从统计力学推导流体状态方程(Ⅱ)——非球形多方阱势硬粒子微扰理论

本文从考虑真实分子的形状与势能出发,引进一新的用级数表示的径向分布函数形式,导出了任意形状硬粒子流体的级数状态方程.用此方程描述参考体系,用多方阱势来近似真实分子的势能曲线,采用Barker与Henderson的方法近似高级微扰项,导出了非球形多方阱势硬粒子微扰理论的通用表达式,以作为进一步导出实用状态方程的基础.     

含临界点的统计缔合流体理论研究(Ⅰ)非极性流体

从适合于临界点的计算出发 ,对统计缔合流体理论方程进行改进 :(1)对链状分子的每个链节考虑其非球形度 ;(2 )提出必须考虑链节成链时对色散作用的影响 .建立了扩展的统计缔合流体理论状态方程 ,对于正构烷烃和异构烷烃的计算表明 ,该方程计算温度范围大 ,从低温区到临界区 ,特别是在临界点附近精度有明显提高 ,临界点的计算值和实验值基本符合 .扩展了理论状态方程的适用性 ,可望用于各种含临界区域流体体系的热力学计算     

A simplified expression for the hard-sphere dimer fluid radial distribution function

Recently, in our laboratory a closed form expression for the correlation function of the hard-sphere dimer fluid obtained from Wertheims multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation was presented by Kim et al. [2001]. However, it is difficult to apply its expression to perturbation theory and vapor-liquid equilibria calculations, since it is of very complex form. In this work, we present a simplified expression for the first shell of the radial distribution function (RDF) of the hard-sphere dimer fluid using a series expansion of the analytical expression. The expansion is carried out in terms of both the packing fraction and the radial distance. Expressions are also obtained for the coordination number and its first and second derivatives as functions of radial distance and packing fraction. These expressions, which are useful in perturbation theory, are simpler to use than those obtained from the starting equation, while giving good agreement with the original expression results. Then we present an simplified equation of state for the square-well dimer fluid of variable well width (λ) based on Barker-Henderson perturbation theory using its expression for the radial distribution function of the hard-sphere dimer fluid, and test its expression with NVT and Gibbs ensemble Monte Carlo simulation data [Kim et al., 2001].     

新的局部组成混合规则模型和汽液平衡数据的关联计算

从径向分布函数理论导出一个简单而合理的分子配位数计算公式,进而建立了新的局部组成模型,该模型简化后与改进的Peng-Robinson状态方程结合,在各类非理想体系汽液平衡计算中取得了满意的结果.     

EQUATIONS OF STATE FOR HARD-SPHERE CHAIN FLUIDS AND SQUARE-WELL CHAIN FLUIDS

Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for HSCFs     

基于化学缔合的链状YUKAWA流体的状态方程

从Yukawa流体出发,采用化学缔合的统计力学理论建立了链状Yukawa流体的分子热力学模型,其亥氏函数由作为参考流体的硬球Yukawa流体的贡献和链节成键的贡献两部分组成.采用链长为2的链状Yukawa流体压缩因子的Monte Carlo模拟结果关联得到成键贡献项中空穴相关函数,对势能函数参数λ=1.8和λ=3.0时链长为4和8的链状Yukawa流体的压缩因子的预测与Monte Carlo数据能很好地吻合,比Wang和Chiew的微扰理论结果更好.     

Estimation of thermodiffusion coefficients in ternary associating mixtures

Following the non‐equilibrium thermodynamics formulation and taking into account the complexities in the structure of aqueous associating mixtures, expressions are proposed to estimate the thermodiffusion coefficients in ternary associating mixtures, such as water and alcohol mixtures. The model expressions are used to estimate the thermodiffusion coefficients in methanol–ethanol–water, dimethyl sulfoxide (DMSO)–ethanol–water and DMSO–t‐butanol–water mixtures at various concentrations. The perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state is used to obtain the mixture properties, such as the derivatives of the chemical potentials needed to evaluate the thermodiffusion coefficient expressions. The results show that at certain concentrations of one component, variation of the concentration of the other two components can cause a sign change in the thermodiffusion coefficients. While the model cannot be evaluated due to the lack of any pertinent experimental data, the model predictions may be used to choose suitable mixture compositions in space experiments to be performed onboard the International Space Station (ISS) in near future. © 2011 Canadian Society for Chemical Engineering     

A new equation of state (hsft) based on fractal theory

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.     

A NEW EQUATION OF STATE (HSFT) BASED ON FRACTAL THEORY

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

Molecular dynamic simulation and equation of state of Lennard-Jones chain fluids

In order to study the thermodynamic properties of chain and polymeric fluids at the molecular level, we perform constant temperature molecular dynamics simulations of ‘repulsive’ and ‘full’ Lennard-Jones (LJ) chain fluids of lengths up to 16. In the simulation, the RATTLE algorithm to determine constraint forces and the Nose-Hoover thermostat to sample the canonical ensemble are used. For repulsive LJ chains, the compressibility factor of the chain fluids is predicted from first-order thermodynamic perturbation theory combined with the Week-Chandler-Andersen (TPT1-WCA) perturbation theory, and is compared to the simulation results. A good agreement between the theory and the simulation results is found particularly at liquid-like densities. For full LJ chains, two different versions of TPT1 are used to calculate the compressibility factor: one is TPT1-WCA, and the other is TPT1 with the Percus-Yevick approximation for the radial distribution function of the LJ spheres (TPT1-PY). At low and intermediate densities, TPT1-PY gives better predictions for the compressibility of the LJ chain fluids, whereas at high densities TPT1-WCA is more reliable.     

一种完全型形状因子对应态原理

In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called “α“ fluid) and the reference fluid(called “o“ fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of “a“ and “o“ fluids are corresponded perfectly by introducing a new pressure shape factor 5. Using methane as the “o“ fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of φ is a function of temperature and volume while θ and δ are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-uolar fluids.     

环状和支链硬球链流体的状态方程

以单体缔合的统计力学理论为基础，建立了链状分子亥氏孙数和状态方程和空们相关函数的关系，并应用于环 状和支链硬球链流体。对这两类流体压缩因子的预测结果与计算机模型值相吻合。     

Predicting the thermodynamic properties and dielectric behavior of electrolyte solutions using the SAFT‐VR+DE equation of state

We extend the SAFT‐VR+DE equation of state to describe 19 aqueous electrolyte solutions with both a fully dissociated and a partially dissociated model. The approach is found to predict thermodynamic properties such as the osmotic coefficient, water activity coefficient, and solution density, across different salt concentrations at room temperature and pressure in good agreement with experiment using only one or two fitted parameters. At higher temperatures and pressures, without any additional fitting, the theory is found to be in qualitative agreement with experimental mean ionic activities and osmotic coefficients. The behavior of the dielectric constant as a function of salt concentration is also reported for the first time using a statistical associating fluid theory (SAFT)‐based equation of state. At high salt concentrations, the stronger electrostatic interactions between the ionic species due to the dielectric decrement, is captured through the inclusion of ion association. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3053–3072, 2015     

Phase equilibria of associating fluid mixtures using the perturbed-hard-sphere-chain equation of state combined with the association model

For developing the equation of state which can be applicable to associating fluids, the Perturbed-Hard-Sphere-Chain-Association (PHSC-AS) equation of state is proposed by incorporating the association term of the SAFT model into the PHSC equation of state which has been widely used to describe phase equilibria for the fluid system containing a large molecule such as polymer. In this work, two different types of PHSC models have been examined. One is the original model proposed by Song et al., and the other is the modified model by Kim and Bae whose chain term was replaced with that of the SAFT model. As a result, two types of PHSC-AS models are obtained, and applied to the calculation of phase equilibria for the binary system containing a self-associating compound such as alcohol, amine and carboxylic acid, etc. The calculated results of vapour-liquid equilibria are in good agreement with the experimental data. The proposed models (PHSC-AS) are also compared to the PC-SAFT model.     

COMMENTS CONCERNING A SIMPLE EQUATION OF STATE OF THE VAN DER WAALS FORM

When the Carnahan-Starling equation of state for hard spheres is combined with a simple attractive term, the molecular size parameter b for argon (as obtained from critical data) is much closer to the “correct” value than that obtained from the empirical Redlich-Kwong equation

For the critical isotherm for argon, the best simple form of the attractive term lies between the two common forms, proposed by van der Waals and by Redlich. At constant temperature, the attractive contribution to the compressibility factor is proportional to (v + 0.2b)^-1 where v is the molar volume. This proportionality is in agreement with results for a square-well fluid recently reported by Sandier.     

Extension to mixtures of two robust hard‐sphere equations of state satisfying the ordered close‐packed limit

Two new hard‐sphere EOS are proposed and tested using the same attractive potential terms used by the SAFT EOS. Generalized expressions for the pair RDF at contact value, the compressibility factor, and the excess chemical potentials have been derived. Extension to mixtures is tested using three mixing rules for multicomponent hard‐sphere fluids. The proposed EOS combined with the Santos et al. and the Barrio‐Solana mixing rules reproduced the compressibility factors and the excess chemical potentials more accurately than the Boublik‐Mansoori‐Camahan‐Starling‐Leland (BMCSL) EOS. However the pair RDF at contact value had larger deviations than those obtained with the BMCSL EOS. The combination of the proposed equations and the Barrio‐Solana mixing rule gave an accurate reproduction of the compressibility factor for binary hard‐sphere fluids with high diameter ratio even in the low concentration regions of the larger spheres.     

Real-time inferencing of solid–liquid phase equilibria in solution polymerization of polyethylene

An algorithm for the real-time prediction of multi-component solid–liquid equilibrium (SLE) in a polyethylene (PE) process flowsheet has been attempted. While most of the available literature assumes the polymer to possess a single average molecular weight and lump the entire polymer as a single component, the present work proposes to consider a polydispersed multi-component fraction, characterized by the pseudo-component approach. The SLE model has been used to study the effects of monomer and polymer polydispersity in solution polymerization process. At first, it has been validated on the solubility data of n-alkanes in n-hexane, polyethylene in M-xylene and on wax precipitation from a mixture of n-paraffins. The SLE model is based on perturbed chain SAFT (PC–SAFT) equation of state (EOS). An algorithm for the real-time prediction of SLE phase boundaries in solution polymerization has been subsequently presented. A simulation experiment on the polyethylene flowsheet highlighted the potential of real-time inferencing for industrial applications.