An isomorphic Peng-Robinson equation for phase-equilibria properties of hydrocarbon mixtures in the critical region

The principle of isomorphism of critical phenomena asserts that the equation of state of fluid mixtures in the critical region has the same form as that of the pure components, provided that the mixture is not considered at a fixed composition but at a fixed value of a constant field variable related to the chemical potentials of the components of the mixtures. This principle has been successfully applied by various investigators to formulate nonclassical equations of state for fluid mixtures in the critical region. In this paper we show how the same principle can be applied to simple classical equations of state using the Peng-Robinson equation as a representative example. The isomorphic Peng-Robinson equation thus obtained is applied to represent phase equilibria properties of some binary mixtures of methane, butane and decane.     

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.     

凝析气相态行为的模拟

针对含重质烃的多元混合物提出了PR模型参数新的关联方法.对多于7个碳的重烃,其状态方程参数a和b改为通过可由实测数据确定的T_B、(?)和T计算,避免了由不同经验关联式计算的临界参数T_c、P_c和(?)值不一致的缺点.作者将经上述改进的PR模型应用于凝析气相态行为的模拟计算(露点压力、恒质量膨胀和恒容衰竭等过程)取得了较满意的结果.     

富硫化氢酸性天然气相态行为的实验测定和模型预测

本文采用无汞抗硫ＰＶＴ装置，测定了三组富硫化氢酸性天然气混合物的Ｐ－Ｔ相包线数据，并比较了三个立方型状态方程：Ｓｏａｖｅ－Ｒｅｄｌｉｃｈ－Ｋｗｏｎｇ，Ｐｅｎｇ－Ｒｏｂｉｎｓｏｎ和Ｐａｔｅｌ－Ｔｅｊａ应用于酸性天然气泡／露点压力及ＰＶＴ数据的预测结果。对泡点压力的预测ＳＲＫ方程误差最小（１．１３％），而对露点压力的预测则ＰＴ方程误差最小（４．７７％）。应用多参数ＭＯＵ／ＧＲＩ方程预测富硫化氢酸性天然气压缩因子数据取得满意的结果，平均误差为０．６３５％。     

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Knowledge of vapor-liquid equilibria is essential for chemical process design. Development of algebraically simple cubic equations of state, particularly Peng-Robinson and Soave-Redlich-Kwong equations of state has encouraged vapor-liquid equilibria calculation using the equation of state approach. To extend applicability to complex mixtures, several modifications to these equations of state were proposed. Also, many new mixing rules have been developed besides the already existing ones that incorporate excess free energy models. Some of these EoS/G^E models are found to be applicable to complex systems in which the components can be highly polar, differ vastly in size or may be forming association. In spite of a large number of publications on this field, this subject is still open for further research. In this article, an overview on the work done using the most successful of the cubic equations of state, i.e., Peng-Robinson and Soave-Redlich-Kwong equations of state is presented. In the later part of this article, VLE predictions (using these two equations of state) of some interesting systems like water/hydrocarbon mixtures, polymer solutions, electrolyte solutions and refrigerant mixtures are discussed. The objective is to present the available information for ready reference that will prove to be useful from a designers point of view. It is seen from the existing literature that with a proper choice of equation of state and mixing rule based on the available knowledge on the properties of the system of interest, VLE of highly complex systems can be predicted with accuracy. Several comparative studies that are cited here (and discussed) will help the designer to pick-up the right combination for the system under investigation.     

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.     

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.     

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.     

利用扩展Tao-Mason状态方程预测天然气混合物容积特性(p-V-T)

A statistical-mechanical-based equation of state(EOS)for pure substances,the Tao-Mason equation of state,is successfully extended to prediction of the(p-v-T)properties of fourteen natural gas mixtures at temperatures from 225 K to 483 K and pressures up to 60.5 MPa.This work shows that the Tao-Mason equation of state for multicomponent natural gas is predictable with minimal input information,namely critical temperature,critical pressure,and the Pitzer acentric factor.The calculated results agree well with the experimental data.From a total of 963 data of density and 330 data of compressibility factor for natural gases examined in this work,the average absolute deviations(AAD)are 1.704%and 1.344%,respectively.The present EOS is further assessed through the comparisons with Peng-Robinson(PR)equation of state.For the all of mixtures Tao-Mason(TM)EOS outperforms the PR EOS.     

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.     

Correlation and prediction of gas solubility in cold lake bitumen

The solubility data for pure light gases, namely N₂, CH₄, CO₂ and C₂H₆, in Cold Lake bitumen are correlated by use of the Peng-Robinson equation of state. Modeling Cold Lake bitumen as a mixture of three pseudocomponents adequately matched two sets of the gas-solubility data. The critical properties and acentric factor for the bitumen pseudocomponents were estimated using the Kesler-Lee correlations. For each gas-bitumen pair, a single constant value of the binary interaction parameter is shown to predict the gas-solubility data with average deviations ranging from 2 to 8%. Subsequently, these calculations were extended to predict the solubility of CO₂+CH₄ gas-mixtures in Cold Lake bitumen. It is shown that the solubility predictions for the gas mixtures data are higher by approximately 6 to 9%.     

立方型+缔合状态方程模拟离子液体的pVT性质和汽液平衡(英文)

Combining Peng-Robinson (PR) equation of state (EoS) with an association model derived from shield-sticky method (SSM) by Liu et al., a new cubic-plus-association (CPA) EoS is proposed to describe the ther-modynamic properties of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall aver-age deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their mo-lecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter kij, satisfactory correlations of vapor-liquid equilibria (VLE) for binary mixtures of ILs + non-associating solvents and + associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs + non-associating mixtures from CPA, lattice-fluid (LF) and square-well chain fluids with variable range (SWCF-VR) EoSs are compared.     

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.     

Multistage multicomponent separation calculations using thermodynamic properties evaluated by the srk/pr equation of state

A computational procedure using thermodynamic properties evaluated by the Soave-Redlich-Kwong' (SRK) equation of state or the Peng-Robinson (PR) equation of state is developed for multistage multicomponent separation processes. The procedure makes use of the Ishii-Otto convergence scheme with the proposed modifications for application with the equation of state. A new technique is developed to improve an initial estimation of temperature profile in a column. The computational procedure is tested on CDC CYBER 172 computer for a wide range of problems including lean oil absorbers, reboiled absorbers and fractionators and a debutaniser operating in a natural gas processing plant in Alberta. The computational results are compared with those obtained using the Chao-Seader model for generating the required thermodynamic properties. It is concluded that the present computational procedure can be used more reliably over a wider range of processing conditions such as those involved in the cryogenic separation of natural gases and in the separation of heavy hydrocarbon mixtures.     

混合工质临界性质的推算研究

采用五种不同的方法计算了四种不同二元混合工质的临界温度和临界压力,研究对比不同方法在推算二元混合临界性质时的精度。其中Peng-Robinson（PR）方程和Soave-Redlich-Kwong（SRK）方程,两种状态方程结合Heidemann等提出的临界点判据计算得到的临界参数与实验结果吻合较好。两种经验公式,改进的Chueh-Prausnitz（MCP）方法和Redlich-Kister方法,以及径向基函数神经网络（RBFNN）在计算混合工质的临界性质时也都有着较高的计算精度。对于临界温度的计算,PR方程、SRK方程、MCP方程、Redlich-Kister方程以及径向基函数神经网络计算结果的绝对平均偏差的最大值分别为1.82%、1.73%、0.95%、0.17%和0.20%。对于临界压力的计算,通过PR方程、SRK方程、MCP方程、Redlich-Kister方程以及径向基函数神经网络计算的绝对平均偏差的最大值分别为6.07%、5.04%、3.49%、1.90%以及0.67%。     

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.     

Phase behaviour prediction in supercritical systems using generalized solute critical properties

Trebble and Sigmund (1990) have recently published a generalized form of the Peng-Robinson (1976) equation of state in which binary interaction parameters are predicted as a function of the species critical volumes, dipole moments, and quadrupole moments. In this study, the critical properties of solutes heavier than normal hexane are correlated against molar mass, normal boiling temperature, and group type (i.e. paraffinic, olefinic, naphthenic or aromatic). This extension further facilitates the use of the generalized Peng-Robinson equation in calculating phase behaviour of supercritical systems in which solute critical properties are unknown or uncertain. Calculation of phase behaviour using the extended correlation is shown to be of the same quality as the previous generalization (which required solute critical constants) for 38 binary systems covering broad temperature and pressure ranges.