NRTL Equation Research Articles

Measurement and correlation of solubility of abietic acid in ethanol + water mixtures

Using a laser monitoring observation technique, the solubility of abietic acid in (ethanol+water) mixtures was measured by a dynamic method at atmospheric pressure. The solubility of abietic acid increased with an increase of temperature and the concentration of ethanol. Experimental solubility data were correlated by means of the Wilson, NRTL and λh equations utilizing parameters derived from the (solid+liquid) equilibrium (SLE) data. The results showed that the three equations are suitable for description of the solubility data of abietic acid in the (ethanol+water) mixtures investigated.

Phase equilibria study of (ionic liquid + water) binary mixtures

The (solid+liquid) and (liquid+liquid) phase equilibria for 10 (ionic liquid+water) binary mixtures have been determined by a dynamic method at a wide temperature range at atmospheric pressure.The mutual immiscibility with an upper critical solution temperature (UCST) for the binary systems {4-(2-methoxyethyl)-4-methylmorpholinium trifluorotris(perfluoroethyl)phosphate, or 4-(2-methoxyethyl)-4-methylmorpholinium bis(trifluoromethylsulfonyl)imide, or 1-(2-methoxyethyl)-1-methylpiperidinium trifluorotris(perfluoroethyl)phosphate, or 1-(2-methoxy-ethyl)-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide, or 1-(2-methoxyethyl)-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, or 4-(2-methoxyethyl)-4-methylpyrrolidinium trifluorotris(perfluoroethyl)phosphate (1)+water (2)} were detected. Complete miscibility in the liquid phase, over the whole range of ionic liquid mole fraction, was observed for the binary mixtures containing: 1-butyl-1-methylpiperidinium dicyanamide, or 1-butyl-1-methylpyrrolidinium dicyanamide, or 1-butyl-4-methylpyridinium dicyanamide, or 1-butyl-4-methylpyridinium thiocyanate.For the tested binary systems with immiscibility gap the parameters of the LLE correlation have been derived using the NRTL equation. The (solid+liquid) phase equilibria have been correlated by means of NRTL, UNIQUAC and Wilson equations and compared to the literature data for different ionic liquids. The influence of the ionic liquid structure on water solubility was discussed.

Liquid–liquid equilibria for the ternary system (water + tetradecane + 1-methyl-2-propoxyethoxy-2-propanol)

Fish-shaped phase diagram at a fixed water/tetradecane mass ratio (1/1) and three triangle phase diagrams at T=(298.15, 308.15, and 318.15)K of the ternary (water+tetradecane+1-methyl-2-propoxyethoxy-2-propanol) were performed under atmospheric pressure. The upper and lower critical solution temperatures of the system were (300.90 and 280.00)K, respectively, according to the fish-shaped phase diagram. The experimental results of the ternary system were satisfactorily correlated by the NRTL equation.

Isobars of the boiling temperature and isotherms of excess thermodynamic functions of isobutanol-alkyl ketone solutions

The boiling temperatures for solutions of five binary systems are measured via ebulliometry in the pressure range of 5.333–101.3 kPa. The isotherms constructed for the pressure of saturated vapor serve as the base for computing the compositions of equilibrium vapor phases of the systems. The excess Gibbs energies, enthalpies, and entropies of solutions are computed from the data on liquid-vapor equilibrium. The laws of changes in the phase equilibria and thermodynamic properties of solutions are determined depending on the composition and temperature of the systems. The vapor-liquid equilibrium of the systems is described by Wilson and NRTL equations.

Solvent extraction of aromatic sulfur compounds from n-heptane using the 1-ethyl-3-methylimidazolium tricyanomethanide ionic liquid

The ionic liquid 1-ethyl-3-methylimidazolium tricyanomethanide ([EMIM][TCM]) has been tested as a solvent for the separation of sulfur compounds from aliphatic hydrocarbon. Liquid–liquid phase equilibrium data have been determined for ternary systems containing the ionic liquid, thiophene or benzothiophene and n-heptane. The influence of temperature on the separation of thiophene from n-heptane was determined. High solubility of sulfur compounds and practical immiscibility of aliphatic hydrocarbon in ionic liquid have been found. The values of selectivity and solute distribution ratios have been calculated for all systems and compared with literature data for other 1-ethyl-3-methylimidazolium-based ionic liquids. High values of selectivity were obtained. The experimental data were correlated using the NRTL equation, and the binary interaction parameters have been reported. The phase equilibria diagrams for the ternary mixtures including the experimental and calculated tie-lines have been presented.

Correlation of Viscosity of Aqueous Solutions of Alkanolamine Mixtures Based on the Eyring's Theory and Wong-Sandler Mixing Rule

A viscosity model, based on Eyring's absolute rate theory combined with a cubic PR equation of state and Wong-Sandler mixing rule, has been proposed in order to correlate viscosities of aqueous solutions of alkanolamine mixtures at atmospheric pressure and different temperatures. In the proposed method, the energy and size parameters in studied Equation of State (EoS) have been obtained using the Wong - Sandler (WS) mixing rule combined with the NRTL and Wilson Gibbs equations. The NRTL and Wilson parameters for aqueous solutions of alkanolamine mixtures have been correlated using measured viscosity data at atmospheric pressure and different temperatures. The overall average deviation between the experimental and calculated viscosities of studied aqueous solutions of alkanolamine mixtures using Wilson model is 0.92%.

Experimental Measurements of Vapor–Liquid Equilibrium Data for the Binary Systems of Methanol + 2-Butyl Acetate, 2-Butyl Alcohol + 2-Butyl Acetate, and Methyl Acetate + 2-Butyl Acetate at 101.33 kPa

The isobaric vapor–liquid equilibrium measurements for the systems of 2-butyl acetate with three chemicals (methanol, 2-butyl alcohol, methyl acetate) were determined respectively in a modified Rose still at 101.33 kPa. Thermodynamic consistency of the three binary vapor–liquid equilibrium data had been confirmed by Herington methods. The three groups of experimental data were all correlated with NRTL and Wilson models, respectively. The binary interaction parameters of both models had been obtained by the simplex method. The NRTL and Wilson equations showed low deviation with respect to the experimental data.

Solubility of Atrazine in Binary Mixtures of Water + Ethanol or 1-Propanol from 283.15 to 343.15 K

The solubility of atrazine (solid) was measured in water + ethanol and water + propanol from 283.15 to 343.15 K. The experimental results showed that in ethanol + water and 1-propanol + water the solubility of atrazine increased slowly with temperature below 308.15 K but increased significantly above 308.15 K. It was also found that the slope of the solubility–temperature curve increases significantly with an increase in the mole fraction of organic solvent in the mixtures. The modified Apelblat and NRTL equations were applied to describe the measured systems. The model parameters of the NRTL equation were expressed as a function of temperature.

(Liquid + liquid) equilibria for benzene + cyclohexane + N,N-dimethylformamide + sodium thiocyanate

(Liquid+liquid) equilibrium (LLE) data for benzene+cyclohexane+N,N-dimethylformamide (DMF) + sodium thiocyanate (NaSCN) were measured experimentally at atmospheric pressure and 303.15K. The selectivity coefficients from these LLE data were calculated and compared to those previously reported in the literature for the systems (benzene+cyclohexane+DMF) and (benzene+cyclohexane+DMF+KSCN). The NRTL equation was used to correlate the experimental data. The agreement between the predicted and experimental results was good. It was found that the selectivity coefficients of DMF+NaSCN for benzene ranged from 2.45 to 11.99. Considering the relatively high extraction capacity and selectivity for benzene, DMF+NaSCN may be used as a potential extracting solvent for the separation of benzene from cyclohexane.

Phase equilibria study of the (N-octylisoquinolinium thiocyanate ionic liquid + aliphatic and aromatic hydrocarbon, or thiophene) binary systems

Binary liquid+liquid phase equilibria for 8 systems containing N-octylisoquinolinium thiocyanate, [C8iQuin][SCN] and aliphatic hydrocarbon (n-hexane, n-heptane), cyclohexane, aromatic hydrocarbon (benzene, toluene, ethylbenzene, n-propylbenzene) and thiophene have been determined using dynamic method. The experiment was carried out from room temperature to the boiling-point of the solvent at atmospheric pressure. For the tested binary systems the mutual immiscibility with an upper critical solution temperature (UCST) for {IL+aliphatic hydrocarbon, or thiophene} were observed. The immiscibility gap with lower critical solution temperature (LCST) for the {IL+aromatic hydrocarbon} were determined. The parameters of the LLE correlation equation for the tested binary systems have been derived using NRTL equation. The phase equilibria diagrams presented in this paper are compared with literature data for the corresponding ionic liquids with N-alkylisoquinolinium, or N-alkylquinolinium cation and with thiocyanate – based ionic liquids. The influence of the ionic liquid structure on mutual solubility with aliphatic and aromatic hydrocarbons and thiophene is discussed.

Reactive vacancy solution theory for correlation and prediction of adsorption equilibria for physical and chemical adsorptions

An isotherm equation was developed in the framework of the vacancy solution theory. In the model, vacancies in the adsorbed phase are dealt with as a kind of reactive entity, which leads to more flexible adsorption isotherm equations. The model can be called as reactive vacancy solution theory (RVST). Practical RVST equations for single-component and binary-component adsorption systems were derived by using Wilson, NRTL and UNIQUAC equations for activity coefficients. The RVST equations were found to coincide with the Langmuir–Freundlich equation when the effect of activity coefficients is assumed to be negligible. Furthermore, it was also found that the RVST model conforms to several simple-theoretical or empirical isotherm equations when the model is simplified. Therefore, it can be stated that the reactive vacancy solution theory can be regarded as more universal and general mathematical description of adsorption equilibria. Validity of the RVST equations for single-component adsorption was tested. The results reveal that the RVST-W and RVST-N equations can appropriately correlate non-ideal adsorption equilibrium data.

Effect of Ionic Liquids on the Isobaric Vapor–Liquid Equilibrium Behavior of Methanol–Methyl Ethyl Ketone

Isobaric vapor–liquid equilibrium (VLE) data for methanol–methyl ethyl ketone (MEK) systems containing ionic liquids (ILs) have been measured with a modified Othmer still at atmospheric pressure (101.32 kPa), and they were correlated by the NRTL equation. Three ILs, composed of an anion tetrafluoroborate ([BF4]−) and a cation from 1-ethyl-3-methylimidazolium ([EMIM]+), over 1-butyl-3-methylimidazolium ([BMIM]+), to 1-octyl-3-methylimidazolium ([OMIM]+), were investigated, and they all gave rise to a change of the relative volatility of methanol to MEK. The results indicated that, among the three ILs studied, [BMIM]+[BF4]− and [OMIM]+[BF4]− eliminated the azeotropic point at mole fraction 30 % and 10 %, respectively, whereas IL [EMIM]+[BF4]− pulled down the azeotropic point. The influence of the variation of the cation’s alkyl chain length of imidazolium tetrafluoroborate-based ILs on VLE of the azeotropic system methanol–MEK was discussed.

Ternary Liquid–Liquid Equilibrium of Biodiesel Compounds for Systems Consisting of a Methyl Ester + Glycerin + Water

Ternary LLE data have been experimentally measured for several systems consisting of biodiesel compounds. Systems measured include mixtures with the methyl esters of lauric, myristic, palmitic, and oleic acids, each with glycerin and water. Data were collected at atmospheric pressure and 60 °C. These ternary systems have been correlated using the NRTL equation. These data and correlation parameters can be used to improve separations efficiency in transesterified biodiesel fuels.

Phase behaviour of ionic liquid 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate with alcohols, water and aromatic hydrocarbons

The phase diagrams for the binary systems of {1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate ([BMPYR][FAP])+an alcohol (1-butanol, 1-hexanol, 1-octanol, 1-decanol, 1-dodecanol), or+water, or+aromatic hydrocarbons (benzene, toluene, ethylbenzene, propylbenzene, or thiophene)} have been determined at atmospheric pressure using a dynamic method. The influence of an alcohol chain length on the liquid–liquid equilibrium diagrams was discussed. A systematic decrease in the solubility was observed with an increase of the alkyl chain length of an alcohol and of the substituent on aromatic ring. The correlation of the experimental data has been carried out using the NRTL equation. The influence of the cation and anion on the phase behaviour has been discussed. The phase diagrams reported here have been compared to the systems published earlier with the 1-butyl-1-methylpyrrolidinium, or tris(pentafluoroethyl)trifluorophosphate-based ionic liquids.

Vapour–liquid equilibria in binary and ternary systems composed of 2,3-dimethylbutane, diisopropyl ether, and 3-methyl-2-butanone at 313.15, 323.15 and 313.15 K

This article reports vapour–liquid equilibrium data in three binary systems, namely 2,3-dimethylbutane+diisopropyl ether, 2,3-dimethylbutane+3-methyl-2-butanone, and diisopropyl ether+3-methyl-2-butanone and in one ternary system, 2,3-dimethylbutane+diisopropyl ether+3-methyl-2-butanone. The data were measured isothermally at 313.15, 323.15, and 333.15K covering the pressure range of 13–108kPa. The binary vapour–liquid equilibrium data were correlated using the Wilson and NRTL equations by means of a robust algorithm for processing all isotherms together. The resulting parameters were then used to calculate phase behaviour in the ternary system and to comparison the calculated with experimental data.

Study of (Solid–Liquid) Phase Equilibria for Mixtures of Energetic Material Stabilizers and Prediction for Their Subsequent Performance

Solid-liquid equilibria for three binary mixtures of 2-nitrodiphenylamine (1) + diphenylamine (2), ethyl centralite (1) + N-ethyl-4-nitro-N-nitrosoaniline (2), and 2,2\(^{\prime }\)-dinitrodiphenylamine (1) + N-ethyl-4-nitro-N-nitrosoaniline (2) were measured using a differential scanning calorimeter. Simple eutectic behaviors for these systems were observed. The experimental results were correlated by means of original and modified NRTL, Wilson, and UNIQUAC equations. The root–mean–square deviations of the solubility temperatures for all measured data vary from 0.63 K to 3.73 K and depend on the particular model used. The best solubility correlation was obtained with the UNIQUAC model.

Solid–liquid phase equilibrium study of n-octadecane + lauryl alcohol binary mixtures

Differential scanning calorimetry (DSC) is used to investigate the thermal properties of n-octadecane and lauryl alcohol and their binary system. The experimental results show that the phase diagram of the n-octadecane+lauryl alcohol binary system presents a eutectic behavior for the solid–liquid equilibrium line, and the corresponding mole fraction of n-octadecane in eutectic point is 0.257. The eutectic melting temperature (TE) is 292K, and the latent heat of melting of eutectic mixture (△fusHE) is 245J·g−1. Furthermore, the activity coefficients of components in mixtures of n-octadecane+lauryl alcohol have been correlated by the Wilson, NRTL and UNIQUAC models, respectively. The best correlation of the solid–liquid equilibrium data has been obtained by the NRTL equation, in which the average root-mean-square deviation of temperature is 0.15K.

Investigation on vapor–liquid equilibrium for 2-propanol + 1-butanol + 1-pentanol at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) data for 2-propanol+1-butanol, 2-propanol+1-pentanol, 1-butanol+1-pentanol and 2-propanol+1-butanol+1-pentanol were measured at 101.3kPa by using an improved Rose still. All the binary VLE data have passed the traditional area test proposed by Herington. The interaction parameters for the Wilson, NRTL and UNIQUAC equations were determined by regressing the binary VLE data. The prediction for ternary system was given by using the three pairs of binary parameters correlated. And the ternary data predicted agreed well with the experiment data.

Experimental determination of liquid-liquid equilibrium data and their representation using the UNIQUAC and NRTL equations

Knowledge of physical and chemical data is essential in process engineering, including the fluid phase equilibria, important phenomena for the design and simulation of many separation processes such as distillation and liquidliquid extraction. One important information concerns the phase diagram. Many researches [1-4] have investigated multicomponent systems in order to understand and provide further information about the thermodynamic properties of such systems and representation of phase equilibria. In this study an apparatus has been specially developed and implemented, it is based on a « staticanalytic » method (similar to the one of Laugier and Richon [5]) with two liquids phase samplers in order to determine experimental « liquid – liquid » equilibrium data [6] ; mixtures of known overall composition were prepared directly inside the equilibrium cell. The analytical work was carried out using a Perichrom (France) gas chromatograph equipped with a thermal conductivity detector (TCD) connected to a data acquisition system. The need to acquire good « liquid – liquid » equilibrium data is important, but it is also essential to be able to represent accurately using appropriate models and thus be able to calculate the phase equilibria in all conditions of use, for this the Simulis software from Prosim (Toulouse, France) is used with the NRTL [7] (Non Random Two Liquids) and UNIQUAC [8] (Universal Quasi Chemical) activity coefficient models to correlate the experimental data In this study the results for the systems (water1propanol1-pentanol) and (waterethanol1-pentanol) were considered. The reliability of the experimental data obtained was successfully verified by applying the Othmer-Tobias [9], Bachman [10] and Hand [11] correlations.

Liquid–Liquid Equilibria of the Methanol + Ethylbenzene + Methylcyclohexane Ternary System at 278.15, 283.15, and 293.15 K

Liquid–liquid equilibria of the methanol + ethylbenzene + methylcyclohexane ternary system are reported at 278.15, 283.15, and 293.15 K. The effect of the temperature on the liquid–liquid equilibrium is discussed. All chemical concentrations were quantified by gas chromatography using a thermal conductivity detector. Experimental data for the ternary system are compared with values calculated by the NRTL and UNIQUAC equations. It was found that both equations gave comparable quality representations of the experimental data for this ternary system. Distribution curves were also analyzed. Data for the ternary system is available from the literature at 303.15 K.