Experimental and Thermodynamic Model Study on Solid and Liquid

Jun 30, 2016 - School of Chemistry and Chemical Engineering, Linyi University, ... at 333.15 K were fitted using the Pitzer and Harvie–Weare (HW) mo...
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Experimental and Thermodynamic Model Study on Solid and Liquid Equilibrium of Ternary System MgBr2−MgSO4−H2O at 333.15 K Rongjian Ying,† Dan Li,*,† Lingzong Meng,†,‡ Tianlong Deng,‡ and Yafei Guo‡ †

School of Chemistry and Chemical Engineering, Linyi University, Linyi 276000, P. R. China Tianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of Science and Technology, Tianjin 300457, P. R. China

‡

ABSTRACT: The solubilities and the refractive indices of the MgBr2−MgSO4−H2O system at 333.15 K were studied with the isothermal equilibrium solubility method. The phase diagram and refractive index diagram were plotted for this system at 333.15 K. The system belongs to hydrate II type. The phase diagram is constituted of three invariant points cosaturated with two salts, four univariant solubility isotherms saturated with one salt, and four stable crystallization fields in the ternary system corresponding to MgSO4· 6H2O (Hex), MgSO4·4H2O (Tet), MgSO4·H2O (Kie), and MgBr2·6H2O (Mb). The calculated refractive index data agree well with the experimental results. Combining the experimental solubility data of the ternary system, the Pitzer binary parameters for MgBr2 and MgSO4, and the Pitzer mixing ion-interaction parameter θBr,SO4, the Pitzer parameter ψMg,Br,SO4 and the solubility equilibrium constants Ksp of solid phases in the ternary system at 333.15 K were fitted using the Pitzer and Harvie−Weare (HW) model. Then the solubilities for the ternary system at 333.15 K were calculated. A comparison between the experimental and calculated solubilities illustrates that the predicted data obtained with the model are in accordance with experimental results.

1. INTRODUCTION The oil field brines in the Qaidam Basin of the Qinghai-Tibet Plateau and underground brines in Laizhou Bay of Shandong Province have high contents of bromine, which mostly reach the industrial grade for comprehensive and single exploitation.1,2 Bromide can be strongly enriched in hydrothermal water compared with seawater.3,4 The solid and liquid equilibrium and the phase diagrams are both the theoretical foundation for the exploitation of the brine resources. The solubility data (phase diagrams) of the brines can be used to predict the path of mineral crystallization and describe the geochemical behavior of brine. Therefore, investigation of the solubility data of bromine-containing systems at high temperatures is important for the comprehensive and effective exploitation of bromine from the brines.5 The MgBr2−MgSO4−H2O system is an important subsystem of the complex brine system. The ternary system has previously been studied at 273.15, 298.15, and 308.15 K since the 1960s,6 but the solubility data and the reports of the corresponding equilibrium solid phases are not complete. Recently, we gave a detailed study on the system at 288.15 and 323.15 K,7,8 it is found that there are three crystallization fields corresponding to MgSO4·7H2O, MgSO4·6H2O, and MgBr2·6H2O at 288.15 K, whereas four crystallization fields corresponding to MgSO4· 6H2O, MgSO4·4H2O, MgSO4·H2O, and MgBr2·6H2O at 323.15 K. The crystallization areas of the ternary system MgBr2−MgSO4−H2O vary greatly at different temperatures; moreover, the ternary system at higher temperature has not been reported in the literature to date. The Pitzer and Harvie− © XXXX American Chemical Society

Weare (HW) model, which is described in our study, was widely used in calculating the solubilities of the salt−water systems.9−13 However, studies on modeling the ternary system MgBr2−MgSO4−H2O at 333.15 K are still lacking in the literature. In this study, the solubilities and the refractive indices of the ternary system MgBr2−MgSO4−H2O at 333.15 K are determined. The Pitzer and HW model was also presented to calculate the solubilities for the MgBr2−MgSO4−H2O system at 333.15 K.

2. EXPERIMENTAL SECTIONS 2.1. Apparatus and Reagents. A thermostatic bath with rotating apparatus (model THZ-82, Jintan Yitong Electronics Co., Ltd., China) was used to study the solid and liquid equilibria. The temperature in the thermostatic bath was controlled at (333.15 ± 0.1) K in this study. The solid phase minerals were determined using Schreinemaker’s method14 and an X-ray diffractometer (D8 Advance, Bruker Ltd., Germany). The chemical sample information is presented in Table 1. All the chemicals were recrystallized before use except kieserite. The purity of the minerals was determined using a titrimetric analysis method.15 The water for chemical analysis was double distilled water (DDW) with conductivity ≤1.2 × 10−4 S·m−1 and pH ≈ 6.60 at 298.15 K. Received: April 5, 2016 Accepted: June 22, 2016

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DOI: 10.1021/acs.jced.6b00290 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Description of the Chemical Samples chemical name

source

initial mass fraction

purification method

final mass fraction

analysis method

MgBr2·6H2O MgSO4·7H2O MgSO4·H2O

Shanghai Xinbao Fine Chemical Plant Chengdu Aike Chemical Reagent Plant Chengdu Aike Chemical Reagent Plant

0.98 0.99 0.99

recrystallization recrystallization none

0.99 0.995 0.99

titration method for Mg2+ and Br− titration method for Mg2+ titration method for Mg2+

Table 2. Solubilities and Refractive Indices for the MgBr2−MgSO4−H2O System at 333.15 K and Pressure p = 0.1 MPaa composition of liquid phase, 100·wb no. 1, A 2 3 4 5 6 7 8 9 10,E 11 12 13 14,F 15 16 17 18 19 20 21,G 22,B

MgBr2 0.00 3.27 6.27 8.64 12.56 15.87 19.27 20.00 22.93 27.60 31.02 31.92 32.43 35.87 36.85 39.84 42.98 46.54 48.56 50.99 52.01 52.41

MgSO4 35.25 32.83 30.17 28.11 24.5 22.02 20.25 18.66 17.04 13.60 11.25 10.2 9.97 7.42 6.31 4.29 2.85 1.74 1.36 1.05 0.82 0.00

composition of wet residue, 100·wb MgBr2

MgSO4

e

1.14 2.87 3.78

44.35 43.2 42.37

8.97 8.14 9.36 13.13 13.53 16.02 15.42 22.00 24.93 26.77 27.67 28.12 29.05 33.20 44.72

39.13 38.86 38.96 38.17 40.48 37.12 38.48 33.09 31.83 31.79 32.6 33.51 34.5 30.80 15.19

refractive index nD expt value

calcd value

relative errord

equilibrium solid phasec

1.3957 1.4006 1.403 1.4039 1.406 1.4082 1.4099 1.4113 1.4141 1.4202 1.4232 1.4239 1.4245 1.4283 1.4292 1.4319 1.4369 1.4447 1.4521 1.4608 1.4648 1.4594

1.3957 1.3992 1.4015 1.4034 1.4061 1.4096 1.4147 1.4133 1.4176 1.4226 1.4267 1.4269 1.4277 1.4314 1.4317 1.4353 1.4405 1.4476 1.4521 1.4578 1.4600 1.4594

0.00 −0.10 −0.11 −0.04 0.01 0.10 0.34 0.14 0.25 0.17 0.24 0.21 0.22 0.22 0.17 0.24 0.25 0.20 0.00 −0.20 −0.33 0.00

Hex Hex Hex Hex Hex Hex Hex Hex Hex Hex + Tet Tet Tet Te Tet + Kie Kie Kie Kie Kie Kie Kie Mb + Kie Mb

a

Standard uncertainties u, u(T) = 0.1 K, u(p) = 0.005 MPa, ur(w) for MgBr2 and MgSO4 are 0.003 and 0.006 in mass fraction, respectively. u(nD) = 0.0001. bw, mass fraction. cHex, MgSO4·6H2O; Tet, MgSO4·4H2O; Kie, MgSO4·H2O; Mb, MgBr2·6H2O. dRelative error = (calculated value − experimental value)/ experimental value. eBlank means not determined.

2.2. Experimental Methods. The isothermal equilibrium solubility method was used in this study, and the experimental methods are available in our previous works.7,8 In briefly, the brines with different quantities of salts and DDW were prepared in the clean polyethylene bottles with volume of 150 mL, which were capped tightly and layed on the rotating apparatus in the thermostatic bath, with the temperature at (333.15 ± 0.1) K. The bottles rotated along with the rotating apparatus with speed at 120 rpm to accelerate the equilibrium. When the compositions of the liquid phase in the bottle became stable, it indicated that the solid and liquid got equilibrium. It is pointed out that the solid phase in the bottle should always exist during the equilibrium process. The equilibrium point usually took about 5 days. After equilibrium achieved, the rotary system was paused for 1 h, and then some clarified liquid phases were taken out for quantitative analysis, and some other solutions were used for the refractive index measurement. Meanwhile, the equilibrium solid phases were determined by the wet residue method14 and further identified by X-ray powder diffraction. The remainder of the mixtures would be used to synthesize another system point. 2.3. Analytical Methods. The ion concentrations of liquid phases and wet residues were analyzed with titrimetric analysis method. The Mg2+ concentration was determined by titration with an EDTA standard solution in the presence of the

indicator Eriochrome Black-T with a standard uncertainty (ur(w)) less than ±0.003 in mass fraction. The Br− ion concentration was determined by titration with a standard solution of Hg(NO3)2 in the presence of mixed indicator of diphenylcarbazone and bromophenol blue (precision: ±0.003 in mass fraction).15 The SO42− was obtained according to ion balance. The liquid phase refractive index (nD) was measured with a WZS-1 type abbe refractometer at (333.15 ± 0.1) K, with an uncertainty of ±0.0001.

3. RESULTS AND DISCUSSION 3.1. Phase Diagram. The experimental solubilities of the MgBr2−MgSO4−H2O system at 333.15 K are tabluated in Table 2. The salt concentrations in the stable equilibrium solutions and the wet residue are expressed as mass fractions. According to the experimental data of Table 2, the phase diagram of the system was plotted, as shown in Figure 1. In Table 2 and Figure 1, the points A, B are the eutectic points of the binary systems MgSO4−H2O and MgBr2−H2O. The phase diagram has four crystallization regions: hexahydrite (MgSO4·6H2O, Hex), tetrahydrite (MgSO4·4H2O, Tet), kieserite (MgSO4·H2O, Kie), and magnesium bromide hexahydrate (MgBr2·6H2O, Mb). The crystallization area of Hex, Kie, Tet, and Mb decreases in sequence. These results illustrate that magnesium sulfate has smaller solubility than that B

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magnesium bromide was considerably smaller than that for hydrated magnesium sulfate. 3.2. Refractive Index Data. Using the experimental results in Table 2, the relationship of the solution refractive indices with concentration of magnesium bromide is presented in Figure 3. It is seen that the refractive indices of solutions

Figure 1. Stable phase diagram of the MgBr2−MgSO4−H2O system at 333.15 K: △, solubility data in this work; , solubility isotherm curve; ..., wet residue line; Hex, MgSO4·6H2O; Tet, MgSO4·4H2O; Kie, MgSO4·H2O; Mb, MgBr2·6H2O.

of magnesium bromide. The concentration of magnesium sulfate decreases with magnesium bromide concentration increasing for the strong salt-out effecting from magnesium bromide. The points E, F, and G are the invariant points saturated with salts (Hex + Tet), (Tet + Kie), and (Kie + Mb), respectively. The curves AE, EF, FG, and GB are the univariant curves saturated with a single salt (Hex, Tet, Kie, and Mb). There are many hydrous salt of magnesium sulfate formed in this system, and double salts and solid solutions were not formed. Therefore, the system belongs to hydrate II type. The solubility data for the ternary system MgBr2−MgSO4− H2O at 273.15, 288.15, 298.15, 308.15, and 323.15 K have been reported in the literature.6−8 Hex, Tet and Kie are found in the system both at 323.15 and 333.15 K, so the comparison for the phase diagrams of the system at 323.15 and 333.15 K was shown in Figure 2. The patterns for the solubility curves at two

Figure 3. Refractive index diagram for the MgBr2−MgSO4−H2O system at 333.15 K: △, experimental data in this work; , experimental curve.

change regularly with the content change of magnesium bromide, and reach the maximum value at the eutectic point G of (Kie + Mb). The following empirical equation of the refractive index in electrolyte solutions developed in the previous study,16,17 was applied to calculate the refractive indices of the solution ⎛n ⎞ ln⎜ D ⎟ = ⎝ nD0 ⎠

∑ Bi × wi

(1)

nD0 (1.327250) is the refractive index of DDW at 333.15 K, wi is the mass fraction of the salt i in the solution, which is the same as that in Table 2. The refractive index coefficient Bi was calculated with the experimental data of the binary system at 333.15 K. The Bi for MgBr2 and MgSO4 were 0.001811 and 0.001427, respectly. Then, the refractive indices were calculated and presented in Table 2. The error between the calculated results and experimental values are no more than 0.34%. The calculated refractive index data agree well with the experimental data. There results illustrate that the coefficients Bi obtained in this study are dependable and can be used to the refractive index calculation in more complicated system.

4. THERMODYNAMIC MODELING Pitzer and HW model was applied to the aqueous solutions in this study, which incorporate the concentration dependent equations showing the specific interactions of the solutes.18,19 These equations are based on the excess free energy, all the activity expressions are consistent, which can be used for parameter evaluation and other thermodynamic properties calculation. By using the activity coefficients and the solubility products of the equilibrium solid phases, the solid and liquid equilibria (solubilities) can be predicted. 4.1. Model Parameterization. The Debye−Hü ckel parameter Aø (0.419008) at 333.15 K was obtained from the literature.20 The Pitzer binary parameters of MgBr2 and MgSO4, the mixing parameters θBr,SO4 were obtained with the

Figure 2. Comparison of the phase diagrams of the MgBr2−MgSO4− H2O system at 323.15 and 333.15 K: ▲, experimental data at 323.15 K;8 △, experimental data at 333.15 K in this work.

temperatures are similar. Compared to the system at 323.15 K, the crystallization area of Kie became bigger, whereas it becomes smaller for Tet at 333.15 K. The areas of the crystallized regions of magnesium bromide and magnesium sulfate decrease as the temperature increasing from 273.15 to 333.15 K. The change of crystallization zone for hydrated C

DOI: 10.1021/acs.jced.6b00290 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Single-Salt and Mixing Ion-Interaction Parameters of the MgBr2−MgSO4−H2O System at 333.15 K species

β(0)

β(1)

MgBr2 MgSO4 Br, SO42− Mg2+, Br−, SO42−

0.461873 0.231323

1.567907 3.705625

β(2)

C(ø)

−44.6211

−0.002099 0.016538

θ

Ψ

ref

0.049506

21 22 23 this work

0.03

fields. Solid solutions and double salts are not formed in this sytem. The refractive indices of the solution are positively correlated with the magnesium bromide concentration, with the maximum value occurring at point G (MgSO4·H2O + MgBr2· 6H2O). The calculated refractive index data are in accordance with the experimental results. Combining the experimental solubility data of the ternary system, the single-salt parameters for MgBr2 and MgSO4, and the mixed ion-interaction parameter θBr,SO4, the Pitzer mixing parameters ψMg,Br,SO4 and the solubility equilibrium constants Ksp of solid phases were fitted with the Pitzer and (HW) model. Then the solubilities for the ternary system at 333.15 K were demonstrated. A comparison of the calculated and experimental solubilities of the ternary system showed that the predicted solubilities are in accordance with experimental values, which illustrates that the obtained Pitzer mixing triple interaction parameters ψMg,Br,SO4 and the solubility equilibrium constants parameters of minerals in the system are dependable for the solubility calculation in the bromide-containing system.

temperature-dependent equations presented in the literature.21−23 The solubility data in the curve AE saturated with Hex for the ternary system MgBr2−MgSO4−H2O in this study were used to fit the mixing parameters ψMg,Br,SO4 through a multiple linear regression procedure. All of the parameters used in the prediction are presented in Table 3. Using the parameters and the solubility data of the ternary system in this work, the equilibrium constants of the salts in the ternary system at 323.15 K were calculated for each stable solution by the activity product constant method. These average equilibrium constants (lnKaver) for the equilibrium solid salts of MgSO4·6H2O, MgSO4·4H2O, MgSO4·H2O, and MgBr2· 6H2O are −2.9542, −0.5721, 3.1702, and 12.3502, respectively. 4.2. Solubility Calculation. The solubilities for the ternary system at 333.15 K were calculated to validate the accuracy of the model. On the basis of the experimental and the calculated data, the phase diagrams were constructed in Figure 4. The

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. and Fax: +86-539-8766600. Funding

This work was supported by the National Natural Science Foundation of China (21406104, 21306136, U1507112 and U1406113), and China Postdoctoral Science Foundation (2015M581303). Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 4. Comparison of the experimental and calculated phase diagrams of the MgBr2−MgSO4−H2O system at 333.15 K. Δ, experimental data; , calculated isotherm curve; Hex, MgSO4· 6H2O; Tet, MgSO4·4H2O; Kie, MgSO4·H2O; Mb, MgBr2·6H2O.

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5. CONCLUSIONS The solubilities and the refractive indices of the MgBr2− MgSO4−H2O system at 333.15 K were studied with the isothermal equilibrium solubility method. The phase diagram and refractive index diagram were presented for this system at 333.15 K. The phase diagram is constituted of three invariant points cosaturated with two salts, four univariant solubility isotherms saturated with one salt, and four stable crystallization D

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equilibria and physicochemical properties of the ternary system MgBr2 + MgSO4 + H2O at 323.15 K. Fluid Phase Equilib. 2013, 342, 88−94. (9) Christov, C. Isopiestic investigation of the osmotic coefficients of aqueous CaBr2 and study of bromide salt solubility in the NaBr− CaBr2−H2O system at 50°C: Thermodynamic model of solution behavior and solid−liquid equilibria in the CaBr2−H2O, and NaBr− CaBr2−H2O systems to high concentration and temperature. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2011, 35, 42−53. (10) Deng, T. L. Phase equilibrium for the aqueous system containing lithium, sodium, potassium, chloride, and borate ions at 298.15 K. J. Chem. Eng. Data 2004, 49, 1295−1299. (11) Meng, L. Z.; Yu, X. P.; Li, D.; Deng, T. L. Solid-liquid metastable equilibria of the reciprocal quaternary system (LiCl + MgCl2 + Li2SO4 + MgSO4 + H2O) at 323.15 K. J. Chem. Eng. Data 2011, 56, 4627−4632. (12) Guo, Y. F.; Liu, Y. H.; Wang, Q.; Lin, C. X.; Wang, S. Q.; Deng, T. L. Phase equilibria and phase diagrams for the aqueous ternary system (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K. J. Chem. Eng. Data 2013, 58, 2763−2767. (13) Liu, Y. H.; Guo, Y. F.; Yu, X. P.; Wang, S. Q.; Deng, T. L. Solid−liquid metastable phase equilibria in the five-component system (Li + Na + K + Cl + SO4 + H2O) at 308.15 K. J. Chem. Eng. Data 2014, 59, 1685−1691. (14) Song, P. S. Studies on the application of the wet residues method in phase equilibrium for the salt-water systems (in Chinese). J. Salt Lake Res. 1991, 1, 42−46. (15) Qinghai Institute of Salt Lakes, Chinese Academy of Science. Analytical methods of brines and salts, 2nd ed.; Chinese Science Press: Beijing, 1988; in Chinese. (16) Song, P. S.; Du, X. H.; Xu, H. C. The phase equilibrium and properties of the saturated solution in the ternary system Li2B4O7− Li2SO4−H2O at 25 °C (in Chinese). Kexue Tongbao 1984, 29, 1072− 1076. (17) Song, P. S.; Du, X. H. Phase equilibrium and properties of the saturated solution in the quaternary system Li2B4O7−Li2SO4−LiCl− H2O at 25 °C (in Chinese). Chin. Sci. Bull. 1986, 3, 209−213. (18) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (19) Harvie, C. E.; Weare, J. H. The prediction of mineral solubilities in natural waters: the Na−K−Mg−Ca−Cl− SO4−H2O system from zero to high concentration at 25 °C. Geochim. Cosmochim. Acta 1980, 44, 981−997. (20) Møller, N. The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na-Ca-Cl-SO4-H2O system to high temperature and concentration. Geochim. Cosmochim. Acta 1988, 52, 821−837. (21) Christov, C. Study of bromide salts solubility in the (m1KBr + m2CaBr2) (aq) system at T = 323.15 K. Thermodynamic model of solution behaviour and (solid + liquid) equilibria in the ternaries (m1KBr + m2CaBr2) (aq), and (m1MgBr2 + m2CaBr2) (aq), and in the quinary (Na + K + Mg + Ca + Br + H2O) systems to high concentration and temperature. J. Chem. Thermodyn. 2012, 55, 7−22. (22) Pabalan, R. T.; Pitzer, K. S. Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O. Geochim. Cosmochim. Acta 1987, 51, 2429−2443. (23) Christov, C. Temperature variable chemical model of bromide− sulfate solution interaction parameters and solid−liquid equilibria in the Na−K−Ca−Br−SO4−H2O system. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2012, 36, 71−81.

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