THE APPLICATIONS OF A GENERALIZED EQUATION OF STATE TO THE CORRELATION AND PREDICTION OF PHASE EQUILIBRIA∗

Two methods of generalizing an equation of state are demonstrated and their limitations are outlined. One method involves the correlation of the equation of state constants and the second method involves a recently proposed Generalized Corresponding States Principle based on the properties of two (nonspherical) reference fluids. The PVT properties of pure fluids are represented by a new cubic equation of slate with four parameters which are obtained from vapor pressure and saturated liquid density data. It is demonstrated how a limited amount of data on key components may be used to obtain phase equilibria in mixtures.     

EVALUATION OF THE ORIGINAL AND THE MODIFIED LEE-KESLER EQUATION OF STATE

In this work, the Lee-Kesler equation of state has been used together with the extended corresponding states principle. In order to improve the predictability of the equation in a more narrow acentric factor range, two new reference fluids have been chosen. The parameters in the Lee-Kesler equation have been estimated for the two reference fluids, CFC12 (dichlorodifluoromethane) and HFC134a (1,1,1,2-tetrafluoroethane), with the Error-in-Variables Model. This model allows both dependent and independent variables to be subject to errors.

Calculations have been made for the two reference fluids as well as for other compounds, and the predicted thermodynamic properties have been compared with experimental values. Comparative calculations have also been carried out for some of the previously suggested modifications of the Lee-Kesler correlation.     

A GENERALIZED EQUATION OF STATE FOR POLAR AND NON-POLAR FLUIDS BASED ON FOUR-PARAMETER CORRESPONDING STATES THEOREM

A new generalized equation of state for polar and non-polar fluids based on the corresponding states theorem is developed, f n addition to two critical parameters, four parameters are required; two for the calculation of volumetric properties and two for the calculation of pressure and departure functions. Parameteres for more than 100 polar and non-polar fluids are given. Comparison with the existing generalized state equations showed that the new method, in general, shows a better agreement with the experimental data. The absolute average deviation is 0.48% for the vapor pressure and 0.32% for the saturated liquid volume.     

A new generalized corresponding-states equation of state for the extension of the Lee-Kesler equation to fluids consisting of polar and larger nonpolar molecules

The Lee-Kesler equation of state for the thermodynamic properties of small nonpolar fluids is extended to all fluids consisting of polar and larger nonpolar molecules, based on the general corresponding-states theory for highly nonspherical fluids. The thermodynamic functions are represented by an analytical equation of state. The results for polar fluids are substantially better than those obtainable from other currently available methods, while the results for nonpolar fluids are equivalent to and mostly better than those obtained by the Lee-Kesler method. The input data required are the critical temperature, the critical volume, the acentric factor and the aspherical factor, which is related to the critical compression factor; the critical volume is therefore required in the present method. The method developed in this work shows good accuracy for 15 representative nonpolar, polar, hydrogen bonding and associating fluids and provides a simple method for industrial applications. Average deviations for the compressibility factor, the heat capacity and the speed of sound for six nonpolar and nine polar fluids from the new equation of state are 0.74%, 2.1% and 2.3%, which are about 8 times smaller than those obtained from the Lee-Kesler equation (about 5.6%, 17% and 29%, respectively).     

COMMENTS ON CUBIC EQUATIONS OF STATE BASED UPON THE INFINITE PRESSURE LIMIT

We examine a recently proposed modification to equations of state of the Van der Waal's type that involves using an infinite pressure limit of the equation to derive new mixing rules for the attractive term parameter. Results on some example systems including both vapor-liquid and solid-supercritical fluid equilibria show that the proposed modification does not appear to enhance the equation over its conventional one-fluid form. It appears that the fundamental inadequacy of the repulsive force term in such equations, for dense fluids, cannot be easily overcome by added complexity for the attractive term expression. Hard sphere reference systems on the other hand provide a more accurate repulsive force term.     

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.     

A new cubic equation of state for fluids and fluid mixtures

A new cubic equation of state for pure fluids is presented in this work. The new equation requires the critical temperature and pressure, as well as two additional parameters to characterize each particular fluid. These parameters have been evaluated by minimizing deviations in saturated liquid densities while simultaneously satisfying the equality of fugacities along the saturation curve. Thus, good predictions of volumetric properties in the liquid region are obtained, while accuracy in vapour—liquid equilibrium calculations is maintained. Parameters for polar as well as nonpolar fluids are presented in this paper. In the case of nonpolar fluids, the two parameters required can be correlated with the acentric factor. No such relationship with independently measured quantities could be found for polar fluids. It is shown that the new equation reproduces many of the good features of the Soave and Peng—Robinson equations of state for nonpolar fluids, whilst overcoming some of the limitations of these equations for polar fluids. Applications of the equation of state to the correlation of phase equilibria are demonstrated.     

A new concept for augmented van der Waals equations of state

A novel approach to perturbed equations of state for simple fluids is presented and its advantages over the traditional perturbed hard sphere equations are demonstrated by its application to several model fluids. The approach is based on a short range Yukawa reference which incorporates, in addition to repulsive interactions, also attractive interactions at short separations. The considered models of common interest are the Sutherland, Lennard-Jones, and EXP6 fluids. It is shown that using the proposed approach the reference system captures a good deal of properties of the studied fluids and that an accurate equation of state can be obtained using only the crude mean field (augmented van der Waals) approach.     

超临界流体p-V-T方程的研究

木文对目前常用的RK、RKS、PR及CS-vdW等状态方程进行了考察,验算了它们对二氧化碳、乙烯、丙烷等十种体系在超临界区、特别在临界点附近区域的适用性.计算结果表明,在上述区域内计算偏差都较大.作者从统计热力学的角度提出了一个“m-RKS”方程:P=RT/(V-b(T))—a(T)/V[V+b(T)],用该方程进行计算,结果与文献报道的实测值之间的偏差大大低于上述常用的诸方程.     

AN IMPROVED PENG-ROBINSON EQUATION OF STATE WITH A NEW TEMPERATURE DEPENDENT ATTRACTIVE TERM

An improved form of the Peng-Robinson cubic equation of state has been proposed. The temperature dependence of the attractive term has been modified so as to accurately represent vapor pressures of several fluids with large acentric factors from triple point to close to the critical point. The prediction of saturated liquid volume is also improved by introducing volume translation term in the equation of state. Comparisons of theoretical results with experimental data are made for the vapor/liquid phase equilibria of 44 pure fluids including nonpolar, polar and associating fluids. Our results show that the modified Peng-Robinson equation of state can represent accurately saturated vapor pressures of the fluids investigated in this paper, and it is more accurate than the Peng-Robinson equation of state and its earlier modifications due to Stryjek and Vera (1986) and Twu et al. (1995rpar;. Incorporation of the volume translation term in the equation of state has been found to improve the accuracy of saturated liquid volume significantly.     

The VIM theory of molecular thermodynamics: Part I: Analytic equation of state of nonpolar fluids

Variational inequality minimization (VIM) theory of statistical mechanics is used to derive analytic equations of state for nonpolar fluids. Pair- and tripletintermolecular potential energy functions are taken into account in the formulation of this equation of state. The VIM theory has made it possible to derive rather simple expressions for the thermodynamic properties of nonpolar fluids. Predictions of the thermodynamic properties of argon and methane in the liquid phase, in the vapor phase, and in the critical region by the VIM equation of state are shown to be in excellent agreement with the experimental data.     

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.     

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.     

EQUATION OF STATE FOR POLAR AND NONPOLAR SUBSTANCES FROM CORRELATIONS OF PURE COMPONENT PROPERTIES

A cubic equation of state of the van der Waals type is presented which is suitable for polar and nonpolar fluids and fluid mixtures. The form is based on the three-parameter equation of lwai, Margerum and Lu. Problems in parameter generalization are avoided by calculating the parameters directly from existing pure component vapor pressure and saturated liquid molar volume correlations. The proposed approach yields excellent representation of pure component saturated and single-phase region properties. Excellent results are also obtained for mixtures.     

A MODIFIED LEE-KESLER EQUATION OF STATE FOR REFRIGERANTS

For calculation of the thermodynamic properties of refrigerants it is proposed that the extended corresponding states principle (ECSP) should be used using two specific reference fluids, CFC12 (CCI₂F₂) and HFC134a (CF₃CH₂F), in order to cover the field of interest for most refrigerants. The specific parameters of these refrigerants have been determined for the Lee-Kesler modification of the Benedict-Webb-Rubin equation of state. In the parameter estimation, it has been taken into accounl that all variables are subject to errors by using the so-called Error-in-Variables-Model (EVM). The parameters have been estimated from experimental pressure-volume-temperature data, vapour pressure and saturated liquid and vapour volume data for CFC12 and HFC134a.

The extended corresponding states principle proposed in this work with CFC12 and HFC134a as reference fluids has been used in calculations of the thermodynamic properties of a number of refrigerants. In comparison with the original Lee-Kesler equation this concept gives improved results in calculations of vapour pressure and liquid volume.     

A REDUCED VAPOR PRESSURE EQUATION BASED ON THE THEOREM OF CORRESPONDING STATES

A reduced vapor pressure equation based on the theorem of corresponding states is proposed in this work by the use of the third parameter to and the fourth parameter X. This equation yields an overall average absolute deviation of 1.09% for 111 normal fluids involving a total of 6968 vapor pressure data points, and 0.67% for 20 polar fluids involving a total of 1516 data points, respectively. A relationship of estimating acentric factors is obtained by applying the reduced vapor pressure equation at the normal boiling point. This relationship is very accurate for the prediction of the values of the acentric factor     

PREDICTION OF PHASE EQUILIBRIA IN BINARY MIXTURES USING AN IMPROVED EQUATION OF STATE AND A THEORETICALLY CONSISTENT MIXING RULE

Prediction of thermodynamic properties and phase equilibria in fluid mixtures using a simple cubic equation of state is still a challenging problem. In this paper, we have predicted vapor/ liquid phase equilibria of several binary fluid mixtures using our previously developed improved Peng-Robinson equation of state and a theoretically consistent mixing rule. Our mixing rule combines the mixing rule of Wong-Sandier with a physically based combination rule. Mixtures are composed of nonpolar, nonassociating polar and associating polar fluids. Comparisons of theoretical predictions with experimental data show a very good performance of our approach in describing vapor/liquid phase equilibria of several mixtures, namely, carbon dioxide/ propane, ethane/hexane, butane/methanol, benzene/methanol, acetone/methanol, methanol/ ethanol, methanol/1-butanol, methanol/water and ethanol/water.     

A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of T_r = 0.3 to 4 and P_r - 0.01 to 10.     

THE CALCULATION OF CRITICAL PROPERTIES OF MIXTURES FROM EQUATIONS OF STATE

The rigorous critical state criteria based on Helmholtz free energy is used with equations of state fordirect calculation of critical properties(T_c,P_c and V_c)of 44 binary and 5 ternary systems.Special at-tention is paid to systems containing polar component(s)and the improvement in critical volume prediction.For extending this method to polar systems,the recently developed Cubic Chain-of-Rotators equation ofstate has been applied.As compared with SRK and PR equations of state,the improvement in V_c pre-diction is most impressive.