Modeling of Liquid-Vapor Equilibrium in Systems Including a Light Oil-Gas Component and Aromatic and Polyaromatic Hydrocarbons

The Victorov-Smirnova's hole lattice quasichemical group-contribution model (HM) is used to simulate the vapor-liquid equilibrium in binary and ternary mixtures systems composed by aromatic (benzene, toluene) and polyaromatic (naphthalene, phenanthrene) hydrocarbons and light oil-gas components (carbon dioxide, hydrogen sulfide, nitrogen, methane, ethane, propane). Eighteen binary and two ternary systems are examined. New group parameters for these systems are estimated. The results of modeling are compared with the experimental data and those predicted by the Peng-Robinson equation of state.     

Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

Modelling of the three phase LLV region for ternary hydrocarbon mixtures with the Soave-Redlich-Kwong equation of state

The prediction of the three phase liquid-liquid-vapour (L2L1V) region for the ternary mixtures ethane + propane + eicosane (C2 + C3 + C20) and methane + ethane + eicosane (C1 + C2 + C20) was performed using the Soave-Redlich-Kwong equation of state. A procedure for finding K- and L-points is presented. It is based on the solution of thermodynamic conditions for the K- and L-point using the Newton iteration technique with carefully chosen starting points. The calculations were performed with all binary interaction parameters set to zero and with binary interaction parameters fitted to vapour-liquid equilibrium data of the binary subsystems. In the latter case for all binary subsystems two adjustable parameters with classical mixing rules were used. The results obtained show only qualitative agreement with experimental data for both sets of interaction parameters.     

Global fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equation

We present here the extension of the crossover soft-statistical associating fluid theory (soft-SAFT) equation of state to mixtures, as well as some illustrative applications of the methodology to mixtures of particular scientific and technological interest. The procedure is based on White's work (White, J. A. Fluid Phase Equilib. 1992, 75, 53) from the renormalization group theory, as for the pure fluids, with the isomorphism assumption applied to the mixtures. The equation is applied to three groups of mixtures: selected mixtures of n-alkanes, the CO2/n-alkane homologous series, and the CO2/1-alkanol homologous series. The crossover equation is first applied to the pure components of the mixtures, CO2 and the 1-alkanol family, while an available correlation is used for the molecular parameters of the n-alkane series (Llovell et al. J. Chem. Phys 2004, 121, 10715). A set of transferable molecular parameters is provided for the 1-alkanols series; these are accurate for the whole range of thermodynamic conditions. The crossover soft-SAFT equation is able to accurately describe these compounds near to and far from the critical point. The theory is then used to represent the phase behavior and the critical phenomena of the selected mixtures. We use binary interaction parameters xi and eta for dissimilar mixtures. These parameters are fitted at some particular conditions (one subcritical temperature or binary critical data) and used to predict the behavior of the mixture at different conditions (other subcritical conditions and/or critical conditions). The equation is able to capture the continuous change in the critical behavior of the CO2/n-alkane and the CO2/1-alkanol homologous series as the chain length of the second compound increases. Excellent agreement with experimental data is obtained, even in the most nonideal cases. The new equation is proved to be a powerful tool to study the global phase behavior of complex systems, as well as other thermodynamic properties of very challenging mixtures.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.     

A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone

The fluid phase behaviour for the binary systems carbon dioxide+cyclobutanone and propane+cyclobutanone has been determined experimentally, using Cailletet equipment. For both the systems bubble points have been determined for a number of isopleths covering the whole mole fraction range. Additionally, for the binary system carbon dioxide+cyclobutanone dew points and critical points could be observed for a number of overall-compositions rich in carbon dioxide. The temperature and pressure range were, respectively, from 278 to 369 K and from 0.1 to 14.0 MPa. Correlation of the experimental data of both systems has been performed using the Soave–Redlich–Kwong (SRK) equation of state. Satisfactory results have been achieved using only one binary interaction parameter.     

Liquid mixtures of xenon with fluorinated species: xenon + sulfur hexafluoride

The vapor-liquid equilibrium of binary mixtures of xenon + SF6 has been measured at nine temperatures from 235.34 to 295.79 K and pressures up to 6.5 MPa. The mixture critical line is found to be continuous between the critical points of the pure components, and hence, the system can be classified as type I phase behavior in the scheme of van Konynenburg and Scott. The excess Gibbs free energies have been calculated, and the experimental results have been interpreted using the statistical associating fluid theory for potentials of variable range (SAFT-VR). Additionally, the SAFT-VR equation has been used to model other systems involving SF6 and alkanes, illustrating the predictability of the approach and further demonstrating the transferability of parameters between binary mixtures involving alkanes and xenon.     

Phase equilibria for the binary mixtures containing hydrogen fluoride and non-polar compound

Isothermal vapor–liquid equilibria for propane+hydrogen fluoride have been measured. The experimental data are correlated with the association model proposed by Lencka and Anderko for the mixtures containing hydrogen fluoride and the relevant parameters are presented. The recalculated parameters of the association model for pure hydrogen fluoride are presented. The problems occurred in the applications of the association model for the mixtures containing hydrogen fluoride are discussed. The correlation was found to be in good agreement with the experimental data. However, the calculated equilibrium pressures at very diluted compositions of hydrogen fluoride below about 0.01 were shown rather higher than the experimental values.     

Isothermal vapor–liquid equilibria and excess molar volumes for the ternary mixtures containing 2-methyl pyrazine

Isothermal vapor–liquid equilibrium (VLE) data at 353.15 K and excess molar volumes (V^E) at 298.15 K are reported for the binary systems of ethyl acetate (EA)+cyclohexane and EA+n-hexane and also for the ternary systems of EA+cyclohexane+2-methyl pyrazine (2MP) and EA+n-hexane+2MP. The experimental binary VLE data were correlated with common g^E model equations. The correlated Wilson parameters of the constituent binary systems were used to calculate the phase behavior of the ternary mixtures. The calculated ternary VLE data using Wilson parameters were compared with experimental ternary data. The experimental excess molar volumes were correlated with the Redlich–Kister equation for the binary mixtures, and Cibulka’s equation for the ternary mixtures.     

Investigation of the surface tension of methane and n-alkane mixtures by perturbed-chain statistical associating fluid theory combined with density-gradient theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) and density-gradient theory are used to construct an equation of state to describe the phase behavior of binary methane–n-alkane mixtures. With the molecular parameters and influence parameters regressed from bulk properties and surface tensions of pure fluids, respectively as input, both the bulk and interfacial properties are investigated. The surface tension of the binary systems methane–propane, methane–pentane, methane–heptane and methane–decane are predicted, and the results are satisfactory compared with the experimental data. Our results show that PC-SAFT combined with density-gradient theory is able to describe the interfacial properties of binary methane–n-alkane mixtures in wide temperature and pressure ranges, and illustrate the influence of the equilibrium bulk properties and chain length of n-alkane molecule on the interfacial properties.     

Equation of state modeling of the phase equilibria of ionic liquid mixtures at low and high pressure

Accurate design of processes based on ionic liquids (ILs) requires knowledge of the phase behavior of the systems involved. In this work, the truncated perturbed chain polar statistical associating fluid theory (tPC-PSAFT) is used to correlate the phase behavior of binary and ternary IL mixtures. Both non-polar and polar solvents are examined, while methyl imidazolium ILs are used in all cases. tPC-PSAFT accounts explicitly for weak dispersion interactions, highly directive polar interactions between permanent dipolar and quadrupolar molecules and association between hydrogen bonding molecules. For mixtures of non-polar solvents, tPC-PSAFT predicts accurately the binary mixture data. For the case of polar solvents, a binary interaction parameter is fitted to the experimental data and the agreement between experiment and correlation is very good in all cases.     

Vapour-liquid equilibrium and critical locus curve calculations with the soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide

Huron, M.-J., Dufour, G.-N. and Vidal, J., 1978. Vapour-liquid equilibrium and critical locus curve calculations with the Soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide. Fluid Phase Equilibria, 1: 247–265The aim of this work is to test the value of the Soave-Redlich-Kwong equation of state for predicting phase behaviour of mixtures. Special attention is paid to systems containing hydrogen sulphide or carbon dioxide with hydrocarbons. The properties analysed are critical loci and liquid vapour equilibria, with calculations of standard deviations for pressures and compositions. Optimum values of binary interaction parameters are proposed for these mixtures. Calculation methods to avoid trivial solutions in phase equilibria calculations and for finding critical loci with temperature extrema are described.     

Solvatochromic parameters for binary mixtures of 1-(1-butyl)-3-methylimidazolium tetrafluoroborate with some protic molecular solvents

The solvatochromic parameters (ET(N), normalized polarity parameter; pi*, dipolarity/polarizability; beta, hydrogen-bond acceptor basicity; alpha, hydrogen-bond donor acidity) were determined for binary solvent mixtures of 1-(1-butyl)-3-methylimidazolium tetrafluoroborate ([bmim]BF4) with water, methanol, and ethanol at 25 degrees C over the whole range of mole fractions. In nonaqueous solutions, the value of the mixture increases with mole the fraction of [bmim]BF4 and then decreases gradually to the value of pure [bmim]BF4. Positive deviation from ideal behavior was observed for the solvent parameters ET(N), pi*, and alpha, whereas the deviation of the beta parameter is negative. The applicability of the combined nearly ideal binary solvent/Redlich-Kister equation for the correlation of various solvatochromic parameters with solvent composition was proved too for the first time. This equation provides a simple computational model to correlate and/or predict various solvatochromic parameters for many binary solvent systems. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute-solvent and solvent-solvent interactions have been applied for interpretation of the results.     

Fluid-phase behavior of binary mixtures in which one component can have two critical points

We investigate theoretically the binary fluid-phase behavior of mixtures in which one water-like component can have two critical points. We consider three equal-sized nonpolar solutes that differ in the strength of their dispersive interactions (a1 < a2 < a3, where a denotes the van der Waals attractive parameter). In each case, we compare the phase behavior predicted using two sets of parameters for water: one giving rise to a pure component low-temperature liquid-liquid transition terminating at a critical point (two-critical-point parameter set), and one in which no such second critical point exists (singularity-free parameter set). Regardless of the parameter values used, we find five mixture critical lines. Using the two-critical-point parameter set, we find that a critical line originates at water's second critical point for aqueous mixtures involving solutes 1, 2, or 3. For mixtures involving solutes 1 or 2, this line extends towards low pressures and high temperatures as the solute mole fraction increases, and is closely related to the critical line originating at water's ordinary vapor-liquid critical point: these two critical lines are loci of upper and lower consolute points corresponding to the same liquid-liquid transition. In mixtures involving solute 2, the critical locus emanating from water's second critical point is shifted to higher temperatures compared to mixtures involving solute 1, and extends up to T approximately 310 K at moderate pressures (ca. 200 bars). This suggests the possibility of an experimentally accessible manifestation of the existence of a second critical point in water. For binary mixtures involving solutes 1 or 2, changing the water parameters from the two critical points to the singularity-free case causes the disappearance of a lower consolute point at moderate pressures. For binary mixtures involving solute 3, the differences between two-critical-point and singularity-free behaviors occur only in the experimentally difficult-to-probe low-temperature and high-pressure region.     

Calculation and prediction of fluid phase equilibria from an equation of state

Liquids or compressed gases consisting of light molecules show deviations from classical mechanics, which are caused by the discontinuity of energy levels. From the assumption that each molecule is confined to a cell with a size depending on the free volume, a quantum correction is derived which extends any van der Waals type equation of state to quantum gases. The correction is applied to a semiempirical equation of state developed by the author. The extended equation yields reasonable critical compressibility factors and gives a better representation of PVT data than the uncorrected equation. Furthermore high pressure phase equilibria in mixtures containing helium and hydrogen have been calculated. Again the agreement with experimental data is improved; the adjustable binary interaction parameters have values close to the Berthelot-Lorentz rules and are less temperature dependent.     

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.