Quaternary liquid-liquid equilibria: Experimental determination and correlation of equilibrium data. Part III. New methods of representation and correlation of liquid-liquid equilibria in quaternary systems

Part III of this work describes two new methods of representation and correlation of liquid-liquid equilibria in quaternary systems. These methods are appropiate for the interpolation of new nonexperimental equilibrium data. The methods suggested are applied to the quaternary systems presented in Parts I and II of this series (Ruiz and Prats, 1982a,b).     

Measurement of vapor-liquid equilibria and determination of azeotropic point

Hiaki, T., Tochigi, K. and Kojima, K., 1986. Measurement of vapor—liquid equilibria and determination of azeotropic point. Fluid Phase Equilibria, 26: 83–102.To measure the azeotropic point, a liquid-vapor ebullition type equilibrium still is developed. Vapor-liquid equilibria at 101.325 kPa are measured for the ternary azeotropic system benzene - cyclohexane - n-propanol, and the three constituted binary azeotropic systems. A method is introduced for graphical determination of the binary azeotropic point on the basis of experimental binary vapor-liquid equilibrium data. Also, a method is evolved for determination of the binary and ternary azeotropic points by using the extended Redlich-Kister equation applicable to the condition of constant pressure, and the azeotropic points are determined for three binary and one ternary systems.     

Hybrid method for phase equilibrium flash calculations

Joulia, X., Maggiochi, P., Koehret, B., Paradowski, H. and Bartuel, J.J., 1986. Hybrid method for phase equilibrium flash calculations. Fluid Phase Equilibria, 26: 15–36.A new algorithm for the calculation of a two-phase equilibrium at a given temperature and pressure using various thermodynamic models is described. This algorithm is a combination of two simultaneous solution methods based on a linearization of the system of equations with or without the partial derivatives of equilibrium ratios with respect to composition. This hybrid method exploits the reliability of the first order methods, which make good progress from a poor starting point, and, if necessary, switches on special application of the Schubert method to accelerate the rate of convergence. Results are reported for liquid—liquid and liquid—vapour equilibria with special attention in the vicinity of critical points.     

A study of simplified molecular models in phase equilibrium prediction

Monfort, J.P. and Rojas R., M.D.L., 1978. A study of simplified molecular models in phase equilibrium prediction. Fluid Phase Equilibria, 2: 181–198.The accuracy of three molecular models of solution (Wilson, UNIQUAC and NRTL) is tested for 34 binary systems and 9 ternary systems. The aim of this paper is to attempt some evaluation of these models. Vapor-liquid calculations show a slight superiority of the UNIQUAC equation in the representation of experimental data, while liquid-liquid calculations using a method of determination of binary energetic parameters from mutual solubility data show a better prediction with the NRTL equation.     

Perfluorodecaline/hydrocarbon systems prediction and correlation of liquid—liquid equilibrium data

Bernardo Gil, M.G. and Soares, L.J.S., 1986. Perfluorodecaline/hydrocarbon systems prediction and correlation of liquid—liquid equilibrium data. Fluid Phase Equilibria, 25: 291–302.Experimental binary, ternary and quaternary liquid-liquid equilibrium data for systems containing perfluorodecaline (PFD) and some hydrocarbons were determined.Binary NRTL, UNIQUAC and UNIFAC parameters were obtained, from the binary, the ternary and the quaternary experimental data: for the calculation of parameters from binary data a Newton-Raphson technique was used and the parameters so obtained—for each temperature (T)-were linearly correlated with T and 1/T. Predicted binary, ternary and quaternary data were then compared with the experimental results; a Nelder-Mead method was used for the calculation of the binary parameters from ternary tie-line data.UNIFAC group parameters for the interaction CH₂/CF₂ and CHCH₂/CF₂ were obtained.Attempts were made, and are discussed, to: correlate UNIFAC parameters with the number of carbon atoms and temperature; obtain a set of NRTL and UNIQUAC parameters yielding the overall best fit for the systems under consideration.     

Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method

Vetere, A., 1986. Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method. Fluid Phase Equilibria, 28: 265–281.A thermodynamic method for vapor-liquid equilibria calculations of mixtures containing supercritical components is described. According to the proposed method the Raoult law is assumed as a reference point also for the supercritical gases, and the non-ideality of the liquid phase is represented by using the NRTL equation in the one parameter form.The vapor phase is described by applying the Redlich-Kwong equation. Literature data of 10 binary systems formed by N₂, CH₄, CO₂, H₂S and CH₃OH are correlated by applying the new procedure. The binary interaction parameters calculated for these systems are used for the prevision of one ternary and two quaternary systems formed by the cited gas in methanol, which is an industrial solvent used for the purification of natural streams from the sour gases.Rules are given to describe the dependence on temperature of the binary interaction parameters.     

Improved binary parameters using GA for multi-component aromatic extraction: NRTL model without and with closure equations

Application of genetic algorithm (GA), which leads to globally optimal binary interaction parameters from multi-component liquid–liquid equilibrium data, has been recently demonstrated for some ternary, quaternary and quinary systems. The binary interaction parameters are related to each other through the closure equations. In this work, the binary interaction parameters based on non-random two liquid (NRTL) activity coefficient model have been estimated using GA, without and with closure equations for 65 multi-component aromatic extraction systems: 53 ternary, 9 quaternary and 3 quinary systems. Parameters that satisfy the closure equations exhibit better root mean square deviations than those that do not satisfy the closure equations. Root mean square deviation value without implementation of closure equations is 0–80% better than literature as compared to 0–90% better with implementation of closure equations.     

Quaternary liquid—liquid equilibrium. Cyclohexane—ethanol—benzene—acetonitrile

Nagata, I., 1986. Quaternary liquid—liquid equilibrium. Cyclohexane—ethanol—benzene—acetonitrile. Fluid Phase Equilibria, 26: 59–68.Experimental liquid—liquid equilibrium results are presented for the ternary acetonitrile—ethanol—cyclohexane and the quaternary cyclohexane—ethanol—benzene—acetonitrile systems at 25°C. The results agree well with the calculated values derived from the extended UNIQUAC equation (Nagata) with parameters from phase equilibrium data for the constituent binary mixtures or ternary tie-line data sets.     

(Liquid + liquid) equilibria of methanol + ethylbenzene + isooctane + methy <Emphasis Type="Italic">tert</Emphasis>-butyl ether quaternary system at <Emphasis Type="Italic">T</Emphasis> = 303.15 K

Tie line data of {methanol + methyl tert-butyl ether + isooctane} ternary systems were obtained at T = 303.15 K, while data for {methanol + ethylbenzene + isooctane} were taken from literature. The ternary system {methanol + methyl tert-butyl ether + ethylbenzene} and {methyl tert-butyl ether + ethylbenzene + isooctane} were completely miscible. A quaternary system {methanol + ethylbenzene + isooctane + methyl tert-butyl ether} was also studied at the same temperature. In order to obtain equilibium data of the quaternary system, four quaternary sectional planes with several methyl tert-butyl ether/methanol ratios were studied. The effect of the addition of methyl tert-butyl ether on the liquid-liquid equilibrium data of {methanol + ethylbenzene + isooctane} ternary system has been investigate at the same temperature. The distribution curves for ternary and quaternary system was analysed. For the quaternary system {methanol + ethylbenzene + isooctane + methyl tert-butyl ether}, experimental data demonstrated that the distribution coefficient of ethylbenzene between the hydrocarbon and methanol phase on a methyl tert-butyl ether–free basis slightly increases with the increase of methyl tert-butyl ether/methanol ratio. Ternary experimental results were correlated with the UNIQUAC and NRTL equation. The NRTL equation is more accurate than the UNIQUAC equation for the ternary systems studied here. The equilibrium data of three ternary systems were used for determining interactions parameters for the UNIQUAC equation. The UNIQUAC equation fitted to the experimental data appeared to be more accurate than the UNIFAC method for the same quaternary system.     

A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems

Vejrosta, J., Novák, J. and Jönsson, J.Å., 1982. A method for measuring infinite-dilution partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems. Fluid Phase Equilibria, 8: 25–35.A method has been developed for measuring the partition coefficients of volatile compounds between the gas and liquid phases of aqueous systems, based on the direct analysis of both phases. A gas mixture containing a known proportion of a volatile compound is drawn through the liquid (water) until equilibrium is established. A defined volume of the liquid phase is then withdrawn through a porous-polymer trap while maintaining the system at equilibrium. The residual water in the trap is then expelled by a stream of nitrogen gas, and the deposit remaining is thermally desorbed and analyzed by gas chromatography. This approach, together with an experimental technique for producing gas mixtures containing an accurately known concentration of hydrocarbon at low values, makes it possible to determine accurately the partition coefficients of low-solubility compounds, such as for hydrocarbons in aqueous systems, at very low solute concentrations in the system. The method has been verified by measuring the partition coefficient of hexane between the gas and liquid phases of an aqueous system at various concentrations and temperatures.     

Gibbs energy based procedure for the correlation of type 3 ternary systems including a three-liquid phase region

Equilibrium data for type 3 ternary systems comprising a liquid–liquid–liquid equilibrium region (LLLE tie-triangle) are not frequently correlated, as is evidenced by a lack of studies in the literature. In the present paper, a robust algorithm to calculate or correlate equilibrium data for this type of system is proposed. This algorithm is based on geometric aspects related to the Gibbs energy of mixing (g^M) and possesses some interesting advantages that are discussed in the text. The methodology put forward is applied to correlate the equilibrium data of three type 3 ternary systems. The NRTL model is used to define g^M, and the common tangent plane criterion to define the equilibrium condition for the calculations. The lack in flexibility of the NRTL equation to model these systems is discussed.     

Systems of fluorides and bromides of lithium, sodium, and cesium with mono- and invariant monotectic equilibria

Phase diagram with mono- and invariant equilibrium were studied by differential thermal analysis by the example of a system of fluorides and bromides of group 1 s-block elements (lithium, sodium, and cesium). Bordering elements were studied, the quaternary reciprocal system Li,Na,Cs∥F,Br was partitioned into simplexes, and a tree of phases was constructed. The liquidi of the systems LiF-NaBr-CsBr and LiF-NaF-CsBr were constructed, the T-x diagrams of polythermal sections passing through phase separation regions were built, and phases being in equilibrium under specific thermodynamic conditions were described.     

A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the gibbs energy

Deiters, U.K., 1985. A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the Gibbs energy. Fluid Phase Equilibria, 19: 287-293.For the solution of the system of nonlinear equation describing the phase equilibrium conditions in fluid mixtures a modified Newton-Raphson method is proposed, which uses numerical differentiation to obtain the chemical potentials. For binary mixtures the new algorithm a little faster, because the same intermediate results that are required for the chemical potentials are also used for the construction of the Jacobian matrix.     

Liquid–liquid equilibria for quaternary mixtures of nonane + undecane + (benzene or toluene or m-xylene) + sulfolane at 298.15 and 313.15 K

Liquid–liquid equilibrium (LLE) data were measured for three quaternary systems containing sulfolane, nonane + undecane + benzene + sulfolane, nonane + undecane + toluene + sulfolane and nonane + undecane + m-xylene + sulfolane, at T = 298.15 and 313.15 K and ambient pressure. The experimental quaternary liquid–liquid equilibrium data have been satisfactorily represented by using NRTL and UNIFAC-LLE models for the activity coefficient. The calculated compositions based on the NRTL model were found to in a better agreement with the experiment than those based on the UNIFAC-LLE model.     

Equilibrium in biphasic aqueous systems: A model for the excess gibbs energy and data for the system H2O−NaCl-1-propanol at 25°C

Liquid-liquid equilibrium data were measured for the 1-propanol-NaCl–H₂O system at 25°C. Liquid-liquid equilibrium in aqueous biphasic salt systems containing salts and alcohols or polymers was modelled using an expression for the excess Gibbs energy of the solution. The model is based on modified forms of the nonprimitive Mean Spherical Approximation, the Bromley equation, and the Flory-Huggins theory and requires three and five adjustable parameters for ternary and quaternary systems, respectively. The model accurately correlated binary water-polymer or water-alcohol vapor-liquid equilibrium data and liquidliquid equilibrium data for seven ternary and three quaternary aqueous biphasic salt systems.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Critical evaluation of methane-hydrocarbon high-pressure experimental vapour-liquid equilibrium data using equations of state

Legret, D., Richon, D. and Renon, H., 1984. Critical evaluation of methane-hydrocarbon high-pressure experimental vapour-liquid equilibrium data using equations of state. Fluid Phase Equilibria, 17: 323–350.An evaluation of literature vapour-liquid equilibrium data for methane-hydrocarbon systems is presented, based on the application of cubic equations of state. Lists of interaction parameters and data sets are presented.     

Liquid-liquid equilibrium data for ternary systems containing organic acid,hydrocarbon and water

Alessi, P., Kikic, I., Fermeglia, M. and Nonino, C., 1984. Liquid-liquid equilibrium data for ternary systems containing organic acid, hydrocarbon and water. Fluid Phase Equilibria, 18: 93–102.Experimental LLE data are presented for the acetic acid-toluene-water system at 60, 70 and 80°C and for the acetic acid-heptane-water, propionic acid-toluene-water, propionic acid-heptane-water and butanoic acid-toluene-water systems at 50, 60 and 70°C. The data are correlated by means of the NRTL and UNIQUAC models and the relevant parameters are given. The UNIFAC method is used to predict the behavior of the systems.     

Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures

Lin, H.-M., 1984. Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures. Fluid Phase Equilibria, 16: 151–169.Binary interaction parameters δ_ij in the Peng-Robinson equation of state have been determined from vapor-liquid equilibrium data for binary mixtures of carbon dioxide with a variety of hydrocarbons. A constant value of δ_ij ? 0.125 appears to represent the experimental data well in most cases. Comments are made on the recent work of Kato, Nagahama and Hirata, who correlated δ_ij as a function of temperature for CO₂ + n-paraffin binary mixtures.     

Liquid-liquid equilibria for ternary systems of water-phenol and solvents: data and representation with models

Alvarez Gonzalez, J.R., Macedo, E.A., Soares, M.E. and Medina, A.G., 1986. Liquid-liquid equilibria for ternary systems of water-phenol and solvents: data and representation with models. Fluid Phase Equilibria, 26: 289–302.Liquid-liquid equilibrium data are presented for the systems water-phenol-benzene, water-phenol-ethylbenzene, water-phenol-nonanoic acid, water-phenol-ethyl acetate, water-phenol-isopropyl acetate, water-phenol-n-butyl acetate, water-phenol-isoamyl acetate and water-phenol-cyclohexyl acetate at 25°C and water-phenol-n-hexyl acetate at 25, 35 and 45°C. These systems are of practical interest for solvent extraction studies, as phenol constitutes a valuable raw material in the production of various chemicals and is recoverable from residual waters.The experimental data presented in this paper are correlated in terms of the NRTL and UNIQUAC models and the relevant parameters are presented.     

A new molecular thermodynamic model for multicomponent Ising lattice

A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.