Pitzer Equations Research Articles

Thermodynamic Model of the H2O–LiCl–NaCl System for Study of Fluid Inclusions: Calculations Using the Pitzer Equations

Thermodynamic Model of the H2O–LiCl–NaCl System for Study of Fluid Inclusions: Calculations Using the Pitzer Equations

Development of a consistent geochemical model of the Mg(OH)2–MgCl2–H2O system from 25°C to 120°C

The formation of magnesium chloride-hydroxide salts (magnesium hydroxychlorides) has implications for many geochemical processes and technical applications. For this reason, a thermodynamic database for evaluating the Mg(OH)2–MgCl2–H2O ternary system from 0 °C–120 °C has been developed based on extensive experimental solubility data. Internally consistent sets of standard thermodynamic parameters (ΔGf°, ΔHf°, S°, and CP) were derived for several solid phases: 3 Mg(OH)2:MgCl2:8H2O, 9 Mg(OH)2:MgCl2:4H2O, 2 Mg(OH)2:MgCl2:4H2O, 2 Mg(OH)2:MgCl2: 2H2O(s), brucite (Mg(OH)2), bischofite (MgCl2:6H2O), and MgCl2:4H2O. First, estimated values for the thermodynamic parameters were derived using a component addition method. These parameters were combined with standard thermodynamic data for Mg2+(aq) consistent with CODATA (Cox et al., 1989) to generate temperature-dependent Gibbs energies for the dissolution reactions of the solid phases. These data, in combination with values for MgOH+(aq) updated to be consistent with Mg2+-CODATA, were used to compute equilibrium constants and incorporated into a Pitzer thermodynamic database for concentrated electrolyte solutions. Phase solubility diagrams were constructed as a function of temperature and magnesium chloride concentration for comparisons with available experimental data. To improve the fits to the experimental data, reaction equilibrium constants for the Mg-bearing mineral phases, the binary Pitzer parameters for the MgOH+ — Cl− interaction, and the temperature-dependent coefficients for those Pitzer parameters were constrained by experimental phase boundaries and to match phase solubilities. These parameter adjustments resulted in an updated set of standard thermodynamic data and associated temperature-dependent functions. The resulting database has direct applications to investigations of magnesia cement formation and leaching, chemical barrier interactions related to disposition of heat-generating nuclear waste, and evaluation of magnesium-rich salt and brine stabilities at elevated temperatures.

A quantitative description of barite thermodynamics, nucleation and growth for reactive transport modelling

The regression of available thermodynamic data in the BaSO4–NaCl–H2O system yielded Pitzer ion interaction parameters that accurately describe the activities of aqueous species and mineral solubilities in this system. This thermodynamics description is compared with published Pitzer parameter sets, and combined with a model for the kinetics of barite nucleation and growth, based on classical nucleation theory. Both the thermodynamic and nucleation/growth models have been incorporated into the PHREEQC computer code to facilitate calculation of the extent and consequences of barite formation in natural and engineered systems. Results of geochemical modelling calculations agree adequately with the amount of barite scale thicknesses derived from calliper measurements from an oil well if the effective surface free energy of barite nuclei is assumed to be ∼50 mJ m−2. Better results, however, are achieved using a temperature dependent effective surface free energy. In contrast, calculations performed by ignoring the effects of barite nucleation lead to a substantial overestimation of the amount of scale formed in our modelled systems. The success of our mineral nucleation and growth model to describe scaling in our modelled system suggests this description of precipitation rates can be applied to many other mineral-aqueous fluid systems, in particular where supersaturation is slight and the solids forming have substantial surface free energy.

Thermodynamics of the Eu(III)-Mg-SO4-H2O and Eu(III)-Na-SO4-H2O systems. Part I: solubility experiments and the full dissociation Pitzer model.

The solubility of Eu(III) was investigated under undersaturated conditions in acidic, dilute to concentrated MgSO4 and Na2SO4 solutions at T = (22 ± 2) °C. After attaining equilibrium conditions, solid phases were characterized by a multi-method approach, including X-ray diffraction (XRD), Raman and infrared (IR) spectroscopy, quantitative chemical analysis (ICP-OES) and thermogravimetric analysis (TG-DTA). A total of 45 solubility samples were investigated for the systems Eu2(SO4)3-MgSO4-H2O (19 samples) and Eu2(SO4)3-Na2SO4-H2O (26 samples). Eu2(SO4)3·8H2O(cr) was found to control the solubility of Eu(III) in all investigated MgSO4 solutions, as well as in dilute Na2SO4 systems. The transformation of Eu2(SO4)3·8H2O(cr) into the double salt Na2Eu2(SO4)4·2H2O(cr) was observed at mNa2SO4 > 0.01 mol kg-1. The latter phase is characterized by significantly lower solubility. Based on these experimental solubility measurements, thermodynamic and activity models were proposed based on the Pitzer equations considering the full dissociation of the Eu(III) species in MgSO4 and Na2SO4 aqueous solutions, i.e. deliberately excluding Eu(III)-sulfate complex formation. A combination of the geochemical calculation code PhreeSCALE and the parameter estimation code PEST was used to determine the values of solubility products and binary and ternary specific interaction parameters (β(0)ij, β(1)ij, Cϕij, θik, Ψijk).

Thermodynamic models for solution behavior and solid-liquid equilibrium in acetate binary systems from low to very high concentration at 25oC

In this study we developed new thermodynamic models for solution behavior and solid-liquid equilibrium in eight acetate binary systems from low to very high concentration at 25oC: six systems of the type 1-1 (X(CH3COO)-H2O with X= (Li, Na, K, Rb, Cs, and Tl)) and two systems of the type 2-1 (Y(CH3COO)2-H2O with Y= (Mg, and Ba)). Models were developed on the basis of Pitzer ion interactions approach. To parameterize models for binary systems we used all available experimental osmotic coefficients data (φ) for the whole concentration range of solutions. To develop models, we used different versions of the standard molality-based Pitzer approach. It was established that for all acetate systems under study application of extended approach with 4 parameters (β0 , β1 , β2 and Cφ ) and variation of 1 and 2 terms in fundamental Pitzer equations leads to the lowest values of standard model-experiment deviation. The predictions of new developed here models are in excellent agreement with experimental φ data, and with recommendations on the mean activity coefficients (±) from low to very high concentration: up to 23.8 m in K(CH3COO)-H2O, up to 39.2 m in Rb(CH3COO)-H2O, and up to 52.2 m in Cs(CH3COO)-H2O. On the basis of evaluated binary parameters important thermodynamic characteristics (Deliquescence Relative Humidity DRH, thermodynamic solubility products Ko sp; standard molar Gibbs free energy of formation, fGo m) for 7 acetate solids were determined at 25oC. The calculated DRH and fGo m values were compared with those reported in the literature. The models described in this study are of high importance, especially in development and improvement of technology for production and purification of acetate solutions and solid phases.

Numerical modeling and experimental validation of heat transfer in a research nuclear reactor evaporator by considering the precipitate formation

One of the wastewater treatment units in the Tehran Research Nuclear Reactor (TRNR) is an evaporator unit, which consists of a semi-batch single-stage kettle-type evaporator with heating coils and auxiliary equipment. The concentrate of this unit is immobilized in cement. So, the precipitate specie, concentrate composition, and its amount are important parameters for further waste treatment steps. In this research, a new bulk mathematical model is developed based on the total mass balance, the partial mass balance of ions in the concentrate and precipitates, as well as the energy balance to investigate the performance of the Tehran Research Nuclear Reactor evaporator. The resulting ordinary differential equations are solved numerically with a proposed algorithm. In this simulation, Pitzer equations are used to calculate the activity coefficient of water and ions, density, and solubility of salts. The temperature and pressure dependence of the developed model parameters are also considered. Moreover, the effect of precipitate formation on the overall heat transfer coefficient with time dependence correlation is also taken into account. Results show a good agreement between the experimental data and the developed model, and the relative error of different parameters is reported between 2% and 13%.

Solid–Liquid Phase Equilibria of the Quaternary System NaCl–CaCl2–H3BO3–H2O at 323.15 K: Solubility Determination and Thermodynamic Model

The solid–liquid phase equilibria of brine systems containing boric acid are the theoretical basis for the development of boric acid from brine resources. The phase equilibria of the systems NaCl–CaCl2–H3BO3–H2O and CaCl2–H3BO3–H2O at 323.15 K were investigated by the isothermal solution method. The phase diagram for the ternary system is composed of one co-saturation point, two univariant solubility curves, and two singe-salt crystallization fields of CaCl2·2H2O and H3BO3. The dry-salt phase diagram for the quaternary system consists of one invariant point, three univariant solubility curves, and three single-salt crystallization fields for NaCl, CaCl2·2H2O, and H3BO3. In the phase diagrams of the quaternary system at 298.15 and 323.15 K, the areas of sodium chloride and calcium chloride salt regions are enlarged, whereas the area of the H3BO3 region is diminished significantly with the increase of temperature. Using the Pitzer model, the lacking Pitzer parameters for H3BO3 were obtained by fitting the solubilities in the CaCl2–H3BO3–H2O system. The calculated solubilities with the Pitzer model were in accord with the experimental data.

Osmotic Coefficients of Gabapentin Drug in Aqueous Solutions of Deep Eutectic Solvents: Experimental Measurements and Thermodynamic Modeling

Most of the applications for aqueous deep eutectic solvent (DES) solutions are directly related to molecular interactions, which can be studied using thermodynamic properties. In this regard, the activity coefficient and osmotic coefficient studies have provided evidence for understanding the depth of ion pair formation, ion solvent, and ion–ion interactions in solutions. In this study, the osmotic coefficients for binary gabapentin (GBP)/water and ternary GBP/DES (ChCl/EG and ChCl/U) aqueous solutions were calculated using vapor pressure osmometry measurements at T = 298.15 K and pressure 872 hPa. Water activities, osmotic coefficients, and vapor pressure depressions were all calculated for binary solutions. The Pitzer equation was used to correlate the osmotic coefficient values. Activity coefficients for GBP in the binary systems were determined by the obtained parameters of this equation. The standard deviation for the osmotic coefficient value in the binary system with the Pitzer equation is 0.0059. In ternary solutions, two different DES concentrations (about molality 1 and 3) were used to investigate the effect of concentration on osmotic coefficients. For ternary solutions, it was also possible to obtain quantities like water activity and osmotic coefficient data. Finally, the predicted values of water activity using the Lin and ECA models were applied to compare the results of water activity in the studied systems. The results showed that the ECA and Lin models have 0.00045 and 0.0011 average standard deviation, respectively.

The Influence of Chemical Activity Models on the Description of Ion Transport through Micro-Structured Cementitious Materials.

The significance of ion activity in transport through a porous concrete material sample with steel rebar in its center and bathing solution is presented. For the first time, different conventions and models of ion activity are compared in their significance and influence on the ion fluxes. The study closes an interpretational gap between ion activity in a stand-alone (stagnant) electrolyte solution and ion transport (dynamic) through concrete pores. Ionic activity models developed in stationary systems, namely, the Debye-Hückel (DH), extended DH, Davies, Truesdell-Jones, and Pitzer models, were used for modeling the transport of ions driven through the activity gradient. The activities of ions are incorporated into a frame of the Nernst-Planck-Poisson (NPP) equations. Calculations were done with COMSOL software for a real concrete microstructure determined by X-ray computed tomography. The concentration profiles of four ions (Na+, Cl-, K+, OH-), the ionic strength, and the electric potential in mortar (with pores) and concrete samples (with aggregates and pores) are presented and compared. The Pitzer equation gave the most reliable results for all systems studied. The difference between the concentration profiles calculated with this equation and with the assumption of the ideality of the solution is negligible while the potential profiles are clearly distinguishable.

Measurements and predictions of phase equilibria in the quaternary system KBr + MgBr2 + SrBr2 + H2O at 273 K and 308 K

The underground brines in Sichuan Basin of China are rich in potassium, magnesium, strontium, bromine. Consequently, the studies of phase equilibria for the underground brines are of great significance. The phase equilibria of the quaternary system KBr + MgBr 2 + SrBr 2 + H 2 O at 273 K and 308 K are determined by the isothermal dissolution equilibrium method in this work. Firstly, the equilibrium liquid phase compositions at two temperatures were measured by chemical analysis. Secondly, the corresponding solid phases were identified by X-ray powder diffraction method. As a result, the corresponding phase diagrams were drawn based on the obtained data. The equilibrium phase diagrams all include four crystallization fields (SrBr 2 ·6H 2 O, MgBr 2 ·6H 2 O, KBr·MgBr 2 ·6H 2 O and KBr), five isothermal solubility curves and two invariant points, which present the same trend at the two temperatures. Furthermore, the mixed ion interaction parameters ( θ Mg , Sr , φ K , Sr , Br , φ Mg , Sr , Br ) of Pitzer model, which have not been reported in the literatures, were obtained by using the solubility data of the ternary system and multiple linear regression. And Pitzer equation and particle swarm optimization algorithm were used to simulate and predict the solubility of salts in the quaternary system. By comparing the calculated phase diagrams at 273 K and 308 K, some obvious deviation in crystalline phase zone of MgBr 2 ·6H 2 O and KBr·MgBr 2 ·6H 2 O at 273 K have been found. And both of them are within the reasonable deviation range. The results show that the fitted parameters and the calculated model of the mixed ion interaction are reliable, and the calculated data agree well with the experimental data.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties. III. Seawater from the freezing point to 45 °C, including acid-base equilibria

A quantitative understanding of pH, acid-base equilibria, and chemical speciation in natural waters including seawater is needed in applications ranging from global change to environmental and water quality management. In a previous study (Humphreys et al., 2022) we implemented a model of solutions containing the ions of artificial seawater, based upon the use of the Pitzer equations for the calculation of activity coefficients and including, for the first time, the propagation of uncertainties. This was extended (Clegg et al., 2022) to include the Tris buffer solutions that are used to calibrate the seawater total pH scale. Here we apply the same methods to develop a model of solutions containing the ions of standard reference seawater, based upon studies by Millero and co-workers. We compare the predictions of the model to literature data for: the dissociation of dissolved CO2 and bicarbonate ion; boric acid dissociation; saturation with respect to calcite, the ion product of water, and osmotic coefficients of seawater. Estimates of the uncertainty contributions of all thermodynamic equilibrium constants and Pitzer parameters to the variance of the calculated quantity are used to determine which elements of the model need improvement, with the aim of agreeing with properties noted above to within their experimental uncertainty. Further studies are recommended. Comparisons made with several datasets for carbonate system dissociation in seawater suggest which are the most reliable, and identify low salinity waters (S < 10) as a region for which dissociation constants of bicarbonate are not yet accurately known. At present, the model is likely to be most useful for the direct calculation of equilibria in natural waters of arbitrary composition, or for adjusting dissociation constants known for seawater media to values for natural waters in which the relative compositions of the major ions are different.

Mean activity coefficients of KCl in the KCl–K2B4O7–H2O solutions at 288.15 K determined by cell potential method and their application to the prediction of solid–liquid equilibria of the KCl–K2B4O7–H2O system

• The unreported mixed ion interaction of Pitzer parameters in KCl–K 2 B 4 O 7 –H 2 O solutions at 288.15 K were obtained in this work. • The experimental and predicted solubilities were compared to verify the rationality of fitting parameters. After measuring the cell potential of the cell without liquid junction K-ISE | KCl ( m 1 ), K 2 B 4 O 7 ( m 2 ) | Cl-ISE with the calibrated potassium ion and chloride ion selective electrode, the mean activity coefficients of KCl in KCl–K 2 B 4 O 7 –H 2 O solutions are calculated by the Nernst equation. The single parameters β (0) , β (1) , C Φ of K 2 B 4 O 7 , and the mixed ion interaction parameters θ Cl, B 4 O 5 (OH) 4 and ψ K,Cl, B 4 O 5 (OH) 4 of the Pitzer model were determined by programming solver and mean activity coefficients in this work. Furthermore, Pitzer equation is also used to evaluate the mean activity coefficient of potassium tetraborate in the KCl–K 2 B 4 O 7 –H 2 O solutions, as well as the osmotic coefficients, water activity and excess Gibbs free energy of the mixed solutions. Additionally, the experimental measurements of phase equilibria in the ternary system KCl–K 2 B 4 O 7 –H 2 O at 288.15 K are investigated in this work. The solubilities of the salts in the ternary system at 288.15 K are predicted by using Pitzer equation and the obtained ion parameters. The comparision of experimental and calculated phase diagram is presented in detail. The prediction results show that the predicted data are in accordance with the experimental data.

Phase Equilibrium of the Ternary System Na2SO3–Na2SO4–H2O at 293.15, 313.15, and 353.15 K

The phase equilibrium data of the ternary system Na2SO3–Na2SO4–H2O at 293.15, 313.15, and 353.15 K were determined by the isothermal dissolution method. There are one invariant point, two univariant isothermal dissolution curves, and three crystallization regions at each temperature. As the temperature increases from 293.15 to 313.15 K, the solubilities of both Na2SO4 and Na2SO3 increase. The single crystallization region of Na2SO4 decreases, while the single crystallization region of Na2SO3 increases. When the temperature increases from 313.15 to 353.15 K, the solubilities of both Na2SO4 and Na2SO3 decrease. The single crystallization region of Na2SO4 decreases, and the single crystallization region of Na2SO3 is basically unchanged. Furthermore, based on the solubility data, the Pitzer ion interaction model was used to calculate the relevant Pitzer parameters and then to calculate the solubilities of Na2SO3 and Na2SO4 theoretically. The calculated Na2SO3 and Na2SO4 solubilities basically agree with the experimental values. The data obtained in this work have important implications for the design and optimization of the Na2SO3 crystallization process from resorcinol production wastewater.

Determination of mean activity coefficients and prediction of phase equilibria of the NaCl‐SrCl2‐H2O solution at 318.15 K

AbstractIn this work, the cell potential method is used to measure activity coefficients of NaCl‐SrCl2‐H2O mixed solution at 318.15 K. The potential values of NaCl in NaCl‐H2O single salt solution were measured, and the standard cell potential E0 and electrode response slope k were fitted with linear regression. Subsequently, the results show that the ion‐selective electrode has a good Nernst response. The mean activity coefficients NaCl in NaCl‐SrCl2‐H2O solution are also determined with Nernst equation, and the total ionic strength in the mixed solution range is from 0.1000 ~ 0.8000 mol·kg−1, the ionic strength fraction of SrCl2 with yb = (0.0, 0.2, 0.4, 0.6, 0.8). Using the mean activity coefficients data and Pitzer model, the Pitzer ion interaction parameters and of Pitzer equations at 318.15 K are fitted. Furthermore, the mean activity coefficients of SrCl2, permeability coefficient Φ, water activity aw, and excess Gibbs free energy GE were also calculated by Pitzer's equations. The phase equilibria of the NaCl‐SrCl2‐H2O solution at 318.15 K are predicted, and corresponding phase diagram of the ternary solution is plotted according to the calculated solubilities in this work, and comparison of phase equilibria at different temperatures is also presented. The results show that the ion interaction parameters of Pitzer equations obtained in this work can be used for calculation of thermodynamic parameters and prediction of phase equilibria of salt‐water solutions containing strontium.

Measurements of mean activity coefficients and solubility prediction in ternary system KBr-K2SO4-H2O at 308.15 K and 288.15 K

In this work, the mean activity coefficients of KBr in KBr-H2O binary system and KBr-K2SO4-H2O ternary system were determined at 308.15 K and 288.15 K by the cell potential method. The potassium ion selective electrode and bromide ion selective electrode are used to measure the cell potential value of single salt electrolyte solution,and the standard potential value E0 and electrode response slope k of the binary system are obtained. The experimental results showed that ion selective electrodes of used in this work had a good Nernst response. The mean activity coefficients KBr in KBr-K2SO4-H2O system are also determined, the total ionic strength in the mixed solution ranging from (0.0100 to 1.0000) mol·kg−1, and ionic strength fractions yb of K2SO4 with yb=(0.8, 0.6, 0.4, 0.2 and 0.0). Using mean activity coefficients obtained in this work and Pitzer model, the Pitzer mixed ion interaction parameters θBr,SO4 and ψK,Br,SO4are fitted respectively. Furthermore, those osmotic coefficient Φ, water activity aw, excess Gibbs free energy GE were also calculated by Pitzer’s equations. The solubilities of salts in the KBr-K2SO4-H2O system at 308.15 K and 288.15 K are predicted by using Pitzer equations and ion interaction parameters fitted in this work, and phase diagrams of the ternary system are also plotted according to the calculated solubilities. The results show that the ion interaction parameters of Pitzer equations by fitting the activity coefficients can be used for calculation thermodynamic parameters and prediction of phase equilibria.

Critical evaluation of CuSO4-H2O system up to solubility limit, from eutectic point to 373.15 K

• CuSO 4 -H 2 O system is modelled from freezing point to boiling point. • The behaviour of the electrolyte solution is described by Pitzer model. • Several parameter sets with different temperature dependency were evaluated. • Only four parameters with eight temperature dependent terms are required. • Model is tested against independent vapour pressure and electrochemical cell data. The solubility of copper(II) sulfate in water as a function of temperature and ionic strength is successfully modelled using Pitzer formalism. Four types of experimental data from the literature were implemented for the assessment, namely activity and osmotic coefficients, freezing point depression and solubility of CuSO 4 in water. This work proved that four Pitzer parameters with eight terms are sufficient to create a consistent thermodynamic model of the CuSO 4 -H 2 O system up to 5 mol/kg-H 2 O of CuSO 4 , from the eutectic point to 373.15 K. The whole optimization study included a critical deviation analysis to sort out less reliable experimental data. To verify the results of this work, comparisons were carried out with experimental data which were not included in the assessment, i.e. the vapour pressure of the saturated solution, thermodynamic values of the cell reaction as well as electrochemical cell potential (EMF).

Study on the Phase Equilibria of the Ternary Mixed Solvent System NaCl–NaBr–CH3OH–H2O at 298 and 323 K

Aiming to improve the utilization of bromine resources in bittern, the solubilities of the ternary NaCl–NaBr–CH3OH–H2O mixed solvent system at 298 and 323 K were measured by the method of isothermal dissolution equilibrium, and the corresponding phase diagrams were constructed. The results show that the phase diagrams at the two temperatures are similar, and both have only one univariant curve and one crystallization region corresponding to a solid solution Na(Cl, Br) without invariant points. Based on the extended Pitzer model, Pitzer parameters were calculated, and the activity product of the solid solution was regressed into a polynomial of Br– mole fraction in the solid solution. The solubilities of the ternary NaCl–NaBr–CH3OH–H2O mixed solvent system at 298 K were calculated. The computed results are in accordance with the experimental values.

Recycling of Lead Pastes from Spent Lead–Acid Batteries: Thermodynamic Constraints for Desulphurization

Lead–acid batteries are important to modern society because of their wide usage and low cost. The primary source for production of new lead–acid batteries is from recycling spent lead–acid batteries. In spent lead–acid batteries, lead is primarily present as lead pastes. In lead pastes, the dominant component is lead sulfate (PbSO4, mineral name anglesite) and lead oxide sulfate (PbO•PbSO4, mineral name lanarkite), which accounts for more than 60% of lead pastes. In the recycling process for lead–acid batteries, the desulphurization of lead sulfate is the key part to the overall process. In this work, the thermodynamic constraints for desulphurization via the hydrometallurgical route for recycling lead pastes are presented. The thermodynamic constraints are established according to the thermodynamic model that is applicable and important to recycling of lead pastes via hydrometallurgical routes in high ionic strength solutions that are expected to be in industrial processes. The thermodynamic database is based on the Pitzer equations for calculations of activity coefficients of aqueous species. The desulphurization of lead sulfates represented by PbSO4 can be achieved through the following routes. (1) conversion to lead oxalate in oxalate-bearing solutions; (2) conversion to lead monoxide in alkaline solutions; and (3) conversion to lead carbonate in carbonate solutions. Among the above three routes, the conversion to lead oxalate is environmentally friendly and has a strong thermodynamic driving force. Oxalate-bearing solutions such as oxalic acid and potassium oxalate solutions will provide high activities of oxalate that are many orders of magnitude higher than those required for conversion of anglesite or lanarkite to lead oxalate, in accordance with the thermodynamic model established for the oxalate system. An additional advantage of the oxalate conversion route is that no additional reductant is needed to reduce lead dioxide to lead oxide or lead sulfate, as there is a strong thermodynamic force to convert lead dioxide directly to lead oxalate. As lanarkite is an important sulfate-bearing phase in lead pastes, this study evaluates the solubility constant for lanarkite regarding the following reaction, based on the solubility data, PbO•PbSO4 + 2H+ ⇌ 2Pb2+ + SO42− + H2O(l).

Thermodynamic modeling of phase equilibrium in aqueous systems to recover boron acid from the brines

• The Pitzer thermodynamic model for the quinary system was constructed. • The calculated solubility data agree well with the experimental data. • The Pitzer model was used to conduct computer simulation of H 3 BO 3 separation. The solid–liquid equilibria in the quinary system HCl−NaCl−MgCl 2 −H 3 BO 3 −H 2 O at 298.15 K was studied with Pitzer thermodynamic model. The Pitzer parameters for H 3 BO 3 in the quinary system were fitted with the solubility data from the literatures. The predicted solubility data of quinary system were obtained by dissolution equilibrium constants and Pitzer parameters. The comparison of calculated data with experimental data shows the Pitzer model of the quinary system was reliable. The phase diagrams and Pitzer model of HCl−NaCl−MgCl 2 −H 3 BO 3 −H 2 O quinary system were conducted for H 3 BO 3 separation from brine with computer simulation. The evaporation crystallization route and the order of salt precipitation were obtained with the model of the quinary system at 298.15 K. The results show that it’s easier to separate H 3 BO 3 under acidic conditions. The pure salt H 3 BO 3 and NaCl were separated with the phase diagrams of NaCl−H 3 BO 3 −H 2 O system at 298.15 K and 323.15 K.

Measurements and predictions of mineral solubilities in the quaternary systems NaCl + KCl + SrCl2 + H2O, NaCl + MgCl2 + SrCl2 + H2O and KCl + MgCl2 + SrCl2 + H2O at 308 K

This paper describes the measurements and predictions for mineral solubilities in the quaternary systems NaCl + KCl + SrCl2 + H2O, NaCl + MgCl2 + SrCl2 + H2O, KCl + MgCl2 + SrCl2 + H2O and subsystem MgCl2 + SrCl2 + H2O at 308 K in detail. The isothermal dissolution equilibrium method was used to determine the solubility of each salt in systems experimentally. Each stable phase diagram was constructed according to the measured results. The ternary system MgCl2 + SrCl2 + H2O has two invariant points, three solubility curves and three crystallization regions (MgCl2·6H2O, SrCl2·2H2O and SrCl2·6H2O). There is one invariant point, three solubility curves and three crystallization regions (NaCl, KCl and SrCl2·6H2O) in the quaternary system NaCl + KCl + SrCl2 + H2O. Two invariant points, five solubility curves and four crystallization regions (NaCl, MgCl2·6H2O, SrCl2·2H2O and SrCl2·6H2O) are included in the quaternary system NaCl + MgCl2 + SrCl2 + H2O. In the quaternary system KCl + MgCl2 + SrCl2 + H2O, the double salts KCl·MgCl2·6H2O were found as its ternary system KCl + MgCl2 + H2O, thus this quaternary system contains three invariant points, seven solubility curves and five crystallization regions (KCl + MgCl2·6H2O + KCl·MgCl2·6H2O + SrCl2·2H2O + SrCl2·6H2O). Using the fitted mixing parameter ΨMg, Sr, Cl and the Pitzer parameters available in literatures, the phase equilibria of four systems listed above were predicted with the Pitzer ion interaction model. The calculations are in adequate agreement with the experimental values.