A new model for predicting solute solubility in supercritical fluids based on the Wilson equation

In this work, a new model based on the Wilson solution theory was proposed for predicting the solubility of solids in supercritical fluid (SCF) with and without cosolvent(s) of binary and ternary systems via computation of activity coefficients. For binary systems the model contains two adjustable parameters, while for ternary systems there are four adjustable parameters. The calculated results of the proposed model were compared with that of the literature models, and it is shown that the proposed model is a more accurate one.     

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.     

Modeling aspirin and naproxen ternary solubility in supercritical CO2/alcohol with a new Peng–Robinson EOS plus association model

A new version of the Peng–Robinson equation of state (PR EOS) is developed through the use of Wertheim's thermodynamic perturbation theory of associating fluids and statistical associating fluid theory (SAFT). The new equation is characterized by two temperature-independent parameters, namely, association strength and association volume, which account for the association interactions between associating molecules. In this work, we employed the equation to model aspirin and naproxen solubility enhancement obtained in the ternary supercritical CO₂/alcohol systems, where the original PR EOS has resulted in large and negative binary interaction parameters between the polar solute and polar cosolvent. Calculated results show that the Peng–Robinson EOS plus association model gives better performance to correlate these ternary solubility data over the ranges of temperature, pressure and cosolvent concentration investigated than its conventional form that uses temperature-dependent parameters.     

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.     

Implementation of electrolyte CPA EoS to model solubility of CO_2 and CO_2+ H_2S mixtures in aqueous MDEA solutions

The electrolyte version of SRK plus association equation of state(e SRK-CPA Eo S) was employed to correlate CO_2 solubility in MDEA aqueous solutions. The applied model comprises the classic form of CPA Eo S including SRK Eo S plus Wertheim association term in addition to MSA theory and Born terms so that the two last terms are responsible for the long-range interactions. A reaction-containing bubble pressure computation technique comprising two nested loops was utilized to model the systems. The internal loop, calculates the liquid phase concentrations via reaction, mass and charge balance equation solving, whereas, the vapor phase concentrations will be obtained in the external one. 470 experimental data were used to correlate binary subsystems and the H_2O + MDEA + CO_2 ternary system. Since, there not exist any binary VLE data for MDEA + CO_2 subsystem, two fitting scenarios were applied. At the first scenario, the binary interaction parameter was assumed equal to zero, while, in second approach the parameter was obtained through ternary system correlation. Both scenarios show very good accuracy in that the Absolute Average Deviation percentages(AAD) obtained were 19.12% and 18.85%, respectively. Also, to show the efficiency of the used model, a comparison between our results and those of the best-known models was made.Finally, having model parameters for H_2S solubility from our previous work [A. Afsharpour, Petroleum Science and Technology 35(3)(2017) 292-298], simultaneous solubility of CO_2+ H_2S mixtures in MDEA solutions was predicted using the e SRK-CPA Eo S with no new optimizable parameters. As the results show,the applied model has a good performance for correlation and prediction of acid gas solubility in a wide range of pressures, temperatures, acid gas loadings, and MDEA concentrations.     

Modeling thermodynamic properties of aqueous single‐solute and multi‐solute sugar solutions with PC‐SAFT

The Perturbed‐Chain Statistical Association Fluid Theory is applied to simultaneously describe various thermodynamic properties (solution density, osmotic coefficient, solubility) of aqueous solutions containing a monosaccharide or a disaccharide. The 13 sugars considered within this work are: glucose, fructose, fucose, xylose, maltose, mannitol, mannose, sorbitol, xylitol, galactose, lactose, trehalose, and sucrose. Four adjustable parameters (three pure‐sugar parameters and a k_ij between sugar and water that was allowed to depend linearly on temperature) were obtained from solution densities and osmotic coefficients of binary sugar/water solutions at 298.15 K available in literature. Using these parameters, the sugar solubility in water and in ethanol could be predicted satisfactorily. Further, osmotic coefficients and solubility in aqueous solutions containing two solutes (sugar/sugar, sugar/salt) were predicted (no additional k_ij parameters between the two solutes) reasonably. The model was also applied to predict the solubility of a sugar in a solvent mixture (e.g., water/ethanol) without additional fitting parameters. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4794–4805, 2013     

Modeling high pressure vapor–liquid equilibrium of ternary systems containing supercritical CO2 and mixed organic solvents using Peng–Robinson equation of state

High pressure vapor–liquid equilibrium (VLE) of CO₂-expanded organic solvents was investigated using Peng–Robinson-LCVM-UNIFAC equation of state. Bubble pressure of several ternary mixtures was predicted using this model and correlations were developed based only on binary experimental data. A sensitivity study of the LCVM parameter numerical value was done by considering the coherence between the mathematical features of the mixing rule and the quality of the simulation. The results provided by PR-LCVM-UNIFAC were compared with those ones given by Peng–Robinson equation of state using the classical quadratic mixing rules (PR-CMR). Despite the use of two adjustable parameters for each binary system, PR-CMR is not able to provide good results when applied to ternary systems. The capability of PR-LCVM-UNIFAC model to predict liquid mixture density for ternary systems using parameters regressed only from bubble pressure experimental data was also investigated. Due to the lack of liquid density experimental data, it was possible to perform only a qualitative assessment of the density curves calculated by this equation of state.     

水-乙酸-乙酸戊酯体系的等压汽液平衡

用改进的Rose釜测定了水-乙酸、乙酸-乙酸戊酯、水-乙酸-乙酸戊酯在101.33 kPa下的等压汽液平衡数据.考虑了乙酸在汽相中的缔合效应,用维里方程和Hayden-O’connell关联式修正了汽相的非理想性,用非线性最小二乘法关联了水-乙酸和乙酸-乙酸戊酯体系的汽液平衡数据,得出了NRTL和UNIQUAC方程的模型参数.用NRTL模型参数预测了三元汽液平衡数据,计算值与实验值吻合良好.     

Molecular thermodynamic analysis for phase transitions of linear and cross-linked poly(N-isopropylacrylamide) in water/2-propanol mixtures

Ternary liquid–liquid phase transitions of linear poly(N-isopropylacrylamide) (PNIPA) and the swelling behavior of cross-linked PNIPA gels in water/2-propanol mixtures were investigated using thermo-optical analysis (TOA) and a photon correlation spectroscopy (PCS) technique, respectively. Closed immiscibility gaps in ternary phase diagrams were obtained below 35 °C although all binary mixtures involved in this system were completely miscible. At a fixed concentration of PNIPA (1.0 wt%), a decrease in the lower critical solution temperature (LCST) occurred first, and with an increasing 2-propanol fraction of the solvent mixture, the upper critical solution temperature (UCST) subsequently developed. Corresponding to the linear PNIPA solution behavior, swollen PNIPA gels in pure water first shrank and then reswelled with increasing 2-propanol content in a typical reentrant transition. For theoretical treatment of the mixtures, a multi-component lattice theory of mixing and Flory–Rehner chain model for elasticity were employed for molecular thermodynamic analysis. A secondary lattice concept of specific interactions was used to model binary water/PNIPA solutions, and a temperature dependence of the intermolecular interactions for 2-propanol/PNIPA was used to describe island type ternary phase diagrams. The swelling transitions of cross-linked PNIPA gels were calculated using model parameters obtained from the ternary phase diagrams of linear PNIPA or from experimental conditions. The predicted results were in good agreement with experimental data without the need for further adjustable parameters.     

One-fluid mixing rules for cubic equations of state : III. Solubility of pure solids in supercritical mixed solvents

Three cubic equations of state are carefully examined to evaluate their capability for correlating the solubility of pure solids in supercritical mixed solvents. After obtaining the pure solute-solvent interaction parameters, the solid solute-cosolvent interaction parameters were directly calculated from the experimental ternary solubility data. The Redlich-Kwong, Soave, and Peng-Robinson equations of state correlate well the solubility data of 32 ternary systems producing AAD(%) errors of 12.54, 12.50 and 12.67% respectively.     

R32+R1234yf+R1234ze（E）混合制冷剂气液相平衡实验研究

基于液相循环法搭建的气液相平衡实验装置,在263.15~323.15 K温度范围内,实验测量了R32+R1234yf和R1234yf+R1234ze（E）二元混合物以及R32+R1234yf+R1234ze（E）三元混合物的气液相平衡数据,利用PRSV状态方程结合WS混合法则和NRTL活度系数模型进行关联拟合,获得二元混合工质的交互参数,并在其基础上预测了三元混合工质气液相平衡性质。计算结果与实验数据对比表明,二元体系R32+R1234yf和R1234yf+R1234ze（E）的压力平均绝对偏差分别为0.71%和0.20%,气相摩尔分数平均绝对偏差均约为0.0016,三元体系R32+R1234yf+R1234ze（E）的压力平均绝对偏差为0.82%,系统组分R32和R1234yf的气相摩尔分数平均绝对偏差均约为0.007。     

Thermodynamic evaluation of the BaO-CaO-YO1.5 system

A series of experiments were performed to study the solid solubility of CaO in BaY₂O₄, and the observed results were then adopted to the present thermodynamic evaluation to derive a set of thermodynamic database for the BaO-CaO-YO_1.5 system. The database was constructed by the CALPHAD method where the binary parameters from the BaO-CaO and CaO-YO_1.5 systems were presently optimized, those from the BaO-YO_1.5 system were simulated by our previous assessments, and only limited amount of ternary parameters were introduced. All the model parameters were emanated from the Bragg-Williams approximation where the liquid and terminal solid-solution phases were treated by the one-sublattice model, and two ternary intermediate phases, named BCY (BaCa₂Y₆O₁₂) and BaY₂O₄, were described by the three-sublattice and two-sublattice models, respectively. Good agreement between the experimental data and the calculated results demonstrates that the present thermodynamic database is self-consistent and credible and able to be used to design novel refractory.     

Electrolytic properties of the MeLn<Subscript>2</Subscript>S<Subscript>4</Subscript>-Ln′<Subscript>2</Subscript> S<Subscript>3</Subscript> phases synthesized using the sol-gel and cryochemical technologies

The possibility of synthesizing sulfide-conducting solid electrolytes based on the ternary sulfides MeLn₂S₄ doped with the binary sulfides Ln′₂S₃ has been approved and the influence of dopants on the electrolytic properties of the basic compounds has been investigated for the first time. The influence of the specific features of the method used for synthesizing complex sulfide phases from nanometer-sized oxide precursors on the important functional properties of the solid electrolytes has been analyzed. The samples have been examined using the X-ray powder diffraction analysis, electron scanning microscopy, and electron microprobe analysis. The region of the existence of the solid solutions has been determined, the total electrical conductivity has been studied, and the activation energy for electrical conduction for samples with different dopant contents has been calculated. The ionic and electronic transfer numbers have been determined using the modified versions of the emf method and the Hebb-Wagner polarization method. A possible mechanism of defect formation has been proposed.     

二溴苯三元物系固液平衡测定与正规溶液模型

采用差示扫描量热法,通过对一系列"拟二元"物系固液平衡数据的测定,得到了邻二溴苯、间二溴苯和对二溴苯三元物系的固液平衡数据.实验结果表明本物系为简单低共熔型,其低共熔摩尔分数组成和温度分别为:邻二溴苯(x1) 间二溴苯(x2) 对二溴苯(x3),x1=0.4259,x2=0.5345,x3=0.0396,Tcu=238.5 K.文中绘制出了其相应的低共熔三元固液平衡相图,并采用正规溶液模型,利用二元溶液的三个相互作用参数对实验数据进行了关联,温度均方根偏差仅为1.32 K,说明正规溶液模型适用于上述弱极性异构体三元物系固液平衡的计算.     

Measurement and prediction of phase diagrams of the enantiomeric 3-chloromandelic acid system

The identification of racemic species of enantiomeric 3-chloromandelic acid (3-ClMA) as well as ternary solubility measurement in a mixture of water and isopropanol (IPA) was studied in this paper. Thermal analyses were carried out for mixtures of the two enantiomers with different compositions. The binary fusion diagram suggested the presence of a racemic compound for racemate 3-ClMA. It was verified with the ternary solubility phase diagram by dissolving various mixtures into the H₂O/IPA solution. Ternary phase diagram revealed a strong temperature dependency of solubility for the 3-ClMA system. In order to shorten the experimental time in the solubility measurement, a semi-empirical thermodynamic model (UNIQUAC) was used to predict the solubility of various compositions of enantiomers at different temperatures. Results indicate that UNIQUAC model can provide good predictions in the solubility of racemate, eutectic and (R)-3-ClMA in both pure water and H₂O/IPA (9/1 weight ratio) system. In addition, structures of racemate and pure (R)-3-ClMA were also studied using a powder X-ray diffractometer. Thermodynamic prediction, thermal analysis, and structural study are in excellent agreement for identifying the enantiomeric 3-ClMA system as a racemic compound forming system.     

Correlation and Prediction of the Solubility of CO<Subscript>2</Subscript> in a Mixture of Organic Solution Solvents

The solubility of carbon dioxide in a mixture of organic solvents was measured at atmospheric pressure in the temperature range of 10–25°C. The solubility of carbon dioxide in the mixture of organic solvents was obtained by using experimental data. In addition, the adjustable parameters of the local composition based models such as the Wilson, the NRTL, and the NRTL-NRF were determined by fitting the experimental data and the results of these models. The results show that the Wilson and the NRTL-NRF models used for the estimation of the CO2 solubility in the mixture of organic solvents used in this work attained relatively better results than the other models.__________From Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 259–263.Original English Text Copyright © 2005 by Pazuki, Pahlavanzadeh.This article was submitted by the authors in English.     

Preparation of sulfide ceramic materials based on BaSm<Subscript>2</Subscript>S<Subscript>4</Subscript>and CaGd<Subscript>2</Subscript>S<Subscript>4</Subscript> with the use of sol-gel and cryochemical technologies

Solid solutions in the MeLn₂S₄?x (mol %) MeS (Ln₂S₃) (Me = Ca, Ba; Ln = Sm, Gd) systems are prepared. The regions of solid solution formation are determined, the unit cell parameters of the crystal lattice are calculated, the total conductivity is investigated, and the activation energies for electrical conduction are calculated for samples with different prehistories. The electrolytic properties of phases based on calcium and barium thiolanthanates are studied, and the mechanism of defect formation is proposed.     

三元体系液液界面张力与溶解度的关联

本文采用界面相模型,推导出一个关联界面张力与溶解度数据的方程.经24个三元体系的检验,方程给出了满意的结果.通过引入部分互溶对的界面张力与互溶度数据所得到的修正方程可作更好的关联     

Physicochemical properties of nanocrystalline composites based on ZrO<Subscript>2</Subscript>, Al<Subscript>2</Subscript>O<Subscript>3</Subscript>, and rare-earth oxides

Powder precursors have been prepared by means of the sol-gel technique and codeposition, and nanoceramics in the ZrO₂-Al₂O₃-rare-earth (RE) oxide system (RE = Ce, Sc, or Y) based on them have been obtained. Physicochemical properties of the resulting ceramic composites have been investigated. The energy model for oxygen-ionic transport processes in a solid solution based on ZrO₂, which relies on computer simulation procedure, has been proposed, and the structural, strength, and electrophysical characteristics of the solid solution have been calculated. The obtained materials are promising as high-melting electrochemical sensors in molten oxides.     

Multicomponent adsorption equilibrium of ethylene,propane, propylene and CO2 on 13X zeolite

Experimental adsorption isotherms of binary, ternary and quaternary mixtures of ethylene, propane, propylene and CO₂ on 13X zeolite have been obtained at 293 K. Experimental data of mixtures were fitted to three theoretical models, the ideal adsorbed solution (IAS), real adsorbed solution (RAS) and spreading pressure dependence (SPD) models to reproduce and predict equilibrium data. With the SPD model, two other temperatures were also studied, 279 and 308 K, in order to calculate the model parameters. The best models for binary and multicomponent mixtures showing the highest deviation from ideality were RAS and SPD, with RAS better than SPD for ternary mixtures.