Equation of state for gaseous ethane determined from isotropic model potentials

A four-term virial equation of state was combined with isotropic model potentials to predict accurate volumetric and caloric thermodynamic properties of ethane in the gas phase. The parameters of the model potentials were determined from a fit to speed-of-sound data alone; no other data were used. The approximation used for the fourth virial coefficient included all interactions that contain up to two triplet potentials. Predicted ordinary second and third virial coefficients are in agreement with the data of Funke et al. [8]; we believe that predicted fourth virial coefficients are reliable and accurate. In the subcritical temperature region, the equation of state predicted compressibility factors that deviate by less than 0.04 percent at densities of up to 2.7 mol/dm³ (≈ 0.4ρ _c ). At supercritical temperatures, compressibility factors deviate by less than 0.02 percent at densities of up to 2.6 mol/dm³; also, in this region predicted isobaric heat capacity agrees with available data to within uncertainties of 0.4 percent at densities above 3 mol/dm³. We demonstrated that the four-term virial equation is more accurate than the three-term analogue.     

Molecular‐based virial coefficients of CO2‐H2O mixtures

We report second and third virial coefficients for the system CO₂‐H₂O, calculated via cluster integrals using quantitative molecular models taken from the literature. Considered models include (1) fits to highly accurate ab initio calculations of the potential energy surfaces, and (2) semiempirical Gaussian Charge Polarizable Models (GCPM). Three‐body effects are found to be essential for obtaining quantitative results. Good agreement with experiment is obtained for the pure‐component coefficients, and for the cross second virial coefficient. For the two cross third virial coefficients, the few experimental data available do not agree well with the calculations; it is not clear whether this is due to problems with the data or deficiencies in the three‐body potentials. The uncertain state of the experimental data, and the relative mutual consistency of values computed from ab initio and GCPM models, suggest that calculated mixture third virial coefficients could be more accurate than values from experiment. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3029–3037, 2015     

圆柱定程干涉法确定工质的第二维里系数

通过圆柱定程干涉法测量了Ar在270~333.15 K,压力至1000 kPa的声学共振频率,修正了热边界层、黏性边界层、声波导管、壳体振动等非理想因素对共振频率测量的影响。通过拟合声学共振频率获得了Ar的第二声速维里系数,实验结果与文献中圆球定程干涉法的测量结果具有较好的一致性。通过第二声速维里系数回归了方阱势能模型的参数,根据回归结果计算了Ar的第二维里系数,在150~450 K范围与标准状态方程的计算偏差小于0.4 cm³·mol^-1。通过圆柱定程干涉法确定的第二维里系数与圆球定程干涉法的精度相当。     

Some properties of the GHC equation of state

The composition functionality of the mixture energy parameter, a_M, used in the Gibbs-Helmholtz Constrained (GHC) equation of state is studied. An analysis is presented that shows that a_M for liquid mixtures is approximately quadratic in composition. All non-quadratic behavior is due solely to ln(T_cM) in the GHC up-scaling equation. If a mean value approximation of this term is used, then a_M^L is quadratic, but non-symmetric, in composition. For vapors, non-quadratic behavior is coupled to the molar volume of the mixture through the term β_M = (V_M + b_M)/V_M. It is shown that the difference between β_M and some average _βM is very small and a_M^V is quadratic in composition. Sensitivity analyses of a_M and resulting molar density to these approximations are also presented. Finally, the non-symmetric composition functionality of a_M is discussed along with GHC predictions of mixture second virial coefficients. Numerical examples are presented to support all claims.     

A Simple Modification of the Pitzer Method to Predict Second Virial Coefficients

A simple modification of the Pitzer relation to calculate second virial coefficients of polar compounds is proposed. The proposed modification is based on the use of a new parameter, β, which embodies both the contributions of acentricity and polarity to second virial coefficient values. The analytical form of the Pitzer relation is preserved and its performances are improved. Rules are given to calculate β for several classes of compounds which require only the knowledge of a few well known properties of pure compounds. A comparison between the new method and the Pitzer-Tsonopoulos relation is made on the basis of the experimental B_i data of nearly 50 compounds.     

多元渗透维里方程通式的表达：双水相系统的液液平衡计算

提出了基于三元系修正Ｐｉｔｚｅｒ模型的多元渗透维里方程通式，并应用于双水相系统液液平衡性质的关联和预测，用汽液平衡数据关联模型参数，预测了聚乙二醇／硫酸镁双水相系统的液液平衡；用汽液平衡数据和尽可能少的液液平衡数据关联模型参数。同时预测了焦点或不含电解质的ＰＥＧ／葡萄糖双水相系统的液液平衡和ＫＣｌ电解质在ＰＥＧ／ＤＥＸ系统中的分配系数。计算结果表明，模型有较好的预测功能。     

Critical isotherms from virial series using asymptotically consistent approximants

The low‐density equation of state of a fluid along its critical isotherm is considered. An asymptotically consistent approximant is formed having the correct leading‐order scaling behavior near the vapor‐liquid critical point, while retaining the correct low‐density behavior as expressed by the virial equation of state. The formulation is demonstrated for the Lennard–Jones fluid, and models for helium, water, and n‐alkanes. The ability of the approximant to augment virial series predictions of critical properties is explored, both in conjunction with and in the absence of critical‐property data obtained by other means. Given estimates of the critical point from molecular simulation or experiment, the approximant can refine the critical pressure or density by ensuring that the critical isotherm remains well‐behaved from low density to the critical region. Alternatively, when applied in the absence of other data, the approximant remedies a consistent underestimation of the critical density when computed from the virial series alone. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3336–3349, 2014     

Vapor liquid equilibrium data for alcohol n-Amylamine binary systems at 333.15 K. Reduction of the experimental data by a novel model-free method

Vapor liquid equilibrium measurements for the binary systems of n-amylamine with methanol, ethanol and 1-propanol at 333.15 K are reported. The measurements were made in a static equilibrium cell of the Van Ness type and the experimental data were reduced using a model-free method. This model-free method is an adaptation of the method of Mixon et al. in which a material balance is introduced to correct for the mols of the gas phase. Second virial coefficients of n-amylamine and cross second virial coefficients for the binary systems were measured in this work and parameters for the Tsonoupolos correlation are reported.     

M-H-EOS的理论基础

根据virialEOS的推导方式 ,从具有分子体积的准理想气体模型出发 ,利用巨正则分布和势能函数 ,从理论上推导了M -H -EOS ,并探讨了M -H -EOS的理论基础。结果表明 ,M -H -EOS与virialEOS具有相同的理论基础 ,只是在考虑实际气体对理想气体在分子体积和分子间相互作用的偏差上做了不同的近似。M -H -EOS为了计算简便 ,在实验的基础上对分子间相互作用做了合理的近似 ,从而避免了高阶virial系数求解困难的问题 ,因此在实用中取得成功。了解M -H -EOS的理论基础 ,对进一步发展和改进M -H -EOS的应用领域和计算准确度具有一定的意义     

A FOUR PARAMETER PITZER-CURL TYPE CORRELATION OF SECOND VIRIAL COEFFICIENTS

The Pitzer-Curl ( 1957) correlation of second virial coefficients is slightly modified to accommodate high temperature data ( TT₄ 4.0) of He and H₂ and extended successfully to “ nonstandard” fluids as defined by Tarakad and Danner (1977), by introducing a fourth parameter per compound. The new version improves results at the high temperature limit while it gives comparable results with the previous versions presented by Pitzer and Curl ( 1957) and Tsonopoulos ( 1974) at lower temperatures. The present approach enhances the applicability of the method for polar and associating compounds by introducing a correcting term for 129 such fluids. The extension of the correlation to mixtures requires an additional parameter per binary. Successful results were obtained for thirty nine binary systems investigated in this work     

GENERALIZED DERIVATIONS FOR MIXTURES USING THE VIRIAL EQUATION: APPLICATION TO FUGACITY

Calculation of mixture properties using the virial equation of state (VEOS) becomes tedious when the expression contains more than the second virial term. This paper describes a derivation procedure which permits relatively simple extension to any number of virial terms. We have used the fugacity derivation as an example of using the new technique and provide an equation for the fugacity coefficient using any number of terms and any number of components.     

SRK方程α的分析和比较

Alpha functions of Soave-Redlich-Kwong （SRK） equation of state proposed by Soave, Twu, and Luo were different in mathematic tendency. They were compared in modeling methane-alkanes equilibria with van der Waals mixing rule and Modified Huron-Vidal （MHV1） mixing rule, respectively. Results showed that Luo＇s alpha function was a little more accurate than Soave＇s, and Twu＇s alpha function lacked accuracy in modeling methane-alkanes equilibrium. SRK equation of state was expanded as virial form, and then the equivalent terms were contrasted with terms of virial equation of state. Results showed that Soave＇s and Luo＇s alpha functions matched the tendency of virial coefficient better than Twu＇s, and Luo＇s alpha function matched better than Soave＇s in wide temperature range, which sustained the conclusions of phase equilibria calculation. Luo＇s alpha function keeps decreasing when Tr〉 1 and becomes negative at sufficient high temperature, thus the conventional cubic equation of state expressed pressure as the sum of repulsion pressure PR （〉0）, and attraction pressure PA （〈0） could be improved to be the sum of hard-sphere repulsion pressure PH （〉0） and intermolecular force pressure P1 （P1〈0 at low temperature and p1〉0 at sufficient high temperature）.     

Second virial coefficients of polar gases for a four-parameter model

The second virial coefficients of polar gases have been studied for a potential function consisting of the Kihara spherical core potential combined with a preaveraged dipole-dipole interaction term. The molecular parameters ?/κ, ρ_o, a*, and y of this potential function were determined for ten substances by a nonlinear least squares analysis of experimental second virial coefficients. These molecular parameters were related to the critical constants, acentric factors, and fourth parameters of the substances. The resulting equations reproduced the second virial coefficients to within the accuracy of the data. Comparisons with experimental data for substances not included in the development of the relationships indicated that good agreement can be obtained for polar fluids by the method of this study.     

Improved accuracy and precision in the light-scattering characterization of homo- and copolymers in THF

A one-point method was developed for the estimation of weight-averaged molecular weights from light-scattering data. The method is based on the calculation of the second virial coefficient from theoretical predictions of the dependence of A₂ on the molecular weight. The second virial coefficient is then regressed for a particular polymer—solvent combination from a series of preexisting measurements over a range of molecular weights. The one-point method is found to yield as accurate molecular weight estimates as obtained from a Debye plot using the conventional dilution technique. The variance in the estimation of the Rayleigh factor has also been found to be highly dependent on the measurement concentration. Therefore, the precision in the estimation of molecular weight can be improved by calculating molecular weights at or near the optimal concentration, which is itself molecular weight-dependent. The one-point method is demonstrated for poly(methyl methacrylate)s of various polydispersities in tetrahydrofuran. The molecular weight of polystyrene and polystyrene-co-acrylic acid were also estimated by the one-point method in THF. In the case of the polystyrene-co-acrylic acid, THF becomes a poorer solvent with increasing levels of acrylic acid in the copolymer, and the parameter (A₂M^0.5) is found to vary with the copolymer composition, as is theoretically predicted. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1303–1316, 1997     

Twenty‐one new theoretically based cubic equations of state for athermal hard‐sphere chain pure fluids and mixtures

Eight new hard‐sphere equations of state (EOS's) were obtained from molecular simulation data for the pair correlation function g_HS(σ) vs. packing fraction η and combined with three theoretical schemes to obtain 21 new cubic EOS's for athermal hard‐sphere chains (AHSC's). The eight new hard‐sphere EOS models successfully reproduced isotropic fluid compressibility factor Z_HS and g_HS(σ) vs. η simulation data and predicted metastable liquid Z_HS vs. η and virial coefficients up through B₁₀. Moreover, calculated Z vs. η and reduced second‐virial coefficient vs. chain length m were compared with molecular simulation data for chains up to m = 201 for a set of representative (eight of twenty‐one) chain equations. Z vs. η for three AHSC binary mixtures was also successfully predicted. The results indicate that the new cubic EOS's give a satisfactory representation of simulation data for chain fluids and can be used to develop theoretically based cubic EOS's for “real” fluids including attractive effects. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1677–1690, 2015     

改进的Burnett法测定N_2-CO_2-CHClF_2体系的压缩因子和维里系数

对DH81型压缩因子计及其数据处理方法进行改造与完善,形成一套完整的能比较精确测量流体PVT性质的改进Burnett法,用以测定含N_2、CO_2、CHClF_2体系在293.15K下的压缩因子和维里系数,其中含CHClF_2体系的有关数据未见文献报导。     

Nitrogen and hydrogen adsorption of activated carbon fibers modified by fluorination

In this study, activated carbon fibers (ACFs) were surface modified with fluorine and mixed oxygen and fluorine gas to investigate the relationship between changes in surface properties by nitrogen and hydrogen adsorption capacity. The changes in surface properties of modified activated carbon fibers were investigated using X-ray photoelectron spectroscopy (XPS) and compared before and after surface treatment. The specific surface area and pore structures were characterized by the nitrogen adsorption isotherm at liquid nitrogen temperature. Hydrogen adsorption isotherms were obtained at 77 K and 1 bar by a volumetric method. The hydrogen adsorption capacity of fluorinated activated carbon fibers was the smallest of all samples. However, the bulk density in this sample was largest. This result could be explained by virial coefficients. The interaction of hydrogen-surface carbon increased with fluorination as the first virial coefficient. Also, the best fit adsorption model was found to explain the adsorption mechanism using a nonlinear curve fit. According to the goodness-of-fit, the Langmuir–Freundlich isotherm model was in good agreement with experimental data from this study.     

CORRELATION FOR THE THIRD VIRIAL COEFFICIENT USING Tc, PC, DIPOLAR POLARIZABILITY AND MEAN RADIUS OF GYRATION AS PARAMETERS

A new semi-empirical correlation for third virial coefficients of pure non-polar gases and their mixtures has been developed. It has been formulated as a sum of three contributions: two for pair additivity and non-additivity to the simple fluids and one for size and shape effects of the molecules. These contributions have been correlated with theoretically calculated data for argon, krypton and xenon and with an important set of emperimental data on third virial coefficients for 12 non-polar gases, The final correlation has been applied to 21 pure non-polar gases, 3 quantum fluids and 12 binary mixtures of classical and quantum gases. The results have been compared with other available methods. The overall comparison shows that this new method is equivalent or better than those, and that its major advantage is its predictive capability and its better theoretical representation thai should allow, in principle, its extension to more complex fluids.     

Self- and mutual diffusion coefficient equation for pure fluids, liquid mixtures and polymeric solutions

Transport properties are important information not only for industrial equipment design but also for many research areas. While there is a well-developed theory for gases at low densities, there is no established theory to calculate diffusion coefficients for dense fluids, especially for polymeric solutions. Recently, a database of 96 self-diffusion coefficient data points were obtained from molecular dynamics (MD) simulations for freely jointed Lennard-Jones chains (LJC) with lengths of 2, 4, 8 and 16 at reduced densities ranging from 0.1 to 0.9 and in the reduced temperature interval of 1.5 to 4. These data were used to develop an equation that correlates MD self-diffusion coefficient points with an overall absolute average deviation of 15.3%. The aim of this work is to show that this equation can be used to calculate diffusivities of pure liquids and liquid mixtures, including polymeric solutions. The proposed equation is used for correlating self-diffusion coefficients for 22 pure real substances and then for predicting mutual diffusion coefficients for 12 binary liquid mixtures. The proposed equation is also used to calculate mutual diffusion coefficients for polymeric systems as: polystyrene-toluene at 110 °C, poly(vinyl acetate)-toluene at 35 °C, and poly(vinyl acetate)-chloroform at 35 and 45 °C. Results show that the model developed here seems to be a promising approach for correlating mutual diffusion coefficients not only for small-molecule systems but also for polymer-solvent systems. One advantage of the equation proposed here is that the parameters have physical meaning and most of them can be estimated without any information on binary diffusion data.