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Phase equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K
Fluid Phase Equilibria 392 (2015) 127–131
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Phase equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K Juanxin Hu a,b , Shihua Sang a,b, * , Meifang Zhou a,b , Wangyin Huang a,b a b
College of Materials, Chemistry and Chemical Engineering, Chengdu University of Technology, Chengdu 610059, PR China Key Laboratory of Mineral Resources Chemistry for the Universities in Sichuan Province, Chengdu 610059, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 18 October 2014 Received in revised form 25 January 2015 Accepted 9 February 2015 Available online 11 February 2015
Solid–liquid equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K were determined with the method of isothermal solution saturation. Also determined are the densities of saturated solutions. According to the experimental data, the equilibrium phase diagrams of the two ternary systems were plotted. The phase diagram of first system has two invariant points, three univariant curves and three crystallization fields (which are saturated with respect to MgBr26H2O, KBrMgBr26H2O and KBr, respectively, where KBrMgBr26H2O is an incongruent double salt). The phase diagram of the second system has one invariant point, two univariant curves and two crystallization fields (which are saturated with respect to MgBr26H2O and NaBr, respectively). The dissolution equilibrium constant of NaBr, KBr, MgBr26H2O and KBrMgBr26H2O at 348.15 K were fitted with Pitzer equations. A chemical model based on Pitzer equations was constructed to calculate the solubilities of salts in the two systems at 348.15 K. The calculated solubilities are in agreement with experimental results. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Solid–liquid equilibrium Pitzer model Solubility Solution density Bromide
1. Introduction Studies of phase equilibria in multicomponent salt–water systems at different temperatures are fundamental for the development and utilization of brine resources. Br-rich brines are widely distributed in the Qinghai-Tibet plateau and the Sichuan basin in China. In particular, the underground brines in the western Sichuan basin contain very abundant liquid mineral resources. The contents of boron, potassium, and bromine in the brines are far beyond the lowest grades for industrial utilization [1,2]. The underground brines have stable chemical properties, and have high concentrations of potassium, sodium, boron, bromine, as well as accompanying lithium, strontium, magnesium, calcium, and many other useful components. The highest content of potassium (K+) in the brines is up to 53.27 g L1, which is much higher than those in the Qarhan salt lake brine in Qinghai (12.1 g L1), the Zabuye salt brine in Tibet, China (27.0 g L1), and the Searles salt lake brine (USA) (23.1 g L1) [1,2]. Underground brines are very complex salt–water systems, whose formation often involves solid–liquid equilibria.
* Corresponding author at: College of Materials, Chemistry and Chemical Engineering, Chengdu University of Technology, Chengdu 610059, PR China. Tel.: +86 13032845233; fax: +86 28 84079074. E-mail addresses: [email protected], [email protected] (S. Sang). http://dx.doi.org/10.1016/j.fluid.2015.02.015 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
Furthermore, the phase diagrams at different temperatures play an important role in exploiting the brine resources and understanding the geochemical behavior of the brine–mineral systems. Therefore, it is very necessary and urgent to investigate the thermodynamic (especially the phase equilibrium) properties of Br-rich brine–mineral systems at varying temperatures. The phase equilibria of some three to five-component bromidecontaining systems that are associated with the above brine– mineral system have been reported, such as the solid–liquid equilibria of the ternary Na–K–Br–H2O and K–Mg–Br–H2O systems at 323 K [3,4]; the quaternary systems Na–K–Br–SO4–H2O at 323 K [5], K–Cl–Br–SO4–H2O [6], the calculated quaternary system Na–K–Br–SO4–H2O at 323 K [7], as well as the phase equilibria of the quinary system Na–K–Mg–Cl–Br–H2O and the partial subsystems at 313 K [8]. Christov applied Pitzer equations to the ternary systems, and developed a thermodynamic model for the multicomponent systems Na–K–Mg–Ca–Br–H2O, Na–K–Mg–Br– H2O and Na–K–Mg–Br–SO4–H2O at high concentrations between 273 K and 373 K [9–11]. In this work, a similar model is adopted for the solid–liquid equilibria of the ternary KBr–MgBr2–H2O systems at 323.15 K [4]. The objectives of this work include three aspects: (1) measure the solubilities of salts in the aqueous solutions and the densities of the saturated solutions in the ternary systems KBr–CaBr2–H2O and NaBr–CaBr2–H2O at 348.15 K, and identify the equilibrium solid
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J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131
Table 1 Chemical sample specifications. Chemical name
Source
Material purity
Experimental pressure
NaBr KBr MgBr26H2O
Tianjin Zhiyuan Chemical Reagent Factory, China Chengdu area of the industrial development zone Xindu Mulan, China Shanghai Xinbao Fine Chemical Plant, China
0.99 mass fraction 0.99 mass fraction 0.98 mass fraction
0.1 MPa
2. Experimental
solution composition should be that of the saturated solution. Experimental results show that the equilibrium states can be attained in 10–15 days under continuous vibration, and the time for the clarification of an aqueous solution is about 4–6 days. Then the liquid samples and the wet residue samples were taken out for chemical analysis. The equilibrium solid phases were determined by the wet residue method.
2.1. Reagents and instruments
2.3. Analytical methods
Distilled water with conductivity less than 104 S m1 and pH 6.6 was used for the phase equilibrium experiments and chemical analysis of samples. An HZ-9613Y type thermostated vibrator with a precision 0.1 K was used in the solid–liquid equilibrium measurements. NaBr, 99.0% pure, was from Tianjin Zhiyuan Chemical Reagent Factory, China; MgBr26H2O, 98% pure, was from Shanghai Xinbao Fine Chemical Plant; KBr, 99.0% pure, was from the industrial development zone Xindu Mulan, Chengdu. The specifications of the chemical samples are summarised in Table 1.
The concentration of K+ was obtained by gravimetric methods using sodium tetraphenylborate (uncertainty: 0.5%). The concentration of Mg2+ was determined by titration with an EDTA standard solution in the presence of the indicator with Eriochrome Black T, ammonium chloride buffer solution was used for maintaining the high pH (10–11) of solutions in the complexometric titration process (uncertainty: 0.3%). The concentration of Br was measured by titration with silver nitrate solution (the Mohr method, uncertainty: 0.3%). The concentration of Na+ is evaluated according to the charge balance of ions. The details of the above analytical methods can be found in the literature [12]. Solution density is measured by the density bottle method with a precision of 0.0002 g.
phases and construct the experimental phase diagrams of the two ternary systems; (2) use Pitzer equations to fit dissolution equilibrium constant of salts; (3) use the thermodynamic parameters available to develop a thermodynamic model for the prediction of bromide solubilities in the two ternary systems.
2.2. Experimental methods Experiments here were conducted by the method of isothermal solution saturation. The samples of ternary systems were prepared by gradually adding the second salt to the binary saturated system at 348.15 K. The solid reagents and water were prepared in 100 mL glass bottles. Then all the bottles are sealed and placed in the thermostated vibrator (HZ-9613Y). The clarified solutions were taken out periodically for chemical analysis. If the solution composition does not change any more, the system can be considered to reach thermodynamic equilibrium. In this state, the
3. Results and discussions 3.1. The KBr–MgBr2–H2O system The solubilities of salts in the system KBr–MgBr2–H2O at 348.15 K are given in Table 2. The ion concentrations in the saturated solution and the wet residue compositions are expressed
Table 2 Salt solubilities and solution densities of the system KBr–MgBr2–H2O at 348.15 K. No
1,A 2 3 4 5 6 7 8 9 10 11 12,E 13 14 15 16 17 18,F 19 20 21 22,B
Composition of liquid, 100w
Composition of wet residue, 100w
KBr
MgBr2
KBr
MgBr2
48.4 47.4 36.5 33.1 26.2 25.2 20.1 16.8 12.2 8.90 6.24 4.57 2.40 1.96 1.74 1.68 1.67 1.62 1.12 0.83 0.33 0.00
0.00 1.30 10.1 13.6 19.3 20.5 24.4 27.9 32.2 35.7 39.3 46.4 50.1 50.9 51.4 51.8 51.9 52.3 52.6 52.7 53.1 53.5
93.7 92.0 89.5 81.4 78.3 67.1 56.8 40.89 22.6 15.3 13.8 7.8 3.34 – 3.26 2.32 – 1.69 – 0.98 0.77 0.00
0.00 1.25 2.28 5.28 7.55 10.3 14.3 21.6 30.4 35.0 39.2 45.3 54.2 – 54.3 54.9 – 55.3 – 55.9 56.0 56.4
w is the mass fraction. b Abbreviations: Car(Br) = KBrMgBr26H2O.
Solution density, r/(g cm3)
Equilibrium solid phaseb
1.4864 1.4871 1.4884 1.4930 1.4931 1.4943 1.4958 1.4966 1.5016 1.5115 1.5316 1.6218 1.6504 1.6591 1.6643 1.6702 1.6719 1.6777 1.6755 1.6730 1.6737 1.6554
KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr + Car(Br) Car(Br) Car(Br) Car(Br) Car(Br) Car(Br) MgBr26H2O + Car(Br) MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O
J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131
129
ternary system. In Fig. 1a, there are three univariant curves (AE, EF and FB) and two co-saturated points (E and F). The solid phases in three crystallization fields are KBrMgBr26H2O, MgBr26H2O and KBr, respectively. The composition of equilibrium solution at the invariant point E is 46.4% MgBr2 and 4.57% KBr, and that of the invariant point F is 52.3% MgBr2 and 1.62% KBr. The crystallization field of MgBr26H2O is smaller than that of KBr, which indicates that the solubility of MgBr2 is greater than that of KBr in the system. The experimental results show that MgBr2 has strong common-ion effect on the dissolution of KBr. 3.2. Comparison of the results of the same system at 313.15 K and 348.15 K The phase diagram of the KBr–MgBr2–H2O system at 313.15 K is shown in Fig. 1b [8] for comparison. It can be seen that Fig. 1a and b has similar solubility curves, although their temperatures are different. The crystallization regions of MgBr2 and KBr enlarge as temperature increases, and this indicate that the solubilities of the two salts are positively correlated with temperature. The phase diagram of the ternary system KBr–MgBr2–H2O at 313.15 K has two cosaturated points, where point F is at 0.25% KBr and 50.2% MgBr2, and point E is at 1.69% KBr, 45.3% MgBr2. However, when the temperature increase to 348.15 K, F moves to 1.62% KBr and 52.3% MgBr2, and E moves to 4.57% KBr and 46.4% MgBr2. The results show that the mass fractions of MgBr2 and KBr in the equilibrium liquid phase increase when temperature increases from 313.15 K to 348.15 K. 3.3. The NaBr–MgBr2–H2O system
Fig. 1. Phase diagram of two ternary systems. (a) KBr–MgBr2–H2O at 348.15 K and (b) KBr–MgBr2–H2O at 313.15 K [8]. Note: MB = MgBr26H2O; Car (Br) = KBrMgBr26H2O.
in mass percentage. The solution density (r) is expressed with mass density (g cm3). According to the data in Table 2, the experimental stable equilibrium phase diagram of the ternary system at 348.15 K is plotted in Fig. 1a. Fig. 1a shows that there is an incongruent double salt with fixed composition 1:1:6 (bromcarnallite, KBrMgBr26H2O) in the
Table 3 gives the experimental solubilities and equilibrium solids of the system NaBr–MgBr2–H2O, as well as the saturated solution density (r). Fig. 2 is the experimental stable equilibrium phase diagram of the system at 348.15 K. In Fig. 2, points C and D are the saturation points of binary systems MgBr2–H2O and NaBr–H2O at 348.15 K, at which the mass percents of salts are 53.5% and 54.4%, respectively. Point C1 represents solid phase MgBr26H2O. Point G is the invariant point of the ternary system at 348.15 K. The phase diagram has two crystallization fields (C–C1–G and D–D1–G), where the equilibrium solids are MgBr26H2O and NaBr, respectively. Apparently, the crystallization field of MgBr26H2O is smaller than that of NaBr, that is, the solubility of MgBr2 is bigger than that of NaBr in the ternary system. The results indicate that MgBr2 has strong common-ion effect on the dissolution of NaBr.
Table 3 Salt solubilities and solution densities of the ternary system NaBr–MgBr2–H2O at 348.15 K. No
1,C 2 3 4 5 6 7 8,G 9 10 11 12 13 14 15,D
Composition of liquid phase, 100w
Composition of wet residue, 100w
NaBr
MgBr2
NaBr
MgBr2
54.4 49.6 45.2 39.9 32.3 15.9 10.4 9.28 7.57 5.65 3.95 2.78 2.14 1.85 0.00
0.00 3.57 6.92 11.9 19.2 35.3 45.6 48.2 48.6 49.8 50.8 51.6 51.9 52.4 53.5
93.9 87.2 80.9 79.3 68.1 44.9 37.9 15.7 6.94 4.65 2.72 2.08 0.97 0.34 0.00
0.00 1.43 3.52 5.03 9.82 24.1 28.7 48.3 56.5 58.5 59.4 59.8 60.7 60.9 61.0
w is the mass fraction.
Solution density, r/(g cm3)
Equilibrium solid phase
1.6168 1.6162 1.6175 1.6157 1.6156 1.6208 1.6762 1.6948 1.6745 1.6641 1.6539 1.6487 1.6437 1.6472 1.6554
NaBr NaBr NaBr NaBr NaBr NaBr NaBr NaBr + MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O
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J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131 Table 5 Dissolution equilibrium constant of salts (K) at 348.15 K calculated in this work versus those in reference [9]. Salt
ln K
NaBr KBr MgBr26H2O KBrMgBr26H2O
K ðMgBr2 6H2 OÞ ¼ 4g 3
m3
This work
Reference
6.414 3.457 12.069 15.951
6.426 3.425 12.039 15.989
a6w
(4)
K ðK BrMgBr2 6H2 OÞ ¼ 9g 2 ðKBrÞg 3 ðMgBr2 Þ m5 a6w
(5)
where Par(T) refers to the parameters of the solution model, T is in Kelvin. The Debye–Hückel term Af. is taken from the literature [15]. The constants in a1,a2, a5 and a6 are from Christov [9] and Spencer et al. [16]. In Eqs. (2)–(5), g i and mi are the activity coefficient and molality of solute species i, respectively.
Fig. 2. Phase diagram of the system NaBr–MgBr2–H2O at 348.15 K.
4. Solubility predictions 4.2. Solubility calculation 4.1. Model parameterization Pabalan and Pitzer [13] proposed a high temperature thermodynamic model for the concentrated electrolyte solution system Na–K–Mg–Ca–SO4–OH–H2O over a large temperature range (from 273.15 K to 473.15 K). Christov developed a thermodynamic model for the MgCl2–H2O and HCl–MgCl2–H2O systems at 273.15– 373.15 K [14]. In order to obtain thermodynamic properties and parameters of ternary solutions, such as osmotic coefficients f, binary and ternary ionic interaction parameters, and dissolution equilibrium constant K, the following equations are applied to the phase equilibria and chemical equilibria of a given solution: ParðTÞ ¼
a1 þ a2 T þ a5 T þ a6 lnT
(1)
KðKBrÞ ¼ g 2 m2
(2)
KðNaBrÞ ¼ g 2 m2
(3)
Based on Pitzer ion-interaction model for aqueous electrolyte solutions and the corresponding temperature-dependent parameter expressions, the dissolution equilibrium constants (K) of solid salts MgBr26H2O, KBrMgBr26H2O, NaBr and KBr were fitted by multiple linear regression. The constants in Eq. (1) for the binary and ternary interaction parameters are taken from the literature [9] (Table 4). Table 5 shows that the calculated dissolution equilibrium constants at 348.15 K agree well with the results in the literature. Harvie and Weare [17] showed that the Pitzer approach can accurately calculate the salt solubilities in complex brines. The solubilities of salts in the present two ternary systems at 348.15 K are calculated with the Pitzer model. As shown in Figs. 3 and 4, the predicted phase diagram of the two ternary systems at 348.15 K are in agreement with the experimental results. Table 6 is a comparison of the calculated and experimental solubilities at the invariant points of the two ternary systems and the saturated solution compositions of relevant binary subsystems. As can be seen from Figs. 3 and 4, there are obvious deviations between the calculated and experimental solubilities. The sources of deviations should include: (1) experimental uncertainty; (2) the deviations of
Table 4 Binary and ternary interaction parameters in Eq. (1). Parameters
a1
a2
a5
a6
b(0)Na,Br(273.15–573.15 K) b(1)Na,Br(273.15–573.15 K)
7.11600256E–01 4.97335195E00 7.34172496E–02 4.79896100E–01 4.13092017E00 5.93226684E–02 7.14660368E00 6.26940853E01 4.20446793E–01 5.02312111E–02 1.73305922E–02 0 6.05037096E + 01 0.07E00 1.69940176E–01
7.51986135E–04 8.57795255E–03 8.71449532E–05 4.17396303E–04 6.85308052E–03 6.33899074E–05 1.02197350E–02 9.95433504E–02 5.9813951E–04 0 3.50504594E–05 0 1.78735421E–02 0 0
1.09266366E + 02 7.38610135E + 02 1.33019597E + 01 9.05196847E + 01 7.04957954E + 02 1.17934031E + 01 1.09274058E03 1.03606736E04 7.29856800E 01 1.40213141E + 01 1.28020967E00 0 1.55748662E03 0 4.93791545E01
0 0 0 0 0 0 0 0 0 0 0 –1.06419353E01 0 0
’
C
Na,Br(273.15–573.15 K)
b(0)K,Br(273.15K–573.15 K) b(1)K,Br(273.15K–573.15 K)
C’K,Br(273.15–573.15 K) b(0)MgBr2(273.15–438.15 K) b(1)MgBr2(273.15–438.15 K) C’MgBr2(273.15–438.15 K) uNa,K a(273.15–523.15 K) cNa,K,Br(273.15–348.15 K) uK,Mgb(273.15–473.15 K) cK,Mg,Br(273.15–323.15 K) uNa,Mgc (273.15–473.15 K) cNa,Mg,Br(273.15–373.15 K) a
[9] [9] [9] [9] [9] [9] [9] [9] [9] [3,9] [3,9] [4,9] [4,9] [9,10] [9,10]
Parameter determined by Greenberg and Moller [18] and validated by Christov and Moller [19]. Parameter in the model of Harvie and Weare at 298.15 K and validated in the T-variable (273.15–473.15 K) model of Pabalan and Pitzer [13] and the model of Balarew et al. [20] for the KBr–MgBr2–H2O system at 298.15 K. c Parameter determined in the model of Harvie and Weare at 298.15 K and used in the T-variable (273.15–473.15 K) model of Pabalan and Pitzer [13]. These parameters are validated in the mixed solution models of Christov [21,22] at 273.15 and 298.15 K and in the T-variable (Na–K–Mg–Ca–Br–H2O) model presented in Refs. [9,10]. b
J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131
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Table 6 Comparison of experimental and calculated invariant points of the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O and the saturated solution compositions of the relevant binary subsystems at 348.15 K.a Points
m/(mol kg1) KBr
B/C B0 /C0 A A0 E E0 F F0 D D0 G G0 a b
Fig. 3. Comparison of calculated and experimental solubilities of salts in the system K Br–MgBr2–H2O at 348.15 K. *: experimental; ~: calculated.
the ion-interaction parameters of Pitzer equations due to the regression and the experimental data used in the regression, although the regression equation is applicable in certain temperature range, the accuracy of the ion-interaction model requires further validation at high temperatures and high concentrations. Overall, the above results indicate that the model in this work is capable of a reasonable prediction of the salt solubilities in the ternary systems in question. 5. Conclusions The solubilities of salts, the densities of saturated solutions and the equilibrium solids in the systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K were determined with the method of isothermal solution saturation. According to the experimental data, the stable equilibrium phase diagrams of the two ternary systems were constructed. Based on Pitzer model and
Equilibrium solid phaseb
NaBr
MgBr2
11.57 11.48 2.12 2.10
6.25 6.22 0.00 0.00 5.15 5.12 6.16 6.12 0.00 0.00 6.16 6.15
0.00 0.00 7.96 7.92 0.78 0.75 0.30 0.30
MgBr26H2O MgBr26H2O KBr KBr KBr + Car (Br) KBr + Car (Br) MgBr26H2O + Car(Br) MgBr26H2O + Car(Br) NaBr NaBr NaBr + MgBr26H2O NaBr + MgBr26H2O
A–G: experimental results; A0 –G0 : calculated results. Car (Br) = KBrMgBr26H2O.
temperature–dependent parameter expressions, the dissolution equilibrium constant of salts are fitted well. Salt solubilities of the ternary systems are predicted at 348.15 K. The results indicate that the Pitzer model based on the temperature–dependent parameter expressions are applicable for the two ternary systems. Acknowledgements This project was supported by the National Natural Science Foundation of China (41373062, U1407108), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20125122110015), and Fund of Key Laboratory of Salt Lake Resources and Chemistry (KLSLRC–KF–13–HX–5), Chinese Academy of Sciences (Qinghai Institute of Salt Lakes). We are grateful to Prof. Jiawen Hu and Christomir Christov give valuable suggestions in improving the manuscript. Our special thanks go to Associate Editor Th. W. De Loos, and two reviewers for their helpful comments on this paper. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
Fig. 4. Comparison of calculated and experimental solubilities of salts in the system Na Br–MgBr2–H2O at 348.15 K. *: experimental; ~: calculated.
[21] [22]
S.B. Shu, Y.L. Xu, E.X. Xu, C.W. Xiao, China Well Rock Salt 2 (2003) 23–26. Y.T. Lin, S.X. Cao, Chin. Geol. (China) 7 (2001) 45–47. C. Christov, Geochim. Cosmochim. Acta 71 (2007) 3557–3569. C. Christov, J. Chem. Thermodyn. 43 (2011) 344–353. S.H. Sang, M.L. Sun, H. Li, X. Zhang, K.J. Zhang, Chin. J. Inorg. Chem. 27 (2011) 845–849. D. Wang, S.H. Sang, X.X. Zeng, H.Y. Ning, Petrochem. Technol. (China) 40 (2011) 285–288. X.X. Zeng, S.H. Sang, D. Wang, J.J. Zhang, J. Chem. Eng. (China) 40 (2012) 32–35. Y.B. Weng, Study on Phase Equilibria of the Quinary System Na+, K+, Mg2+//Cl, Br–H2O at 313 K, Tianjin University, Tianjin, 2008. C. Christov, J. Chem.Thermodyn. 55 (2012) 7–22. C. Christov, J. Chem. Thermodyn. 47 (2012) 335–340. C. Christov, CALPHAD 36 (2012) 71–81. Institute of Qinghai Salt-Lakes, Chinese Academy of Sciences, Analytical Methods of Brines and Salts, second ed., Science Press, Beijing, 1988. R. Pabalan, K.S. Pitzer, Geochim. Cosmochim. Acta 51 (1987) 2429–2443. C. Christov, J. Chem. Eng. Data 54 (2009) 2599–2608. J. Ananthaswamy, Gordon Atklnson, J. Chem. Eng. Data 29 (1984) 81–87. R.J. Spencer, N. Møller, J.H. Weare, Geochim. Cosmochim. Acta 54 (1990) 575–590. C.E. Harvie, J.H. Weare, Geochim. Cosmochim. Acta 44 (1980) 981–997. J. Greenberg, N. Moller, Geochim. Cosmochim. Acta 53 (1989) 2503–2518. C. Christov, N. Moller, Geochim. Cosmochim. Acta 68 (2004) 1309–1331. C. Balarew, C. Christov, S. Petrenko, V. Valyashko, J. Solut. Chem. 22 (1993) 173–181. C. Christov, J. Chem. Thermodyn. 37 (2005) 1036–1060. C. Christov, CALPHAD 20 (1996) 501–509.
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Phase equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K Juanxin Hu a,b , Shihua Sang a,b, * , Meifang Zhou a,b , Wangyin Huang a,b a b
College of Materials, Chemistry and Chemical Engineering, Chengdu University of Technology, Chengdu 610059, PR China Key Laboratory of Mineral Resources Chemistry for the Universities in Sichuan Province, Chengdu 610059, PR China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 18 October 2014 Received in revised form 25 January 2015 Accepted 9 February 2015 Available online 11 February 2015
Solid–liquid equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K were determined with the method of isothermal solution saturation. Also determined are the densities of saturated solutions. According to the experimental data, the equilibrium phase diagrams of the two ternary systems were plotted. The phase diagram of first system has two invariant points, three univariant curves and three crystallization fields (which are saturated with respect to MgBr26H2O, KBrMgBr26H2O and KBr, respectively, where KBrMgBr26H2O is an incongruent double salt). The phase diagram of the second system has one invariant point, two univariant curves and two crystallization fields (which are saturated with respect to MgBr26H2O and NaBr, respectively). The dissolution equilibrium constant of NaBr, KBr, MgBr26H2O and KBrMgBr26H2O at 348.15 K were fitted with Pitzer equations. A chemical model based on Pitzer equations was constructed to calculate the solubilities of salts in the two systems at 348.15 K. The calculated solubilities are in agreement with experimental results. ã 2015 Elsevier B.V. All rights reserved.
Keywords: Solid–liquid equilibrium Pitzer model Solubility Solution density Bromide
1. Introduction Studies of phase equilibria in multicomponent salt–water systems at different temperatures are fundamental for the development and utilization of brine resources. Br-rich brines are widely distributed in the Qinghai-Tibet plateau and the Sichuan basin in China. In particular, the underground brines in the western Sichuan basin contain very abundant liquid mineral resources. The contents of boron, potassium, and bromine in the brines are far beyond the lowest grades for industrial utilization [1,2]. The underground brines have stable chemical properties, and have high concentrations of potassium, sodium, boron, bromine, as well as accompanying lithium, strontium, magnesium, calcium, and many other useful components. The highest content of potassium (K+) in the brines is up to 53.27 g L1, which is much higher than those in the Qarhan salt lake brine in Qinghai (12.1 g L1), the Zabuye salt brine in Tibet, China (27.0 g L1), and the Searles salt lake brine (USA) (23.1 g L1) [1,2]. Underground brines are very complex salt–water systems, whose formation often involves solid–liquid equilibria.
* Corresponding author at: College of Materials, Chemistry and Chemical Engineering, Chengdu University of Technology, Chengdu 610059, PR China. Tel.: +86 13032845233; fax: +86 28 84079074. E-mail addresses: [email protected], [email protected] (S. Sang). http://dx.doi.org/10.1016/j.fluid.2015.02.015 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
Furthermore, the phase diagrams at different temperatures play an important role in exploiting the brine resources and understanding the geochemical behavior of the brine–mineral systems. Therefore, it is very necessary and urgent to investigate the thermodynamic (especially the phase equilibrium) properties of Br-rich brine–mineral systems at varying temperatures. The phase equilibria of some three to five-component bromidecontaining systems that are associated with the above brine– mineral system have been reported, such as the solid–liquid equilibria of the ternary Na–K–Br–H2O and K–Mg–Br–H2O systems at 323 K [3,4]; the quaternary systems Na–K–Br–SO4–H2O at 323 K [5], K–Cl–Br–SO4–H2O [6], the calculated quaternary system Na–K–Br–SO4–H2O at 323 K [7], as well as the phase equilibria of the quinary system Na–K–Mg–Cl–Br–H2O and the partial subsystems at 313 K [8]. Christov applied Pitzer equations to the ternary systems, and developed a thermodynamic model for the multicomponent systems Na–K–Mg–Ca–Br–H2O, Na–K–Mg–Br– H2O and Na–K–Mg–Br–SO4–H2O at high concentrations between 273 K and 373 K [9–11]. In this work, a similar model is adopted for the solid–liquid equilibria of the ternary KBr–MgBr2–H2O systems at 323.15 K [4]. The objectives of this work include three aspects: (1) measure the solubilities of salts in the aqueous solutions and the densities of the saturated solutions in the ternary systems KBr–CaBr2–H2O and NaBr–CaBr2–H2O at 348.15 K, and identify the equilibrium solid
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Table 1 Chemical sample specifications. Chemical name
Source
Material purity
Experimental pressure
NaBr KBr MgBr26H2O
Tianjin Zhiyuan Chemical Reagent Factory, China Chengdu area of the industrial development zone Xindu Mulan, China Shanghai Xinbao Fine Chemical Plant, China
0.99 mass fraction 0.99 mass fraction 0.98 mass fraction
0.1 MPa
2. Experimental
solution composition should be that of the saturated solution. Experimental results show that the equilibrium states can be attained in 10–15 days under continuous vibration, and the time for the clarification of an aqueous solution is about 4–6 days. Then the liquid samples and the wet residue samples were taken out for chemical analysis. The equilibrium solid phases were determined by the wet residue method.
2.1. Reagents and instruments
2.3. Analytical methods
Distilled water with conductivity less than 104 S m1 and pH 6.6 was used for the phase equilibrium experiments and chemical analysis of samples. An HZ-9613Y type thermostated vibrator with a precision 0.1 K was used in the solid–liquid equilibrium measurements. NaBr, 99.0% pure, was from Tianjin Zhiyuan Chemical Reagent Factory, China; MgBr26H2O, 98% pure, was from Shanghai Xinbao Fine Chemical Plant; KBr, 99.0% pure, was from the industrial development zone Xindu Mulan, Chengdu. The specifications of the chemical samples are summarised in Table 1.
The concentration of K+ was obtained by gravimetric methods using sodium tetraphenylborate (uncertainty: 0.5%). The concentration of Mg2+ was determined by titration with an EDTA standard solution in the presence of the indicator with Eriochrome Black T, ammonium chloride buffer solution was used for maintaining the high pH (10–11) of solutions in the complexometric titration process (uncertainty: 0.3%). The concentration of Br was measured by titration with silver nitrate solution (the Mohr method, uncertainty: 0.3%). The concentration of Na+ is evaluated according to the charge balance of ions. The details of the above analytical methods can be found in the literature [12]. Solution density is measured by the density bottle method with a precision of 0.0002 g.
phases and construct the experimental phase diagrams of the two ternary systems; (2) use Pitzer equations to fit dissolution equilibrium constant of salts; (3) use the thermodynamic parameters available to develop a thermodynamic model for the prediction of bromide solubilities in the two ternary systems.
2.2. Experimental methods Experiments here were conducted by the method of isothermal solution saturation. The samples of ternary systems were prepared by gradually adding the second salt to the binary saturated system at 348.15 K. The solid reagents and water were prepared in 100 mL glass bottles. Then all the bottles are sealed and placed in the thermostated vibrator (HZ-9613Y). The clarified solutions were taken out periodically for chemical analysis. If the solution composition does not change any more, the system can be considered to reach thermodynamic equilibrium. In this state, the
3. Results and discussions 3.1. The KBr–MgBr2–H2O system The solubilities of salts in the system KBr–MgBr2–H2O at 348.15 K are given in Table 2. The ion concentrations in the saturated solution and the wet residue compositions are expressed
Table 2 Salt solubilities and solution densities of the system KBr–MgBr2–H2O at 348.15 K. No
1,A 2 3 4 5 6 7 8 9 10 11 12,E 13 14 15 16 17 18,F 19 20 21 22,B
Composition of liquid, 100w
Composition of wet residue, 100w
KBr
MgBr2
KBr
MgBr2
48.4 47.4 36.5 33.1 26.2 25.2 20.1 16.8 12.2 8.90 6.24 4.57 2.40 1.96 1.74 1.68 1.67 1.62 1.12 0.83 0.33 0.00
0.00 1.30 10.1 13.6 19.3 20.5 24.4 27.9 32.2 35.7 39.3 46.4 50.1 50.9 51.4 51.8 51.9 52.3 52.6 52.7 53.1 53.5
93.7 92.0 89.5 81.4 78.3 67.1 56.8 40.89 22.6 15.3 13.8 7.8 3.34 – 3.26 2.32 – 1.69 – 0.98 0.77 0.00
0.00 1.25 2.28 5.28 7.55 10.3 14.3 21.6 30.4 35.0 39.2 45.3 54.2 – 54.3 54.9 – 55.3 – 55.9 56.0 56.4
w is the mass fraction. b Abbreviations: Car(Br) = KBrMgBr26H2O.
Solution density, r/(g cm3)
Equilibrium solid phaseb
1.4864 1.4871 1.4884 1.4930 1.4931 1.4943 1.4958 1.4966 1.5016 1.5115 1.5316 1.6218 1.6504 1.6591 1.6643 1.6702 1.6719 1.6777 1.6755 1.6730 1.6737 1.6554
KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr KBr + Car(Br) Car(Br) Car(Br) Car(Br) Car(Br) Car(Br) MgBr26H2O + Car(Br) MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O
J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131
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ternary system. In Fig. 1a, there are three univariant curves (AE, EF and FB) and two co-saturated points (E and F). The solid phases in three crystallization fields are KBrMgBr26H2O, MgBr26H2O and KBr, respectively. The composition of equilibrium solution at the invariant point E is 46.4% MgBr2 and 4.57% KBr, and that of the invariant point F is 52.3% MgBr2 and 1.62% KBr. The crystallization field of MgBr26H2O is smaller than that of KBr, which indicates that the solubility of MgBr2 is greater than that of KBr in the system. The experimental results show that MgBr2 has strong common-ion effect on the dissolution of KBr. 3.2. Comparison of the results of the same system at 313.15 K and 348.15 K The phase diagram of the KBr–MgBr2–H2O system at 313.15 K is shown in Fig. 1b [8] for comparison. It can be seen that Fig. 1a and b has similar solubility curves, although their temperatures are different. The crystallization regions of MgBr2 and KBr enlarge as temperature increases, and this indicate that the solubilities of the two salts are positively correlated with temperature. The phase diagram of the ternary system KBr–MgBr2–H2O at 313.15 K has two cosaturated points, where point F is at 0.25% KBr and 50.2% MgBr2, and point E is at 1.69% KBr, 45.3% MgBr2. However, when the temperature increase to 348.15 K, F moves to 1.62% KBr and 52.3% MgBr2, and E moves to 4.57% KBr and 46.4% MgBr2. The results show that the mass fractions of MgBr2 and KBr in the equilibrium liquid phase increase when temperature increases from 313.15 K to 348.15 K. 3.3. The NaBr–MgBr2–H2O system
Fig. 1. Phase diagram of two ternary systems. (a) KBr–MgBr2–H2O at 348.15 K and (b) KBr–MgBr2–H2O at 313.15 K [8]. Note: MB = MgBr26H2O; Car (Br) = KBrMgBr26H2O.
in mass percentage. The solution density (r) is expressed with mass density (g cm3). According to the data in Table 2, the experimental stable equilibrium phase diagram of the ternary system at 348.15 K is plotted in Fig. 1a. Fig. 1a shows that there is an incongruent double salt with fixed composition 1:1:6 (bromcarnallite, KBrMgBr26H2O) in the
Table 3 gives the experimental solubilities and equilibrium solids of the system NaBr–MgBr2–H2O, as well as the saturated solution density (r). Fig. 2 is the experimental stable equilibrium phase diagram of the system at 348.15 K. In Fig. 2, points C and D are the saturation points of binary systems MgBr2–H2O and NaBr–H2O at 348.15 K, at which the mass percents of salts are 53.5% and 54.4%, respectively. Point C1 represents solid phase MgBr26H2O. Point G is the invariant point of the ternary system at 348.15 K. The phase diagram has two crystallization fields (C–C1–G and D–D1–G), where the equilibrium solids are MgBr26H2O and NaBr, respectively. Apparently, the crystallization field of MgBr26H2O is smaller than that of NaBr, that is, the solubility of MgBr2 is bigger than that of NaBr in the ternary system. The results indicate that MgBr2 has strong common-ion effect on the dissolution of NaBr.
Table 3 Salt solubilities and solution densities of the ternary system NaBr–MgBr2–H2O at 348.15 K. No
1,C 2 3 4 5 6 7 8,G 9 10 11 12 13 14 15,D
Composition of liquid phase, 100w
Composition of wet residue, 100w
NaBr
MgBr2
NaBr
MgBr2
54.4 49.6 45.2 39.9 32.3 15.9 10.4 9.28 7.57 5.65 3.95 2.78 2.14 1.85 0.00
0.00 3.57 6.92 11.9 19.2 35.3 45.6 48.2 48.6 49.8 50.8 51.6 51.9 52.4 53.5
93.9 87.2 80.9 79.3 68.1 44.9 37.9 15.7 6.94 4.65 2.72 2.08 0.97 0.34 0.00
0.00 1.43 3.52 5.03 9.82 24.1 28.7 48.3 56.5 58.5 59.4 59.8 60.7 60.9 61.0
w is the mass fraction.
Solution density, r/(g cm3)
Equilibrium solid phase
1.6168 1.6162 1.6175 1.6157 1.6156 1.6208 1.6762 1.6948 1.6745 1.6641 1.6539 1.6487 1.6437 1.6472 1.6554
NaBr NaBr NaBr NaBr NaBr NaBr NaBr NaBr + MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O MgBr26H2O
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J. Hu et al. / Fluid Phase Equilibria 392 (2015) 127–131 Table 5 Dissolution equilibrium constant of salts (K) at 348.15 K calculated in this work versus those in reference [9]. Salt
ln K
NaBr KBr MgBr26H2O KBrMgBr26H2O
K ðMgBr2 6H2 OÞ ¼ 4g 3
m3
This work
Reference
6.414 3.457 12.069 15.951
6.426 3.425 12.039 15.989
a6w
(4)
K ðK BrMgBr2 6H2 OÞ ¼ 9g 2 ðKBrÞg 3 ðMgBr2 Þ m5 a6w
(5)
where Par(T) refers to the parameters of the solution model, T is in Kelvin. The Debye–Hückel term Af. is taken from the literature [15]. The constants in a1,a2, a5 and a6 are from Christov [9] and Spencer et al. [16]. In Eqs. (2)–(5), g i and mi are the activity coefficient and molality of solute species i, respectively.
Fig. 2. Phase diagram of the system NaBr–MgBr2–H2O at 348.15 K.
4. Solubility predictions 4.2. Solubility calculation 4.1. Model parameterization Pabalan and Pitzer [13] proposed a high temperature thermodynamic model for the concentrated electrolyte solution system Na–K–Mg–Ca–SO4–OH–H2O over a large temperature range (from 273.15 K to 473.15 K). Christov developed a thermodynamic model for the MgCl2–H2O and HCl–MgCl2–H2O systems at 273.15– 373.15 K [14]. In order to obtain thermodynamic properties and parameters of ternary solutions, such as osmotic coefficients f, binary and ternary ionic interaction parameters, and dissolution equilibrium constant K, the following equations are applied to the phase equilibria and chemical equilibria of a given solution: ParðTÞ ¼
a1 þ a2 T þ a5 T þ a6 lnT
(1)
KðKBrÞ ¼ g 2 m2
(2)
KðNaBrÞ ¼ g 2 m2
(3)
Based on Pitzer ion-interaction model for aqueous electrolyte solutions and the corresponding temperature-dependent parameter expressions, the dissolution equilibrium constants (K) of solid salts MgBr26H2O, KBrMgBr26H2O, NaBr and KBr were fitted by multiple linear regression. The constants in Eq. (1) for the binary and ternary interaction parameters are taken from the literature [9] (Table 4). Table 5 shows that the calculated dissolution equilibrium constants at 348.15 K agree well with the results in the literature. Harvie and Weare [17] showed that the Pitzer approach can accurately calculate the salt solubilities in complex brines. The solubilities of salts in the present two ternary systems at 348.15 K are calculated with the Pitzer model. As shown in Figs. 3 and 4, the predicted phase diagram of the two ternary systems at 348.15 K are in agreement with the experimental results. Table 6 is a comparison of the calculated and experimental solubilities at the invariant points of the two ternary systems and the saturated solution compositions of relevant binary subsystems. As can be seen from Figs. 3 and 4, there are obvious deviations between the calculated and experimental solubilities. The sources of deviations should include: (1) experimental uncertainty; (2) the deviations of
Table 4 Binary and ternary interaction parameters in Eq. (1). Parameters
a1
a2
a5
a6
b(0)Na,Br(273.15–573.15 K) b(1)Na,Br(273.15–573.15 K)
7.11600256E–01 4.97335195E00 7.34172496E–02 4.79896100E–01 4.13092017E00 5.93226684E–02 7.14660368E00 6.26940853E01 4.20446793E–01 5.02312111E–02 1.73305922E–02 0 6.05037096E + 01 0.07E00 1.69940176E–01
7.51986135E–04 8.57795255E–03 8.71449532E–05 4.17396303E–04 6.85308052E–03 6.33899074E–05 1.02197350E–02 9.95433504E–02 5.9813951E–04 0 3.50504594E–05 0 1.78735421E–02 0 0
1.09266366E + 02 7.38610135E + 02 1.33019597E + 01 9.05196847E + 01 7.04957954E + 02 1.17934031E + 01 1.09274058E03 1.03606736E04 7.29856800E 01 1.40213141E + 01 1.28020967E00 0 1.55748662E03 0 4.93791545E01
0 0 0 0 0 0 0 0 0 0 0 –1.06419353E01 0 0
’
C
Na,Br(273.15–573.15 K)
b(0)K,Br(273.15K–573.15 K) b(1)K,Br(273.15K–573.15 K)
C’K,Br(273.15–573.15 K) b(0)MgBr2(273.15–438.15 K) b(1)MgBr2(273.15–438.15 K) C’MgBr2(273.15–438.15 K) uNa,K a(273.15–523.15 K) cNa,K,Br(273.15–348.15 K) uK,Mgb(273.15–473.15 K) cK,Mg,Br(273.15–323.15 K) uNa,Mgc (273.15–473.15 K) cNa,Mg,Br(273.15–373.15 K) a
[9] [9] [9] [9] [9] [9] [9] [9] [9] [3,9] [3,9] [4,9] [4,9] [9,10] [9,10]
Parameter determined by Greenberg and Moller [18] and validated by Christov and Moller [19]. Parameter in the model of Harvie and Weare at 298.15 K and validated in the T-variable (273.15–473.15 K) model of Pabalan and Pitzer [13] and the model of Balarew et al. [20] for the KBr–MgBr2–H2O system at 298.15 K. c Parameter determined in the model of Harvie and Weare at 298.15 K and used in the T-variable (273.15–473.15 K) model of Pabalan and Pitzer [13]. These parameters are validated in the mixed solution models of Christov [21,22] at 273.15 and 298.15 K and in the T-variable (Na–K–Mg–Ca–Br–H2O) model presented in Refs. [9,10]. b
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Table 6 Comparison of experimental and calculated invariant points of the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O and the saturated solution compositions of the relevant binary subsystems at 348.15 K.a Points
m/(mol kg1) KBr
B/C B0 /C0 A A0 E E0 F F0 D D0 G G0 a b
Fig. 3. Comparison of calculated and experimental solubilities of salts in the system K Br–MgBr2–H2O at 348.15 K. *: experimental; ~: calculated.
the ion-interaction parameters of Pitzer equations due to the regression and the experimental data used in the regression, although the regression equation is applicable in certain temperature range, the accuracy of the ion-interaction model requires further validation at high temperatures and high concentrations. Overall, the above results indicate that the model in this work is capable of a reasonable prediction of the salt solubilities in the ternary systems in question. 5. Conclusions The solubilities of salts, the densities of saturated solutions and the equilibrium solids in the systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K were determined with the method of isothermal solution saturation. According to the experimental data, the stable equilibrium phase diagrams of the two ternary systems were constructed. Based on Pitzer model and
Equilibrium solid phaseb
NaBr
MgBr2
11.57 11.48 2.12 2.10
6.25 6.22 0.00 0.00 5.15 5.12 6.16 6.12 0.00 0.00 6.16 6.15
0.00 0.00 7.96 7.92 0.78 0.75 0.30 0.30
MgBr26H2O MgBr26H2O KBr KBr KBr + Car (Br) KBr + Car (Br) MgBr26H2O + Car(Br) MgBr26H2O + Car(Br) NaBr NaBr NaBr + MgBr26H2O NaBr + MgBr26H2O
A–G: experimental results; A0 –G0 : calculated results. Car (Br) = KBrMgBr26H2O.
temperature–dependent parameter expressions, the dissolution equilibrium constant of salts are fitted well. Salt solubilities of the ternary systems are predicted at 348.15 K. The results indicate that the Pitzer model based on the temperature–dependent parameter expressions are applicable for the two ternary systems. Acknowledgements This project was supported by the National Natural Science Foundation of China (41373062, U1407108), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20125122110015), and Fund of Key Laboratory of Salt Lake Resources and Chemistry (KLSLRC–KF–13–HX–5), Chinese Academy of Sciences (Qinghai Institute of Salt Lakes). We are grateful to Prof. Jiawen Hu and Christomir Christov give valuable suggestions in improving the manuscript. Our special thanks go to Associate Editor Th. W. De Loos, and two reviewers for their helpful comments on this paper. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
Fig. 4. Comparison of calculated and experimental solubilities of salts in the system Na Br–MgBr2–H2O at 348.15 K. *: experimental; ~: calculated.
[21] [22]
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