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.     

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.     

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.     

Solubility of hinokitiol in supercritical fluids; measurement and correlation

Supercritical fluid technology has been an alternative for purification and separation of biological compounds in cosmetic, food, and pharmaceutical products. Solubility information of biological compounds in supercritical fluids is essential for choosing a supercritical fluid processes. The equilibrium solubility of hinokitiol was measured in supercritical carbon dioxide and ethane with a static method in the pressure range from 8 to 40MPa and at temperatures equal to 313.2, 323.2 and 333.2 K. The experimental data were correlated well by Peng-Robinson equation of state and quasi-chemical nonrandom lattice fluid model.     

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 comparison among three equations of state in predicting the solubility of some solids in supercritical carbon dioxide

Equations of state play an important role in chemical engineering designs, and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. In this report, a modified Peng-Robinson equation of state by Danesh et al., a modified Peng-Robinson equation of state by Gasem et al., and the Mansoori-Mohsen Nia-Modarress equation of state are used to predict the solubility of some solids in supercritical carbon dioxide. The systems studied were binary mixtures containing supercritical carbon dioxide with Ascorbic acid, Ascorbyl palmitate, Butyl hydroxyl anisole, Dodecyl gallate and Propyl gallate. Interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.     

Measurement and correlation of vapor-liquid equilibria of the binary carbon dioxide-chloroform mixture system

Binary vapor liquid equilibrium data of the carbon dioxide+chloroform system were measured at five isotherms from 310.13 K to 333.32 K. A circulating type apparatus with on-line gas chromatography was used in this study. The experimental data were correlated by classical Peng-Robinson equation of state using van der Waals one fluid mixing rules and the multi-fluid nonrandom lattice fluid (MF-NLF) equation of state.     

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.     

Prediction of the infinite-dilution partial molar volumes of organic solutes in supercritical carbon dioxide using the Kirkwood-Buff fluctuation integral with the hard sphere expansion (HSE) theory

Two thermodynamic models were used to predict the infinite dilution partial molar volumes (PMVs) of organic solutes in supercritical carbon dioxide: (1) the Kirkwood Buff fluctuation integral with the hard sphere expansion (HSE) theory incorporated (KB-HSE fluctuation integral method) and (2) the Peng-Robinson equation of state with the classical mixing rule. While an equation of state only for pure supercritical carbon dioxide is needed in the KB-HSE fluctuation integral model, and thus, there is no need to know the critical properties of solutes, two molecular parameters (one size parameter σ₁₂ and one dimensionless parameter α₁₂) in the KB-HSE fluctuation integral model are determined to fit the experimental data published on the infinite dilution PMVs of solutes. The KB-HSE fluctuation integral method produced better results on the infinite dilution PMVs of eight organic solutes tested in this work than the Peng-Robinson equation of state with the classical mixing rule.     

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.     

A MODIFIED PENG-ROBINSON EQUATION OF STATE

A modified form of the Peng-Robinson equation of state is proposed. This equation shows its greatest advantage in the predictions of the volumetric properties in the single-phase region for mixtures, while it performs as good as original Peng-Robinson equation for the predictions of thermodynamic properties of pure components, and vapor-liquid equilibria of mixtures. Also the equation gives apparently more realistic Joule-Thomson inversion curves than both the SRK and PR equations.     

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.     

High pressure phase behavior for the binary mixture of pentafluoropropyl methacrylate and poly(pentafluoropropyl methacrylate) in supercritical carbon dioxide and dimethyl ether

Pressure-composition isotherm is obtained for the carbon dioxide+2,2,3,3,3-pentafluoropropyl methacrylate (PFPMA) using static apparatus with a variable volume view cell at temperature range from 40 °C to 120 °C and pressure up to 130 bar. This system exhibits type-I phase behavior with a continuous mixture-critical curve. The experimental result for carbon dioxide+PFPMA mixture was modeled using the Peng-Robinson (P-R) and multi-fluid nonrandom lattice fluid (MF-NLF) equation of state. Experimental cloud-point data of pressure up 470 bar and temperature to 182 °C were reported for the binary mixture of poly(2,2,3,3,3-pentafluoropropyl methacrylate) [Poly(PFPMA)] in supercritical carbon dioxide and dimethyl ether (DME). The Poly(PFPMA)+carbon dioxide and Poly(PFPMA)+DME systems showed LCST behavior.     

Peng-Robinson状态方程及保形溶液混合规则用于汽-液平衡计算

Peng-Robinson状态方程式用于推算三组二元系统的汽-液平衡:甲烷、二氧化碳及氢与烃类.对含甲烷及二氧化碳的二元系统.推荐了经过关联的相互作用参数.将保形溶液(Conformal Solu-tion)混合规则及本文提出的对温度有关的系数α的修正式应用于高度非对称的含氢二元系统,较Peng-Robinson的原始工作更为精确地表述了汽-液平衡.     

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.     

THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

THE MODIFIED PGR EQUATION OF STATE: ASYMMETRIC MIXTURE VLE REPRESENTATIONS AND PREDICTIONS

A set of mixing rules was proposed for the modified Park-Gasem-Robinson (PGR) equation of state (EOS) to extend its predictions to mixtures. The phase behavior predictive capability of this segment-segment interaction model was evaluated for selected binary asymmetric mixtures involving ethane, carbon dioxide, and hydrogen in normal paraffins. The predicted bubble point pressures for the ethane + n-paraffin and carbon dioxide + n-paraffin binaries were compared to those of the Peng-Robinson (PR), simplified perturbed hard-chain theory (SPHCT), and original PGR equations. The a priori predictive capability of the modified PGR EOS is significantly better than that of the PR, SPHCT, and original PGR equations of state for ethane binaries with absolute-average percent deviation (%AAD) of 5%. However, this EOS produces comparable representations for ethane binaries (%AAD of 1.9%) and carbon dioxide binaries (%AAD of 2.0). For hydrogen binaries, the modified PGR EOS showed much better representations (%AAD of 1.7) than the original PGR equation and was comparable to the PR equation.     

实用温度函数型PR方程及其在低碳醇混合物中的应用——(Ⅰ)纯物质饱和蒸汽压

本文在对立方型状态方程的详细分析基础上,采用一种实用的与温度有关的a函数表达式,修正了Peng-Robinson状态方程式.用其计算包括非极性,极性和量子流体的52种性质广泛的纯物质,特别是低碳醇混合物中各组分的饱和蒸汽压,获得了令人满意的结果.与多种常见的状态方程式相比较,尤其是对极性流体,本文有明显改进.     

Calculation of phase equilibrium for water+carbon dioxide system using nonrandom lattice fluid equation of state

For the geological sequestration of carbon dioxide to prevent global warming, the phase equilibrium data for water and carbon dioxide mixture play an important role in process design and operation. In this work, the nonrandom lattice fluid equation of state with hydrogen bonding (NLF-HB EOS) was applied for the prediction of phase equilibrium of mixtures containing water and carbon dioxide. A new set of pure component parameters for carbon dioxide above critical condition was found and optimum binary interaction parameters were reported to correlate mutual solubility of mixtures. The calculated results were compared with the Peng-Robinson Equation of State with the conventional mixing rule (PR-EOS) and the Wong-Sandler mixing rule (PR-WS-EOS). The calculation results show that NLF-HB EOS can correlate mutual solubility of water+carbon dioxide mixtures with reasonable accuracy within a single theoretical framework.     

超临界二氧化碳和醇类体系的相平衡计算

应用Peng-Robinson(P-R)状态方程对超临界CO2系统进行了相平衡模拟。对超临界CO2和醇类二元系统进行了汽液相平衡计算,结果表明,P-R状态方程模拟高压下CO2系统的相平衡具有较高的精度。