Generalized LIQUAC model for the single‐ and mixed‐solvent strong electrolyte systems

A generalized strong electrolyte LIQUAC model is presented to describe the vapor–liquid equilibria, osmotic coefficients, mean ion activity coefficients, and solid–liquid equilibria for the single‐ and mixed‐solvent electrolyte systems over the entire concentration range from infinite dilution to saturated solutions. An appropriate reference state for the ions was first applied to test the capability of the model in simultaneously describing the mean ion activity coefficients and the solubility of a salt in a binary solvent mixture. The influence of salt on the vapor–liquid equilibrium behavior is predicted with the new correlated parameters. The generalized activity coefficient formulations are presented through the investigation of thermodynamic properties and phase phenomena in the single‐ and mixed‐solvent electrolyte systems. This work is a continuous study for the LIQUAC activity coefficient model. A reliable representation of the single‐ and mixed‐solvent salt solutions is obtained. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

初级的强电解质水溶液热力学模型

提出了1个电解质溶液的热力学模型,它由两步组成,即电解质与溶剂的混合和电解质在溶剂中的电离.据此,导得了电解质离子的平均活度系数和溶剂（水）的渗透系数方程.并能方便地推广到混合电解质溶液.用实验数据广泛检验结果表明,这个模型能很好地适用于较高浓度下的强电解质溶液.     

MBr(M=Na,K)在离子液体[Bmim]Br水溶液中的溶解度

为探索溴化1-丁基-3-甲基咪唑([Bmim]Br)离子液体对无机溴化物MBr(M=Na,K)在水中溶解度的影响,采用等温溶解平衡法在常压下测定了298.15~328.15 K范围内MBr在[Bmim]Br(1)+H₂O(2)溶液中的溶解度,考察了离子液体含量对溶解度的影响。实验结果表明,[Bmim]Br的加入会显著降低MBr(M=Na,K)在水中的溶解度,离子液体[Bmim]Br对KBr的盐析作用比对NaBr的盐析作用大。不同温度下的溶解度数据可用Pitzer混合电解质溶液模型进行关联,得到了混合离子相互作用参数以及MBr在混合溶剂中的平均活度因子和溶剂的渗透系数。模型计算的溶解度与实验结果吻合良好,平均活度因子和溶剂的渗透系数均随离子液体含量的增加而增加。     

A simple model for precisely describing liquid–liquid equilibrium and better understanding extraction mechanism

Describing distribution of solute equilibrium concentrations between two solvents is important for liquid–liquid equilibrium (LLE). Due to non-ideality of solutions, the distribution usually possesses non-linear characteristic. In this work, the non-ideality was simply represented by pseudo reaction (or chemical interaction) between the solute and the solvent without recourse to the complicated activity coefficient models. On this basis, a simple model, which combined physical partition and pseudo reaction equilibriums, was proposed and can precisely correlate various LLE systems, for example, the immiscible, the partially miscible, the organic, and even the electrolyte. More interestingly, the model can accurately reflect intrinsic mechanism by fitted parameters, that is, stoichiometric ratio of the pseudo reaction and total equilibrium constant for the interaction intensity. Besides, influence of the solute, the extractant, and temperature on the parameters was discussed deeply. This simple model is promising for precisely describing the LLE systems and better understanding their intrinsic extraction mechanism.     

Modeling for mean ion activity coefficient of strong electrolyte system with new boundary conditions and ion-size parameters

A rigorous approach is proposed to model the mean ion activity coefficient for strong electrolyte systems using the Poisson–Boltzmann equation. An effective screening radius similar to the Debye decay length is introduced to define the local composition and new boundary conditions for the central ion. The crystallographic ion size is also considered in the activity coefficient expressions derived and non-electrostatic contributions are neglected. The model is presented for aqueous strong electrolytes and compared with the classical Debye–Hückel (DH) limiting law for dilute solutions. The radial distribution function is compared with the DH and Monte Carlo studies. The mean ion activity coefficients are calculated for 1:1 aqueous solutions containing strong electrolytes composed of alkali halides. The individual ion activity coefficients and mean ion activity coefficients in mixed sol-vents are predicted with the new equations.     

A new model in correlating and calculating the solid–liquid equilibrium of salt–water systems

In this work, a new activity coefficient model was deduced for the correlation of solid–liquid equilibrium(SLE) in electrolyte solutions. The new excess Gibbs energy equation for SLE contains two parts: the single electrolyte item and the mixed electrolyte item. Then a new hypothesis for the reference state of activity coefficients was proposed in the work. Literature data for single electrolyte solution and mixed electrolyte solution systems,with temperature spanning from 273.15 to 373.15 K, were successfully correlated using the developed model.     

Association-based activity coefficient model for electrolyte solutions

This work presents an association-based activity coefficient model that explicitly considers the solution nonideality due to associations among ions and solvent species. Built upon the electrolyte nonrandom two-liquid (eNRTL) model, the model greatly improves the accuracy of eNRTL model for strongly associating electrolyte solutions due to presence of ionic species with high surface charge density. The model successfully correlates mean ionic activity coefficients of 46 aqueous single-salt systems from 10 cations and 5 anions at 298.15 K up to their solubility limits. With the ion-specific association parameters identified, the model accurately predicts activity and osmotic coefficients for aqueous mixed-salt systems at 298.15 K. The temperature dependence of the model results has also been examined at 273–373 K. With superior accuracy over a wide range of concentration and temperature, the model represents a major advancement over eNRTL model and has a great potential to be a next-generation model for electrolyte solutions.     

电解质混合溶剂体系汽液平衡的推算

本文建立了由混合溶剂中电解质活度系数推算汽液平衡的数值计算方法。在电解质活度系数测定的盐浓度范围内,NaBr(1)-H_2O(2)-MeOH(3)和HCl(1)-H_2O(2)-MeOH(3)两体系在101.3 kPa下的汽液平衡计算结果与文献值平均绝对偏差分别为:汽相摩尔分率,平衡温度和,对前一体系还能正确地推测出交叉的盐效应规律。     

含盐溶液汽液平衡预测

本文提出一种新的预测含盐溶液汽液平衡的方法。对Pitzer(1980年)模型进行扩展后,将其简化成单参数形式,推广至多元电解质溶液;经过适当假定,得到计算含盐挥发性强电解质和水体系及含盐水醇体系的活度系数公式,这些公式仅含有二元相互作用参数;由二元溶液的活度关联出参数后,可用于含盐体系各温度下汽液平衡的预测。关联了四十个二元电解质水溶液及七个电解质甲醇溶液298.15K时的简化Pitzer方程的单参数;用以推算六个水盐体系和二个甲醇盐体系在320-403K的蒸汽压,得到满意的结果,182个数据点的平均偏差小于0.65kPa;用以预测五个不同类型的含盐三元体系的等温、等压汽液平衡,所得的平均偏差对于汽相组成、沸点、压力分别为0.015、1K、1.92kPa。     

含盐溶液汽液平衡预测(Ⅰ)——Pitzer模型的扩展及其在多元体系中的应用

本文提出一种新的预测含盐溶液汽液平衡的方法.对Pitzer(1980)模型进行扩展后,将其简化成单参数形式,推广至多元电解质溶液;经过适当假定,得到计算含盐挥发性强电解质和水体系及含盐水醇体系的活度系数公式,这些公式仅含二元相互作用参数;由二元溶液的活度关联出该参数后,可用于含盐体系各种温度下汽液平衡的预测.关联了40个二元电解质水溶液及7个电解质甲醇溶液298.15K时的简化Pitzer方程的单参数;用以推算6个水盐体系和2个甲醇盐体系在320-403K的蒸汽压,得到满意的结果,182个数据点的平均偏差小于0.65kPa;用以预测5个不同类型的含盐三元体系的等温、等压汽液平衡,所得的平均偏差对于汽相组成、沸点、压力分别为0.015、1K和1.92kPa.     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Revisiting electrolyte thermodynamic models: Insights from molecular simulations

Pitzer and electrolyte nonrandom two‐liquid (eNRTL) models are the two most widely used electrolyte thermodynamic models. For aqueous sodium chloride (NaCl) solution, both models correlate the experimental mean ionic activity coefficient (γ_±) data satisfactorily up to salt saturation concentration, that is, ionic strength around 6 m. However, beyond 6 m, the model extrapolations deviate significantly and diverge from each other. We examine this divergence by calculating the mean ionic activity coefficient over a wide range of concentration based on molecular simulations and Kirkwood–Buff theory. The asymptotic behavior of the activity coefficient predicted by the eNRTL model is consistent with the molecular simulation results and supersaturation experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3728–3734, 2018     

Liquid–liquid equilibrium extraction of ethanol with mixed solvent for bioethanol concentration

The extraction of ethanol with the solvents of aldehydes mixed with m-xylene was studied for the bioethanol concentration process.Furfural and benzaldehyde were selected as extraction solvents,with which the solubility of water is small,expecting large distribution coefficient of ethanol.The liquid–liquid two-phase region was the largest with m-xylene solvent,followed by benzaldehyde and furfural.The region of two liquid–liquid phase became larger with the mixed solvent of m-xylene and furfural than that with furfural solvent.The NRTL model was applied to the ethanol–water–furfural–m-xylene system,and the model could well express the liquid–liquid equilibrium of the system.For any solvent used in this study,the separation selectivity of ethanol relative to water decreased as the distribution coefficient of ethanol increased.The separation selectivity with m-xylene was the largest among the employed solvents,but the distribution coefficient was the smallest.The solvent mixture of furfural and m-xylene showed relatively high distribution coefficient of ethanol and separation selectivity,even in the higher mass fraction of m-xylene in the solvent phase.The ethanol extraction with a countercurrent multistage extractor by a continuous operation was simulated to evaluate the extraction performance.The ethanol content could be concentrated in the extract phase with relatively small number of extraction stages but low yield of ethanol was obtained.     

水盐体系汽液平衡的热力学模型研究

水盐体系的相平衡性质是化工单元操作的基础,在化学化工、海洋、地质等领域有着重要的研究价值。国内外许多学者对水盐体系汽液平衡进行了实验和理论的研究,构筑了各具特色的经验和半经验的模型。针对水盐体系,在NRTL理论的基础上,基于水化作用和混合盐假设建立了能够预测混合体系汽液平衡的活度系数扩展模型。通过对21组二元水盐体系和14组混合体系的关联计算,验证了该模型的可行性;同时,该模型可以采用二元体系参数直接预测计算混合水盐体系汽液平衡。     

利用变阱宽方阱链流体状态方程计算1：1电解质溶液热力学性质

将变阱宽方阱链流体状态方程拓展到1：1强电解质水溶液热力学性质的计算中,通过关联溶液的平均离子活度系数和溶剂的渗透系数得到了22种离子的链节直径和方阱能量参数,40余种电解质溶液的平均离子活度系数和溶剂渗透系数的总平均相对偏差分别为6.03%和5.83%。计算结果表明,建立的电解质型状态方程可以满意预测电解质溶液的密度和宽广温度下溶液的蒸气压,总体平均相对偏差分别为0.22%和4.69%。进一步说明模型参数的可靠性。     

A modified entropic expression for the analysis of swelling behavior of polymeric membranes in solutions

The linear mixed relation for mixed molar volume and free-volume were modified to derive our new activity expression attributed to the combined combinatorial and free volume contributions. The validity and applicability of this expression were demonstrated by calculating the solvent activity in polymer solutions and analyzing the swelling behaviors for polymeric membranes. The average absolute deviation (AAD) of these calculated results from the experimental values of solvent activities for polymer solutions was employed for comparison. It is shown that the modified model can yield better results than the original one for most of the systems considered. The swelling behavior of poly vinyl alcohol (PVA) membranes in water/glycol (EG) mixture over a wide range of concentrations was analyzed. The activity of solvents in the liquid and the membrane was calculated by the UNIQUAC model and this present modified model, respectively. The estimations are consistent with experimental data roughly at temperatures of 333 and 343 K. It is found that the modified model is a suitable alternative to the Flory-Huggins equation for the analysis of the swelling behaviors of polymeric membranes in solutions.     

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg2+–Ca2+–Cl− binary and ternary systems

Salt lake brine is a complex salt-water system under natural environment. Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution, the multi-temperature characteristics and predictability are still the goals of model development. In this study, a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements: (1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range; (2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients, the liquid parameters, which associated with Gibbs energy, enthalpy, and heat capacity contribution; and (3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range. Together the activity coefficient model, property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl₂–CaCl₂–H₂O binary and ternary systems, and it shows excellent agreement with the literature data for the ternary and binary systems. The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-ideality system, and the ability to extrapolate the temperature.     

Berechnung und Modellierung komplexer Phasen- und Reaktionsgleichgewichte in wäßrigen Elektrolytlösungen

In many natural and industrial processes the thermodynamic properties of aqueous electrolyte solutions play an important role. Systems of interest are frequently characterized by a large number of components and possible reactions. Due to low solubility, some reaction products precipitate as solids. The thermodynamic modelling therefore implies the computation of simultaneous phase and chemical equilibria. The minimization of the Gibbs free energy and the K-value method are powerful algorithms for numerical computation and permit the simulation of complex electrolyte systems. The behaviour of the liquid solution has to be described by suitable activity coefficient models.     

TERNARY NaCl+LiCl+H2O MIXED ELECTROLYTE SYSTEM: DETERMINATION OF ACTIVITY COEFFICIENTS BASED ON POTENTIOMETRIC METHOD

The mean activity coefficients for NaCl in a ternary electrolyte system were determined by the potentiometric method, at 25°C, using a solvent polymeric (PVC) sodium-selective membrane electrode (Na⁺ ISE), containing N,N'-dibenzyl-N,N'-diphenyl-1,2-phenylenedioxydiacetamide as ionophore, and combined with an Ag/AgCl electrode. The potentiometric measurements were performed at the same ionic strengths in different series of mixed salt solutions, each characterized by a fixed salt molal ratio r (where r = m₁/m₂ = 1, 10, 50, 100). The nonideal behavior of the ternary NaCl(m₁) + LiCl(m₂) + H₂O electrolyte system was described based on the Pitzer ion-interaction model for mixed salts over the ionic strength ranging from 0.01 up to about 4 mol/kg. Two- and three-particle Pitzer interaction parameters for a mixed electrolyte system were determined based on potentiometric data, and the critical role of potentiometric selectivity coefficient (K₁₂) of ISE as limiting factor in the potentiometric measurements was analyzed.