyvale, CA) with 20 mM methanesulfonate as the eluent, and those of the chloride anions in the collected samples were detected using an AS11HC column (Dionex Co., Sunnyvale, CA) using 20 mM KOH as the eluent. Both the detection limits of the cations and anions are less than 0.05 mg/L. Prior to testing, all samples need to be diluted 100 times to meet the injection requirement of IC. According to the analytical results, there are no severe difference between the measured sodium and the measured chlorine concentration. Therefore, in this study, only the sodium concentration was used to represent the measured sodium chloride concentration and to evaluate the conformity with previous work. The units of solubility were transferred 3378



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Table 2. Solubility of Sodium Chloride in Subcritical Water at Similar Water Density Conditions Measured in This Work and Reported in Literaturea T

P

ρb

S1,c −1

K

MPa

mol L

671.20 669.35 671.85 670.95

17.40 18.50 19.50 20.40

4.46 4.99 5.38 5.74

T

mmol.kg

−1

1.54 2.02 2.29 2.96

ρb

P

S2,c −1

K

MPa

mol L

673.72 673.34 673.42 673.42 673.57 673.27 673.04 672.96

17.05 17.07 17.95 17.98 19.01 19.01 20.06 20.08

4.27 4.28 4.63 4.64 5.09 5.10 5.61 5.63

mmol.kg 1.53 1.44 2.60 2.68 3.89 3.59 5.05 5.53

T −1

ρb

P

S3,c −1

K

MPa

mol L

773.15 723.15 773.15

20.00 20.00 25.00

3.76 4.37 4.99

mmol.kg−1 0.54 1.09 1.73

The standard uncertainties u are u(T) = 0.45 K, u(p) = 0.03 MPa, ur(S) = 0.03. bρ represents the density of water at experimental temperature and pressure conditions. The values of water density were obtained by the IAWPS-IF97 water and steam physical properties calculation software with certain temperature and pressure values. cS is the molality of sodium chloride in water; 1experimental solubility data; 2literature data from Leusbrock et al.; 3literature data from Armellini et al.

a

Table 3. Solubility Data of Sodium Chloride in Subcritical Water at Temperature (568 to 598) K and Pressure (10 to 25) MPaa and the pH Value of Sample T K

ρb mol L

Sc −1

mmol·kg

T −1

pH

K

ρb

Sc −1

mol L

p/MPa = 10 567.95 568.95 573.35 573.85 569.80 570.50 570.80 571.60 582.05 584.00 586.10 586.60 588.90 589.45 589.65 592.85 596.60 597.50 571.05 572.05

40.37 40.25 39.71 39.65 p/MPa = 15 40.69 40.61 40.58 40.49 39.23 38.98 38.70 38.63 38.32 38.24 38.21 37.75 37.18 37.04 p/MPa = 20 41.04 40.93

mmol·kg−1

pH

p/MPa = 20 160.68 143.30 85.26 69.80

5.34 5.12 5.11 5.00

175.02 158.51 146.82 120.79 62.60 62.36 62.40 62.31 62.21 59.64 59.46 57.41 57.23 57.05

4.94 4.87 4.82 4.86 5.62 5.41 5.82 5.20 6.68 6.72 5.13 6.67 6.68 6.73

341.45 240.85

4.72 5.20

577.55 577.65 580.25 580.80 581.15 587.10 589.75 589.50 594.00 594.70

40.33 40.32 40.03 39.97 39.93 39.22 38.89 38.92 38.34 38.24

575.65 580.25 586.45 587.55 588.15 589.45 590.35 592.15 595.30 597.10 598.80

41.03 40.54 39.86 39.74 39.67 39.52 39.41 39.20 38.82 38.60 38.39

121.38 113.73 81.54 74.90 74.43 62.91 62.36 61.03 60.29 59.66

4.86 4.92 4.73 6.46 6.51 6.20 6.78 6.60 6.84 6.62

268.90 122.06 69.96 66.39 64.15 63.29 62.51 62.46 61.95 61.23 60.85

5.22 5.25 6.30 6.39 6.22 6.28 6.70 6.67 6.80 6.71 6.75

p/MPa = 25

a The standard uncertainties u are u(T) = 0.8 K, u(p) = 0.06 MPa, u(pH) = 0.1, ur(S) = 0.02. bρ represents the density of water at experimental temperature and pressure conditions. The values of water density were obtained by the IAWPS-IF97 water and steam physical properties calculation software with certain temperature and pressure values. cS is the molality of sodium chloride in water.

that the solvation capacity of water for inorganic salts changed with the density of water. In general, the density of water increases with the increase of pressure, but decreases with the increase of temperature. As a result, with the increase of density, the solvation capacity of water increases, and more salt molecules interacted with water molecules and dissolved in water, thus resulting in an increase in solubility. However, as water density decreases, the situation is exactly opposite. Specifically, in the low-density range of (37.02 to 39.70) mol/L, the solubility changed from 57.05 × 10−3 to 66.39 × 10−3 mol/kg; with the increase of density, the solubility did not significantly change. In the low-density range, it is possible that the increase in the density of water could not significantly

calculated via the IAWPS-IF97 water and steam physical properties calculation software.48 As shown in Table 3 and Figure 4, at constant pressure, the solubility decreases with the increase of temperature. Also, under the similar temperature conditions, the solubility increases with system pressure. Whereas, in the temperature range of 585−598 K, the differences between the solubility data at different pressure are not significant. Figure 5 shows the solubility curve and the solubility correlated results obtained using the models mentioned above. As can be seen in Figure 5, the solubility of sodium chloride generally increased with the increasing density over the investigated temperature and pressure range. The above results were attributed to the fact 3379



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Figure 5. Measured solubility of sodium chloride as a function of water density and comparison with correlated results from different solubility models: (red ●) experimental data. () empirical model; (aqua dashdot line) enthalpy model; (light green dash line) Cp-model; (orange dash line) ionization model; (brown dash-dot line) Flory−Huggins model; (dark blue dash dot line) second-order polynomial model; (dark green dash dot line) third-order polynomial model.

Figure 3. Temperature−pressure phase diagram of pure water.

Actually, the parallel hydrolysis of cations in supercritical water has been observed by researchers.15,27,49,50 Whether or not a significant cation hydrolysis reaction occurred in subcritical water was explored by measuring the pH values of the collected samples. As shown in Table 3 and Figure 6, the

Figure 4. Measured solubility of sodium chloride in water at different temperature and pressure conditions: (■) 10 MPa; (red ●) 15 MPa; (blue ◆) 20 MPa; (green ▲) 25 MPa.

influence the solubility of the solute. Although the solvation effect of the solute molecules was enhanced, the effects of the solute solvation and the strong hydrogen bonding between water molecules on the solubility balanced each other, which leads to the minor changes in solubility. In contrast, in the highdensity range of (39.71 to 41.39) mol/L, the solubility changed from 69.80 × 10−3 to 341.45 × 10−3 mol/kg; thus, the solubility increased significantly with the density. This increase potentially occurred because the hydration of the salt molecules became dominant and the hydrogen bonds between the water molecules are weakened. From the experimental results, the solubility of sodium chloride in subcritical water is much higher than in supercritical water. Unlike the approximate linear relationship between the solubility of sodium chloride and the water density in the supercritical region, there is a sudden change in solubility as the density of the subcritical water increased. The unique changes in the polarity and solvation ability of subcritical water were potentially attributed to this solubility tendency, which is different from that in supercritical water.

Figure 6. Measured pH value of sodium chloride samples as a function of water density.

pH values ranged between 4.72 and 6.84, indicating the presence of the hydrolysis reaction of sodium ions, which is responsible for the pH decrease in the sample solution. The hydrolysis mechanism can be depicted as eq 22: NaCl + H 2O ⇔ NaOH(s) + HCl

(22)

The cation hydrolysis at higher densities is more severe than that at lower densities, which is related to the complicated interactions between the cations and water molecules, which may be stronger at higher densities than those at lower densities. Notably, the degree of cation hydrolysis had no significant effect on the decrease in the solute solubility. 4.2. Experimental Solubility Data Correlation. To evaluate the correlation results of seven solubility models, the average absolute relative deviations (AARD) between the 3380



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Table 4. Correlated Results of Seven Empirical and Semiempirical Models with the Experimental Solubility Data of Sodium Chloride in Subcritical Water correlated parameter

a

no.

correlation model

a

b

1 2 3 4 5 6 7

empirical model enthalpy model Cp- model ionization model Flory−Huggins modela second-order polynomial model third-order polynomial model

16.048 5045.61 −61.79 −1.224 −4.474 0.224 0.264

−61.315 −513.48 604.44 −36172.97 429777.12 −17.17 −30.96

c 16.45 4.173 × 10−3 9664.78 326.25 1208.68

d

16.45

−15725.23

AARD (%) 27.58 27.61 27.56 27.02 28.00 13.19 46.01

The fitting parameters βs and Δμs of the Flory−Huggins model corresponding to the parameter a and b in the table, respectively.

experimental and fitting data were calculated using the following formula (eq 23): AARD(%) =

100 N

N

∑ 1

y cal − y exp y exp

not significant and the deviations only occurred at a high density range of (ρ > 40.5 mol/L). Since the enthalpy and Cp-models were derived from the same dissolution equilibrium theory, these two models provided almost identical correlated results. As for the empirical and ionization models, they also gave almost the same correlated results which are similar to the fitting curves obtained by the enthalpy and Cp-models. The correlated results from these four models are almost the same. Actually, it is difficult to explain why the fitted results of two purely empirical models, that is, the empirical and ionization models, are almost identical to those of the two thermodynamic mechanism models, that is, the enthalpy and Cp-models. Although the Flory−Huggins model was derived from one additional thermodynamic theory, this model does not significantly improve the description of the solubility in comparison to the four models mentioned, which is far less than the intended consequence. The linear prediction curves obtained by enthalpy, Cp- and Flory−Huggins models are not consistent with the solubility curve of sodium chloride in subcritical water. One reason is that undoubtedly, the water properties and the complicated interactions between water molecules and solid solute molecules at the subcritical state is definitely different from those at the supercritical water. The dissolution equilibrium theory, Flory−Huggins theory, and regular solution theory on which these theoretical models are based do not appropriately apply to the description of the dissolution of inorganic salts in subcritical water. In addition, perhaps a series of simplified assumptions made in the derivation of the theoretical model also make it difficult for these models to be applied to correlate solubility in subcritical water. For example, the assumption that the complicated interaction among solvated salt complex, salt molecules, and water molecules is neglected was made during the derivation of the enthalpy model.25 Maybe this assumption is suitable for a description at supercritical state but cannot be adapted in the subcritical state. The properties of water such as the dielectric constant and solvation capacity do not linearly change with the density of water from subcritical to supercritical state. This tendency cannot be described by the models that express a linear relationship between solubility and water density. Hence, it is important to study the properties of water and the complicated interaction between solid solute and solvent in inorganic salt + subcritical water systems to better correlate and predict the solubility in subcritical water. The second-order polynomial model and third-order polynomial model only consider the solubility as a function of density. Perhaps in the subcritical region, the effect of temperature on the solubility is not significant with respect to

(23)

where y cal is the calculated value of the solubility and y exp is the experimental solubility data of the solute. The variable N is the number of experimental data points. The adjustable parameters in the models were calculated via the function f iminsearch in the optimization toolbox of the Matlab software which was demonstrated to be accurate and efficient by Luo et al. for correlating the solubility of several acids in acetic acid + cyclohexanone mixtures.51 The optimal adjustable parameters and AARD values are shown in Table 4 and Figure 7.

Figure 7. AARD value of each model used to correlate the measured solubility of sodium chloride in subcritical water: (1) empirical model; (2) enthalpy model; (3) Cp-model; (4) ionization model; (5) Flory− Huggins model; (6) second-order polynomial model; (7) third-order polynomial model.

As shown in Table 4 and Figure 7, the second-order polynomial model results in the best correlation to the experimental data with a lowest AARD value of 13.21. In contrast, the third-order polynomial model gave the worst fit with an AARD value of 46.01, which is the highest among the models. The correlated results of empirical, enthalpy, Cp- and ionization models are almost identical, which can be evidenced by the AARD values. The differences between the correlation of the Flory−Huggins model and that of four models above are 3381



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Table 5. Experimental Solubility Data of Sodium Chloride in Sub-, Near- and Supercritical Water Reported in the Literature and Presented in This Work no.

inorganic salt

temp (T/K)

pressure (P/MPa)

solubility (S/mmol·kg−1)

ref

1 2 3 4 5

NaCl

654.0−684.5 623.0−673.0 723.0−823.0 723.0−823.0 568.0−598.0

17.10−23.50 9.00−12.00 10.00−25.00 1.38−10.34 10.00−25.00

4.270−9.840 0.020−0.203 0.015−1.730 (0.019−19.040) × 10−3 57.050−341.450

25 26 15 27 this work

Table 6. Correlated Results of Seven Empirical and Semiempirical Models with Literature Data correlated parameter

a

no.

correlation model

1 2 3 4 5 6 7

empirical model enthalpy model Cp- model ionization model Flory−Huggins modela second-order polynomial model third-order polynomial model

a

b −12.116 −228.010 −11976.467 4638.182 115198.907 1.209 0.113

4.065 −84754.091 −44.348 −19.033 −5.751 −4.321 × 10−2 −7.410 × 10−3

c 4.174 2.213 2761.989 −10.540 0.178

d

4.105

−8.391

AARD (%) 20.39 18.29 18.80 19.01 25.93 20.55 19.79

The fitting parameters βs and Δμs of Flory−Huggins model corresponding to the parameter a and b in the table, respectively.

As shown in Table 6 and Figure 8, the enthalpy model provides the best correlated result with the lowest AARD value of 18.29. The poorest correlated results were given by the Flory−Huggins model with the highest AARD value of 25.93. The other models, empirical, Cp-, ionization, second-order, and third-order polynomial models, had AARD values of 20.39, 18.80, 19.01, 20.55, and 19.79, respectively. Actually, in addition to the Flory−Huggins model, the difference between the correlated results of the other models is not significant. The solubility data reported by different researchers and the fitted curves obtained by different models were plotted in Figure 9. As shown in Figure 9, second-order and third-order polynomial models are shown to give a greater deviation with

the other properties of water. Hence, the second-order polynomial model is more suitable to correlate the solubility of sodium chloride in subcritical water. In contrast, high-order density polynomials are not helpful for improving the correlated precision of the experimental data. 4.3. Comparison Results of the Different Solubility Data. To compare the solubility data of sodium chloride in sub-, near-, and supercritical water, the details of the temperature, pressure, and solubility data in the present study and literature are listed in Table 5. 4.3.1. Comparison between the Reported Solubility Data in Literature. The solubility models above were used to correlate and predict the solubilities in near- and supercritical water which were reported in the literature. The optimal adjustable parameters and AARD values can be observed in Table 6 and Figure 8.

Figure 9. Comparison of the predicted solubilities obtained by different models with literature data: (red ◆) Leusbrock et al. 2008; (blue ▼) Higashi et al. 2005; (pink ◀) Armellini et al. 1993; (orange ▲) Galobardes et al. 1981; () empirical model; (aqua dash dot line) enthalpy model; (green dash line) Cp-model; (brown dash line) ionization model; (dark blue dash dot line) Flory−Huggins model; (blue dash dot line) second-order polynomial model; (purple dash dot line) third-order polynomial model.

Figure 8. AARD value of each model used to correlate the literature data: (1) empirical model; (2) enthalpy model; (3) Cp-model; (4) ionization model; (5) Flory−Huggins model; (6) second-order polynomial model; (7) third-order polynomial model. 3382



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Table 7. Correlated Results of Seven Empirical and Semiempirical Models with Experimental Solubility Data and Literature Data correlated parameter no.

correlation model

a

b

1 2 3 4 5 6 7

empirical model enthalpy model Cp- model ionization model Flory−Huggins modele second-order polynomial model third-order polynomial model

1.689 92225.756 −332.554 19.611 −7.728 −6.958 × 10−3 1.070 × 10−3

−7.651 60.486 −15685.438 −19512.112 88202.751 0.400 −8.031 × 10−2

c 2.645 46.029 1874.295 −6.915 1.765

d

2.853

−12.922

AARD (%) 97.21 89.67 89.18 96.63 98.87 78.65 22.42

The fitting parameters βs and Δμs of Flory−Huggins model corresponding to the parameter a and b in the table, respectively.

e

the solubility data over medium low density range (ρ < 3.5 mol/L). Maybe in this density range, the effect of temperature on solubility becomes more remarkable, but these two polynomial models do not account for the temperature effect on solubility. The other five models suggest a linear relationship between the logarithm of solubility (ln y) and the solvent density (ln ρ or ρ) as well as consider the temperature (T) effect on the changes in the solubility. The predicted results of enthalpy, Cp- and ionization models are basically uniform and are in agreement with solubility data. As discussed in the literature, the dissolution equilibrium theory is suitable for describing the solubility of inorganic salts in near- and supercritical water.25,49,50,52 The predictions of empirical and Flory−Huggins models show a deviation from that of the three solubility-density linear relationship models above, especially with respect to the literature data in the low density range (ρ < 2.5 mol/L). 4.3.2. Comparison between the Reported Data and Experimental Data in This Work. To evaluate the correlative and predictive capability of these models for the solubility data in sub-, near-, and supercritical water, which is of great significance in the design and optimization of an industrial SCWO system, the data sets of both the present study and the available literature were used to evaluate the correlations and predicitons of different models. The optimal adjustable parameters and AARD values are shown in Table 7 and Figure 10. As presented in Table 7 and Figure 10, the AARD value is 22.42 for the third-order polynomial model, which is much better than those obtained by other models. The enthalpy, Cpand second-order polynomial model gave relative poor correlated results with an AARD of 89.67, 89.20, and 78.65, respectively. The worst fitting results were provided by the empirical, ionization, and Flory−Huggins models with AARDs of 97.29, 96.63, and 98.93, respectively, which are almost close to 100. This indicated that, in addition to the third-order polynomial model, the other models almost cannot be used to correlate the solubility in sub-, near-, and supercritical water. These solubility data were considered as a function of water density and shown in Figure 11. Figure 11 clearly indicates that the solubility of sodium chloride increased with an increase of the whole water density range, because the greater is the density of water, the stronger is the dissolution of inorganic salts. In near- and supercritical water, the solubility almost increases linearly with density. However, from supercritical to subcritical water, the increases of solubility with density do not show a linear relationship and are not significant. The fitted curves were also presented in Figure 11, it can be seen that only the third-order polynomial model can well fit and predict the

Figure 10. AARD value of each model used to correlate the measured solubility and literature data: (1) empirical model; (2) enthalpy model; (3) Cp-model; (4) ionization model; (5) Flory−Huggins model; (6) second-order polynomial model; (7) third-order polynomial model.

Figure 11. Comparison of the predicted solubilities obtained by different models with the measured solubilities and literature data: (◆) experimental solubility data; (red ●) Leusbrock et al. 2008; (blue ▼) Higashi et al. 2005; (pink ◀) Armellini et al. 1993; (orange ▲) Galobardes et al. 1981. () Empirical model; (aqua dash dot line) enthalpy model; (light green dash line) Cp-model; (orange dash line) ionization model; (brown dash dot line) Flory−Huggins model; (dark blue dash dot line) second-order polynomial model; (dark green dash dot line) third-order polynomial model. 3383



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regular; they basically exhibited rod, flaky, and polygonal shapes. Figure 12(2) was obtained by enlarging the region (a) in Figure 12(1). In Figure 12(2), many fine dots covered the surfaces of the relatively large grains and were arranged very closely. The sizes of these tiny grains were substantially less than 1.00 μm. Figure 13 panels (1) and (2) show the inner surface morphologies of the new and corroded 316L SS tubes, respectively. Significant morphology changes can be observed. As can be seen in Figure 13(1), the inner surface morphology of the new 316L SS tubes was uniform, whereas in Figure 13(2), the surface morphology became relatively flat and the gully structure disappeared because a layer of oxide film covered the inner surface of the 316L SS tube. In contrast, many pits and crack structures existed on the oxide films. These morphological structures were caused by the pitting corrosion and stress cracking corrosion of the 316L SS. In previous works, many researchers have found that severe pitting corrosion and significant stress cracking corrosion in 316L SS would occur during the oxidization of supercritical water containing chloride.53−56 When the oxide film was formed, chloride ions, as the aggressive ions, continuously attacked the oxide scales and caused decomposition of the oxides. The stainless steel would suffer further corrosion because the matrix was exposed to the corrosion medium. Kim et al. proposed that severe pitting corrosion and stress cracking corrosion would occur in austenitic stainless steel under the direct attack of chlorides in supercritical water.57 However, the corrosion of 316L SS discussed in this work was more severe than that of the steels reported by Kim et al.53 This observation demonstrates that the coexistence of the oxidizing and aggressive ions caused more serious pitting and stress cracking corrosion in subcritical water than in supercritical water. This difference may occur because the solubility of the chlorides in subcritical water is higher than that in supercritical water; hence, more aggressive ions could attack the protective oxide films and metals, causing seriously dealloying corrosion.19,23,29,30,58 The cross-section morphologies of the 316L SS tubes after corrosion are shown in Figure 13(3) and Figure 13(4) which presents a high-magnification (×5000) SEM image of the oxide film. As illustrated in these two images, the thicknesses of the oxide film formed at different locations on the inner surface of the corroded 316L SS tube were different, with an average thickness of 12.6 μm. As shown in Figure 13(4), the formed oxide film was not uniformly coated on the inner surface of the tube. These characteristics resulted from the spallation of the oxide film and the further corrosion of the metal matrix. Under the condition of subcritical water containing chlorine, aggressive ions, such as chloride ions, could continuously attack the protective oxide layer as well as dissociate and spall the oxide scales. The exposed metal matrix was further oxidized by the oxidant. Therefore, the oxide film appeared concave and convex. 5.2. Chemical Analysis of the Corrosion Powder and 316L SS Tube Inner Surface. As shown in Figure 14, the mass percentages of the main metal elements were analyzed via energy diffraction spectroscopy (EDS). Figure 14 panels a−e represent the chemical compositions of the different areas of the corrosion powder and oxide film in Figure 12(1) and Figure 13(3),(4), respectively. The results in 14a indicated that Ni and Mo were dominant in the corrosion powder, and the intensity of iron was less than that of Ni and Mo. In general, iron is easily attacked in the presence of aggressive ions.59 Therefore, it is

trend of experimental data in the high density range (ρ > 2 mol/L). As discussed above, because of the complicated changes of solvation capability of water and of the interaction between solvated salt complex molecule and water molecule from the subcritical and near-critical, to the supercritical state, the current thermodynamic theories cannot be adapted to describe and predict the solubility over the whole range. According to the predicted result of the third-order polynomial model, the solubility value increases first and then decreases when the density of water reduces from subcritical to the supercritical region within a wide range. Because the third-order polynomial model is a purely empirical model, the trends in predicted solubility by this model cannot be explained from the perspective of mechanism. In some cases, the change of solvation property of water from subcritical to supercritical state may result in this special solubility tendency. Further measurement needs to be conducted to verify the predictive results of the third-order polynomial model for the solubility of sodium chloride in water over the range from subcritical to supercritical state. Unfortunately, none of the predictions of these models are in good agreement with the data set over the low density range (0.1 < ρ < 2 mol/L). Actually, water properties are significantly different among the sub-, near- and supercritical regions. In addition, the relationship between the changes of water properties and the changes of temperature and pressure is complex. This relationship is not something that can be easily grasped and understood. The complicated interaction between ions and molecules in an inorganic salt + water system at different states is also difficult to interpret. Therefore, it is difficult to correlate the whole region from sub- to supercritical conditions. Also, the models that have been reported in the literature lack the rich and accurate theoretical mechanism for describing the solubilities of inorganic salts in sub-, near-, and supercritical water. Maybe the correlation of solubility in the subcritical and supercritical water needs to be separated. If the whole region needs to be correlated, it is necessary to propose a more complicated correlation which must consider water properties.

5. CORROSION CHARACTERIZATION SECTION The corrosion behavior of the experimental apparatus was characterized using SEM, XRD, and XPS methods. The chemical compositions of the 316L SS and Hastelloy C-276 are shown in Table 8. Table 8. Chemical Compositions of Metals (in wt %) compositions (wt %) metal

Ni

Cr

Mo

C

Fe

Mn

316L SS Hastelloy C-276

12.0 45.1

17.0 15.81

2.5 15.97

0.08 0.01

68.4 5.33

2.0 0.56

5.1. The Surface Morphologies of the Corrosion Powder and 316L SS Tube Interiors. Figure 12 shows the SEM images of the corrosion powders obtained from the filter after experimentation. The resulting powder should have been the corrosion product of the appartus. As shown in Figure 12, the sizes and shapes of the grains in the powder were different, and the distribution of these grains was very loose. In Figure 12(1), the size of the relatively large grains ranged from 3.53 to 8.06 μm, while the size of the relatively small grains was less than 2.55 μm. The shapes of the various grains were not 3384



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Figure 12. (1) Surface morphologies of corrosion powder, (a) the part region of corrosion powder; (2) high magnification (×10000) SEM images of the region (a) in Figure 1.

Figure 13. Morphologies of the inner surface and cross-section of 316L SS tube: (1) inner surface morphologies of the new 316L SS tubes; (2) inner surface morphologies of the corroded 316L SS tubes; (3) cross-section morphologies of the corroded 316L SS tubes: (b) 316L SS matrix; (4) highmagnification (×5000) SEM image of the oxide film covering the inner surface of 316L SS tubes: (c−e) different degrees of formed oxide film.

strongest peak in the spectra indicates the major metallic components of the steels. According to the XRD results, almost all the elements in the alloy and stainless steel were corroded by oxygen and produced various oxides. Zhang et al. noted that a dual-layer structure oxide scale, which consisted of an outer NiO layer and inner Cr2O3/NiCr2O4-mixed layer, was formed on the surface of Hastelloy C-276 in oxidizing supercritical water.60 Choudhry et al. reported that an oxide layer formed in an oxidizing SCW environment on 316L SS that consisted of Fe3O4, Cr2O3, Fe, Mn, etc.61 In this study, due to the synergistic effect of the aggressive ions and oxidants, these typical oxides that existed in the inner and outer layers of the oxide film were all stripped from the oxide film and appeared in the powder. This demonstrated that the corrosion caused by the coexistence of oxygen and salt was more serious than that caused by a single condition, especially in subcritical water.

believed that severe corrosion also occurred in the Hastelloy C276 cell because the contents of Ni and Mo in the Hastelloy C276 are relatively high. Figure 14 panels b and c−e show the compositions of the 316 L SS matrix and formed oxide film, respectively. The results indicated that Fe was dominant in the 316 L SS matrix and oxide film and the content of Ni and Mo were reduced. The intensity of the oxygen decreased gradually from panel c to e, which could be explained by the fact that different locations of the tubes incurred different degrees of pitting and stress cracking corrosion. Particularly for Figure 14 panels d and e, these two images indicated that the matrix had not been completely corroded. No chlorine was detected in the corrosion powder or in the oxide layer, implying that chloride did not form stable and insoluble compounds with the main metal elements. XRD and XPS analyses were performed to identify the compositions of the corrosion powders. In Figure 15, the 3385



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core level spectra, namely, NiOOH and MoCl5, respectively. On the whole, the results of the XPS analysis were basically in accord with those of the XRD analysis. However, some metallic components such as KMnO4, MoOx, and MoCl5 detected by XPS cannot be found in the XRD results. This may occur because the content of these components was so low in the corrosion powder that XRD cannot accurately analyze the existence of them. 5.3. Discussion of the Corrosion Mechanism. In previous studies, several mechanisms have been proposed to explain the complex corrosion processes of metals in oxidizing sub- and supercritical water containing salts, such as the oxide film growth mechanism, metal dissolution mechanism, and metal salt precipitation mechanism.76−78 In the present work, the corrosion mechanism of 316L SS and Hastelloy C-276 is briefly discussed in this section. The corrosion mechanism was considered to consist of three steps. The first step was the formation of the oxide scales on the surface of the metals. Under the subcritical water environment, the metal matrix reacted with oxygen to produce various oxides, such as Fe3O4, Cr2O3, and NiO. The resulting oxides formed an oxide film layer that covered the surface of the metals. The whole process is shown by eqs 24−27.

Figure 14. Composition of corrosion powder and inner surface of corroded 316L SS tube: (a) corrosion powder; (b) 316L SS matrix; (c−e) different degrees of formed oxide film.

Fe + O2 → FeO + O2 → Fe2O3

(24)

FeO + Fe2O3 → Fe3O4

(25)

Cr + O2 → Cr2O3

(26)

Ni + O2 → NiO

(27)

During the second step, the metal oxides were spalled from the corroded surface into the fluid phase. Under the attack of aggressive ions, such as chloride ions, the oxide scales constantly departed from the corroded surface and transformed into a liquid phase. Further corrosion of the metal matrix occurred in the corrosion pit. The dissolved metal ions did not form stable compounds with the chloride ions. The whole process is shown by eqs 28−30.

Figure 15. XRD spectra of corrosion powder.

To determine the chemical states of the Cl, Ni, Cr, Mn, Fe, and Mo, the oxides of the corrosion powder were examined using XPS. Figure 16 shows the core level spectra of Fe 2p, Mn 2p, Mo 3d, Cr 2p, Ni 2p, and Cl 2p, and the binding energy (BE) and assignments of the peaks according to the literature data are listed in Table 9.62−75 According to the analysis results, the composition of the powder was very complex. In the Fe 2p core level spectra, only two components were found. The peaks located at the BEs of 710.4 and 724.0 eV were assigned to Fe3O4, and the signals of 713.6 and 718.6 eV were assigned to Fe. For Mn, there were four substances that appeared in the Mn 2p core level spectra. Mn was indicated by the BEs of 638.4 and 649.5 eV, Mn3O4 was indicated by the BEs of 641.3 and 653.1 eV, and MnO2 and KMnO4 were indicated by the BEs of 643.4 and 647.0 eV, respectively. The detected KMnO4 may have been due to the interfusion of potassium impurities into the measuring system. In the Mo 3d core level spectra, the signals of 232.65 and 235.08 eV belonged to MoOx, and the peaks of 229.7 and 231.7 eV were assigned to MoO2 and MoO3, respectively. Mo mainly formed several different oxides. In the Cr 2p core level spectra, several complex compounds were found; the signals of 576.3, 586.0, and 587.4 eV were assigned to Cr2O3, the peaks of 576.0 and 585.9 eV were assigned to NiCr2O4, and the signal of 577.9 eV was assigned to Na4CrO4. Only one compound was found in the Ni and Cl 2p

Cl−

Fe3O4 ⎯→ ⎯ Fe 2 + + Fe3 + + O2 −

(28)

Cl−

Cr2O3 ⎯→ ⎯ Cr 3 + + O2 − Cl−

NiO ⎯→ ⎯ Ni 2 + + O2 −

(29) (30)

During the third step, the metal oxides regenerated in the aqueous phase. The metal ions that dissolved in the fluid phase during the second step reacted with the oxygen anions in the aqueous phase, resulting in insoluble, stable oxides, and were deposited from the fluid phase. The whole process is shown by eqs 31−35.

3386

Fe 2 + + O2 − → FeO

(31)

Fe3 + + O2 − → Fe2O3

(32)

FeO + Fe2O3 → Fe3O4

(33)

Cr 3 + + O2 − → Cr2O3

(34)

Ni 2 + + O2 − → NiO

(35) DOI: 10.1021/acs.jced.7b00436 J. Chem. Eng. Data 2017, 62, 3374−3390


Article

Figure 16. XP spectra: (1) Fe; (2) Mn; (3) Mo; (4) Cr; (5) Ni; (6) Cl.

6. CONCLUSIONS

capacity of water in the subcritical region. The strong hydrolysis effect of sodium chloride also exists in subcritical water. The seven different empirical and semiempirical models were applied to correlate the solubility data determined in this work and collected from the literature. The results indicated that the second-order polynomial model accurately correlated the solubility data in subcritical water with the lowest AARD value. As for the correlation and prediction of solubility data in near- and supercritical water, the performance of the enthalpy model is much better than that of other models. Moreover, only the third-order polynomial model is able to correlate and

In this work, the solubility of sodium chloride in subcritical water was determined over the temperature range of (568 to 598) K and the pressure range of (10 to 25) MPa. Overall, there is a sudden change in the solubility of sodium chloride in subcritical water. In the low-density range, the solubility almost did not significantly increase with the increase of the density of water. In contrast, the solubility increased sharply with the density over the high-density range. This tendency may be related to the unique changes in the polarity and solvation 3387



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Table 9. Assignments of Peaks in Figure 16 for Corrosion Powder Element: Cl

Element: Fe

BE(eV)

BE(eV)

2p

cmpd

2p3/2

2p1/2

199.8

MoCl5

710.4 713.6

724.0

2p3/2,sat

718.6 Element: Mo

Element: Mn BE(eV)

BE(eV)

2p3/2

2p1/2

cmpd

3d5/2

3d3/2

cmpd

638.4 641.3 643.4 647.0

649.5 653.1

Mn Mn3O4 MnO2 KMnO4

232.65 229.7 231.7

235.08

MoOx MoO2 MoO3

Element: Cr

Element: Ni

BE(eV) 2p2/3

2p1/2

576.3

586.0

BE(eV) 2p2/3,sat 587.4

576.0 577.9

585.9

cmpd

2p2/3

2p1/2

Cr2O3 Cr2O3 NiCr2O4 Na4CrO4

855.55

873.0

2p2/3,sat

2p1/2,sat

cmpd

861.35

879.7

NiOOH NiOOH

Funding

predict the solubility in sub-, near-, and supercritical water over high density. In consideration of the significant changes of water properties and of the complicated interaction within the inorganic salt + water system from subcritical and near-critical to the supercritical state of the whole region, the current solubility models are difficult to correlate and can hardly predict the solubility trends over a wide range. A more complicated correlation model which must consider the multiple influencing factors needs to be developed for study of the solubilities of inorganic compounds. During the design and optimization of the SCWO industrial application, the experimental solubility data of sodium chloride + subcritical water system and the correlation conclusions might be of great value as a reference. On the basis of the results of corrosion characterization, it was concluded that the most severe pitting and intercrystalline corrosion occurred in the experimental apparatus. The significant spallation of the oxide scales was caused by a synergistic effect between the chloride and oxygen, which was observed from the corrosion powder. The composition of the corrosion powder reveals that the some of the oxides which were supposed to be present in the inner oxide layer were found to be present in the powder. This indicated that the aggressive ions eroded the entire oxide layer which resulted in the continuous corrosion of the metal matrix. The corrosion of the experimental apparatus in the oxidizing subcritical water containing chloride was far more serious than that in the oxidizing supercritical water. Actually, the substances produced by metal corrosion may affect the dissolution and deposition of inorganic salts in water. Hence, the measured solubility data may be slightly deviated from the true value. However, no relevant studies have been reported in the literature. This content will be the research focus in future work.

■

cmpd Fe3O4 Fe Fe

The authors would like to acknowledge the following financial supports: PetroChina Innovation Foundation (2014D-50060401), National Natural Science Foundation of China (No. 21376186), the Ministry of Education (Doctoral Special Study Foundation No. 20110201110032), China. Notes

The authors declare no competing financial interest.

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Tao Fang: 0000-0001-8966-1902 3388



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Experimental Determination and Modeling of the Solubility of Sodium

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