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.     

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     

硬球链流体在平板和硬球表面分布的密度泛函理论

采用Yethiraj和Woodward的密度泛函理论方法,结合胡英和刘洪来等发展的硬球链流体状态方程,得到了自由连接硬球链流体在平板狭缝中和球形固体颗粒表面附近的密度分布表达式,并计算了在两平行壁所组成的狭缝中和直径大小不同的球形固体颗粒周围硬球链分子的链节密度分布.理论计算结果与作者采用Dickman 和Hall 的方法进行Monte Carlo计算机模拟结果非常吻合.颗粒直径对链状分子的密度分布有一定的影响,随着固体颗粒直径的增加,靠近颗粒表面附近的链节密度降低.     

Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT)

A semi-empirical equation of state for the freely jointed square-well chain fluid is developed. This equation of state is based on Wertheim’s thermodynamic perturbation theory (TPT) and the statistical associating fluid theory (SAFT). The compressibility factor and radial distribution function of square-well monomer are obtained from Monte Carlo simulations. These results are correlated using density expansion. In developing the equation of state the exact analytical expressions are adopted for the second and third virial coefficients for the compressibility factor and the first two terms of the radial distribution function, while the higher order coefficients are determined from regression using the simulation data. In the limit of infinite temperature, the present equation of state and the expression for the radial distribution function are represented by the Carnahan-Starling equation of state. This semi-empirical equation of state gives at least comparable accuracy with other empirical equation of state for the square-well monomer fluid. With the new SAFT equation of state from the accurate expressions for the monomer reference and covalent terms, we compare the prediction of the equation of state to the simulation results for the compressibility factor and radial distribution function of the square-well monomer and chain fluids. The predicted compressibility factors for square well chains are found to be in a good agreement with simulation data. The high accuracy of the present equation of state is ascribed to the fact that rigorous simulation results for the reference fluid are used, especially at low temperatures and low densities. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

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。     

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.     

用改进的密度泛函理论预测三元硬球混合物的结构

在Ronsenfeld的权重函数的基础上,在计算流体自由能密度时利用硬球混合物流体的Boublik—Mansoori—Canahan-Starling-Leland状态方程来代替硬球的定标粒子理论,从而得到了改进的密度泛函理论。结合测试粒子法,对不同组成的三元硬球混合物流体的径向分布函数进行了计算：与分子模拟数据比较结果表明,使用合适的密度泛函理论,测试粒子法能够成功地计算多元硬球混合物流体的结构性质。本研究为使用统计力学理论计算其它复杂流体的热力学性质提供了一种方法。     

IMPROVING CUBIC EQUATIONS OF STATE FOR HEAVY RESERVOIR FLUIDS AND CRITICAL REGION

It is shown that by considering the “b” parameter in a cubic equation of state (EOS) as acentric factor/temperature-dependent, liquid densities especially for heavy compounds and the region near the critical point can be estimated more accurately. The proposed equation can also be used for accurate estimation of critical compressibility factors of different compounds, Although the method is applied to Peng-Robinson equation of state (PR-EOS), it can be used for any other cubic equation of state. The proposed method is particularly useful for phase equilibrium calculations of reservoir fluids. The proposed equation requires critical temperature, critical pressure and acentric factor as the input parameters. The proposed equation of stale estimates properties of liquids, vapor-pressure and critical compressibility factors with greater accuracy for pure compounds and mixtures as well as light and heavy compounds found in reservoir fluids.     

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.     

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.     

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.     

修正的硬球三参数状态方程(Ⅰ)计算流体的饱和性质

对硬球三参数状态方程(CSPT)引力参数的温度校正系数α和拟临界压缩因子(?)提出了新的温度关系式.用修正的CSPT方程(MCSPT)计算了105种纯物质的饱和性质.结果表明,新的方程改善了原CSPT方程在低对比温度下物质的饱和性质,以及临界区域内热力学性质的计算精度.并用于计算超临界状态下物质的热力学性质,有良好的外推性.     

硬球链流体在狭缝中密度分布的Monte Carlo模拟

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurationai-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurationai entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various eauations of state of HSCFs by different authors.     

带电硬哑铃流体的分子热力学

Chemical potentials of charged hard-dumbbell fluids are obtained by Monte Carlo simulations using Widom‘s test-particle method, corresponding compressibility factors are achieved by integration of chemical potentials at different densities. A molecular thermodynamic model is also developed for these charged hard-dumbbell fluids where the residual Helmholtz function is composed of two terms: a reference term responsible for the charged hard spheres and a bonding contribution measuring the sticky interactions between positive and negative hard ions.Model predictions are in good agreement with simulation results.     

An analytical equation of state for water and alkanols

An analytical equation of state extended from statistical associating fluid theory (SAFT) is modified to describe the thermodynamic properties of fluids with high polarity such as water and alkanols up to the region close to the critical point. Five terms are used in the equation of state: the term for hard convex body, the term for dispersion energy, the term for the chain formation of hard convex body, the term for the change of the dispersion energy because of chain formation, and the term for dipole-dipole interaction. This equation of state is still called SAFT-CP (across critical points). Six fluids water, methanol, ethanol, 1-propanol, 1-butanol and 1-pentanol are used as examples. The new equation of state reproduces saturated pressures and densities in vapor-liquid equilibrium, critical properties (as temperature, pressure and density), and densities in the one-phase region with rational accuracies. The comparison of the calculated critical exponent β with the experimental one for methanol shows the improvement up to the region only with 20 K difference of temperature to the critical point. The result coincides with the estimation of the critical region on the basis of Ginzburg number and also with the available opinion that crossover methods and renormalization theories are necessary in the near-critical region.     

Tao-Mason状态方程扩展用于重正烷烃(英文)

In our previous paper we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. This is a continuation for evaluating TM EOS in predicting PVT properties of heavy n-alkanes. Liquid density of long-chain n-alkane systems from C 9 to C 20 have been calculated using an analytical equation of state based on the statistical-mechanical perturbation theory. The second virial coefficients of these n-alkanes are scarce and there is no accurate potential energy function for their theoretical calculation. In this work the second virial coefficients are calculated using a corresponding state correlation based on surface tension and liquid density at the freezing point. The deviation of calculated densities of these alkanes is within 0.5% from experimental data. The densities of n-alkanes obtained from the TM EOS are compared with those calculated from Ihm-Song-Mason equation of state and the corresponding-states liquid densities (COSTALD). Our results are in favor of the preference of the TM EOS over other two equations of state.     

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.     

Extension of Tao-Mason Equation of State to Heavy n-Alkanes

In our previous paper we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids, using the speed of sound data. This is a continuation for evaluating TM EOS in predicting PVT prope...     

A CUBIC EQUATION OF STATE BASED ON A SIMPLIFIED HARD-CORE MODEL

The Redlich-Kwong (RK) equation of state introduced in 1949 has been considered the most accurate two-constant-parameter cubic equation of state. The other cubic equations which are more accurate than the RK equation contain either three, or more, parameters and/or their parameters are temperature- dependent. A New two-constant-parameter cubic equation of state, $ is introduced using a simplified molecular theory of hard-sphere fluids for its repulsive term. This two-constant-parameter cubic equation of state appreciably increases the accuracy of thermodynamic property predictions and phase equilibria of pure fluids and flluid mixtures over the equations of this category.     

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