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.     

High-pressure phase equilibria for the carbon dioxide–2-methyl-1-butanol,carbon dioxide–2-methyl-2-butanol,carbon dioxide–2-methyl-1-butanol–water,and carbon dioxide–2-methyl-2-butanol–water systems

High-pressure vapor–liquid equilibria for the binary carbon dioxide–2-methyl-1-butanol and carbon dioxide–2-methyl-2-butanol systems were measured at 313.2 K. The phase equilibrium apparatus used in this work is of the circulation type in which the coexisting phases are recirculated, on-line sampled, and analyzed. The critical pressure and corresponding mole fraction of carbon dioxide for the binary carbon dioxide–2-methyl-1-butanol system at 313.2 K were found to be 8.36 MPa and 0.980, respectively. The critical point of the binary carbon dioxide–2-methyl-2-butanol was also found 8.15 MPa and 0.970 mole fraction of carbon dioxide. In addition, the phase equilibria of the ternary carbon dioxide–2-methyl-1-butanol–water and carbon dioxide–2-methyl-2-butanol–water systems were measured at 313.2 K and several pressures. These ternary systems showed the liquid–liquid–vapor phase behavior over the range of pressure up to their critical point. The binary equilibrium data were all reasonably well correlated with the Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Patel–Teja (PT) equations of state with eight different mixing rules the van der Waals, Panagiotopoulos–Reid (P&R), and six Huron–Vidal type mixing rules with UNIQUAC parameters.     

Vapor–liquid equilibria for nitrogen with 2-propanol, 2-butanol,or 2-pentanol binary systems

Isothermal vapor–liquid equilibrium (VLE) data were measured for the binary systems of nitrogen with 2-propanol, 2-butanol, or 2-pentanol at temperatures from 333.15 to 393.15 K and pressure up to 100 bar. Henry's constants of nitrogen in these three sec-alcohols were determined by using the Krichevesky–Ilinskaya equation. The experimental VLE data were also correlated by the Peng–Robinson and the Patel–Teja equations of state with various mixing rules.     

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.     

Mixing rules for van-der-Waals type equation of state based on thermodynamic perturbation theory

A concept based on the thermodynamic perturbation theory for a `simple fluid' has been applied to the attractive term of a van-der-Waals type equation of state (EOS) to derive a simple mixing rule for the a parameter. The new mixing rule is a small correction to the original one-fluid approximation to account for the influence of particles of j-type on the correlation function of ii-type in a mixture consisting of particles of i and j types. The importance of the correction has been shown by comparison of the calculated results for binary mixtures of Lennard–Jones fluids with the data obtained by numerical method (Monte-Carlo simulation). The new mixing rules can be considered as a flexible generalization of the conventional mixing rules and can be reduced to the original v-d-W mixing rules by defaulting the extra binary parameters to zero. In this way the binary parameters already available in the literature for many systems can be used without any additional regression work. Extension of the new mixing rules to a multicomponent system do not suffer from `Michelsen–Kistenmacher syndrome' and provide the correct limit for the composition dependence of second virial coefficients. Their applicability has been illustrated by various examples of vapor–liquid and liquid–liquid equilibria using a modified Patel–Teja EOS. The new mixing rules can be applied to any EOS of van-der-Waals type, i.e., EOS containing two terms which reflect the contributions of repulsive and attractive intermolecular forces.     

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.     

由L-J流体的FMSA状态方程计算流体的PVT性质

运用Tang等提出的Lennard-Jones (L-J)流体两参数的一阶平均球形近似(FMSA)状态方程, 计算了流体的汽液共存相图和饱和蒸汽压曲线, 以及非饱和区的PVT性质, 并与文献数据进行比较. L-J参数由Tr＜0.95的汽液相共存数据回归得到. 计算结果表明, 对于分子较接近球形的流体, 除临界点附近外, 该方程可以在较大的温度和压力范围内计算真实流体的PVT性质, 结果满意. 对于球形分子, 该方程的精确度随分子尺寸的变大基本保持稳定. 该方程不适用于强极性物质. 在高密度区, 该方程的计算结果明显优于P-R方程. 对于分子偏离球形较远的流体, 该方程的适用性变差, 此时要考虑分子形状的影响, 可采用三参数的FMSA状态方程进行计算.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Estimation of second-order derivative thermodynamic properties using the crossover cubic equation of state

In this research, we apply the crossover cubic equation of state (XCubic EOS) [1] to the calculations of thermodynamic second-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, the Joule–Thomson coefficient, and speed of sound). This equation of state is used to calculate those properties of pure systems (carbon dioxide, normal alkanes from methane to propane). We show that, over a wide range of states, the equation of state yields each property with a much better accuracy than the original PT equation of state and near the critical region, represents the singular behaviour well.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.     

Estimation of 2nd-order derivative thermodynamic properties using the crossover lattice equation of state

We apply the crossover lattice equation of state (xLF EOS) [M.S. Shin, Y. Lee, H. Kim, J. Chem. Thermodyn. 40 (2007) 174–179] to the calculations of thermodynamic 2nd-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, Joule–Thompson coefficient, and sound speed). This equation of state is used to calculate the same properties of pure systems (carbon dioxide, normal alkanes from methane to propane). We show that, over a wide range of states, the equation of state yields properties with better accuracy than the lattice equation of state (LF EOS), and near the critical region, represents singular behavior well.     

Modeling hydrate formation conditions in the presence of electrolytes and polar inhibitor solutions

In this paper, a new predictive model is proposed for prediction of gas hydrate formation conditions in the presence of single and mixed electrolytes and solutions containing both electrolyte and a polar inhibitor such as monoethylene glycol (MEG), diethylene glycol (DEG) and triethylene glycol (TEG). The proposed model is based on the γ–φ approach, which uses modified Patel–Teja equation of state (VPT EOS) for characterizing the vapor phase, the solid solution theory by van der Waals and Platteeuw for modeling the hydrate phase, the non-electrolyte NRTL-NRF local composition model and Pitzer–Debye–Huckel equation as short-range and long-range contributions to calculate water activity in single electrolyte solutions. Also, the Margules equation was used to determine the activity of water in solutions containing polar inhibitor (glycols). The model predictions are in acceptable agreement with experimental data. For single electrolyte solutions, the model predictions are similar to available models, while for mixtures of electrolytes and mixtures of electrolytes and inhibitors, the proposed model gives significantly better predictions. In addition, the absolute average deviation of hydrate formation pressures (AADP) for 144 experimental data in solutions containing single electrolyte is 5.86% and for 190 experimental data in mixed electrolytes solutions is 5.23%. Furthermore, the proposed model has an AADP of 14.13%, 5.82% and 5.28% in solutions containing (Electrolyte + MEG), (Electrolyte + DEG) and (Electrolyte + TEG), respectively.     

Modification of Simha–Somcynsky equation of state for small and large molecules

The Simha–Somcynsky equation of state (SS EOS) represents the PVT behavior of polymers quite satisfactorily, but cannot be applied to gases at low pressures. This work proposes a modification of the free volume contribution of the SS EOS to allow representation of gaseous state of low molecular-weight substances by introducing the perturbed hard-chain theory of Beret and Prausnitz into the EOS. In addition to this modification, two universal constants are introduced to the free volume term for better representation of properties of low molecular-weight substances. Characteristic parameters in the modified SS EOS were determined for 44 low molecular-weight substances and 64 polymers. The absolute average deviations (AADs) for critical temperature, critical pressure and vapor pressures were 0.86, 2.38 and 2.01%, respectively, while AAD for critical density and saturated liquid density at normal boiling point were somewhat larger, being 20.46 and 5.30%, respectively. The high performance of the original SS EOS for polymer PVT behavior was maintained in the modified EOS with grand AAD of 0.050% for densities.     

A novel approach to thermophysical properties prediction for chloro-fluoro-hydrocarbons

In this paper we present a new procedure, based on quantum/molecular (QM/MM) mechanics and molecular dynamics (MD) computer simulations, for estimating the Perturbed Hard Sphere Chain Theory (PHSCT) equation of state (EOS) parameters of a set of 14 alternative chloro-fluoro-hydrocarbons (CFH) of industrial relevance and to predict their thermophysical properties and PVT behavior. Force field and quantum-mechanical techniques were employed in molecular modeling and for the calculation of geometrical and chemico-physical parameters. The Connolly surface algorithm, corrected for quantum-mechanical effects, was used in the evaluation of molecular surfaces and volumes. From these data, the parameters of the PHSCT EOS, V* and A*, were obtained. The third parameter, E*, was calculated from extensive MD simulations under NPT conditions. The new, original method proposed in this work gives good results, is relatively inexpensive, is absolutely general and can be applied in principle to any EOS, provided the parameters have a physical meaning. The tuning of the energetic parameter to a generated data set accounts for the degree of empiricism introduced at a certain stage in the development of any EOS.     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Measurements of HmE and VmE for (n-butane + sulphur hexafluoride) in the supercritical region at the pressure 6.00 MPa

A flow mixing calorimeter followed by a vibrating-tube densimeter has been used to measure excess molar enthalpies H_m^E and excess molar volumes V_m^E of {xC₄H₁₀+(1−x)SF₆}. Measurements over a range of mole fractions x have been made in the supercritical region at the pressure p=6.00 MPa and at seven temperatures in the range T=311.25 K to T=425.55 K. The H_m^E(x) measurements at T=351.35 K were found to exhibit an unusual double maximum. Measurements at all temperatures are compared with the Patel–Teja equation of state with the parameters determined by solving a cubic equation as recommended, and also with parameters determined by the method suggested by Valderamma and Cisternas who proposed equations which are a function of the critical compression factor. The overall fit to the H_m^E and V_m^E measurements obtained using Valderamma and Cisternas equations was found to be better than that obtained using the parameters according to the method suggested by Patel and Teja.     

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.