Harvie – Weare Research Articles

Calculation of Solubility of Borate in the Brine Systems Using Pitzer Thermodynamic Model

The solubility calculation of the system Na+//Cl–, $${\text{SO}}_{4}^{{2 - }}$$, borate–H2O and its subsystems Na+//Cl–, borate–H2O, Na+//$${\text{SO}}_{4}^{{2 - }}$$, borate–H2O were carried out with two models on the basis of Pitzer and Harvie-Weare (HW) model. The first model (model I) is to assume that there is only one boron ion B4O5(OH)$$_{4}^{{2 - }}$$ in the solution. The other model (model II) is to assume that there are four forms for boron corresponding to B(OH)3, B(OH)$$_{4}^{ - }$$, B3O3(OH)$$_{4}^{ - }$$, and B4O5(OH)$$_{4}^{{2 - }}$$ in the solution. The data calculated with model II are closer to the experimental data than those with model I. The model I can also be used for solubility calculation in the systems containing borate with the fitted solubility product of borate if the parameters for boron ions are lacking. The results of solubility calculation in this study are essential for the development of universal thermodynamic models for brine systems containing borate.

Solid–Liquid Metastable Phase Equilibria in the Ternary System (MgCl2 + MgSO4 + H2O) at 323.15 K

The solubilities and the densities in the aqueous ternary system (MgCl2 + MgSO4 + H2O) at 323.15 K were determined by the isothermal evaporation method. The phase diagram was drawn for this system at 323.15 K. The phase diagram consists of two invariant points, three univariant curves, and three crystallization regions corresponding to bischofite (MgCl2 · 6H2O), tetrahydrate (MgSO4 · 4H2O) and hexahydrite (MgSO4 · 6H2O). Neither double salts nor solid solution was found. Based on the Pitzer and Harvie–Weare (HW) model, the solubility equilibrium constants for the salts were fitted with the solubilities in this research work, and the solubilities of the ternary system at 323.15 K were calculated. Comparisons between the calculated and measured solubilities show that the predicted data agree well with the experimental results.

Thermodynamic Study of Solid–Liquid Equilibrium in NaCl–NaBr–H2O System at 288.15 K

The solubility data, composition of the solid solution and refractive indices of the NaCl–NaBr–H2O system at 288.15 K were studied with the isothermal equilibrium dissolution method. The solubility diagram and refractive index diagram of this system were plotted at 288.15 K. The solubility diagram consists of two crystallization zones for solid solution Na(Cl,Br) · 2H2O and Na(Cl,Br), one invariant points cosaturated with two solid solution and two univariant solubility isothermal curves. On the basis of Pitzer and Harvie-Weare (HW) chemical models, the composition equations and solubility equilibrium constant equations of the solid solutions at 288.15 K were acquired using the solubility data, the composition of solid solutions, and binary Pitzer parameters. The solubilities calculated using the new method combining the equations are in good agreement with the experimental data.

Experimental and thermodynamic modeling study of solid-liquid equilibrium in ternary systems NaBr–SrBr2–H2O and KBr–SrBr2–H2O at 288.15 K and 0.1 MPa

The solubilities and refractive indices of the NaBr–SrBr2–H2O and KBr–SrBr2–H2O systems at 288.15K were investigated with the isothermal dissolution method. The phase diagrams and refractive index diagrams were plotted for the two systems at 288.15K. The phase diagrams consist of one two-salt cosaturated invariant point, two univariant solubility isotherms, and two stable crystallization fields. The two systems belong to the simple eutectic type, and neither double salt nor solid solution was found. The refractive indices change regularly with the strontium bromide concentration increasing in solution, and reach the maximum value at the eutectic point. On the basis of Pitzer and Harvie-Weare (HW) model, the binary and mixing Pitzer parameters and solubility equilibrium constants of equilibrium solid salts for the two ternary systems at 288.15K were acquired. And then, the solubilities for the ternary systems at 288.15K were demonstrated. A comparison shows that the calculated solubilities agree well with the experimental data.

Solid-liquid equilibria in the ternary system NaBr–KBr–H2O at 398 K

The solubilities of the ternary system NaBr–KBr–H2O were investigated by isothermal method at 398 K. On the basis of the experimental data, the phase diagram was plotted. In the phase diagram of ternary system NaBr–KBr–H2O at 398 K, no complex salt or solid solution was found. It belongs to simple co-saturation type. There are only one invariant point, two univariant curves, and two crystallization fields corresponding to NaBr and KBr. Using the equilibrium solubilities data of the ternary system at 398 K, mixing ioninteraction parameter ΨNa,K,Br of Pitzer’s equation was fitted by multiple linear regression method. Based on the Pitzer model and its extended Harvie–Weare (HW) model, the solubilities of phase equilibrium in the ternary system NaBr–KBr–H2O at 398 K were calculated. The phase diagram of the ternary system was plotted. The results show that calculated values have a good agreement with measured experimental data. It can demonstrate the accuracy of the experimental data, and it also shows that reasonable parameters of the Pitzer model can be used in ternary system NaBr–KBr–H2O at 398 K.

Experimental and Thermodynamic Model Study on Solid and Liquid Equilibrium of Ternary System MgBr2–MgSO4–H2O at 333.15 K

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...

Solid–liquid equilibria in the NaCl–SrCl2–H2O system at 288.15 K

The phase equilibria in the ternary system NaCl–SrCl2–H2O at 288.15 K were studied with the isothermal equilibrium solution method. The phase diagram and refractive index diagram were plotted for this system at 288.15 K. The phase diagram contains one invariant solubility point, two univariant solubility curves, and two crystallization fields of NaCl and SrCl2 · 6H2O. The refractive indices of the equilibrium solution change regularly with w(NaCl) increase. The calculated refractive index data are in good agreement with the experimental data. Combining the experimental solubility data of the ternary system, the Pitzer binary parameters for NaCl at 288.15 K and SrCl2 at 298.15 K, the Pitzer mixing parameters θNa, Sr, ΨNa, Sr, Cl and the solubility equilibrium constants Ksp of solid phases existing in the ternary system at 288.15 K were fitted using the Pitzer and Harvie-Weare (HW) models. The mean activity coefficients of sodium chloride and strontium chloride, and the solubilities for the ternary system at 288.15 K were presented. A comparison between the calculated and measured solubilities shows that the predicted data agree well with the experimental results.

Solid–Liquid Equilibria in the Systems CaBr2–MgBr2–H2O and NaBr–KBr–SrBr2 at 348 K

The solid–liquid equilibria in the ternary system CaBr2–MgBr2–H2O and quaternary system NaBr–KBr–SrBr2–H2O at 348 K were determined with the method of isothermal solution saturation. Also determined are the densities of saturated solutions. The phase diagram of the ternary system CaBr2–MgBr2–H2O has two invariant points, three univariant curves and three crystallization fields (which are saturated with MgBr2·6H2O, 2CaBr2·MgBr2·12H2O, and CaBr2·2H2O, respectively). The phase diagram of the quaternary system NaBr–KBr–SrBr2–H2O includes one invariant point, three univariant curves and three crystallization fields (which are saturated with SrBr2·6H2O, NaBr, and KBr, respectively). On the basis of the extended Harvie–Weare (HW) model and its temperature-dependent equation, the mixing ion interaction parameters θMg,Ca, ΨMg,Ca,Br and the dissolution equilibrium constant K for MgBr2·6H2O, CaBr2·2H2O, and 2CaBr2·MgBr2·12H2O in the ternary system at 348 K were fitted by using the Pitzer equations and the multiple l...

Experimental determination and modeling of the solubility phase diagram of the ternary system (Li2SO4 + K2SO4 + H2O) at 288.15 K

The solubility and density in the thermodynamic phase equilibria ternary system (Li2SO4+K2SO4+H2O) at 288.15K and 0.1MPa were investigated experimentally with the method of isothermal dissolution equilibrium. This system at 288.15K consists of two invariant points, three univariant isothermal dissolution curves; and three crystallization regions. The salt Li2SO4·K2SO4 belongs to the incongruent double salt, and no solid solution was found. Based on the Pitzer model and its extended Harvie–Weare (HW) model, the mixing ion-interaction parameters of θLi,K, ψLi,K,SO4 at 288.15K and the solubility equilibrium constants Ksp of solid phases Li2SO4·H2O and Li2SO4·K2SO4, which are not reported in the literature were acquired. A comparison between the calculated and experimental results at 288.15K for the ternary system shows that the calculated solubilities obtained with the extended HW model agree well with experimental data.

Measurement and Thermodynamic Modeling Study on the Solid and Liquid Equilibrium of Ternary System NaBr–CaBr2–H2O at 288.15 K

The solubilities and refractive indices of the NaBr–CaBr2–H2O system at 288.15 K were determined using the isothermal equilibrium solution method. The phase diagram and refractive index diagram were drawn for this system at 288.15 K. The system belongs to the hydrate II type. The phase diagram is comprised of two invariant solubility points, three univariant solubility curves, and three areas of crystallization: NaBr·2H2O, NaBr and CaBr2·6H2O. Using the temperature-dependent formulas from the literature, the Pitzer parameters and the solubility product constants (ln Ksp) of NaBr·2H2O and NaBr were determined. Applying the Pitzer and Harvie–Weare (HW) model, the solubility product constant of CaBr2·6H2O was fit with the solubilities in this research work, and then, the mean activity coefficients of sodium bromide and calcium bromide and the solubilities for the ternary system at 288.15 K were demonstrated. Comparisons between the calculated and measured solubilities show that the predicted data have good accordance with the experimental results.

Solubility measurement and solid-liquid equilibrium model for the ternary system MgBr2 + MgSO4 + H2O at 288.15 K

The solubility of magnesium minerals and the refractive index of the ternary system MgBr2 + MgSO4 + H2O at 288.15 K were investigated using an isothermal dissolution method. It was found that there are two invariant points in the phase diagram and the solubility isotherm of this ternary system consists of three branches, corresponding to equilibrium crystallization of Epsomite (MgSO4·7H2O, Eps), hexahydrite (MgSO4·6H2O, Hex) and magnesium bromide hexahydrate (MgBr2·6H2O, Mb). Neither solid solutions nor double salts were found. The refractive indices calculated from empirical equation are in good agreement with the experimental data. Combining the results from solubility measurements with the single-salt parameters for MgBr2 and MgSO4, and the mixed ion-interaction parameter θBr,S04, the parameter ψMg,Br,S04 at 288.15 K was fitted using the Pitzer theory and Harvie-Weare (HW) approach. In addition, the average equilibrium constants of the stable equilibrium solids at 288.15 K were obtained by a method using the activity product constant. A chemical model, which combined the Pitzer parameters and the average equilibrium constants, was constructed to calculate the solid + liquid equilibria in the ternary system MgBr2 + MgSO4 + H2O at 288.15 K. The model agreed well with the equilibrium solubility data for the magnesium salts.

Phase Equilibria and Phase Diagrams for the Aqueous Ternary System (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K

The solubility and density of the thermodynamic phase equilibria ternary system (Na2SO4 + Li2SO4 + H2O) at (288 and 308) K were determined using the isothermal dissolution method. According to the experimental results of the ternary system at (288 and 308) K, the phase diagrams and the diagrams of density versus composition were plotted. In the ternary system at 308 K, four crystallization regions corresponding to thenardite (Na2SO4, Th), two congruent double salts of Li2SO4·3Na2SO4·12H2O (Db1) and Li2SO4·Na2SO4 (Db2), and lithium sulfate monohydrate (Li2SO4·H2O, Ls) were found, whereas only three crystallization regions corresponding to Ls, one incongruent double salt of Db1, and mirabilite (Na2SO4·10H2O, Mir) were found in the system at 288 K. No solid solution was found at either temperature. When the experimental phase diagram at 308 K was compared with that at 288 K, it shows that (1) a new phase region of double salt Db2 was formed and the mineral of Mir transformed into Th with the increase of temperature from (288 to 308) K and (2) the area of the crystallization region of sodium sulfate was decreased sharply and those of the crystallized regions of Li2SO4·H2O and double salt Db1 increased obviously. The solution densities of the ternary system both at (288 and 308) K change regularly with increasing lithium sulfate concentration in solution. Based on the Pitzer model and its extended Harvie-Weare (HW) model, the mixing triple interaction parameter of ΨLi,Na,SO4 at (288 and 308) K and the solubility equilibrium constants Ksp of solid phases Ls, Db1, Db2, Th, and Mir at (288 and 308) K, which are not reported in the literature, were acquired by fitting the experimental solubility data of the ternary system (Li2SO4 + Na2SO4 + H2O) by the lease-square method. A comparison between the calculated and experimental results at (288 and 308) K for the ternary system shows that the predicted solubilities obtained with the extended HW model agree well with experimental data.

Measurement and thermodynamic model study on solid + liquid equilibria and physicochemical properties of the ternary system MgBr2 + MgSO4 + H2O at 323.15 K

The solubility of magnesium minerals and the physicochemical properties (density and refractive index) of the ternary system MgBr2+MgSO4+H2O at 323.15K were investigated using an isothermal evaporation method. It was found that there are three three-salt cosaturated invariant points, four univariant solubility isotherms and four stable crystallisation fields in the ternary system corresponding to hexahydrite (MgSO4·6H2O, Hex), tetrahydrite (MgSO4·4H2O, Tet), kieserite (MgSO4·H2O, Kie) and magnesium bromide hexahydrate (MgBr2·6H2O, Mb). Neither solid solutions nor double salts were found. The densities and refractive indices calculated from empirical equations are in good agreement with the experimental data. Combining the results from solubility measurements with the single-salt parameters for MgBr2 and MgSO4, and the mixed ion-interaction parameter θBr,SO4, the parameter ψMg,Br,SO4 at 323.15K was fitted using the Pitzer and Harvie–Weare (HW) model. In addition, the average equilibrium constants of the stable equilibrium solids at 323.15K were obtained by a method using the activity product constant. A chemical model, which combined the Pitzer parameters and the average equilibrium constants, was constructed to calculate the solid+liquid equilibria in the ternary system MgBr2+MgSO4+H2O at 323.15K. The model agreed well with the equilibrium solubility data for the magnesium salts.

The phase diagrams of the systems MgCl2 + MgB6O10 + H2O and MgSO4 + MgB6O10 + H2O at 323.15 K and Pitzer model

The solubilities and the relevant physicochemical properties of the systems MgCl2 + MgB6O10 + H2O and MgSO4 + MgB6O10 + H2O at 323.15 K were determined by the method of isothermal dissolution, and the phase diagrams and the diagrams of physicochemical properties versus composition were plotted. Both of the systems belong to a simple eutectic type, and neither double salts nor solid solution were found. Based on the extended Harvie-Weare (HW) model and its temperature-dependent equations, the value of the singlesalt Pitzer parameters β(0), β(1), β(2), and CO for MgCl2, MgSO4, and Mg(B6O7)(OH)6, the mixed ion-interaction parameters \(\theta _{Cl, B_6 O_{10} }\), \(\theta _{SO_4 , B_6 O_{10} }\), \(\Psi _{Mg, Cl, B_6 O_{10} }\), \(\Psi _{Mg, SO_4 , B_6 O_{10} }\), the average equilibrium constants (lnKaver) of solids in the systems and the Debye-Huckel parameter AO were fitted. Using the Pitzer parameters and the average equilibrium constants of solids at equilibrium, the solubilities of the two systems at 323.15 K have been calculated. Comparisons between the calculated and experimental results show that the predicted solubilities agree well with experimental data.

Stable Phase Equilibrium of the Aqueous Quaternary System (MgCl2 + MgSO4 + MgB6O10 + H2O) at 323.15 K

The solubilities and relevant physicochemical properties including density and pH values of the aqueous quaternary system (MgCl2 + MgSO4 + MgB6O10 + H2O) at 323.15 K were determined for the first time with the method of isothermal dissolution. According to the experimental results, the dry-salt-phase diagram, water-phase diagram, and physicochemical properties versus composition diagrams were plotted. It was found that there are three three-salt cosaturated invariant points, seven univariant solubility isotherm curves, and five stable crystallization fields corresponding to bischofite (MgCl2·6H2O, Bis), kieserite (MgSO4·H2O, Kie), tetrahydrite (MgSO4·4H2O, Tet), hexahydrite (MgSO4·6H2O, Hex), and mcallisterite (Mg(B6O7)(OH)6·4.5H2O, Mca). Neither solid solution nor double salts were found. On the basis of the extended Harvie–Weare (HW) model and its temperature-dependent equation, single-salt parameters β(0), β(1), β(2), and Cϕ for MgCl2, MgSO4, and Mg(B6O7)(OH)6, mixed ion-interaction parameters θC1,SO4, θC1,B6O7 (OH)6, θSO4,B6O7(OH)6, ΨMg,Cl,SO4, ΨMg,Cl,B6O7(OH)6, and ΨMg,SO4,B6O7(OH)6, and the Debye–Hückel parameter Aϕ at 323.15 K were obtained. In addition, the average equilibrium constants of stable equilibrium solids at 323.15 K were obtained with the method of the activity product constant. The prediction of solubilities of the quaternary system is then demonstrated. A comparison between the calculated and the experimental results shows that the predicted solubilities agree well with experimental data.

Solid–Liquid Metastable Equilibria of the Reciprocal Quaternary System (LiCl + MgCl2 + Li2SO4 + MgSO4 + H2O) at 323.15 K

Experimental studies on the metastable solubilities and the physicochemical properties (density, pH value, conductivity, and viscosity) of the aqueous reciprocal quaternary system (LiCl + MgCl2 + Li2SO4 + MgSO4 + H2O) at 323.15 K were determined with the isothermal evaporation method. According to the experimental results, the dry-salt phase diagram, water-phase diagram, and the physicochemical properties versus composition diagram were plotted. It was found that there are four invariant points, nine metastable solubility isotherm curves, and six metastable crystallization fields corresponding to lithium chloride monohydrate (LiCl·H2O), bischofite (MgCl2·6H2O), starkeyite (MgSO4·4H2O), hexahydrite (MgSO4·6H2O), lithium sulfate monohydrate (Li2SO4·H2O), and the double salt lithium-carnallite (LiCl·MgCl2·7H2O). No solid solution was found. On the basis of the extended Harvie–Weare (HW) model and its temperature-dependent equation, the values of the Pitzer parameters β(0), β(1), β(2), and Co for Li2SO4, MgCl...

Equilibria in the Quaternary System KCl−NaCl−CaCl2−H2O at 283.15 K

The solubilities and physicochemical properties in the quaternary system KCl−NaCl−CaCl2−H2O at 283.15 K have been measured with the isothermal method. The dry-salt phase diagram, water-phase diagram, and physicochemical properties vs composition in the system were plotted according to the measured data. The system contained only the forms of single salts, and no double salts or solid solution were found. On the basis of the extended Harvie−Weare (HW) model and the temperature coefficients of the single-salt parameters obtained from the calorimetric data, the Pitzer parameters for KCl, NaCl, and CaCl2 and the mixed ion-interaction parameters at 283.15 K were obtained. In addition, the average equilibrium constants of the solids at the same temperature were obtained using a method derived from the activity coefficient model of the electrolyte solution theory. Using the average equilibrium constants of the solids at equilibrium, the solubility predictions for the quaternary system are presented. A comparison between the calculated and experimental results suggests that the predicted solubility data obtained with the extended HW model agree well with the experimental data.

Metastable Phase Equilibrium in the Aqueous Ternary System (MgCl2+ MgSO4+ H2O) at 308.15 K

The metastable solubilities and the refractive indices in the aqueous ternary system (MgCl2 + MgSO4 + H2O) at 308.15 K were determined with the method of isothermal evaporation, and the metastable phase diagram and the diagram of refractive index versus composition were plotted. Four two-salt cosaturated points of epsomite (MgSO4·7H2O, Eps) + hexahydrite (MgSO4·6H2O, Hex), Hex + pentahydrite (MgSO4·5H2O, Pen), Pen + tetrahydrite (MgSO4·4H2O, Tet), and Tet + bischofite (MgCl2·6H2O, Bis), five isothermal univariant curves, and five metastable crystallization fields corresponding to Eps, Hex, Pen, Tet, and Bis were formed in the metastable ternary system. A comparison of the stable and metastable phase diagrams of the ternary system at 308.15 K shows that one more metastable crystallization field is formed. Neither a solid solution nor double salts are found. The solubility predictions of the metastable ternary system at 308.15 K based on Pitzer’s ion-interaction model and its extended Harvie−Weare (HW) model are presented, and the calculated results were in good agreement with the experimental results.

Solid–liquid metastable equilibria in the quaternary system Li 2SO 4 + MgSO 4 + Na 2SO 4 + H 2O at T = 263.15 K

Solubility in the liquid–solid metastable system Li 2SO 4 + MgSO 4 + Na 2SO 4 + H 2O at T = 263.15 K was studied using the isothermal evaporation method. Based on experimental data, dry-salt phase and water-phase diagrams of the system were plotted. The dry-salt phase diagram of the system includes one three-salt co-saturation point, three metastable solubility isotherm curves, and three crystallization regions corresponding to lithium sulphate monohydrate (Li 2SO 4·H 2O), epsomite (MgSO 4·7H 2O), and mirabilite (Na 2SO 4·10H 2O). Neither a solid solution nor double salts were found. Based on the extended Harvie–Weare (HW) model and its temperature-dependent equation, the values of the Pitzer parameters β (0), β (1), β (2), and C Φ for Li 2SO 4, MgSO 4, and Na 2SO 4, the mixed ion-interaction parameters θ Li,Na, θ Li,Mg, θ Na,Mg, Ψ Li,Na,S O 4 , Ψ Li,Mg,S O 4 , and Ψ Na,Mg,S O 4 , and the Debye–Hückel parameter A Φ in the quaternary system at 263.15 K were obtained. The solubility of the quaternary system Li 2SO 4 + MgSO 4 + Na 2SO 4 + H 2O at T = 263.15 K was also calculated. A comparison between the calculated and experimental results shows that the predicted solubility agrees well with experimental data.

Liquid-solid metastable phase equilibria for the quaternary system (NaCl-KCl-CaCl2-H2O) at 308.15 K

The solubility and the physicochemical properties (densities, viscosities, refractive indices, conductivities and pH) in the liquid-solid metastable system (NaCl-KCl-CaCl2-H2O) at 308.15 K have been investigated using the isothermal evaporation method, and the dry-salt phase diagram, water-phase diagram, and the diagram of physicochemical properties vs. composition in the system were plotted. One three-salt cosaturated point, three metastable solubility isotherm curves, and three crystallization regions corresponding to sodium chloride, potassium chloride and calcium chloride tetrahydrate were formed, and neither solid solution nor double salts were found. On the basis of the extended Harvie-Weare (HW) model and its temperature-dependent equation, the values of the Pitzer parameters β(0), β(1), Cϕ for NaCl, KCl and CaCl2, the mixing ion-interaction parameters θNa,K, θNa,Ca, θK,Ca, ΨNa,K,Cl, ΨNa,Ca,Cl, ΨK,Ca,Cl, and the Debye-Huckel parameter Aϕ and the chemical potentials of the minerals in the quaternary system at 308.15 K were fitted, and the predictive solubility based on the temperature-dependent equation and the chemical potentials of the minerals agrees well with the experimental data.