Local-composition models and prediction of binary liquid-liquid binodal curves from heats of mixing

The temperature dependence of several local-composition models has been studied in conjunction with the Gibbs-Helmholtz identity. Binary heat-of-mixing data at temperatures near but above the critical solution temperature have been used to fit parameters obtained from excess-free-energy models in conjunction with the Gibbs-Helmholtz equation. These models, if the temperature dependence is adequate, should allow prediction of liquid-liquid equilibria (LLE) from the fitted parameters. The NRTL, UNIQUAC, and modified NRTL and UNIQUAC models (modified by inclusion of temperature-dependent parameters) seldom provide even qualitatively correct LLE predictions. A new local-composition model due to Wang and Chao (1983) yields reasonably good predictions for some systems but incorrect results for others. Reasons for these model inadequacies are discussed in terms of a local-composition model for the excess enthalpy which can be used to predict binodal curves accurately, including reasonably accurate values for the critical solution temperature, if reference excess-free-energy data at higher temperatures are available from VLE maesurements.     

A new density-dependent mixing rule for the SRK equation of state

A new procedure for obtaining density-dependent mixing rules is applied to the Soave-Redlich-Kwong equation of state. The result is a one-parameter local-composition mixing rule which adequately represents the nonidealities possible in dense fluid mixtures but approaches the classical mixing rule at low densities. A three-parameter version of the mixing rule is also presented which allows for the local-composition effect in the low density limit. The expressions are tested with the Soave-Redlich-Kwong equation of state. Results for vapor-liquid and gas-liquid systems are discussed.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.     

Phase equilibria in solvent mixture–ion exchange resin catalyst systems

Phase equilibria for solvent mixtures and strong acidic ion exchange resins in H⁺ form are investigated. Experimental data on ternary non-reactive solvent–solvent–polymer systems as well as reactive multicomponent systems are presented for moderately and highly cross-linked poly(styrene-co-divinylbenzene) (PS-DVB) resins. Esterification of acetic acid with ethanol is used as a model reaction. The data are correlated with a combination of thermodynamic models derived for polymer solutions and gels. Independently determined data is used whenever possible with a goal of reducing cross-correlations between the model parameters. The limitations of the thermodynamic modeling approach for solvent–ion exchange resin systems are discussed. It is shown that, due to glass transition of the polymer matrix, the underlying assumptions are not entirely valid in low dielectric constant media and at high cross-link densities.     

Measurement and correlation of excess molar enthalpies for the partially miscible systems 2-butanone+water and methanol+hexane

The excess molar enthalpies of the systems 2-butanone+water and methanol+hexane which show limited miscibility were measured at 283.15–298.15 K using a flow microcalorimeter. The experimental data were correlated using three local-composition (LC) models (NRTL, modified Wilson and modified EBLCM). These models were also used to predict the liquid–liquid equilibria for both systems with the parameters obtained from the excess enthalpy data.     

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.     

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.     

A new formulation of the predictive NRTL-PR model in terms of kij mixing rules. Extension of the group contributions for the modeling of hydrocarbons in the presence of associating compounds

A generalized NRTL model was previously proposed for the modeling of non ideal systems and was extended to the prediction of phase equilibria under pressure according to the cubic NRTL-PR EoS. In this work, the model is reformulated with a predictive k_ij temperature and composition dependent mixing rule and new interaction parameters are proposed between permanent gases, ethane and nitrogen with hydrocarbons, ethane with water and ethylene glycol. Results obtained for excess enthalpies, liquid-vapor and liquid-liquid equilibria are compared with those provided by the literature models, such as VTPR, PPR78, CPA and SRKm. A wide variety of mixtures formed by very asymmetric compounds, such as hydrocarbons, water and ethylene glycols are considered and special attention is paid to the evolution of k_ij with respect to mole fractions and temperature.     

Thermodynamics of mixtures of amines with n-alkanes and 1-alkanols

The LFAS (Lattice-Fluid Associated Solution) model, which has been applied to alkanol + alkane and to alkanol + alkanol mixtures is now extended to mixtures consisting of one self-associated and one active or weakly self-associated component. The types of association complexes considered are A_nB_m and A_nB with a single A-B bond each. The model is subsequently applied to binary alkanol + amine mixtures with an emphasis on vapor-liquid equilibria. Self-association constants for n-alkyl amines and dialkyl amines are presented along with the pure component lattice-fluid scaling constants. These parameters are used for correlating pure component data on vapor pressures, heats of vaporization, and orthobaric densities as well as mixing properties of amine + alkane mixtures.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Application of association models to mixtures containing alkanolamines

Two association models, the CPA and sPC-SAFT equations of state, are applied to binary mixtures containing alkanolamines and hydrocarbons or water. CPA is applied to mixtures of MEA and DEA, while sPC-SAFT is applied to MEA-n-heptane liquid-liquid equilibria and MEA-water vapor-liquid equilibria. The role of association schemes is investigated in connection with CPA, while for sPC-SAFT emphasis is given on the role of different types of data in the determination of pure compound parameters suitable for mixture calculations. Moreover, the performance of CPA and sPC-SAFT for MEA-containing systems is compared. The investigation showed that vapor pressures and liquid densities were not sufficient for obtaining reliable parameters with either CPA or sPC-SAFT, but that at least one other type of information is needed. LLE data for a binary mixture of the associating component with an inert compound is very useful in the estimation. The simple 4-site scheme is suitable for both CPA and sPC-SAFT and little is gained by using more complex association schemes. Finally, the results of CPA and sPC-SAFT are overall similar and whatever differences are seen appear to be more related to details in the parametrization rather than the different functional forms of the two equations of state.     

Gas solubility calculations. II. Application of a new group-contribution equation of state

A new equation of state has been developed for polar as well as nonpolar components. It is based on the generalized van der Waals partition function and uses local-composition mixing rules. The group-contribution version of this equation of state (the GC-EOS) is described and tables containing parameters for 14 solvent groups and 9 gases (H₂, N₂, CO, O₂, CH₄, C₂H₄, CO₂, C₂H₆ and H₂S) are presented.The GC-EOS predicts vapor-liquid equilibria well for all kinds of systems involving the groups considered. The method requires only information concerning readily accessible pure-component properties. Calculations for multicomponent systems show that the method suggested provides very good predictions of multicomponent high-pressure vapor-liquid equilibria and fairly good predictions of Henry's constants in mixed solvents.     

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.     

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures

Huron, M.-J. and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilibria, 3: 255-271.Good correlations of vapour-liquid equilibria can be achieved by applying the same two-parameter cubic equation of state to both phases. The results primarily depend on the method used for calculating parameters and, for mixtures, on the mixing rule. True parameters are the covolume b and the energy parameter a/b. For this latter one, deviations from a linear weighting rule are closely connected to the excess free energy at infinite pressure. Thus any mixing rule gives a model for the excess free energy, or any accepted models for this property can be used as mixing rules.From the above, an empirical polynomial mixing rule is used for data smoothing and evaluation, while for practical work a local composition model is used. The mixing rule thus obtained can be reduced to the classical quadratic rule for some easily predicted values of the interaction energies. For highly polar systems, it includes three adjustable parameters. Using literature data, the new mixing rule is applied, in the low and high pressure range, to binary mixtures with one or two polar compounds, giving good data correlation and sometimes avoiding false liquid-liquid immiscibility.     

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.     

Thermodynamics of complex formation in chloroform-oxygenated solvent mixtures

Complex formation equilibria in binary mixtures of chloroform with dipropyl ether (PE), diisopropyl ether (IPE), methyl tert-butyl ether (MBE), tetrahydrofuran (THF). 1,4-dioxane (DOX), acetone (AC), and methyl acetate (MA) have been analyzed in detail using several association models. Vapor-liquid equilibria, excess enthalpy and excess heat capacity data for these mixtures have been correlated using a multiproperty global fitting procedure. The thermodynamic properties for chloroform +PE, +IPE, +MBE, +AC, and +MA are best correlated using the ideal association model while for chloroform +THF and +DOX the best model is an athermal solvation model where the Flory-Huggins expression for the species activity coefficients is considered. The model parameters, i.e., the equilibrium constant, enthalpies and heat capacities of complexation, were found to be reliable, well representing the chloroform-oxygenated solvent H-bonded complexes. A detailed discussion is given on the test proposed by McGlashan and Rastogi to decide whether the solution contains only 11 complexes or 21 complexes as well. The complex formation equilibria in chloroform mixtures is compared to those previously examined for halothane (2-bromo-2-chloro-1,1,1-trifluoroethane) mixed with the same oxygenated solvents. It was found that the H-bonds formed by halothane are stronger than those formed by chloroform.     

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.     

Thermodynamics and diffusion in size-symmetric and asymmetric dense electrolytes

MD simulation results for model size-symmetric and asymmetric electrolytes at high densities and temperatures (well outside the liquid-gas coexistence region) are generated and analyzed focusing on thermodynamic and diffusion properties. An extension of the mean spherical approximation for electrolytes originally derived for charged hard sphere fluids is adapted to these systems by exploiting the separation of short range and Coulomb interaction contributions intrinsic to these theoretical models and is found to perform well for predicting equation of state quantities. The diffusion coefficients of these electrolytes can also be reasonably well predicted using entropy scaling ideas suitably adapted to charged systems and mixtures. Thus, this approach may provide an avenue for studying dense electrolytes or complex molecular systems containing charged species at high pressures and temperatures.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.