High pressure isothermal vapor-liquid equilibria for the binary system of carbon dioxide (CO<Subscript>2</Subscript>)+1,1,1-trifluoroethane (R-143a)

Isothermal vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO₂)+1,1,1-trifluoroethane (HFC-143a) were measured within the temperature range of 273.15–333.15 K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continuously recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EOS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model. The values calculated by the PR EOS with the W-S mixing rules show good agreement with our experimental data.     

SRK方程结合超额Gibbs自由能规则预测汽液平衡

SRK方程结合范德华混合规则应用于极性体系会产生较大误差,而结合超额Gibbs自由能(GE)型混合规则能得较好的结果。Wong-Sandler(WS型)混合规则是基于无穷大压力的GE型混合规则,文中对提出一种基于常压的改进型WS(MWS型)混合规则,利用SRK方程分别结合WS型和MWS型混合规则对多个二元极性体系汽液平衡进行预测。比较结果表明,采用SRK方程结合MWS型混合规则预测汽液平衡结果一般优于WS型混合规则。     

PSRK模型的修正混合规则及其应用于聚合物溶液汽液平衡的预测

To extend the PSRK(predictive Soave-Redlich-Kwong equation of state)model to vapor-liquid equilibria of polymer solutions,a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi)in the PSRK mixing rule for the parameter a,and the combinatorial part in the original universal functional activity coefficient(UNIFAC)model are cancelled.To take into account the free volume contribution to the excess Gibbs energy in polymer solution,a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied [b1/2 ij= 1/2(b1/2 i b1/2 j)].The literature reported Soave-Redlich-Kwong equation of state(SRK EOS)parameters of pure polymer are employed.The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium(VLE)of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.     

Thermodynamic modeling of vapor-liquid equilibrium of binary systems ionic liquid + supercritical {CO2 or CHF3} and ionic liquid + hydrocarbons using Peng-Robinson equation of state

Vapor-liquid equilibrium (VLE) data from literature for binary systems involving several ionic liquids were correlated. The Peng-Robinson equation of state, coupled with the van der Waals and Wong-Sandler mixing rules, was used as the thermodynamic model to evaluate the fugacity coefficients. The UNIQUAC and NRTL models were used to calculate the excess Gibbs free energy in the Wong-Sandler mixing rule. A molecular modeling strategy using the software ChemOffice was used to calculate the volume and surface area parameters of ionic liquids for UNIQUAC, while the binary interaction energy parameters for UNIQUAC and NRTL models, as well as the binary interaction parameter of the van der Waals and Wong-Sandler mixing rules were estimated through a method based on the genetic algorithm. The results show that, as expected, the Wong-Sandler mixing rules represented better the data, with both activity coefficient models showing high accuracy. However, in one case, NRTL predicted an erroneous azeotropic condition, while UNIQUAC was able to correlate the data without this error.     

Vapor-liquid equilibria for the binary mixtures of dimethyl ether (DME)+ dimethyl carbonate (DMC)

Isothermal vapor-liquid equilibrium data for the binary system of dimethyl ether (DME)+dimethyl carbonate (DMC) were measured at 303.15, 313.15, 323.15, 333.15 and 343.15 K using a circulation-type equilibrium apparatus with on-line gas chromatography analysis. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the van der Waals one fluid mixing rule and the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rule combined with the NRTL excess Gibbs free energy model. This system showed negative deviation from Raoult’s law, and no azeotropic behavior was observed for all the temperature ranges studied here. Calculated results with PR-EoS using both two mixing rules showed good agreement with experimental data.     

应用PSRK状态方程预测高压汽液平衡

为预测高压汽液平衡,将过量吉布斯自由能混合规则和UNIFAC活度系数模型与SRK状态方程相结合,建立基团贡献状态方程PSRK。利用该状态方程对5个体系在不同压力和温度下的汽液平衡数据进行了关联实验测定的汽相压力和汽相组成与计算结果相比所得的相对平均偏差分别为2．16％和1．01％。结果表明,PSRK状态方程可以成功地预测高压下汽液平衡,其精度高于MHV1和MHV2模型。     

Calculation of the solid solubilities in supercritical carbon dioxide using a new G mixing rule

The aim of this study is to develop a new EOS/G^ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO₂, by using six mixing rules, namely, the Wong-Sandler (WS) rule, the Orbey-Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide.The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO₂.     

Correlation of vapor-liquid equilibria for binary mixtures with free energy-based equation of state mixing rules: Carbon dioxide with alcohols, hydrocarbons, and several other compounds

The correlation of vapor-liquid equilibrium data for high-pressure carbon dioxide systems is of interest in a number of industrial applications, including supercritical extraction. Here, we consider the correlation of data for 12 binary systems of carbon dioxide separately with alcohols, with hydrocarbons, and with acetone, benzene, and water. The Wong-Sandler (W-S) and modified Huron — Vidal first order (MHV1) free energy-based equation of state mixing rules (the W-S and MHV1 models) were used in the calculations. Both combined equation of state+free energy models generally resulted in good correlations of the experimental data over wide ranges of temperature and pressure with temperature — independent parameters. However, for the carbon dioxide+water system, the W-S model produced an 11% average absolute deviation in pressure, while no parameter that resulted in an AAD in pressure of less than 20% could be found for the MHV1 model.     

一种新的WS型混合法则

立方形状态方程被广泛应用于相平衡计算中．绝大多数状态方程是结合简单的van der Waals混合法则来进行VLE数据关联的．然而对于应用这些方程关联高度非理想混合物的复杂的相行为,仅用van der waals单维流体混合法则是不够的．甚至在van der Waals混合法则引入另外一个参数都不能够精确地关联含有极性物质的混合物．     

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     

PR方程结合改进的WS混合规则预测汽液平衡

对WS型混合规则加以适当改进提出一种新的G^E型混合规则（MWS型）,并将其与PR状态方程相结合应用于多个二元极性体系汽液平衡数据的预测。结果表明,采用PR方程结合MWS型混合规则预测汽液平衡结果一般优于WS型混合规则,能广泛应用于工程实践。     

Isothermal vapor-liquid equilibria for the binary systems of ethylene glycol monopropyl ether with 2,2-dimethylbutane and 2,3-dimethylbutane

Isothermal vapor liquid equilibria for the binary system of ethylene glycol monopropyl ether with 2,2-dimehylbutane and 2,3-dimethylbutane were measured in a circulating water bath at 303.15, 318.15, and 333.15 K. The apparatus was in-house designed and manufactured. Consistency testing of the apparatus was done by comparing the measured vapor pressures to the calculated vapor pressures from the Antoine equation. The measured systems were correlated with a Peng-Robinson equation of state (PR) combined with Wong-Sandler mixing rule for the vapor phase, and NRTL, UNIQUAC, and Wilson activity coefficient models for the liquid phase. All the measured systems showed good agreement with the correlation results.     

非对称烃类体系高压汽液平衡的预测

本文基于London色散力理论和Pitzer对比态原理等统计力学基础提出了一个RKS方程改进的混合规则,进而导出一个非对称烃类体系通用二元相互作用参数的表达式:使用该RKS方程改进的混合规则,较满意地预测了21个非对称烃类的高压汽液平衡,从而显著地提高了原RKS方程假定K_(ij)=0时的预测精度。     

Extending the range of COSMO‐SAC to high temperatures and high pressures

The range of the predictive Gibbs energy of solvation model, COSMO‐SAC, is extended to large ranges of density, pressure, and temperature for very nonideal mixtures by combining it with an equation of state (EOS) using the Wong‐Sandler mixing rule. The accuracy of isothermal vapor‐liquid equilibria (VLE) calculations based on using the predictive COSMO‐SAC model and separately the correlative NRTL model is compared, each combined with three different forms of the Peng‐Robinson equation of state. All the models considered require the value of the EOS mixing rule binary parameter k_ij. The NRTL model also requires three other parameters obtained from correlation low pressure VLE data. The PRSV + COSMO‐SAC model is showed, with its one adjustable parameter obtained from low temperature data leads good predictions at much higher temperatures and pressures. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1806–1813, 2018     

热力学状态方程二元交互作用参数估算模型开发

基于气液平衡理论,建立了热力学状态方程二元交互作用参数估算模型。首先,结合气液平衡理论、状态方程以及相应的混合规则建立气液相平衡数学模型;然后以气相组成误差平方和与压力相对误差平方和之和作为目标函数,并使用计算机编程,利用单纯形法进行优化求解,实现了热力学状态方程二元交互作用参数估算模型的开发;最后,用该模型对5组二元气液平衡体系中的组分二元交互作用参数进行估算,并根据估算出的参数对各体系的气相组成进行预测,结果显示,预测值与实验值的平均相对偏差均小于1％,表明该模型计算结果准确,可应用于气液平衡计算中。     

Vapor-liquid equilibrium correlations for systems containing amines using a lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of vapor-liquid equilibria (VLE) for binary amine and hydrocarbon mixture at various temperatures. For these mixtures, the consideration of hydrogen bondings in the lattice equation of state clearly improves the prediction for VLE. The amines were divided into four groups due to the different strength of the hydrogen bonding. For all groups, different hydrogen bonding parameters were obtained and evaluated. The effects of varying hydrogen bonding energies for NLF-HB EOS are discussed. For systems containing lower amines, the NLF-HB EOS showed excellent agreement with the experimental data. For the correlation of systems containing tertiary amine molecules, binary interaction parameter had to be involved instead of hydrogen bonding parameters.     

状态方程模拟醇胺系统的密度和汽液相平衡

通过考虑醇胺分子间的缔合作用,结合先前开发的非缔合变阱宽链流体状态方程(SWCF-VREOS)建立了一个缔合方阱链流体状态方程,并利用方程模拟了醇胺系统的密度和汽液相平衡。通过关联不同温度下醇胺的饱和蒸气压和液体体积得到了18种醇胺流体的分子参数,新方程计算的饱和蒸气压和液体密度总的平均误差分别为0.94%和0.88%。结合简单的混合规则,将此方程扩展到混合系统。研究发现,建立的方程可预测二元和三元醇胺混合物的密度。当引入一个与温度无关的可调参数时,方程能满意关联二元系统的汽液相平衡数据,并可进一步预测多元混合系统的汽液相平衡,预示着新方程可模拟醇胺系统的相行为。     

Calculation of phase equilibrium for water+carbon dioxide system using nonrandom lattice fluid equation of state

For the geological sequestration of carbon dioxide to prevent global warming, the phase equilibrium data for water and carbon dioxide mixture play an important role in process design and operation. In this work, the nonrandom lattice fluid equation of state with hydrogen bonding (NLF-HB EOS) was applied for the prediction of phase equilibrium of mixtures containing water and carbon dioxide. A new set of pure component parameters for carbon dioxide above critical condition was found and optimum binary interaction parameters were reported to correlate mutual solubility of mixtures. The calculated results were compared with the Peng-Robinson Equation of State with the conventional mixing rule (PR-EOS) and the Wong-Sandler mixing rule (PR-WS-EOS). The calculation results show that NLF-HB EOS can correlate mutual solubility of water+carbon dioxide mixtures with reasonable accuracy within a single theoretical framework.     

从纯组分蒸汽压方程计算混合物汽液平衡

本文运用双流体对应态方法,在常低压区,直接从纯组分蒸汽压方程计算混合物的汽液平衡.此法兼有状态方程法理论严密和活度系数法计算简便的优点.用vdW和Wong两种已有的混合法则配合此法计算,取得一定效果,但限于同系物体系,为此发展了一种新的能量混合法则,用一个调节参数,配合此法计算了大量非(弱)极性-非(弱)极性、极性-极性、极性-非(弱)极性各类体系的汽液平衡,精度相当于活度系数法,关联的参数值有一定规律.