A new cubic equation of state for reservoir fluids

A new three-parameter cubic equation of state is developed with special attention to the application for reservoir fluids. One parameter is taken temperature dependent and others are held constant. The EOS parameters were evaluated by minimizing saturated liquid density deviation from experimental values and satisfying the equilibrium condition of equality of fugacities simultaneously. Then, these parameters were fitted against reduced temperature and Pitzer acentric factor. For calculating the thermodynamic properties of a pure component, this equation of state requires the critical temperature, the critical pressure, the acentric factor and the experimental critical compressibility of the substance. Using this equation of state, saturated liquid density, saturated vapor density and vapor pressure of pure components, especially near the critical point, are calculated accurately. The average absolute deviations of the predicted saturated liquid density, saturated vapor density and vapor pressure of pure components are 1.4%, 1.19% and 2.11%, respectively. Some thermodynamic properties of substances have also been predicted in this work.     

A new two-parameter cubic equation of state for predicting phase behavior of pure compounds and mixtures

In this work, a new two-parameter cubic equation of state is presented based on perturbation theory for predicting phase behavior of pure compounds and of hydrocarbons and non-hydrocarbons. The parameters of the new cubic equation of state are obtained as functions of reduced temperature and acentric factor. The average deviations of the predicted vapor pressure, liquid density and vapor volume for 40 pure compounds are 1.116, 5.696 and 3.083%, respectively. Also the enthalpy and entropy of vaporization are calculated by using the new equation of state. The average deviations of the predicted enthalpy and entropy of vaporization are 2.393 and 2.358%, respectively. The capability of the proposed equation of state for predicting some other thermodynamic properties such as compressibility, second virial coefficient, sound velocity in gases and heat capacity of gases are given, too. The comparisons between the experimental data and the results of the new equation of state show the accuracy of the proposed equation with respect to commonly used equations of state, i.e. PR and SRK. The zeno line has been calculated using the new equation of state and the obtained result compared with quantities in the literatures. Bubble pressure and mole fraction of vapor for 16 binary mixtures are calculated. Averages deviations for bubble pressure and mole fraction of vapor are 9.380 and 2.735%, respectively.     

Application of an improved simplified perturbed hard chain theory equation of state for pure compounds and binary asymmetric mixtures

The simplified perturbed hard chain theory equation of state is modified using recently developed repulsive and attractive terms. Both terms meet the low density and close-packed density boundary conditions and are in reasonable agreement with molecular simulation data. The modified equation of state accurately predicts pure component properties including saturated vapor volume, liquid density, vapor pressure and enthalpy of vaporization. Compared with the original equation, the modified one predicts physical properties more accurately. However, the improvement of predicting enthalpy of vaporization is marginal. The two equations are tested for predicting the phase behavior of binary asymmetric mixtures. It is shown that the difference in predicting the phase behavior is not appreciable.     

A new three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.     

Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.     

Molecular thermodynamics on the basis of an equation of state for argon. III. Systems of appreciably nonspherical linear molecules

A molecular model based on an equation of state for pure argon is applied to various systems involving appreciably nonspherical molecules. Since the pure components are not described adequately, their potential parameters are fitted at each temperature separately to ensure the proper vapor pressures and liquid volumes. Used in this way, the model makes reasonable predictions of the thermodynamic behavior of the binary mixtures considered. Again, the introduction of a binary parameter in the dispersion potential does not lead to any significant overall improvement.     

Development of a five-parameter cubic equation of state

A five-parameter van der Waals type cubic equation of state has been developed specifically for representing pure-component volumetric properties. The justification of such an equation is based on the analysis of the variation of the attraction term contribution with reduced density. The parameters have been evaluated on the basis of optimal representation of the three saturated properties (vapor pressure, liquid volume and vapor volume) and the compressed liquid volume, and generalized in terms of critical temperature and the acentric factor. The calculated densities for 17 fluids are compared with those obtained from seven selected equations of state.In addition, individual parameters for carbon dioxide, ethylene, ethane and propane are presented for predicting volumetric behaviors in the critical region useful for supercritical fluid extraction processes.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃(C1-C20)的跨接比容平移Soave-Redlich-Kwong(SRK)(跨接VTSRK)状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数.比较结果表明,跨接方程对烷烃(C1-C20)饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善.进一步将方程推广到环烷烃(环丙烷、环戊烷和环己烷)和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

A crossover cubic equation of state near to and far from the critical region

In this research, we use the Patel–Teja (PT) cubic equation of state [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37 (1982) 463–473.] and develop a crossover cubic model near to and far from the critical region, which incorporates the scaling laws asymptotically close to the critical point and it transformed into original classical cubic equations of state far away from the critical point. This equation of state is used to calculate thermodynamic properties of pure systems (carbon dioxide, normal alkanes from methane to heptane). We show that, over a wide range of states, the equation of state yields the saturated vapour pressure data and the saturated density data with a much better accuracy than the original PT equation of state.     

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃（C1-C20）的跨接比容平移Soave-Redlich-Kwong（SRK）（跨接VTSRK）状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数. 比较结果表明,跨接方程对烷烃（C1-C20）饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善. 进一步将方程推广到环烷烃（环丙烷、环戊烷和环己烷）和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

A New Association Term for SAFT Equation of State

This work is devoted to present a new expression for association part of SAFT equation of state. This expression is obtained by calculating the mole fraction of not bonded molecules through a general chemical theory of association. The new equation of state is named CSAFT and has one adjustable parameter less than original SAFT for pure associating fluids. The performance of CSAFT is investigated by PVT calculations for pure fluids and LLE calculations for binary and ternary mixtures. Results show that CSAFT correlates vapor pressure and liquid density data of pure associating components more accurate than SAFT. Also the accuracy of CSAFT model is much better than SAFT for LLE prediction of binary and ternary mixtures, considering SAFT has one pure component parameter more than CSAFT.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state

Stryjek, R. and Vera, J.H., 1986. Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state. Fluid Phase Equilibria, 25: 279–290.The PRSV cubic equation of state and a new Margules-type composition-dependent mixing rule previously proposed have been used to correlate vapor—liquid equilibrium data for hydrochloric acid solutions. In total, four adjustable parameters are used for pure hydrogen chloride, pure water and their mixtures. The two binary parameters are determined from azeotropic point data. Results obtained for this highly nonideal system, presenting negative deviations from ideality, are better than those obtained with the modified cubic equation of Gibbons and Laughton.     

An improved perturbed hard-sphere equation of state

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the Patel–Teja equation of state (PT) and the Peng–Robinson equation of state (PR) and the original CSPT model. The new CSPT combined with temperature-dependent functions was applied to the vapour–liquid equilibrium data available for 45 pure substances. The results indicate that the new CSPT model can accurately reproduce the experimental vapour–liquid equilibria in the whole temperature and pressure range. The successful calculations of the PVT in the critical region suggest the new CSPT has wide applicability. The new CSPT model is also superior to PR and the original CSPT for calculating the phase behaviour of binary mixtures.     

Modelling the VLE properties using van der Waals-type equation of state

The vapour–liquid equilibrium (VLE) properties of polar and non-polar fluids have been modelled by the use of two modified van der Waals (vdW)-type equations of state (EOSs). In this article, a revised method is applied to the above-mentioned EOSs to improve the representation of VLE properties of different class of fluids. In this respect, the repulsion parameter b is considered to be temperature dependent and also a temperature-dependent revision factor α(T) is introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration to reproduce the vapour pressure (P^s) of pure liquids. The present method is also extended to represent the VLE properties of binary mixtures containing noble gases, refrigerants and hydrocarbons. This method outperforms the original vdW-type EOSs in predicting the VLE and pressure-volume-temperature (PVT) properties of 22 pure substances and 7 binary mixtures.