Extension of polar GC-SAFT to systems containing some oxygenated compounds: Application to ethers, aldehydes and ketones

The GC-SAFT equation of state proposed by Tamouza et al. (2004) [51], extended to polar molecular fluids NguyenHuynh et al. (2008) [32], is here applied to model vapor-liquid phase equilibria of various binary mixtures containing at least one oxygenated compound belonging to ethers, ketones or aldehydes chemical families.These systems are modeled using a polar version of the three different versions of SAFT-EOS (original, VR-SAFT and PC-SAFT) in a predictive manner: binary interaction parameters k_ij and l_ij are all set to zero.In the case of alcohol + ether, +ketone, +aldehyde systems, a cross-association interaction between an oxygenated compound (non self-associating compound) and an alcohol is necessary to model/predict accurately the mixture VLE. The corresponding association parameters are assumed to be equal to the self-association parameters of pure 1-alkanols.The above-cited systems have been treated in a comprehensive manner. The general agreement between polar GC-SAFT and experimental data is good (within 4-5% deviation on pressure), similar to the one obtained on previously investigated systems using GC-SAFT.     

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

Measurement and prediction of vapor–liquid equilibria of ternary systems containing ionic liquids

For the first time vapor–liquid equilibrium (VLE) data for ternary systems containing ionic liquids are reported. The data were measured by means of a computer-operated static VLE apparatus at 353.15 K with the ionic liquids 1-ethyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [EMIM]⁺[(CF₃SO₂)₂N]⁻ and 1-butyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [BMIM]⁺[(CF₃SO₂)₂N]⁻ and acetone, 2-propanol and water. The experimental VLE data of the binary systems were correlated using the Wilson, NRTL and UNIQUAC models. The errors using Wilson, NRTL, and UNIQUAC are 3.92%, 1.45%, and 1.53%. The g^E-model parameters of the binary systems were used to predict the VLE behavior of the ternary systems and the predictions were compared to the experimental datasets. The errors using Wilson-, NRTL-, and UNIQUAC-parameters are 5.61%, 7.22%, and 5.02%.     

Modelling the VLE properties using van der Waals-type equation of state

The vapour–liquid equilibrium (VLE) properties of polar and non-polar fluids have been modelled by the use of two modified van der Waals (vdW)-type equations of state (EOSs). In this article, a revised method is applied to the above-mentioned EOSs to improve the representation of VLE properties of different class of fluids. In this respect, the repulsion parameter b is considered to be temperature dependent and also a temperature-dependent revision factor α(T) is introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration to reproduce the vapour pressure (P^s) of pure liquids. The present method is also extended to represent the VLE properties of binary mixtures containing noble gases, refrigerants and hydrocarbons. This method outperforms the original vdW-type EOSs in predicting the VLE and pressure-volume-temperature (PVT) properties of 22 pure substances and 7 binary mixtures.     

Prediction of ternary vapor–liquid equilibria for 33 systems by molecular simulation

A set of molecular models for 78 pure substances from prior work is taken as a basis for systematically studying vapor–liquid equilibria (VLE) of ternary systems. All 33 ternary mixtures of these 78 components for which experimental VLE data are available are studied by molecular simulation. The mixture models are based on the modified Lorentz–Berthelot combining rule that contains one binary interaction parameter which was adjusted to a single experimental binary vapor pressure of each binary subsystem in prior work. No adjustment to ternary data is carried out. The predictions from the molecular models of the 33 ternary mixtures are compared to the available experimental data. In almost all cases, the molecular models give excellent predictions of the ternary mixture properties.     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach

The GC-PPC-SAFT equation of state (EoS) is a combination of a group contribution method [S. Tamouza et al., Fluid Phase Equilib. 222-223 (2004) 67-76; S. Tamouza et al., Fluid Phase Equilib. 228-229 (2005) 409-419] and the PC-SAFT EoS [J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244-1260] which was adapted to the polar molecules [D. Nguyen-Huynh et al., Fluid Phase Equilib. 264 (2008) 62-75]. It is here applied to the vapour pressure and liquid molar volume of primary, secondary and tertiary amines and their mixtures with n-alkanes, primary and secondary alcohols, using previously published group parameters. The mixing enthalpy is also evaluated for the binary systems. Binary interaction parameters k_ij are computed using a group-contribution pseudo-ionization energy, as proposed by Nguyen-Huynh [D. Nguyen-Huynh et al., Ind. Eng. Chem. Res. 47 (2008) 8847-8858]. A unique corrective parameter for the cross-association energy between amines and alcohols is used.The agreement with experimental data in correlation and prediction were found rather encouraging. The mean absolute average deviation (AAD) on bubble pressure is about 3.5% for pure amines. The mean AAD on the vapour-liquid equilibria (VLE) are respectively 2.2% and 5.5% for the amine mixtures with n-alkanes and alcohols. The AADs on saturated liquid volume are about 0.7% for the pure compounds and 0.9% for the mixtures. Prediction results are qualitatively and quantitatively accurate and they are comparable to those obtained with GC-PPC-SAFT on previously investigated systems.     

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.     

Isobaric (vapour + liquid) equilibria for N-formylmorpholine with ethylbenzene,n-butylbenzene,iso-propylbenzene and 1,2,4-trimethylbenzene at 101.33 kPa

The isobaric (vapour + liquid) equilibrium (VLE) of N-formylmorpholine with aromatics (ethylbenzene, n-butylbenzene, isopropylbenzene, 1,2,4-trimethylbenzene) at 101.33 kPa was investigated. The experimental VLE data for the four binary systems were tested and verified to be thermodynamically consistent by the Herington analysis method. At the same time, the non-random two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) activity coefficient models were used to correlate the experimental data with temperature-independent parameters. The average absolute deviations of the temperature correlated by NRTL model and UNIQUAC model for all the systems are below 0.62 K and the average absolute deviations for the vapour phase compositions are all below 0.083. In addition, the UNIFAC (Do) group contribution model was used to correlate and estimate the VLE data. The N-formylmorpholine was treated as a group (NFM). The group interaction parameters for CH₂-NFM, ACH-NFM and ACCH₂-NFM were regressed. The UNIFAC (Do) model can correlate the experimental data well. The group interaction parameters were used to estimate VLE data of the (o-xylene + N-formylmorpholine), (m-xylene + N-formylmorpholine) and (p-xylene + N-formylmorpholine) binary systems. The estimated data fit well with the literature data. The average absolute deviations of the temperature for N-formylmorpholine with (o-xylene, m-xylene, p-xylene) are 1.67 K, 1.77 K and 1.35 K, respectively, and the average absolute deviations for the vapour phase compositions of o-xylene, m-xylene and p-xylene are 0.0133, 0.0057 and 0.0059, respectively.     

Measurements of VLE,vE and hE for binary mixtures of n-alkanes with chloro-alkylbenzenes

Results of a series of experimental investigations of the binary mixtures n-heptane—chlorobenzene and n-octane—benzyl chloride are reported: T, p, x, y data of vapour—liquid equilibria (VLE); h^E, T, x data of calorimetric measurements and v, T, x data of volumetric measurements. VLE data are checked for thermodynamic consistency and used to fit parameters of several g^E models. UNIFAC predictions and experimental data are compared. h^E and v^E data were correlated with Redlich-Kister polynomials.     

Extension of the new proposed association equation of state (AEOS) to associating fluid mixtures

Recently, a new statistical mechanic-based equation of state has been proposed by Mohsen-Nia and Modarress [M. Mohsen-Nia, H. Modarress, Chem. Phys. 336 (2007) 22–26] for associating pure fluids. The new association equation of state (AEOS) was successfully applied to calculate the saturated properties of water, methanol, and ammonia. In this work, the new proposed AEOS is used to evaluate the (vapour + liquid) equilibrium (VLE) of 25 associating pure compounds and the adjusted parameters are reported. The new AEOS is also extended to mixtures containing associating and non-associating compounds. The calculated saturated properties of the pure compounds are compared with those calculated by other AEOSs. The results of VLE calculation for various binary mixtures such as: alcohol/hydrocarbon, alcohol/CO₂, alcohol/aromatic-hydrocarbons, and the quaternary system (H₂O/CH₄/CO₂/H₂S) indicate the capability of the new proposed AEOS for associating pure and mixture calculations.     

Isothermal (vapour + liquid) equilibrium (VLE) for binary mixtures containing diethyl carbonate,phenyl acetate,diphenyl carbonate,or ethyl acetate

The isothermal (vapour + liquid) equilibrium (VLE) (P–T–x_i–y_i) was determined the binary systems of (ethyl acetate + diethyl carbonate) from T = (373.2 to 453.2) K, (ethyl acetate + phenyl acetate) at T = 373.2 K, and (diethyl carbonate + phenyl acetate) at T = 373.2 K, while the VLE (P–T–x_i) of three diphenyl carbonate-containing binary systems was also determined experimentally at temperatures from (373.2 to 453.2) K. The experimental results show no azeotrope formation and near ideal solution behaviour for each binary system. These new VLE (P–T–x_i–y_i) data have been passed by the point, area, and infinite dilution thermodynamic consistency tests. The Wilson-HOC, the NRTL-HOC, and the UNIQUAC-HOC models were applied to correlate the VLE results and the optimal values of the model parameters have been determined through data reduction. Comparable results were obtained from these three models.     

Comparison of three models for permeation of CO2/CH4 mixtures in poly(phenylene oxide)

Two models for the permeability of pure gases have been extended to include binary gas mixtures. The first is an extension of a pure gas permeability model, proposed by Petropoulos, which is based on gradients of chemical potential. This model predicts the permeability of components in a gas mixture solely on the basis of competition for sorption sites within the polymer matrix. The second mixed gas model follows an earlier analysis by Barrer for pure gases which includes the effects of saturation of Langmuir sites on the diffusion as well as the sorption processes responsible for permeation. This generalized “competitive sorption/diffusion” model includes the effect of each gas component on the sorption and diffusion of the other component in the mixture. The flux equations from these two models have been solved numerically to predict the permeability of gas mixtures on the basis of pure gas sorption and transport parameters. Both the mixed gas Petropoulos and competitive sorption/diffusion model predictions are compared with predictions from the earlier simple competitive sorption model based on gradients of concentration. An analysis of all three models is presented for the case of CO₂/CH₄ permeability in poly(phenylene oxide) (PPO). As expected, the competitive sorption/diffusion model predicts lower permeability than either of the models which consider only competitive sorption effects. The permeability depression of both CO₂ and CH₄ predicted by the competitive sorption/diffusion model is roughly twice that predicted by the competitive sorption model, whereas the mixed gas Petropoulos model predictions for both gases lie between the other two model predictions. For the PPO/CO₂/CH₄ system, the methane permeability data lie above the predictions of all three models, whereas CO₂ data lie below the predictions of all models. Consequently, the competitive sorption/diffusion model gives the most accurate prediction for CO₂, while the simple competitive sorption model is best for methane. The effects of mixed gas sorption, fugacity, and CO₂-induced dilation were considered and do not explain the inaccuracies of any of the models. The relatively small errors in mixed gas permeability predictions using either of the three models are likely to be related to “transport plasticization” of PPO owing to high levels of CO₂ sorption and its effect on polymer segmental motions and gas diffusivity.     

Molecular models for 267 binary mixtures validated by vapor–liquid equilibria: A systematic approach

By assessing a large number of binary systems, it is shown that molecular modeling is a reliable and robust route to vapor–liquid equilibria (VLE) of mixtures. A set of simple molecular models for 78 pure substances from prior work is taken to systematically describe all 267 binary mixtures of these components for which relevant experimental VLE data is available. The mixture models are based on the modified Lorentz–Berthelot combining rule. Per binary system, one state independent binary interaction parameter in the energy term is adjusted to a single experimental vapor pressure. The unlike energy parameter is altered usually by less than 5% from the Berthelot rule. The mixture models are validated regarding the vapor pressure at other state points and also regarding the dew point composition, which is a fully predictive property in this work. In almost all cases, the molecular models give excellent predictions of the mixture 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.     

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.     

High pressure phase behavior in systems containing CO2 and heavier compounds with similar vapor pressures

The separation of the para and ortho isomers of xylene as well as the azeotropic mixture of butyl ether/o-xylene using carbon dioxide at high pressure was investigated. The phase behavior of carbon dioxide and each of these compounds along with the ternary systems; CO₂/p-xylene/o-xylene and CO₂/butyl ether/o-xylene were experimentally determined. The relative volatilities of p-xylene to o-xylene in the CO₂/p-xylene/o-xylene system compared favorably with those obtained in distillation. The results also indicated a substantial shift in the butyl ether/o-xylene azeotrope to higher butyl ether concentrations in the presence of carbon dioxide thus indicating a potential for the separation of these mixtures using carbon dioxide at low temperatures. Thermodynamic models using the Peng—Robinson equation of state were developed and better predictions of the bubble point pressures were obtained when the interaction parameter, δ_ij, was allowed to vary with phase density. This approach results in an analytically solvable quartic equation in volume and gives different δ_ij's for the vapor and liquid phases. In this model, the temperature dependence of the binary interaction parameter is contained within its density dependence and, δ_ij's obtained from fitting VLE data at a single temperature could be used for accurate prediction of equilibrium data at other temperatures. The results of such predictions were better than predictions obtained by fitting the actual data using the conventional VDW-1 mixing rules.     

Extending the GC-SAFT-VR approach to associating functional groups: Alcohols, aldehydes, amines and carboxylic acids

The statistical associating fluid theory is a widely used molecular-based equation of state that has been successfully applied to study a broad range of fluid systems. It provides a framework in which the effects of molecular shape and interactions on the thermodynamics and phase behavior of fluids can be separated and quantified. In the original approach, molecules were modeled as chains composed of identical segments; the heterogeneity of molecules in terms of structure and functional groups was described implicitly through effective parameters. To overcome this limitation, in recent works [Peng et al. Fluid Phase Equilib. 227(2), 131 (2009); Ind. Eng. Chem. Res. 49(3), 1378 (2010)] the GC-SAFT-VR approach has been developed to extend the theory to model chains composed of segments of different size and/or energy of interaction and enable the development of a group-contribution approach within the SAFT-VR framework in which molecular heterogeneity and connectivity is explicitly accounted for. The parameters for several key functional groups (CH₃, CH₂, CH, CH₂CH, CO, C₆H₅, esters, ethers, cis-alkenes and trans-alkenes groups) were determined by fitting to experimental vapor pressure and saturated liquid density data for a number of small molecules containing the functional groups of interest and transferability of the parameters tested by comparing the theoretical predictions with experimental data for pure fluids not included in the fitting process and binary mixtures of both simple fluids and the VLE and LLE of small molecules in polymer systems. In this work, we further extend the applicability of the GC-SAFT-VR approach through the study of the vapor-liquid phase behavior of associating systems, such as linear and branched alcohols, primary and secondary amines, aldehydes, and carboxylic acids, and their mixtures. In the study of these new molecules several new functional groups (OH (linear and branched), HCO, NH₂, NH and COOH) are defined and their molecular parameters characterized. The transferability of the parameters is again tested by comparing the theoretical predictions with experimental data for pure fluids and binary mixtures not included in the fitting process. The GC-SAFT-VR approach is found to predict the phase behavior of the systems studied in most cases in good agreement with experimental data and accurately captures the effects of changes in structure and molecular composition on phase behavior.     

Thermodynamics of liquid mixtures containing a very strongly polar compound: Part 6. DISQUAC characterization of N,N-dialkylamides

Systems of N,N di(n-alkylamides) (hereafter, N,N-dialkylamides) with alkane, benzene, toluene, 1-alkanol or 1-alkyne have been investigated in the framework of the DISQUAC model. The corresponding interaction parameters are reported. They change regularly with the molecular structure of the mixture components. This variation is similar to those encountered when treating other systems in terms of DISQUAC. The model describes consistently a whole set of thermodynamic properties: liquid–liquid equilibria (LLE), vapor–liquid equilibria (VLE), solid–liquid equilibria (SLE), molar excess Gibbs energies (G^E), molar excess enthalpies (H^E), molar excess heat capacities at constant pressure (C_P^E), partial molar excess properties at infinite dilution, enthalpies and heat capacities. The model also provides good results for the Kirkwood–Buff integrals and for the linear coefficients of preferential solvation. For ternary systems, DISQUAC predictions on VLE and H^E, obtained using binary parameters only, are in good agreement with the experimental data. A short comparison between DISQUAC and Dortmund UNIFAC results is shown. DISQUAC improves UNIFAC results on H^E and C_P^E, magnitudes which strongly depend on the molecular structure. The investigated mixtures behave similarly to those characterized by thermodynamic properties which arise from dipolar interactions. Association/solvation effects do not play, as a whole, an important role in the studied systems. This may explain that the ERAS model fails when representing the thermodynamic properties of dimethylformamide + 1-alkanol mixtures.