PREDICTION OF MOLAR VOLUMES, VAPOR PRESSURES AND SUPERCRITICAL SOLUBILITIES OF ALKANES BY EQUATIONS OF STATE

A generalized cubic equation of state which can represent all the cubic equations is introduced and thermodynamic property relations for it are presented. Five cubic equations of states with respective mixing rules are used to predict molar volumes and vapor pressures of pure alkanes (from methane till n-tritriacontane) and solubilities of solid wax components (high molecular weight alkanes) in supercritical solvents. They are the RK (Redlich-Kwong), MMM (Mohsennia-Modarress-Mansoori), RM (Riazi-Mansoori), PR (Peng-Robinson), and SRK (Soave-Redlich-Kwon) equations of state. The experimental data necessary to compare the equations of state are taken from the literature. It is demonstrated that the SRK equation of state is more accurate for predicting vapor pressures of alkanes. The RM equation of state is shown to be more accurate for predicting molar volumes of saturated and sub-cooled liquid alkanes as well as molar volumes of alkanes in their supercritical condition. For the solubility of wax components in supercritical solvents it is shown that the MMM equation of state gives the least AAD% for the 270 data points of 10 binary systems studied consisting of a high molecular weight alkane and supercritical ethane and carbon dioxide.     

Van der waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling

A new concept for the development of mixing rules for cubic equations of state consistent with statistical-mechanical theory of the van der Waals mixing rules is introduced. Utility of this concept is illustrated by its application to the Redlich-Kwong (RK) and the Peng-Robinson (PR) equations of state. The resulting mixing rules for the Redlich-Kwong and the Peng-Robinson equations of state are tested through prediction of solubility of heavy solids in supercritical fluids. It is shown that the new mixing rules can predict supercritical solubilities more accurately than the original mixing rules of the Redlich-Kwong and Peng-Robinson equations of state.     

用SRK方程与PR方程求算双组分混合气体热力学性质

流体热力学性质的计算是化工热力学中的一类重要计算,立方型方程经常用于这类计算中。SRK方程与PR方程是在RK方程基础上发展而来的,具有比RK方程更好的计算精度。但现有教材中没有给出PR方程和SRK方程的剩余焓、剩余熵的计算公式,缺失了流体热力学性质计算的系统性。本文通过立方型状态方程的一般形式推导出PR方程和SRK方程的剩余焓、剩余熵的计算公式,利用Excel电子表格计算双组分混合气体的热力学性质。计算过程简捷明了,利于学生更好地理解混合物热力学性质的计算过程。     

Parameters for the attractive coefficient of the patel-teja-valderrama equation of state

A three-parameter form of the temperature dependence of the attractive term in cubic van der Waals type equations of state (AS; Almeida et al., 1991; Aznar and Silva-Telles, 1992) has been applied to a generalized equation of state known as the Patel-Teja-Valderrama equation (PTV; Valderrama, 1990). The parameters of the AS model in the PTV equation of state were calculated for 457 substances of different polarity, molecular size, and chemical nature. The parameters were calculated using vapor pressure data determined through accurate equations available in the literature (Wagner 1973, Antoine 1888, Frost and Kalkwarf, 1953). The deviations between the equation of state calculations and vapor pressure information are lower than 0.5% for most fluids. The study shows that both the generalized PTV cubic equation and the AS represent good tools for pressure-temperature calculations in engineering applications.     

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.     

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.     

常用立方型状态方程系数的推导

为了更深入理解、掌握立方型状态方程,笔者将临界点特征微分式应用于多个经典立方型状态方程(vdW方程、RK方程、SRK方程、PR方程),借助微积分、迭代,分别求出方程中的常数,vdW方程中的a=(27R2TC2)/(64pC),b=(RTC)/(8pC);RK方程中的a=0.42748(R2TC2.5)/(pC),b=0.08664(RTC)/(pC);SRK方程中的aC=α(T)×0.42748(R2TC2)/(pC),b=0.08664(RTC)/(pC);PR方程中的aC=α(T)×0.45725(R2TC2)/(pC),b=0.07779(RTC)/(pC);求解出的常数与教科书中提供的数值一致。立方型方程系数的推导,学生较好地锻炼了区分变量的问题,能为其后续剩余性质、偏摩尔性质的学习打下坚实的基础。     

状态方程在气固相平衡计算中的应用

状态方程法是研究气固平衡的一种常用方法,但是目前仅有SRK和PR方程运用于元素硫沉积机理的研究。采用RK、SRK、PR、PT和LHSS状态方程对含硫天然气气固相平衡进行了计算,并且比较了不同状态方程对计算结果的影响。通过算例分析可知,对含硫天然气气固相平衡进行计算时每种状态方程都会存在误差,而误差主要来源于实验过程中的误差、状态方程参数设置的误差、数值计算方法的误差等。计算结果表明,采用RK和SRK方程计算误差较大,PR和PT方程两者计算误差差别不大,LHSS方程更适合描述含硫天然气的气固相平衡。     

One-fluid mixing rules for cubic equations of state: II. Solubility of solid mixtures in supercritical fluids

Three cubic equations of state are carefully examined to evaluate their capability for correlating the solubility of solid mixtures in supercritical fluids. After obtaining the pure solute-solvent interaction parameters, the solute-solute interaction parameters were directly calculated from the experimental ternary solubility data. The Redlich-Kwong, Soave, and Peng-Robinson equations of state correlate well the ternary data. However, the Redlich-Kwong equation of state gives the best result among them.     

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.     

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.     

二参数三阶状态方程

在确定M M.Abbott三阶方程一般式最佳T_c等温线的基础上,提出了一个新的二参数三阶状态方程.在p_r=0—30、T_r=0.5—15之间,方程用于符合或近似符合普遍化压缩因子图表的流体,其误差一般均小于4%.同其它二参数三阶方程相比,本方程能获得更高的精度,同时也具备简便的特点.     

普遍化立方型状态方程中Wong-Sandler型混合规则的建立

<正>自70年代末期Huron和Vidal将过量Gibbs自由能模型引入状态方程的混合规则以来,状态方程新混合规则的研究引起了人们的高度重视并取得了重要成就,已成功地将状态方程推广到多种复杂体系的计算,其中近年来由Wong和Sandler等发展的Wong-San-dler（WS）混合规则模型受到了广泛的关注。他们工作的意义在于可以使用由低压汽液平衡数据得到的活度系数模型参数及二元交互作用参数直接推算高压汽液平衡。 但该模型的导出仅限于两参数的立方型状态方程,这样对于广泛应用WS型混合规则势必产生局限性,因此将此类型的混合规则推广到普遍化的立方型状态方程是十分必要的。本文报道了以五参数的Modified Kumar-Starling（MKS）立方型状态方程为工作方程,建立了将WS型混合规则推广到多参数立方型状态方程的途径。     

A new four-parameter cubic equation of state for fluids

A simple cubic equation of state of the van der Waals type has been developed and successfully applied to both nonpolar and polar fluids. It contains four parameters and only one parameter is temperature-dependent. The parameters have been determined by using reliable data of vapour pressure and saturated liquid volume, and correlated in terms of critical properties and acentric factor. The P-V-T relationships, vapour pressures, volumes, and enthalpies of vapourization were calculated for a variety of substances. Comparison of the calculated results with experimental data and with results obtained from other equations shows that the proposed equation is a superior one in overall performance.     

CO2-C2H6共沸物分离的立方型状态方程选取

汽液平衡热力学模型的准确选取对CO₂-C₂H₆共沸物分离流程的设计和操作分析至关重要。在汽液平衡实验数据的基础上,依据逸度平衡原则,评估vdW、RK、SRK和PR立方型状态方程结合vdW、Margles和CVD混合规则预测CO₂纯物质、CO₂-C₂H₆共沸物和n-C₅H₁₂-CO₂-C₂H₆三元体系汽液平衡的可靠性,采用平均绝对误差的方法进行状态方程的选取。结果表明：SRK状态方程计算CO₂纯物质汽液平衡性质的精度最高;PR状态方程结合Margles混合规则可以准确计算CO₂-C₂H₆共沸体系汽液平衡特性;对于n-C₅H₁₂-CO₂-C₂H₆三元体系,SRK状态方程结合Margles混合规则计算精度明显优于vdW、RK和PR状态方程。通过试差迭代法优化CO₂-C₂H₆共沸体系和n-C₅H₁₂-CO₂-C₂H₆三元体系的二元交互作用参数,状态方程的计算精度得到明显提高。     

GENERALIZED SEMI-EMPIRICAL NON CUBIC EQUATION OF STATE FOR THE REPRESENTATION OF PROPERTIES OF PURE SUBSTANCES

The analytical equation of state first introduced by Ponce and Renon was modified. At a given temperature, the addition of a corrective term in virial form yields an equation with four parameters. All parameters are assumed temperature dependent and properties of pure substances can be represented with 11 parameters. A corresponding state form using the characteristic parameters T_c, P_c, ω was developed. It yields an improvement in representation of molar volumes compared with the generalized cubic (Soave, Peng-Robinson) and non cubic (Simonet) equations. Enthalpy can also be calculated.     

COMPARISON OF A PAIR OF THREE PARAMETER EQUATIONS OF STATE

The lattice fluid (LF) equation of state derived by Sanchez and Lacombe from a lattice model is compared to the empirical Peng-Robinson (PR) equation for normal alkane fluids ranging from methane to heptadecane in molecular weight. With respect to vapor pressure predictions, the equations are both good. The LF equation is superior, especially for higher molecular weight fluids, to the Peng-Robinson equation in predicting saturated liquid densities. For carbon numbers less than 6, the PR equation predicts heats of vaporization more accurately, whereas for carbon numbers greater than 9 the LF equation is more accurate than the PR one for temperatures lower than about 95% of critical.     

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.     

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.