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Calculation of critical point coordinates of ternary miscibility gap from experimental tie-lines
Abstract
Demixing phenomena in liquid ternary systems are widely used in chemical engineering processes. When a critical point is observed, the composition of this invariant point of major interest is experimentally difficult to determine. A simple calculation method for the critical point is proposed using the experimental tie-lines. The computing treatment is based on the application of the barycentric weighting of the binodal points in order to extend the rectilinear diameter method and the exploitation of the modulus of the experimental tie-lines. A systematic study was carried out on a large set of ternary systems taken from DECHEMA and NIST. The results are compared with those available in literature or calculated by standard methods using binary interaction parameters. Very good agreements are obtained when the experimental tie-lines are located close to the critical point.
The purpose of the present work is to study the effect of adding different mass quantities of a light alcohol (methanol) to dimethyl sulfoxide, in order to extract o-xylene from octane. Experimental liquid–liquid equilibrium data for the quaternary systems {octane + o-xylene + dimethyl sulfoxide + (0.2, 0.4, 0.6, and 0.8) mass fraction of methanol} were determined at T = 298.15 K under atmospheric pressure. For the four quaternary systems, the selectivity and distribution coefficient of o-xylene were applied to assess the efficacy of (dimethyl sulfoxide + mass fraction of methanol) as mixed solvents. The triangular phase diagrams for all studied systems were sketched. The Non Random Two-Liquid activity coefficient model was employed to correlate experimental results and fitting parameters were reported.
The water-phosphoric acid-cyclohexane ternary system was studied at 25 and 35 °C under atmospheric pressure, and the binodal curve was determined by the cloud-point method. In addition, the isoplethic section between 2H3PO4·H2O-cyclohexane was investigated using a Tammann diagram based on the thermal analysis of different samples with the determination of hemihydrate melting temperature. The concentration of phosphoric acid and cyclohexane was assayed by volumetric titration and gas chromatography, respectively; the amount of water was calculated by the material balance equation. The miscibility between phosphoric acid and cyclohexane was found to be very low with the appearance of a three-phase stability domain liquid-liquid-solid by the presence of phosphoric acid crystals: hemihydrate (2H3PO4·H2O) and anhydrous phosphoric acid (H3PO4).
Ternary miscibility data, usually reported in the Roozeboom triangular diagram, have been analyzed in Cartesian coordinates defined by X=(xi-xj)/3 and Y=xk where xi, xj, and xk are the mole fractions of the two solvents and of the solute, respectively. This has allowed for an easy analytical representation of all the elements which are characteristic of the system: binodal curve, tie lines, plait point. Three novel methods for determining the plait point composition have been proposed based only on its fundamental properties. The results have been presented by applying the methods to some systems described in the literature. Differences between the values obtained with the proposed methods and those obtainable with the NRTL and UNIQUAC models have been found and are discussed.
In many cases of miscibility gap in ternary systems, one critical point at least, stable or metastable, can be observed under isobaric and isothermal conditions. The experimental determination of this invariant point is difficult but its knowledge is essential. The authors propose a method for calculating the composition of the invariant solution starting from the composition of the liquid phases in equilibrium. The computing method is based on the barycentric properties of the conjugate solutions (binodal points) and an extension of the straight diameter method. A systematic study was carried out on a large number of ternary systems involving diverse constituents (230 sets ternary systems at various temperatures). Thus the results are presented and analyzed by means of consistency tests.
The formulation of the so-called law of rectilinear diameter for the determination of the critical volume of substances in the concluding decades of the nineteenth century became in a very useful and acceptably exact alternative tool for researchers in the field of critical phenomena. Its corresponding original expression, and even those of its early few modifications, were so mathematically simple that their use did not limit to exclusively contribute to remove the by then experimental obstacle for the estimating of this critical parameter, but also extended along several decades in the increasing applications of the principle of corresponding states.
Isoplethic thermal analysis was used to determine the solid-liquid-liquid equilibria in the ternary system water-sodium sulfate-piperidine. The changes in state observed on the thermogram recorded during the displacement in a quasi-binary section permit the identification of the different phases and the delimitation of the corresponding equilibrium domains. Two isotherms were established at 25°C and 40°C because these temperatures frame the peritectic decomposition of the sodium sulfate decahydrate. Miscibility gaps were completely delimited and each critical point was calculated. This study permitted to determine the optimal conditions for separating the organic phase by liquid-liquid extraction.
There are a great amount of substances found in the must distillations and at very low concentrations (called congeners). Other than that, ethanol and water are the major compounds. These facts make it difficult to simulate and optimize this industrial process. To extend the scarce knowledge of mixing thermodynamics related to these compounds, this paper contains the results of a new experimental study of liquid-liquid equilibrium (LLE) at temperatures of (298.15, 308.15, and 318.15) K for the ternary mixtures ethanol + water + (ethyl acetate or 1-pentanol) under atmospheric conditions. Ethyl acetate and 1-pentanol are important natural and legal congeners in common alcoholic distillation. A comparative analysis was performed by application of different group contribution methods to predict experimental equilibria behavior of these mixtures. The experimental tie line data were correlated to test consistency with the Othmer-Tobias equation. Disposable literature was revised and commented upon.
This article reports the solubilities and equilibrium data of the ternary mixture water + acetic acid + methyl ethyl ketone at 25, 35 and 45°C, and the equilibrium data of the binary system water + methyl ethyl ketone over the range 20–55°C. NRTL and UNIQUAC equations have been fitted to the experimental data for the ternary system, which are also compared with the values predicted by the UNIFAC method.
Mutual solubility and tie-line data are presented for six ternary liquid-liquid systems containing acetone, water, and the esters methyl acetate, ethyl acetate, propyl acetate, amyl acetate, ethyl propionate and ethyl butyrate at 30°C. For comparison, equilibrium data for the system acetone-water-n-butyl acetate reported in literature has been plotted on the mutual solubility, equilibrium distribution and selectivity diagrams. The tie-line data for the six systems have been correlated satisfactorily by the methods of Hand and Othmer and Tobias and the plait points are located by the method of Treybal, Weber and Daley. From the comparative plot of the distribution of acetone between the ester and aqueous layers for the various systems, it is found that acetone favours the ester layer in all the cases. The system, propyl acetate-acetone-water is observed to exhibit solutropy. Among the various esters studied, amyl acetate is observed to be the most selective of all the solvents.
Phase equilibrium data are presented for the ternary liquid systems, namely, acetic acid-water-hexane, ethylene glycol-water-n-butanol, ethylene glycol-water-ethyl methyl ketone, and ethyl methyl ketone-water-cyclohexane. The tie-line data for all the systems have been analysed by the methods of correlation of Othmer & Tobias and Hand, and fitted reasonably with the respective plots. For the system acetic acid-water-hexane, the tie-lines, when produced beyond the binodal curve, meet at a point on the extended base line of the ternary equilibrium diagram and this facilitates the interpolation and extrapolation of the tie-line data. A comparison of the present data for glycol-water systems with the literature data for the corresponding systems containing n-pentanol and n-hexanol respectively as solvents, has confirmed earlier conclusions, namely, that for any solute-water combination, when the solvent is changed in a homologous series in the order of increasing molecular weight, the area of heterogeneity increases, and the solute favours the aqueous phase more and more.
Liquid−liquid equilibria for the acetic acid + water + amyl acetate and acetic acid + water + 2-methyl ethyl acetate ternary systems were measured at (304.15, 332.15, and 366.15) K under atmospheric pressure. The experimental data were correlated with the NRTL model, and its interaction parameters were obtained.
We report liquid−liquid equilibrium data for the quaternary system 1-octanol + 2-methoxy-2-methylpropane (MTBE) + water + methanol at 25 °C. Experiments were performed with mixtures with bulk compositions equivalent to systems of the form {water + methanol + [m1-octanol + (1 − m)MTBE]}, where m = [xoctanol]/[xoctanol + xMTBE] and takes values of 0 (the ternary system water + methanol + MTBE), 0.2, 0.4, 0.6, 0.8, and 1.0 (the ternary system water + methanol + 1-octanol). The quaternary liquid−liquid equilibrium data were correlated by the TK-Wilson, UNIQUAC, and NRTL equations; the UNIQUAC correlation afforded the smallest deviations between experimental and calculated compositions. The quaternary data were satisfactorily predicted by the UNIFAC method.
This study is part of a wider program of research on the recovery of light alcohols from dilute aqueous solutions using high molecular weight solvents. The authors report liquid-liquid equilibrium data and binodal curves for the systems water + methanol + 1-octanol and water + ethanol + 1-octanol at 25, 35, and 45 C. The data were fitted to the NRTL and UNIQUAC equations.
The liquid-liquid and the vapor-liquid phase equilibria of the ternary system 1-butanol + water + 2-propanol have been measured at ambient pressure. Compositions along the binodal curve have been determined gravimetrically at 0, 20, 50, and 60 C. The lines were determined for 0, 20, and 60 C. The data were compared to reported measurements at 80 C. Furthermore, the vapor-liquid equilibrium at ambient pressure has been measured for both one-phase and two-phase liquid mixtures using a recirculation still proposed by Roeck and Sieg.
The enhancement of phase splitting was investigated for the liquid mixtures of water+ethanol+ethyl acetate in the presence of a hydrophilic agent (glycerol) or an electrolyte compound (potassium acetate, KAc, or calcium chloride, CaCl2). The liquid–liquid equilibrium (LLE) properties were measured for ternary systems of water+ethanol+ethyl acetate and water+ethyl acetate+CaCl2, and three quaternary systems, including water+ethanol+ethyl acetate+auxiliary agent (glycerol, potassium acetate, or calcium chloride), at temperatures ranging from 283.15K to 313.15K. The region of heterogeneity was found to increase as one of the auxiliary agents was introduced into the aqueous mixtures. By adding the same percentage of auxiliary agents, the magnitudes of phase-splitting enhancement follow the order of CaCl2>KAc>glycerol. The Electrolyte-NRTL model was used to correlate the new LLE data for the investigated mixtures. In general, the model reproduces reasonably for the LLE phase envelops.
The effect of sodium chloride, calcium chloride and zinc chloride at concentrations 5–20% by weight on the liquid—liquid equilibrium (LLE) data of the ternary system ethyl acetate(S)—methanol(C)—water(A) has been investigated experimentally at 30 °C. The region of heterogeneity is significantly increased with the addition of sodium and calcium chloride salts. A change in the direction of tie-line was observed for 10% sodium chloride, 20% calcium chloride and saturated zinc chloride exhibiting thereby a tendency to form solutropism for this system, which is non-solutropic under a no-salt condition. The selectivity values are also altered in comparison with that of a no-salt condition. The tie-line data have been correlated by the Eisen—Joffe equation. The solubility envelopes for the salt systems have been predicted using the NRTL model, from a knowledge of the binary vapor—liquid equilibria (VLE) determined experimentally in our laboratory employing the iso-activity criterion.
Liquid-liquid equilibrium (LLE) data for the ternary systems 3-methyl-1-butanol + ethanol + water and 2-methyl-1-propanol + ethanol + water were measured at 293.15 K and atmospheric pressure. The NRTL and UNIQUAC models were used to correlate the experimental data. Good agreement was obtained with both models.
(Liquid + liquid) equilibrium data for the quaternary systems (water + 2-propanol + 1-butanol + potassium bromide) and (water + 2-propanol + 1-butanol + magnesium chloride) were measured at T = 313.15 K and T = 353.15 K. The overall salt concentrations were 5 and 10 mass percent. Ternary (liquid + liquid) equilibrium data for the salt-free system (water + 2-propanol + 1-butanol) were also determined and found to be in good agreement with data from the literature. The NRTL model for the activity coefficient was used to correlate the data. New interaction parameters were estimated, using the Simplex minimization method and a concentration-based objective function. The results are very satisfactory, with root mean square deviations between experimental and calculated compositions of both phases being less than 0.5%.
Alcohol flushing is a new in-situ remediation technique for the removal of water-immiscible solvents from contaminated soil and groundwater. Understanding the changes in the physical and chemical properties of chlorinated solvents and the aqueous-phase solution during flushing is prerequisite for the successful application of this technology. The overall objectives of these experiments were to characterize the ternary-phase behavior, interfacial tension, viscosity, and density for mixtures containing a chlorinated solvent, water and alcohol. Two chlorinated solvents were used: tetrachloroethylene and trichloroethylene. The alcohols studied included methanol, ethanol, and propan-2-ol. Results showed that the single-phase region of the ternary relationships increased as the molecular weight of the alcohol increased. The interfacial tension between the chlorinated solvents and aqueous solutions decreased with increasing alcohol concentration and increasing molecular weight of the alcohol. Changes in the viscosity of water + alcohol mixtures due to the addition of the solvents were only evident at high alcohol concentrations. Small changes in density were noted for the chlorinated solvents in equilibrium with water + alcohol solutions except in the case of trichloroethylene and propan-2-ol solutions, which exhibited considerable swelling.
Liquid−liquid equilibria for the ternary systems water + acetic acid + ethyl acetate and water + acetic acid + isophorone (3,5,5-trimethyl-2-cyclohexen-1-one) were measured over the temperature range (283 to 313) K. The results were used to estimate the interaction parameters between each of the three compounds of the systems studied for the NRTL and UNIQUAC models. The estimated interaction parameters were successfully used to predict the equilibrium compositions by the two models; experimental data were successfully reproduced. The UNIQUAC model was the most accurate in correlating the overall equilibrium composition of the studied systems. Also the NRTL model satisfactorily predicted the equilibrium composition. Isophorone experimentally resulted in a better extraction capacity for acetic acid and in a lower miscibility with water.
Liquid−liquid phase equilibrium (LLE) data have been measured for the ternary system 2-butanone + 2-butanol + water at (293.25, 313.15, 323.15, and 333.15) K. Experimental results show the extreme phase sensitivity of this system to temperature. At (293.15 and 313.15) K the ternary system has two separate biphasic regions, while at (323.15 and 333.15) K the system has only one region of immiscibility. The nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) models were applied to correlate the ternary system at (323.15 and 333.15) K; the interaction parameters obtained from both models successfully correlated the equilibrium compositions. Moreover, isobaric vapor−liquid−liquid equilibrium (VLLE) is measured for this ternary mixture at 101.3 kPa. The experimental data were compared with the estimation from LLE binary interaction parameters using NRTL and UNIQUAC models and with the prediction of universal functional activity coefficient (UNIFAC) model.
Calculation of ternary (and higher) liquid-liquid equilibria is based on a model for the excess Gibbs energy using only binary parameters. Since these are not unique, meticulous care must be taken to obtain optimum binary parameters for yielding reliable multicomponent results. In many cases binary data are not sufficient to fix optimum binary parameters; limited ternary tie-line data are often also required. The principle of maximum likelihood provides a convenient data-reduction method for obtaining optimum binary parameters. Using UNIQUAC, illustrative examples are given for a variety of ternary (and higher) systems.
A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two-liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α12 which makes it applicable to a large variety of mixtures. By proper selection of α12, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor-liquid and ternary liquid-liquid equilibria based on binary data alone.
To obtain a semi-theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi-chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi-chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters.
The UNIQUAC equation gives good representation of both vapor-liquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well-defined simplifying assumptions are introduced into the generalized quasi-chemical treatment, the UNIQUAC equation reduces to any one of several well-known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations.
The effects of molecular size and shape are introduced through structural parameters obtained from pure-component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.
Sodium and potassium chloride were experimentally shown to be effective in modifying the liquid–liquid equilibrium (LLE) of water/acetic acid/1-butanol system in favour of the solvent extraction of acetic acid from an aqueous solution with 1-butanol, particularly at high salt concentrations. Both the salts enlarged the area of the two-phase region; decreased the mutual solubilities of water and marginally decreased the concentrations of 1-butanol and acetic acid in the aqueous phase while significantly increased the concentrations of the same components in the organic phase. These effects essentially increased the heterogeneity of the system, which is an important consideration in designing a solvent extraction process. The equilibrium data were well correlated by Eisen–Joffe equation with respect to the overall molar ratio of salt to water in the liquid phases. By expressing the salt–solvent interaction parameters as a third order polynomial of salt concentration in the liquid phase, Tan's modified NRTL model [T.C. Tan, Trans. Inst. Chem. Eng., Part A 68 (1990) 93–103.] for solvent mixtures containing salts or dissolved non-volatile solutes was able to provide good correlation of the present LLE data. Using the regressed salt concentration coefficients for the salt–solvent interaction parameters and the solvent–solvent interaction parameters obtained from the same system without salt, the calculated phase equilibria compared satisfactorily well with the experimental data.
An apparatus has been constructed to measure mutual solubilities and vapor pressures for aqueous—organic liqui—liquid systems in the region of 200°C. Both liquid phases are sampled and analyzed using gas chromatography. Special care must be taken to ensure reliable sampling because mutual solubilities are very small; it is especially important to avoid entrainment, phase change (due to temperature gradients or pressure drop) and adsorption when removing samples for chemical analysis.Experimental results are reported for the temperature range 100–200°C for binary aqueous mixtures containing benzene, toluene, m-xylene and thiophene, and for ternary aqueous mixtures containing benzene and pyridine. The binary results are in good agreement with diverse data reported in the literature.
Letcher T.M. and Siswana P.M., 1992. Liquid-liquid equilibria for mixtures of an alkanol +water+a methyl substituted benzene at 25°C. Fluid Phase Equilibria, 74: 203-217.The tie-line and liquid-liquid equilibrium data are presented for mixtures of an alkanol + water + toluene or mesitylene at 25°C. The alkanols are methanol, ethanol, propanol, 2-propanol, butanol, 2-butanol, 2-methyl-1-propanol and 2-methyl-2-propanol. The tie-lines and liquid-liquid equilibria for the systems 2-propanol + o-xylene or m-xylene + water were also measured. The results are compared with data for related ternary mixtures containing benzene, p-xylene, cyclohexane or hexane. The plait points were determined by both Treybal's method and the Bachman method.
Liquid–liquid equilibrium data for the ternary system 1-pentanol–ethanol–water have been determined experimentally at 25, 50, 85 and 95ºC. These results have been correlated simultaneously by the UNIQUAC method obtaining two sets of interaction parameters: one of them independent of the temperature and the other with a linear dependence. Both sets of parameters fit the experimental results well. The authors wish to thank the Generalitat Valenciana Spain for the financial help of the Project GV-3174r95 and to DGES for the financial aids of project PB96-0338.
Enhancement of liquid phase splitting of water+ethanol+ethyl acetate mixtures in the presence of a hydrophilic agent or an electrolyte 335 substance Liquid-liquid and vapor-liquid-liquid equilibrium of the 2-butanone+2-butanol+water system
- H M Lin
- C E Yeh
- G B Hong
- M J Lee
- E Lladosa
- J B Monton
- J De La Torre
- N F Martinez
Lin, H.M., Yeh, C.E., Hong, G.B., Lee, M.J., 2005. Enhancement of liquid phase splitting of water+ethanol+ethyl acetate mixtures in the presence of a hydrophilic agent or an electrolyte 335 substance. Fluid Phase Equilib. 237, 21. Lladosa, E., Monton, J.B., De la Torre, J., Martinez, N.F., 2011. Liquid-liquid and vapor-liquid-liquid equilibrium of the 2-butanone+2-butanol+water system. J. Chem. Eng. Data. 56, 1755.