Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state

We have discussed the capability of the soft-SAFT equation of state (EoS) to predict second order thermodynamic derivative properties of pure fluids in a recent paper [F. Llovell, L.F. Vega, J. Phys. Chem. B 110 (2006) 11427–11437]. The goal of this work is to extend these calculations to selected binary mixtures. The equation was applied in a semi-predictive manner: the pure component molecular parameters needed to apply soft-SAFT to experimental systems were obtained by fitting vapor–liquid equilibrium data and used, without further fitting, to calculate isochoric and isobaric heat capacities of selected alkane + n-alkane and n-alkane + 1-alkanol binary mixtures; isentropic compressibility coefficients and the speed of sound of selected n-alkane + 1-alkanol mixtures were calculated following the same procedure. We have used the crossover soft-SAFT equation which explicitly incorporates a renormalization group term in order to take into account the long range fluctuations appearing in the near critical region. Soft-SAFT was able to capture the qualitative behavior of the mixture properties studied, for a wide range of conditions, showing quantitative agreement with experimental data in some of the cases. As a further test to the equation, we have also calculated excess properties. The equation was able to capture the non-ideal behavior upon mixing experienced by these properties. This work shows the robustness of the molecular parameters and the equation to calculate properties not included in the fitting procedure, in a predictive manner.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

Soft-SAFT modeling of vapor–liquid equilibria of nitriles and their mixtures

Nitriles are strong polar compounds showing a highly non-ideal behavior, which makes them challenging systems from a modeling point of view; in spite of this, accurate predictions for the vapor–liquid equilibria of these systems are needed, as some of them, like acetonitrile (CH₃CN) and propionitrile (C₂H₅CN), play an important role as organic solvents in several industrial processes. This work deals with the calculation of the vapor–liquid equilibria (VLE) of nitriles and their mixtures by using the crossover soft-SAFT Equation of State (EoS). Both polar and associating interactions are taken into account in a single association term in the crossover soft-SAFT equation, while the crossover term allows for accurate calculations both far from and close to the critical point. Molecular parameters for acetonitrile, propionitrile and n-butyronitrile (C₃H₇CN) are regressed from experimental data. Their transferability is tested by the calculation of the VLE of heavier linear nitriles, namely, valeronitrile (C₄H₉CN) and hexanonitrile (C₅H₁₁CN), not included in the fitting procedure. Crossover soft-SAFT results are in excellent agreement with experimental data for the whole range of thermodynamic conditions investigated, proving the robustness of the approach. Parameters transferability has also been used to describe the isomers n-butyronitrile and i-butyronitrile. Finally, the nitriles soft-SAFT model is further tested in VLE calculation of mixtures with benzene, carbon tetrachloride and carbon dioxide, which proved to be satisfactory as well.     

Thermodynamics of mixtures containing linear monocarboxylic acids II. Binary systems showing cross-association between components: DISQUAC characterization of linear monocarboxylic acid + 1-alkanol,or + linear monocarboxylic acid mixtures

Binary mixtures containing compounds which show cross-association between them are investigated in terms of DISQUAC: namely, systems with two linear monocarboxylic acids, or with one acid and one 1-alkanol. In the former, the interactions between the COOH groups of the acids are represented by dispersive parameters only. Binary systems involving two 1-alkanols behave similarly. In the linear monocarboxylic acids + 1-alkanol mixtures, the COOH/OH interactions are represented by structure-dependent dispersive and quasichemical parameters. It is shown that those solutions with methanol and ethanol do not fit into the general scheme followed by the higher members of each homologous series considered here. A similar behaviour is found when mixtures containing methanol and benzene or CCl₄ are compared with those involving higher alkanols in the frameworks of DISQUAC or of the Barker's theory.Vapor-liquid equilibria, VLE, and excess enthalpy, H^E, data are consistently described by DISQUAC. Discrepancies are analysed.The UNIQUAC association model or an equation of state (Carnahan-Starling) with the association built in have been applied in the literature as pure correlations of the experimental data for acids + 1-alkanols systems. Their results are compared with those reported in this work by DISQUAC.     

Solvatochromic behavior of phenol blue in CO2+ethanol and CO2+n-pentane mixtures in the critical region and local composition enhancement

The UV-Vis spectra of probe phenol blue in CO(2)+ethanol and CO(2)+n-pentane binary mixtures were studied at 308.15 K and different pressures. The experiments were conducted in both supercritical region and subcritical region of the mixtures by changing the compositions of the mixed solvents. On the basis of the experimental results the local compositions of the solvents about phenol blue were estimated by neglecting the size difference of CO(2) and the cosolvents. Then the local composition data were corrected by a method proposed in this work, which is mainly based on Lennard-Jones sphere model. It was demonstrated that the local mole fraction of the cosolvents is higher than that in the bulk solution at all the experimental conditions. In the near critical region of the mixed solvents the local composition enhancement, defined as the ratio of cosolvent mole fraction about the solute to that in the bulk solution, increased significantly as pressure approached the phase boundary from high pressure. The local composition enhancement was not considerable as pressure was much higher than the critical pressure. In addition, in subcritical region the degree of composition enhancement was much smaller and was not sensitive to pressure in the entire pressure range as the concentration of the cosolvents in the mixed solvents was much higher than the concentration at the critical point of the mixtures.     

Prediction of thermodynamic derivative properties of pure fluids through the Soft-SAFT equation of state

We present in this work the application of the soft-SAFT equation of state (EoS) to the calculation of some main derivative properties, including heat capacities, reduced bulk modulus, Joule-Thomson coefficient, and speed of sound. Calculations have been performed analytically through the derivation of a primary thermodynamic potential function. The application to the n-alkanes, n-alkenes, and 1-alkanols families has been done in a semipredictive manner, with the molecular parameters of the equation obtained from previous fitting to vapor-liquid equilibrium data of the same compounds. The equation is able to capture the typical extrema isothermal derivative properties exhibit with respect to density, providing quantitative agreement with experimental (or correlation) data in some cases. Results in the vicinity of the critical point are improved by adding a crossover treatment to take into account the long-range fluctuations present in this region. By taking advantage of the molecular nature of the equation, we have been able to separate and quantify the different contributions (reference fluid, chain, and association) to the total derivative properties. The association plays a predominant role in energetic properties, such as the heat capacities, while there is a competition between association and chain length as the chain length of the compound increases for volumetric properties, such as the isothermal compressibility. These results act in favor of the molecular-based equations, like soft-SAFT, as predictive tools for several applications.     

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.     

Liquid—liquid coexistence curves for binary systems

The liquid—liquid coexistence curves of polar+non-polar binary systems have been determined experimentally. The polar compounds studied were ethanenitrile, methanol and N-methylpyrrolidone, whereas the non-polar compounds were chosen from the n-alkane series. The upper critical solution temperature for each set of mixtures increases with increasing n-alkane chain length, and the critical composition of the polar component also increases in this fashion.     

Thermodynamics of 1-alkanol+linear alkanoate mixtures

1-Alkanol?+?linear alkanoate mixtures have been investigated in the framework of the DISQUAC model. The interaction parameters for the OH/COO contacts are reported. The quasichemical parameters are independent of the mixture compounds. The dispersive parameters change with the molecular structure of the components. The same behaviour is observed for the OH/CO (carbonyl) and OH/OCOO (carbonate) contacts. DISQUAC represents well the molar excess Gibbs energies, coordinates of azeotropes and molar excess enthalpies. Using binary parameters only, DISQUAC improves meaningfully predictions on this property from the UNIFAC model for 1-alkanol?+?linear alkanoate?+?hydrocarbon systems. In contrast, the Nitta–Chao and the DISQUAC models yield similar results for the thermodynamic properties of the binary and ternary mixtures considered. 1-Alkanol?+?linear alkanoate mixtures are characterized by strong dipolar interactions between like molecules. In 1-alkanol?+?CH₃COO(CH₂) _{u ?1}CH₃ systems, dipole–dipole interactions between ester molecules are more important for u?≤?7. For u?≥?8, the more important contribution to the excess molar enthalpy comes from the disruption of the alkanol–alkanol interactions. For systems containing a polar compound such as alkanone, alkanoate or linear organic carbonate, dipolar interactions increase in the order: alkanone?<?alkanoate?<?carbonate.     

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.     

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.     

Thermodynamic modeling of solute adsorption equilibrium from near-critical carbon dioxide

Modeling of adsorption equilibrium for supercritical fluid mixtures, with as few parameters as possible, is important in applications of the technology of supercritical fluid adsorption. In this paper, a correlative model has been developed to represent the adsorption equilibria of solutes from the near-critical CO(2) fluid. A two-dimensional van der Waals equation of state and the three-dimensional P - R equation of state were used to describe the adsorbed and bulk phases, respectively. This model contains five parameters for adsorption equilibrium isotherms at finite concentrations and two parameters for adsorption equilibrium constants at infinite dilution. All the parameters are independent of temperature and pressure. By applying the model to the experimental data from the literature, it was shown that this model is capable of describing the adsorption behavior of solutes from supercritical carbon dioxide over relatively wide temperature and pressure ranges. In addition, the adsorption behavior of supercritical fluid mixtures was investigated at finite and infinite dilution conditions.     

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.     

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.     

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.     

How does the critical point change during a chemical reaction in supercritical fluids? A study of the hydroformylation of propene in supercritical CO(2).

An understanding of homogeneous catalysis in supercritical fluids requires a knowledge of the phase behavior and the variation in critical point as the reaction proceeds. In this paper, the critical temperatures, T(c) and pressures, P(c), have been measured for a considerable number of mixtures representing the various stages of the hydroformylation reaction of propene in supercritical CO(2) and different reactant concentrations. Critical point data have also been measured for all of the binary mixtures of the components (CO(2), H(2), CO, propene, n- and isobutyraldehyde) which are not available from the literature or can be deduced from published data. We use the stoichiometry of the reacting system to simplify greatly the phase behavior problem by defining a path through the otherwise multidimensional "phase space". Satisfactory modeling of the data (0.3% in T(c) and 3.0% in P(c)) has been achieved using the Peng-Robinson equation of state and ignoring all binary interactions which do not involve CO(2). The model is used to explore the strategies needed to avoid phase separation in continuous and batch reactions. At a given temperature, a batch reactor may need to be run under much higher pressures than a flow reactor if single-phase conditions are to be preserved throughout the course of the reaction. Most of the critical point data were measured acoustically, but a selection of points were validated using more traditional view-cell procedures.     

Thermodynamic modeling of the phase behavior of binary systems of ionic liquids and carbon dioxide with the group contribution equation of state

The group contribution equation of state (GC-EOS) was applied to predict the phase behavior of binary systems of ionic liquids of the homologous families 1-alkyl-3-methylimidazolium hexafluorophosphate and tetrafluoroborate with CO2. Pure group parameters for the new ionic liquid functional groups [-mim][PF6] and [-mim][BF4] and interaction parameters between these groups and the paraffin (CH3, CH2) and CO2 groups were estimated. The GC-EOS extended with the new parameters was applied to predict high-pressure phase equilibria in binary mixtures of the ionic liquids [emim][PF6], [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], and [omim][BF4] with CO2. The agreement between experimental and predicted bubble point data for the ionic liquids was excellent for pressures up to 20 MPa, and even for pressures up to about 100 MPa, the agreement was good. The results show the capability of the GC-EOS to describe phase equilibria of systems consisting of ionic liquids.