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.     

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.     

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.     

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.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Molecular simulation and macroscopic modeling of the diffusion of hydrogen, carbon monoxide and water in heavy n-alkane mixtures

The self-diffusion coefficient of hydrogen (H(2)), carbon monoxide (CO) and water (H(2)O) in n-alkanes was studied by molecular dynamics simulation. Diffusion in a few pure n-alkanes (namely n-C(8), n-C(20), n-C(64) and n-C(96)) was examined. In addition, binary n-C(12)-n-C(96) mixtures with various compositions as well as more realistic five- and six-n-alkane component mixtures were simulated. In all cases, the TraPPE united atom force field was used for the n-alkane molecules. The force field for the mixture of n-alkanes was initially validated against experimental density values and was shown to be accurate. Moreover, macroscopic correlations for predicting diffusion coefficient of H(2), CO and H(2)O in n-alkanes and mixtures of n-alkanes were developed. The functional form of the correlation was based on the rough hard sphere theory (RHS). The correlation was applied to simulation data and an absolute average deviation (AAD) of 5.8% for pure n-alkanes and 3.4% for n-alkane mixtures was obtained. Correlation parameters vary in a systematic way with carbon number and so they can be used to provide predictions in the absence of any experimental or molecular simulation data. Finally, in order to reduce the number of adjustable parameters, for the n-alkane mixtures the "pseudo-carbon number" approach was used. This approach resulted in relatively higher deviation from MD simulation data (AAD of 18.2%); however, it provides a convenient and fast method to predict diffusion coefficients. The correlations developed here are expected to be useful for engineering calculations related to the design of the Gas-to-Liquid process.     

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.     

Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model

In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.     

Molecular thermodynamics of flexible-molecule fluids

Some of the most important problems encountered -in the statistical-mechanical treatment of dense, complex molecular fluids are indicated. Particular attention is given to the application of the generalized van der Waals concept to flexible-molecule fluids. Perturbed-hard-chain theory and chain-of-rotators theory are reviewed. This is followed by a brief summary of recent experimental work on thermodynamic excess properties of liquid mixtures of type (Y + an n-alkane). Several novel effects connected with local correlation of molecular orientation in the n-alkanes, with medium-induced conformational changes and with preferential orientation of strongly polar molecules are discussed (order/disorder phenomena).     

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.