A modification to the Peng–Robinson-fitted equation of state for pure substances

In this work we present two modifications to the Peng–Robinson-Fitted equation of state where pure component parameters are regressed to vapor pressure and saturated liquid density data. The first modification (PR-f-mod) is a method that enhances the equation of state pure component property predictions through simple temperature dependent pure component parameters. In the second modification (PR-f-prop) we propose a temperature dependency for co-volume b in the repulsive parameter of the EoS, and revise the temperature function in the attractive term. The agreement with experimental data for 72 pure substances, including highly polar compounds, is remarkably good. We obtain average absolute deviations in saturated liquid density of less than 1% for all substances studied.     

Density-and-temperature-dependent volume translation for the SRK EOS: 1. Pure fluids

A mathematical framework for applying a density-and-temperature-dependent volume translation in a thermodynamically consistent manner was developed. Volumetric equations of state (EOS)s that incorporate this translation procedure can be used to generate derived properties, such as fugacity and enthalpy departure, that are based on isothermal departure or residuals from ideal gas state conditions. This kind of translation serves to improve the original EOS and not simply act as a correlation for molar volumes. A density-and-temperature-modified translation of this type was applied to the Soave–Redlich–Kwong EOS and was shown to possess accuracy for saturation pressure predictions equivalent to the untranslated EOS, as well as greatly improved density predictions compared to what is available when using only constant valued translation. The EOS translated in this manner retains many of the important features of the untranslated EOS, such as explicit calculation of volume roots, while having the representation capabilities of substantially more complicated models, such as the extended virial equation of Benedict, Webb, Rubin, and Starling.     

Mutual solubilities of hydrocarbons and water with the CPA EoS

The knowledge of hydrocarbon/water phase equilibria is important in the design and operation of equipment for petroleum transport and refining and petrochemical plants. The presence of water in a hydrocarbon mixture can affect the product quality and damage the operation equipment due to corrosion and formation of gas hydrates. Tracing the concentration of hydrocarbons in aqueous media is also important for technical purposes like preventing oil spills and for ecological concerns such as predicting the fate of these organic pollutants in the environment.     

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

High-pressure vapor–liquid equilibria of systems containing ethylene glycol,water and methane: Experimental measurements and modeling

This work presents new experimental phase equilibrium measurements of the binary MEG–methane and the ternary MEG–water–methane system at low temperatures and high pressures which are of interest to applications related to natural gas processing. Emphasis is given to MEG and water solubility measurements in the gas phase. The CPA and SRK EoS, the latter using either conventional or EoS/G^E mixing rules are used to predict the solubility of the heavy components in the gas phase. It is concluded that CPA and SRK using the Huron–Vidal mixing rule perform equally satisfactory, while CPA requires fewer interaction parameters.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

A comparison of mixing rules for the combination of COSMO-RS and the Peng–Robinson equation of state

In this work, the COSMO-RS model is combined with a volume-translated Peng–Robinson equation of state (EOS) via a G^E$G^{\text{E}}$-based mixing rule. The performance of several mixing rules previously published for this purpose is compared and semi-empirical modifications to one of them are introduced to improve its performance in our application. The new mixing rule contains three internal parameters that are adjusted to achieve consistency between the mixing rule and COSMO-RS. No experimental binary data is needed for our EOS. The new COSMO-RS-based, predictive EOS introduces a density dependence into COSMO-RS and extends its applicability to higher pressures and to mixtures containing supercritical components.     

Equation of state for square-well chain molecules with variable range. I: Application for pure substances

An equation of state (EOS) for square-well chain molecules with variable range developed on the basis of statistical mechanics for chemical association in our previous work is employed for the calculations of pVT properties and vapor–liquid equilibria (VLE) of pure non-associating fluids. The molecular parameters for 73 normal substances and 46 polymers are obtained from saturated vapor pressure and liquid molar volume data for normal fluids or pVT data for polymers. Linear relations are found for the molecular parameters of normal fluids with their molecular weight of homologous compounds. This indicates that the model parameters of homologous series, subsequently pVT and VLE, can be predicted when experimental data are not available. The predicted saturated vapor pressures and/or liquid volumes are satisfactory through the generalized model parameters. The calculated VLE and pVT for normal fluids and polymers by this EOS are compared with those from other engineering models, respectively.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

A generalised perturbation-based equation of state for thermodynamic modelling of fluids over a wide range of density

A new generalized perturbed thermodynamic nonlinear isotherm regularity (GPTNLIR) equation of state (EoS) has been proposed for the fluids over the entire density range from gas to liquid. The GPTNLIR has been derived on the basis of an effective nearest neighbor pair interaction of an extended average effective pair potential (AEPP) in the framework of the thermodynamic perturbation theory (TPT). The selected AEPP is an extended Lennard-Jones (12, 6, 3) type which considers the repulsive, dispersion, dipole-dipole and longer-range interactions between pair molecules, respectively. Based on the EoS, a non-linear relationship exists between (Z– Z_CS)v² and ρ for each isotherm of fluid, where Zis the compression factor, v=1/ρis the molar volume, Z_CS is Carnahan–Starling (CS) expression for the compression factor of the reference fluid with the temperature-dependent effective hard-core diameter (σ_eff). The validity of EoS against the experimental p–v–Tdata were tested for a variety of fluids, including polar, non-polar, hydrogen bonded and quantum fluids. This EoS provides the estimation of σ_eff at T>T_c, T=T_c and T<T_c, in which T_c is critical temperature, for each real fluid using its experimental p–v–T data and the extension of TPT theory as well.     

Thermodynamic derivative properties and densities for hyperbaric gas condensates: SRK equation of state predictions versus Monte Carlo data

The ability of Soave–Redlich–Kwong cubic equation of state (SRK EoS) to predict densities and thermodynamic derivative properties such as thermal expansivity, isothermal compressibility, calorific capacity, and Joule–Thompson coefficients, for two gas condensates over a wide range of pressures (up to 110 MPa) was studied. The predictions of the EoS were compared to Monte Carlo simulation data obtained by Lagache et al. [M.H. Lagache, P. Ungerer, A. Boutin, Fluid Phase Equilibr. 220 (2004) 221]. Two completely different alpha functions for the SRK EoS attractive term were used and their respective effects on the predictions of such properties were analyzed. Also, two different forms of the crossed terms of the attractive parameter, a_ij, and three expressions of the crossed terms of the repulsive parameter, b_ij, were combined in different ways, and predictions were carried out. Little sensitivity of the properties on the chosen alpha function, except for the calorific capacities, was found in the systems studied. The most commonly used combination rules to model phase behavior of reservoir fluids, i.e. geometric and arithmetic forms of a_ij and b_ij, respectively, predicted very deficient results for these fluids at extreme conditions, specially for density calculations.     

Association equation of state (AEOS) based on aggregate formation for pure substance

Based on the statistical mechanical theories and by using the concept of grand canonical ensemble a new equation of state for aggregate formations in the association fluids has been proposed. The compressibility factor for aggregate formation in an association fluid is represented by the following equation:

Z=Z^dis+Z^agg-1$Z=Z^{\text{dis}}+Z^{\text{agg}}-1$

Subcritical and supercritical thermodynamic properties calculations for quantum light molecules using an extended LJ potential-based equation of state

In this work, the extended Lennerd-Jones potential-based equation of state (ELJ-based EoS) on which the effective near-neighbour pair interactions are LJ (12,6,3) type has been extended to predict the density and other thermodynamic properties of quantum light molecules in subcritical (liquid) and supercritical regions. There are no upper and lower density limitations in the applicability of the model for these systems. Having the temperature dependence of the parameters of new EoS, the parameters can be determined at any temperature for each of quantum light molecules, including H₂, p-H₂, D₂, He, and Ne. A comparison with literature data has been made. The results show that the ELJ-based EoS can be used to predict the density and other thermodynamic properties of quantum light molecules within experimental errors. The average absolute deviations for density are better than 0.2% in the subcritical region and 0.12% in the supercritical region for all studied molecules.     

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.     

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.     

Joule-Thomson coefficients and Joule-Thomson inversion curves for pure compounds and binary systems predicted with the group contribution equation of state VTPR

In this work the accuracy of the prediction of Joule-Thomson coefficients for the gases CO₂ and Ar and the binary systems CO₂-Ar and CH₄-C₂H₆ was examined using the group contribution equation of state VTPR. Furthermore the experimental and correlated data of Joule-Thomson inversion curves of a few compounds including carbon dioxide, nitrogen, benzene, toluene, methane, ethane, ethylene, propyne, and SF₆ were compared with the results of the group contribution equation of state VTPR, the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR) and the Helmholtz equation of state (HEOS). Moreover, Joule-Thomson inversion curves for pure fluids, binary (CH₄-C₂H₆, N₂-CH₄, CO₂-CH₄), and ternary systems (CO₂-CH₄-N₂, CH₄-C₂H₆-N₂, CO₂-CH₄-C₂H₆) were calculated with VTPR and compared to the results of SRK, PR, HEOS and the molecular simulation results of Vrabec et al. It was found that the calculated values for the Joule-Thomson coefficients and Joule-Thomson inversion curves are in good agreement with the experimental findings.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.