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.     

Vapor–liquid equilibria and critical points of the CO2 + 1-hexanol and CO2 + 1-heptanol systems

Vapor–liquid equilibria (VLE), vapor–liquid–liquid equilibria (VLLE) and critical point (CP) data for the carbon dioxide+1-hexanol (at 324.56, 353.93, 397.78, 403.39, 431.82 and 432.45 K up to 20 MPa) and carbon dioxide+1-heptanol (at 313.14, 333.16, 373.32, 411.99 and 431.54 K up to 21 MPa) systems are reported. Phase behavior measurements were made in a new equilibrium cell based on the static-analytic method and capable of measurements up to 60 MPa and 673 K. The Peng–Robinson equation of state (EoS) with the Wong–Sandler mixing rules and temperature independent parameters was able to correlate and extrapolate the VLE for the carbon dioxide+1-hexanol system. However, in order to obtain good agreement with experimental data for the carbon dioxide+1-heptanol system, the mixture EoS parameters were adjusted to the experimental VLE data at each temperature.     

An activity coefficient model for predicting salt effects on vapor–liquid equilibria of mixed solvent systems

In the present study, an activity coefficient model, based on the concept of local volume fractions and the Gibbs–Helmholtz relation, has been developed. Some modifications were made from Tan–Wilson model (1987) and TK–Wilson model (1975) to represent activity coefficients in mixed solvent–electrolyte systems. The proposed model contains two groups of binary interaction parameters. One group for solvent–solvent interaction parameters corresponds to that given by the TK–Wilson model (1975) in salt-free systems. The other group of salt–solvent interaction parameters can be calculated either from vapor pressure or bubble temperature data in binary salt–solvent systems. It is shown that the present model can also be used to describe liquid–liquid equilibria. No ternary parameter is required to predict the salt effects on the vapor–liquid equilibria (VLE) of mixed solvent systems. By examining 643 sets of VLE data, the calculated results show that the prediction by the present model is as good as that by the Tan–Wilson model (1987), with an overall mean deviation of vapor phase composition of 1.76% and that of the bubble temperature of 0.74 K.     

Modification of PSRK mixing rules and results for vapor–liquid equilibria, enthalpy of mixing and activity coefficients at infinite dilution

The predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) is a well-established method for the prediction of thermodynamic properties required in process simulation. But there are still some problems to be solved, e.g. the reliability for strong asymmetric mixtures of components which are very different in size. The following modifications are introduced in the PSRK mixing rules: the Flory–Huggins term in the mixing rule for the EOS parameter a, and the combinatorial part in the UNIFAC model are skipped simultaneously; a nonlinear mixing rule for the EOS parameterb, instead of the linear mixing rule, is proposed. With these two modifications better results are obtained for vapor–liquid equilibria and activity coefficients at infinite dilution for alkane–alkane systems, specially for asymmetric systems. In order to obtain better results for enthalpy of mixing, temperature-dependent parameters are used. Group interaction parameters have been fitted for several groups, and the results are compared with the Modified UNIFAC (Dortmund), and the PSRK methods.     

Liquid–liquid and liquid–liquid–solid equilibrium in Na2CO3–PEG–H2O

The phase diagram was determined for the Na₂CO₃–PEG–H₂O system at 25°C using PEG (poly(ethylene glycol)) with a molecular weight of 4000. Compositions of the liquid–liquid and the liquid–liquid–solid equilibria were determined using calibration curves of density and index of refraction of the solutions, and atomic absorption (AA) and X-ray diffraction analyses were made on the solids. The solid phase in equilibrium with the biphasic region was Na₂CO₃·H₂O. Binodal curves were described using a three-parameter equation. Tie lines were described using the Othmer–Tobias and Bancroft correlation’s. Correlation coefficients for all equations exceeded 0.99. The effects of temperature (25 and 40°C) and the molecular weight of the PEG (2000, 3000, and 4000) on the binodal curve were also studied, and it was observed that the size of the biphasic region increased slightly with an increase in these variables.     

Vapor–liquid equilibria in the ternary system isobutyl alcohol + isobutyl acetate + butyl propionate and the binary systems isobutyl alcohol + butyl propionate,isobutyl acetate + butyl propionate at 101.3 kPa

Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system isobutyl alcohol (IBA) + isobutyl acetate (IBAc) + butyl propionate (BUP) and two constituent binary systems: IBA + BUP and IBAc + BUP. The IBA + BUP system show lightly positive deviation from Raoult's law and IBAc + BUP system exhibits no deviation from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is very well predicted from binary interaction parameters. BUP eliminates the IBA–IBAc binary azeotrope. The change of phase equilibria behaviour is significant therefore this solvent seems to be an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.8.The binary VLE data measured in the present study passed the thermodynamic consistency test of Fredenslund et al. [A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, A Group Contribution Method, Elsevier, Amsterdam, 1977], and were correlated by the Wilson, NRTL and UNIQUAC models to relate activity coefficients with mole fractions. The VLE data obtained for the ternary system passed both the Wisniak L–W [J. Wisniak, Ind. Eng. Chem. Res. 32 (1993) 1531–1533] and McDermott–Ellis [C. McDermott, S.R. Ellis, Chem. Eng. Sci. 20 (1965) 293–296] consistency test. The parameters obtained from binary data were utilized directly to predict the phase behaviour of the ternary system. The results showed an excellent agreement with experimental values.     

On the mean spherical approximation for the Lennard–Jones fluid

Subtle details on the mean spherical approximation (MSA) theory for the Lennard–Jones potential [Fluid Phase Equilib. 134 (1997) 21] are presented. In order to enhance the appreciation of the theory, the accuracy of the mapping method and the contact approximation used in the theory are demonstrated by comparing with the exact results at certain extreme conditions. Technical derivation of internal energy of the MSA is also fully displayed. In addition, the typographic errors appeared in [Fluid Phase Equilib. 134 (1997) 21] are also corrected in this work.     

Modification of Esmaeilzadeh–Roshanfekr equation of state to improve volumetric predictions of gas condensate reservoir

The Peneloux–Rauzy–Freze (PRF) method of improving volumetric predictions by introducing the volume shift into the equation of state, is applied to the Esmaeilzadeh–Roshanfekr equation of state (ER-EOS). The ER-EOS is a new three parameter equation of state that was developed in 2006 aiming to be applied to reservoir fluids. First, this equation of state was developed for pure hydrocarbons and then was extended to mixtures by using mixing rules [M. Bonyadi, F. Esmaeilzadeh, Fluid Phase Equilib. 260 (2007) 326–334]. The modified ER-EOS (mER-EOS) is expected to improve volumetric predictions of gas condensate by applying volume shift for heavy end(s). In this study, three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as two samples from literature have been used to check the validity of the modified ER-EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. Relative volume and condensate drop-out in CCE and CVD tests were predicted by ER-EOS, mER-EOS, PR-EOS and SRK-EOS [D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1), (1976) 59–64; G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203]. Comparison results between experimental and calculated data indicate that the mER-EOS has smaller error than the ER-EOS, PR-EOS and SRK-EOS. By this modification, the total average absolute deviations of the predicted liquid saturation from CVD experiments and relative volume from CCE experiments are 13.17% and 0.99%, respectively.     

Isobaric vapor–liquid equilibria for acetone + methanol + lithium nitrate at 100 kPa

Isobaric vapor–liquid equilibria for the ternary system acetone + methanol + lithium nitrate have been measured at 100 kPa using a recirculating still. The addition of lithium nitrate to the solvent mixture produced an important salting-out effect and the azeotrope tended to disappear for small contents of salt. The experimental data sets were fitted with the electrolyte NRTL model and the parameters of the Mock's model were estimated. These parameters were used to predict the ternary vapor–liquid equilibrium which agreed well with the experimental one.     

Thermodynamic representation of phase equilibrium behavior of aqueous solutions of amino acids by the modified Wilson model

The polymer–electrolyte Wilson model [R. Sadeghi, J. Chem. Thermodyn. 37 (2005) 323–329] which has a molecular thermodynamic framework has been extended to model the vapor–liquid and liquid–solid equilibrium behavior of amino acids and small peptides in aqueous solutions as functions of temperature, ionic strength and amino acid compositions. The utility of the model is demonstrated with a successful representation of the activity coefficients and the solubility of several amino acids in different aqueous solutions and the results are compared with those obtained from the NRTL model.     

Binary vapor–liquid equilibrium of methyl glycolate and ethylene glycol

Vapor pressure of methyl glycolate and the binary isothermal vapor–liquid equilibrium of ethylene glycol and methyl glycolate were measured by using static method. The experimental data was correlated with the Wilson and NRTL activity coefficient models. Good agreement between the experimental data and model is achieved.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

The liquid–gas interface of oxygen–nitrogen solutions 2: Description in the Framework of the van der Waals gradient theory

The van der Waals gradient theory (vdW GT) is used to calculate surface tension, density profiles, adsorption, the Tolman length and to determine the position of dividing surfaces in the liquid–gas interface of an oxygen–nitrogen solution. The Helmholtz energy density (HED) is determined via an equation of state (EOS), unified for a liquid and gas, which describes stable, metastable and two-phase states of solutions. The influence parameters are calculated from data on the surface tension of pure components with the use of the mixing rule. At temperatures T > 100 K the vdW GT describes experimental data on the surface tension of oxygen–nitrogen solutions [V.G. Baidakov, A.M. Kaverin, V.N. Andbaeva, The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension, Fluid Phase Equilib. 270 (2008) 116–120] within the experimental error. It is shown that the Tolman length, which determines the dependence of surface tension on the curvature of the dividing surface, depends considerably on the solution concentration.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Vapor–liquid equilibria and excess properties for methyl tert-butyl ether (MTBE) containing binary systems

Methyl tert-butyl ether (MTBE) is recently widely used in the chemical and petrochemical industry as a non-polluting octane booster for gasoline and as an organic solvent. The isobaric or isothermal vapor–liquid equilibria (VLE) were determined directly for MTBE+C₁–C₄ alcohols. The excess enthalpy (H^E) for butane+MTBE or isobutene+MTBE and excess volume (V^E) for MTBE+C₃–C₄ alcohols were also determined. Besides, the infinite dilute activity coefficient, partial molar excess enthalpies and volumes at infinite dilution (γ^∞, H^E,∞, V^E,∞) were calculated from measured data. Each experimental data were correlated with various g^E models or empirical polynomial.     

Solubility of light hydrocarbons and their mixtures in pure water under high pressure

New solubility data of methane, ethane, n-butane and their mixtures in pure water are obtained at 344.25 K, from 2.5 to 100 MPa. The results agree well with those of the literature in the case of pure hydrocarbons in water, but differ significantly for hydrocarbon mixtures. In contrast to the conclusion reached by Amirijafari and Campbell [B. Amirijafari, J. Campbell, Solubility of gaseous hydrocarbon mixtures in water, Soc. Pet. Eng. J. (1972) 21–27.], the experimental solubility data of methane–ethane mixtures shows an ideal solution behavior, while the solubility data of methane–n-butane mixtures shows a weaker non-ideality than that observed by McKetta and Katz [J.J. McKetta, D.L. Katz, Methane–n-butane–water system in two-and three-phase regions, Ind. Eng. Chem. 40 (1948) 853–863]. The pure hydrocarbon solubility data are satisfactorily correlated using the Soreide and Whitson modification [I. Soreide, C.H. Whitson, Peng–Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine, Fluid Phase Equilib. 77 (1992) 217–240] of the Peng–Robinson equation of state.     

Vapor–liquid equilibria and excess volumes of the binary systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate at 101.325 kPa

Isobaric vapor–liquid equilibrium data have been experimentally determined at 101.3 kPa for the binary systems ethanol + ethyl lactate, isopropanol + isopropyl lactate and n-butanol + n-butyl lactate. No azeotrope was found in any of the systems. All the experimental data reported were thermodynamically consistent according to the point-to-point method of Fredenslund. The activity coefficients were correlated with the NRTL and UNIQUAC liquid-phase equations and the corresponding binary interaction parameters are reported. The densities and derived excess volumes for the three mixtures are also reported at 298.15 K.