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 ∑xiln(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 [bij^1/2=1/2(bi1/2 bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters of i3 - 2- 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.     

EOS状态下基于多相流有规栅格理论的水-碳氢化合物两相体系的临界轨迹关系

Quantitative representation of complicated behavior of fluid mixtures in the critical region by any of equation-of-state theories remains as a difficults thermodynamic topics to date.In the present work,a computational efforts were made for representing various types of critical loci of binary water with hydrocarbon systems showing Type Ⅱ and Type Ⅲ phase behavior by an elementary equation of state[called multi-fluid nonrandom lattice fluid EOS(MF-NLF EOS)]based on the lattice statistical mechanical theory.The model EOS requires two molecular parameters which representing molecular size and interaction energy for a pure component and single adjustable interaction energy parameter for binary mixtures.Critical temperature and pressure data were used to obtain molecular size parameter and vapor pressure data were used to obtain interaction energy parameter.The MF-NLF EOS model adapted in the present study correlated quantitatively well the critical loci of various binary water with hydrocarbon systems.     

用活度系数模型和PCOR状态方程预测聚合物溶液中的亨利常数（英文）

In this paper, the polymer chain of rotator (PCOR) equation of state (EOS) was used together with an EOS/GE mixing rule (MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers. The results of the proposed method compared with two equation of state (van der Waals and GC-Flory) and three activity coefficient models (UNIFAC, UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results. The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR, a and b, were fitted with experimental volume data (Tait equation). As a result, the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.     

PREDICTIVE EQUATION OF TRACER LIQUID DIFFUSION COEFFICIENT FROM VISCOSITY

1 INTRODUCTIONAccurate data on molecular diffusion are required for the design of chemical and physi-cal processes where mass transfer plays an important role.Expressions for estimatingtracer diffusion coefficients(i.e.binary diffusion coefficients at infinite dilution)areavailable for a number of different systems .The Akgerman and Gainer equa-tion has been known to give good predictions for the diffusion coefficients of gases inliquids.This study provides an approximation approach for predicting diffusioncoefficients of binary liquid systems from their viscosities.     

SRK状态方程用于聚合物体系的汽液和气液平衡

A simple extension of cubic equations of state （EOS） to polymer systems has been proposed. The Soave-Redlich-Kwong （SRK） EOS was taken as a prototype to be used to describe the PVT behavior of polymer melts in a wide temperature and pressure range. Combined with a modified Huron-Vidal gE-mixing rule it was applied for modeling vapor-liquid equilibria of polymer-solvent solutions and the solubility of supercritical gases in polymer melts. Satisfactory results are obtained.     

离子液体[BMIM][DBP]+水+甲醇/乙醇三元工质溶液蒸汽压的测量和预测(英文)

The ionic liquid, 1-butyl-3-methylimidazolium dibutylphosphate ([BMIM][DBP]) was prepared and the vapor pressures of three set of binary solutions H2O(1)/CH3OH(1)/C2H5OH(1) + [BMIM][DBP](2) were measured at different temperature and in the ILs mole fraction range from 0.1 to 0.6 with a static equilibrium apparatus. The measured vapor pressures were correlated with Non-Random Two Liquid (NRTL) activity coefficient model and the average relative deviations (ARD) between experimental and correlated vapor pressures for these binary solutions were 3.19%, 2.42% and 2.95%, respectively. Then, the vapor pressures of two set of ternary solutions H2O(1) + CH3OH(2)/C2H5OH(2) + [BMIM][DBP](3) were measured with an inclined boiling apparatus and further predicted with NRTL activity coefficient model based on the binary interaction parameters coming from fitting the vapor pressures of the binary solutions. The results indicated that the ternary solutions containing [BMIM][DBP] were shown a strong negative deviation from Raoult’s Law when the mole fraction of [BMIM][DBP] was larger than 0.2, which meant that ternary solutions could absorb the refrigerant vapors at the same or below solution temperature. Meanwhile, the average relative deviations between experimental and predicted vapor pressures for ternary solutions were 2.92% and 3.06%, respectively. Consequently, the NRTL active coefficient model used for non-electrolyte solutions was still valid for predicting vapor-liquid equilibrium of binary or ternary solutions containing ILs.     

水杨酸苯酯与C4醇固液平衡测定与关联

In an equilibrium vessel,the solid-liquid equilibria(SLE) for three binary mixtures of phenyl salicylate with 1-butanol,2-butanol,and 2-methyl-1-propanol,respectively,have been measured from 283.15 K to the melting temperature of the solute using a method in which an excess amount of solute was equilibrated with the alcohol solution.The liquid concentrations of the investigated phenyl salicylate in the saturated solution were analyzed by UV spectrometry.Activity coefficients for phenyl salicylate have been calculated by means of the Wilson,NRTL,and UNIQUAC equations and with them were correlated solubility data that were compared with the experimental ones.The best correlation of the solubility data has been obtained by the Wilson equation by which the average root-mean-square deviation of temperature for the three systems is 1.03 K.     

A four parameter cubic equation of state with temperature dependent covolume parameter

A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.     

Measurement and correlation of physical properties of aqueous solutions of tetrabutylammonium hydroxide,piperazine and their aqueous blends

The density, viscosity and refractive index of aqueous solutions of tetrabutylammonium hydroxide (TBAOH), pi-perazine (PZ) and their aqueous blends are determined at several temperatures (303.15 to 333.15 K). All these measured physicochemical properties decreases with an increase in temperature. The density data is used to cal-culate the coefficient of thermal expansion and excess molar volume of al aqueous binary and ternary solutions. The coefficient of thermal expansion increases with increase in temperatures and concentrations. The negativity of excess molar volume for al the aqueous solution decreased with increase in temperature. Each physical prop-erty is correlated with temperature by least square method and the corresponding coefficients for each property are presented. The prediction values from correlations for the physical properties are in good agreement with the experimental values.     

Calculation of Viscosities of Liquid Mixtures Using Eyring’s Theory in Combination with Cubic Equations of State

1 INTRODUCTON The viscosity, particularly that of liquid mixtures is very important in engineering calculations involved in the process design for petroleum and other chemica industries. Since the successful development of a one-parameter equation for correlating the liquid vis cosity of nonpolar mixtures by Grunberg and Nissan[1] many other models have been proposed. Most of them are based on the corresponding state principle, the absolute rate theory of Eyring[2], or the free volume the…     

RG-CPA方程计算超临界CO2-醇体系汽液相平衡

综合考虑缔合作用和密度涨落的影响,将经重整化群修正的CPA方程（RG-CPA方程）扩展到二元体系汽液相平衡的计算。通过一个温度下的汽液相平衡数据回归得到二元交互作用参数,预测其他温度下的相平衡。采用这种方法计算了超临界CO₂与醇二元体系的汽液相平衡性质和临界曲线。结果表明,RG-CPA方程预测超临界CO₂与醇二元体系的气液相组成和密度具有较高的精度,液相组分平均绝对偏差为0.032,气相组分平均绝对偏差为0.019。与原始CPA方程相比,RG-CPA方程能更好地预测气液临界曲线。     

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     

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。     

AN EMPIRICAL VIRIAL-LIKE CUBIC EQUATION OF STATE FOR PHASE EQUILIBRIUM CALCULATIONS

An empirical cubic equation of state(EOS) was obtained by truncating the virial expansion in reciprocal of molar volume after the third term. The constants of the EOS was generalized in terms of critical temperature, critical pressure and Pitzer's acentric factor.

In pure component applications the EOS exhibited a performance comparable to Peng-Robinson (1976) EOS in the reduced temperature range of 0.5 to 1. The present EOS tends to predict better saturation liquid volumes at reduced temperatures below 0.8, and better estimations for second virial coefficient at high reduced temperatures.

The EOS was successfully employed for vapor liquid equilibrium calculations for some mixtures of normal or slightly polar fluids with traditional one binary parameter mixing rule at moderately high pressures. At low reduced temperatures, where conventional one adjustable parameter applications of the cubic equations compare unfavorably with dual methods based on excess Gibbs energy functions for the liquid phase, a new two constant mixing rule introduced by Stryjek and Vera (1986) was employed for the present equation of state.     

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     

含氢系统的新混合规则及其在工业氮洗塔中的应用(Ⅱ)

将本研究第(Ⅰ)部分中所提出的混合规则Ⅱ,结合PR方程用于合成氨厂原料气净化工艺中氮洗塔模拟。由各二元分系统的二元交互作用参数,推算了氮洗塔中五元相平衡,并模拟了(?)海和山西化肥厂的氮洗塔工况,结果与国外设计公司推荐值符合很好。因此证实了本文提出的模型具有实用价值。     

有机物水溶液粘度的关联和预测

在Eyring的液体粘性流动模型的基础上,根据Sandler的水溶液过量自由焓溶质聚集模型,导出有机物水溶液的粘度模型。利用该模型方程参数与温度的关系,可预测低压下各种温度和不同组成的有机物水溶液的粘度。用该模型计算了7个体系442个不同温度和组成的二元水溶液和3个体系164个不同温度和组成的三元水溶液的粘度,计算值与实验值的总平均相对偏差分别为1.554%和2.588%,计算值与实验数据吻合很好。     

Measurement of excess enthalpies using a high-pressure flow microcalorimeter and determination of binary interaction parameters for thermodynamic models

While an equation of state (EOS) plays a critical role in estimating thermodynamic properties, employing it in the determination of binary interaction parameters is extremely important. In general, these parameters can be determined from phase equilibrium data. However, data collection from experiments is a time-consuming and tedious process. In this study, after measuring the excess enthalpies of binary systems containing CO₂ by high-pressure flow isothermal microcalorimetry (IMC), we determined the EOS binary interaction parameters, specifically, the Peng-Robinson EOS binary interaction parameters. These binary interaction parameters obtained by IMC were compared with those obtained by vapor-liquid equilibrium (VLE) experiments. Hence, high-pressure flow IMC appears to be an effective method for the determination of interaction parameters that are used in the estimation of thermodynamic properties. Further, the Flory-Huggins interaction parameters of a binary mixture CO₂ containing with various mole compositions were also estimated by employing high-pressure IMC.