Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.     

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H₂S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures.For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole-dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H₂S, the association interactions between H₂S molecules and between the ionic liquids and H₂S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H₂S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.     

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.     

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.     

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.     

Vapor-liquid and vapor-liquid-liquid equilibria of carbon dioxide/n-perfluoroalkane/n-alkane ternary mixtures

Perfluoroalkanes have numerous applications (e.g., in the medical field and the chemical industry), and their high affinity for carbon dioxide makes them attractive as surfactants and cosolvents. Although research in this area has grown in the past few years, very little phase-equilibrium data is available in the open literature for these systems. In this work, we present, for the first time, predictions of vapor-liquid and vapor-liquid-liquid equilibria of binary and ternary systems of carbon dioxide/n-perfluoroalkane/n-alkane. Our results are based on the SAFT-VR EOS (statistical associating fluid theory of variable range, equation of state), and we study the influence of temperature, pressure, composition, and chain length on the phase diagram. The predicted phase diagrams are based on temperature-independent binary interaction parameters, and no ternary parameters are introduced. Comparisons to the available experimental and molecular simulation data show that the predicted diagrams should provide a good representation of the phase equilibria.     

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.     

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.     

Pressure dependence of the vapor-liquid-liquid phase behavior in ternary mixtures consisting of n-alkanes, n-perfluoroalkanes, and carbon dioxide

Expansion of an organic solvent by an inert gas can be used to tune the solvent's liquid density, solubility strength, and transport properties. In particular, gas expansion can be used to induce miscibility at low temperatures for solvent combinations that are biphasic at standard pressure. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to investigate the vapor-liquid-liquid equilibria and microscopic structures for two ternary systems: n-decane/n-perfluorohexane/CO2 and n-hexane/n-perfluorodecane/CO2. These simulations employed the united-atom version of the transferable potential for phase equilibria (TraPPE-UA) force field. Initial simulations for binary mixtures of n-alkanes and n-perfluoroalkanes showed that special mixing parameters are required for the unlike interactions of CHx and CFy pseudoatoms to yield satisfactory results. The calculated upper critical solution pressures for the ternary mixtures at a temperature of 298 K are in excellent agreement with the available experimental data and predictions using the SAFT-VR (statistical associating fluid theory of variable range) equation of state. The simulations yield asymmetric compositions for the coexisting liquid phases and different degrees of microheterogeneity as measured by local mole fraction enhancements.     

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO₂) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6 MPa and two different temperatures (303.2 and 323.2 K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO₂ solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO₂ in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.     

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.     

Solubility of perfumery and fragrance raw materials based on cyclohexane in 1-octanol under ambient and high pressures up to 900 MPa

The (solid + liquid) phase equilibria (SLE) of binary mixtures containing 1-octanol and fragrance raw materials based on cyclohexane were investigated. The systems {1-octanol (1) + cyclohexyl carboxylic acid (CCA), or cyclohexyl acetic acid (CAA), or cyclohexyl acetate (CA), or 2-cyclohexyl ethyl acetate (2CEA), or 2-cyclohexyl ethanol (2CE)(2)} have been measured by a dynamic method in wide range of temperatures from (220 to 320) K and ambient pressure. For all systems SLE diagrams were detected as eutectic mixtures with complete miscibility in the liquid phase. The experimental data were correlated by means of the Wilson and NRTL equations, utilizing parameters derived from the (solid + liquid) equilibrium. The root-mean-square deviations of the solubility temperatures for all calculated data are dependent upon the particular system and the particular equation used.Additionally, the SLE in binary mixture that contain {1-octanol (1) + CCA (2)} has been measured under very high pressures up to about 900 MPa at the temperature range from T = (303.15 to 353.15) K. The thermostatted apparatus for the measurements of transition pressures from the (liquid + solid) state was used. The freezing and melting temperatures at a constant composition increase monotonously with pressure. The high pressure experimental results obtained at isothermal conditions (p–x) were interpolated to more convenient T–x diagram. Data of the (pressure + temperature) composition relation at the high pressure (solid + liquid) phase equilibria was correlated by the polynomial based on the Yang model.The basic thermodynamic properties of pure substances viz. the melting point, enthalpy of fusion, enthalpy of solid–solid phase transition, and glass transition, have been determined by the differential scanning calorimetry (DSC).