Isobaric vapor–liquid equilibrium of systems containing triethyl orthoformate at 101.3 kPa

Isobaric vapor–liquid equilibrium data of ethanol(1)-triethyl orthoformate(2), benzene(1)-triethyl orthoformate(2) and ethanol(1)-benzene(2)-triethyl orthoformate(3) were measured at 101.3 kPa and under a wide range of temperatures (349–420 K), using the Rose–Williams still modified by the authors. The experimental data of binary systems were tested for thermodynamic consistency with the method of Fredenslund and coworkers and correlated satisfactorily with SRK equation and PR equation of state. The VLE data of ethanol(1)-benzene(2)-triethyl orthoformate(3) ternary system were tested with the method of McDermont–Ellis and were predicted with the parameters of SRK and PR equation of state obtained from binary systems.     

PVTx measurements of the N-methylpyrrolidone/methanol mixed solvent: cubic and SAFT EOS analyses

The PVTx behavior for the x N-methylpyrrolidone (NMP) + (1 - x) methanol compressed liquid solvent is reported over the full composition range and within wide pressure and temperature ranges. The derived excess properties were analyzed in terms of structural effects and intermolecular interactions and revealed strong H-bonding heteroassociations between the two components. The cubic equations of state by Soave (SRK), Peng-Robinson (PR), Patel-Teja (PT), and Sako-Wu-Prausnitz (SWP), and the statistical associating fluid theory (SAFT) equation of state, combined with a number of selected mixing rules, were used to correlate and predict the behavior of both the pure components and mixed solvent. While the classical cubic equations of state were not successful in describing the properties of this system, the SWP equation of state and the SAFT yielded reasonably good results.     

On the compatibility between vapor pressure data and the critical constants: Use of the van der Waals family of cubic equations of state to study the cases of 2-methoxyethanol and 2-ethoxyethanol

The performance of five cubic equations of state (EOSs) for the correlation of vapor-pressure data of 2-methoxyethanol and 2-ethoxyethanol are compared. The cubic EOSs considered are the van der Waals EOS, modified with Soave's approach (MvdW), the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR), and the two versions of the Peng-Robinson-Stryjek-Vera EOSs: PRSV and PRSV2. Three sets of critical constants for 2-methoxyethanol are considered and new acentric factor is proposed for this compound. New critical constants and acentric factor for 2-ethoxyethanol are proposed. Pure compound parameters for the PRSV and the PRSV2 EOSs for 2-methoxyethanol and 2-ethoxyethanol are evaluated using a genetic algorithm (GA) optimization technique. The results show the importance of using compatible information in vapor liquid equilibrium studies.     

Molecular simulation of the Joule–Thomson inversion curve of carbon dioxide

The complete Joule–Thomson (JT) inversion curve for carbon dioxide is calculated using molecular simulations. A two center Lennard–Jones model with an embedded point quadrupole is used to model the fluid–fluid interactions. The simulation results agree quantitatively with all available experimental data. Comparison with commonly used equations of state provides only a modest agreement, with the highest discrepancies being observed at the high temperature branch of the inversion curve.     

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.     

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.     

Modeling of three-phase vapor–liquid–liquid equilibria for a natural-gas system rich in nitrogen with the SRK and PC-SAFT EoS

In this work, we present the modeling of three-phase vapor–liquid–liquid equilibria for a mixture of natural gas (Hogback gas) containing high concentrations in nitrogen (51.8 mol%) with the SRK and PC-SAFT equations of state. The interest of studying this mixture is due to the experimental evidence of the occurrence of multiple equilibrium liquid phases for this mixture over certain ranges of temperature and pressure. The calculation of the multiphase equilibria was carried out by using an efficient numerical procedure based on the minimization of the system Gibbs energy and thermodynamic stability tests to find the most stable state of the system. The results of the calculated vapor–liquid–liquid equilibria (VLLE) show that the PC-SAFT equation of state predicts satisfactorily the phase behavior that experimentally exhibits this mixture, whereas the SRK equation of state predicts a three-phase region wider than the experimentally observed. The two-phase boundary for this mixture was also calculated through flash calculations, and the results showed that this mixture does not present any gas-liquid critical point.     

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.     

Modeling adsorption in binary associating solvents using the extended MPTA model

Application of the MPTA model has been extended to associative liquid adsorption. The MPTA model describes fluid–fluid interactions using an equation of state (EoS) term, and fluid–solid interactions using a potential equation. In order to extend the application to associative liquid adsorption, an association term has been considered for fluid–fluid interactions. Sixteen binary mixtures containing associating and non-associating components in equilibrium with various adsorbents have been studied; fluid–fluid interactions have been modeled using the Peng–Robinson, Soave–Redlich–Kwong, volume-translated SRK and CPA equations of state, while the effects of fluid–solid interactions have been taken into account using Dubinin–Radushkevich–Astakhov (DRA) and Steele potential functions. The model parameters have been obtained by fitting the model to experimental data on surface excess. For the studied systems, the accuracy of fitted isotherms has been found to be more dependent on the fluid–solid potential equation rather than the applied EoS. Calculations show that the SRK equation is a suitable choice for non-associating systems, while the CPA equation is found to be more appropriate for associating systems, as would be expected. The results also show that the Steele potential function is in better agreement with experimental data than the DRA potential function.     

Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids

Making use ofWeierstrass's theorem and Chebyshev's theorem and referring to the equations of state of the scaled-particle theory and the Percus-Yevick integration equation, we demon-strate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.     

Thermodynamic phase equilibria of wax precipitation in crude oils

Economic loss due to wax precipitation in oil exploitation and transportation has reached several billion dollars a year recently. Development of a model for better understanding of the process of wax precipitation is therefore very important to reduce the loss. In this paper, a new thermodynamic model for predicting phase equilibriums of crude oils is proposed. The modified SRK EOS and the UNIQUAC equations are used to describe the vapor, liquid phase and the wax, respectively. New correlations have been introduced to calculate the volume parameter, c, in SRK EOS and the heat of vaporization in UNIQUAC equation. The model can be used to describe the systems which contain paraffin, naphthene and aromatic fractions. New correlations for the enthalpies, temperatures of solid–solid transitions and fusion enthalpies of paraffins are established in this paper based on data obtained from open literature. By using the proposed modified model, the wax precipitation in hydrocarbon fluids has been predicted for three crude oil systems. The calculation results have been compared with experimental observations and those results obtained using regular solution models. It is found that wax precipitation in complex systems can be better predicted by using this new model.     

Vapor–liquid equilibrium prediction at high pressures using activity coefficients at infinite dilution from COSMO-type methods

Predictions of vapor–liquid equilibria at high temperatures and pressures were obtained by applying a modified procedure using the Huron–Vidal mixing rule based on available activity coefficients at infinite dilution and low pressures. These activity coefficients were calculated with so-called conductor-like screening model for real solvents (COSMO-RS) and with a variation of this model, known as segment activity coefficient (COSMO-SAC) model.In this work, the performances of the mixing rule (HVID model) coupled with the SRK equation of state and a reduced UNIQUAC model are presented for six binary systems and a ternary system, whose VLE data are available over a large temperature and pressure range.     

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.     

Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals?

The PC-SAFT equation of state is a very popular and promising model for fluids that employs a complicated pressure-explicit mathematical function (and can therefore not be solved analytically at a specified pressure and temperature, contrary to classical cubic equations). In this work, we demonstrate that in case of pure fluids, the PC-SAFT equation may exhibit up to five different volume roots whereas cubic equations give at the most three volume roots (and yet, only one or two volume roots have real significance). The consequence of this strongly atypical behaviour is the existence of two different fluid–fluid coexistence lines (the vapour-pressure curve and an additional liquid–liquid equilibrium curve) and two critical points for a same pure component, which is obviously physically inconsistent. In addition to n-alkanes, nearly 60 very common pure components (branched alkanes, cycloalkanes, aromatics, esters, gases, and so on) were tested out and without any exception, we can claim that all of them exhibit this undesired behaviour. In addition, such similar phenomena (i.e. existence of more than three volume roots) may also arise with mixtures. From a computational point of view, most of the algorithms used for solving equations of state only search for three roots at the most and are thus likely to be inefficient when an equation of state gives more than three volume roots. To overcome this limitation, a simple procedure allowing to identify all the possible volume roots of an equation of state is proposed.     

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.     

Permeation models for mixed matrix membranes

Permeation models for mixed matrix membranes (MMMs) are discussed. A new model is proposed for the effective permeability of a species in MMMs. The model takes into account the presence of interfacial layer (shell) at the surface of the core filler particles. According to the proposed model, the relative permeability (Pr) of a species in MMM, defined as permeability in MMM divided by matrix permeability, is a function of five variables, namely: ratio of interfacial shell-to-core particle radii (delta), ratio of interfacial shell-to-matrix permeabilities (lambdaIm), ratio of core particle-to-interfacial shell permeabilities (lambdadI), volume fraction of composite core-shell particles (phi), and maximum packing volume fraction of particles (phim). The predictions of the model are discussed and compared with available experimental data on permeability and selectivity of mixed matrix membranes.     

Computational aspects of master equation transformation in terms of moments

The master equation describing the temporal evolution of a gaseous system in contact with a heat bath can be transformed into a system of linear, constant-coefficient, first-order differential equations of moments of the population distribution. While it has the advantage that populations are obtained directly from observables (moments), this system of equations is not too well-conditioned and unless precautions are taken, unsurmountable numerical problems appear. These are principally associated with manipulations (inversion and taking the exponential of a matrix) involving slightly modified Vandermonde matrices whose elements span a very wide range of orders of magnitude. This article discusses ways to avoid these pitfalls which consist principally of a suitable matrix normalization.     

Effect of various types of equations of state for prediction of simple gas hydrate formation with or without the presence of kinetic inhibitors in a flow mini-loop apparatus

This paper compares the effects of using various types of equations of state (PR,¹ SRK,² ER,³ PT⁴ and VPT⁵) on the calculated driving force and rate of gas consumption based on the Kashchiev and Firoozabadi model for simple gas hydrate formation for methane, carbon dioxide, propane and iso-butane with experimental data points obtained in a flow mini-loop apparatus with or without the presence of kinetic inhibitors at various pressures and specified temperatures. For this purpose, a laboratory flow mini-loop apparatus was set up to measure gas consumption rate when a hydrate forming substance (such as C₁, C₃, CO₂ and i-C₄) is contacted with water in the presence or absence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The total average absolute deviation was found to be 15.4%, 16.3%, 15.8%, 17.8% and 17.4% for the PR, ER, SRK, PT and VPT equations of state for calculating gas consumption in simple gas hydrate formation with or without the presence of kinetic hydrate inhibitors, respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in flow loop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations of state for this model.