NRTL Equation Research Articles

Liquid-Liquid equilibrium Behavior and intermolecular interactions of Levulinic acid and water with isopropyl ether and methyl Tert-Butyl ether

Levulinic acid (LA) is a crucial bio-based chemical with extensive industrial applications. Due to its significant share in the cost of production, the development of efficient techniques for the separation of LA is essential. Traditional separation using sulphuric acid raises environmental and cost concerns, making liquid–liquid extraction a more sustainable and cost-effective alternative. liquid–liquid equilibrium (LLE) investigation was carried out for two ternary mixtures of water + LA + isopropyl ether / methyl tert-butyl ether (MTBE) at two temperatures and 101.3 kPa. The results indicated that the solvent MTBE, as an extractant, showed a higher partition coefficient and selectivity for LA than isopropyl ether, demonstrating its superior effectiveness in recovering LA. The interaction insights between LA and the extractants were explored using quantum chemistry calculations, which aligned well with the collected results. The ascertained LLE data was modeled using the NRTL equation, achieving the RMSD values below 0.01, demonstrating a good concordance between the collected data and computed values. The fitted NRTL model parameters are conducive to the designing and optimizing the LA separation process.

Excess Enthalpies Analysis of Biofuel Components: Sunflower Oil-Alcohols Systems.

This study addresses the pressing issues of energy production and consumption, in line with global sustainable development goals. Focusing on the potential of alcohols as "green" alternatives to traditional fossil fuels, especially in biofuel applications, we investigate the thermochemical properties of three alcohols (n-propanol, n-butanol, n-pentanol) blended with sunflower oil. The calorimetric analysis allows for the experimental determination of excess enthalpies in pseudo-binary mixtures at 303.15 K, revealing similarities in the trends of the curves (dependence on concentrations) but with different values for the excess enthalpies for each mixture. Despite the structural differences of the alcohols studied, the molar excess enthalpy values exhibit uniformity, suggesting consistent mixing behavior. The peak values of excess enthalpies for systems with sunflower oil and n-propanol, n-butanol and n-pentanol are, respectively, 3255.2 J/mole, 3297.4 J/mole and 3150.1 J/mole. Both the NRTL and Redlich-Kister equations show satisfactory agreement with the obtained values.

Investigation on the solvent and temperature effect of climbazole solubility

The thermodynamic behavior of objective compounds plays an important role in crystallization and purification. In this work, the solubility of climbazole in nine pure solvents at (288.15–318.15 K) and in a water–ethanol mixed solution at (278.15–313.15 K) was determined by a gravimetric method. It was found that the solubility is positively related to temperature and ethanol content. Three well-known thermodynamic models (modified Apelblat equation, NRTL equation, λh equation) were used to correlate the experimental data, and the modified Apelblat equation showed better correlation results. Meanwhile, the thermodynamic properties of climbazole in selected solvents were investigated, and it was found that the dissolution process of climbazole is spontaneous, endothermic and entropy driven. Furthermore, the solvent effect was evaluated and discussed by Kamlet and Taft linear solvation energy relationship model (KAT-LSER) and Hansen solubility parameters (HSPs). The solvent–solvent interactions and the nonspecific dipolarity/polarizability interactions have a great influence on solubility. Additionally, the molecular surface characteristics and intermolecular interactions were studied by molecular simulation to reveal the molecular mechanism behind the solubility behavior of climbazole.

Vapor-Liquid Equilibrium in the Acetic Acid-Ethanol-Ethyl Acetate-Water Quaternary System: Critical Literature Review and Thermodynamic Consistency of the Experimental Data

This study presents a critical review of the experimental vapor-liquid equilibrium (VLE) data for the quaternary acetic acid-ethanol-ethyl acetate-water system and its subsystems that are reported in the literature. The thermodynamic consistency of the VLE data were verified using two integral tests: the Redlich–Kister test and the direct integration of the Gibbs–Duhem equation. The VLE data were correlated using the NRTL equation for further integration. Additionally, the reliable value of the integral derived from the direct integration of the Gibbs–Duhem equation for multicomponent systems under isothermal-isobaric conditions was estimated. This integral can be used for testing the thermodynamic consistency of experimental VLE data.

Liquid-Liquid Equilibria for Ternary Systems Citronellal + Ethanol + Water and Citronellol + Ethanol + Water at 303.15 and 323.15 K

The liquid-liquid equilibria (LLE) for the ternary systems citronellal + ethanol + water and citronellol + ethanol + water are reported. The LLE of the systems have been measured at 303.15 and 323.15 K under atmospheric pressure as a reference for citronella oil production using solvent extraction method. The experimental data obtained were correlated using NRTL and UNIQUAC equations. The non-randomness parameter (αij) of the NRTL model is 0.2-0.47 and fits the experimental data satisfactorily. Both the NRTL and UNIQUAC models gave relatively good results for the systems investigated with the average Root Mean Square Deviation (RMSD) are 0.92% and 0.85% respectively. Based on the ternary diagram obtained in this work, it was found that the system followed the type I classification by Treybal [19]. The binary interaction parameters generated in this study can also be used for LLE calculation in the design of extraction columns.

A study on the vapor–liquid equilibria of vinyl acrylate-acetic acid and vinyl acetate-acetic acid with GEMC method

Vinyl acetate (VAc) is one of the widely utilized industrial organic raw materials. In the acetoxylation of ethylene to vinyl acetate, there is a by-product vinyl acrylate. However, the vapor–liquid phase equilibrium data of this component with acetic acid and vinyl acetate have not been reported. Here, by Density Functional Theory calculations, we fitted the TraPPE-UA force field parameters of vinyl acrylate. The vapor–liquid phase equilibrium data of the vinyl acrylate-acetate and vinyl acrylate-vinyl acetate binary systems were calculated using the Gibbs Ensemble Monte Carlo (GEMC) method. The calculated phase equilibrium data were utilized to fit the binary interaction parameters of the NRTL equations for the binary systems which were used for the separation process simulation of the vinyl acrylate, acetic acid and vinyl acetate systems. It was verified that the TraPPE-UA force field parameters fitted in this paper have high accuracy. The results clarify the concentration distribution of vinyl acrylate gas–liquid phase components in the distillation column, which builds the foundation for the development of the separation process.

VLE measurement of binary systems 1-butyl-3-methylimidazolium-based ionic liquids and ethanol or water

Experimental vapor–liquid equilibrium (VLE) data for binary systems of ethanol or water with four ionic liquids (ILs) comprising 1-butyl-3-methylimidazolium cation and different anions were measured at atmospheric pressure within a broad region of IL concentrations, IL mole fraction ranging between 0 and 0.7 or even 0.87. Siwoloboff procedure of vapor–liquid phase transition temperature measurement was applied to estimate VLE of the binary mixtures. Obtained t–x data were fitted assuming ideal vapor and non-ideal liquid phase behavior, using the original NRTL equation to calculate component activity coefficients. VLE description results are presented in form of equilibrium diagrams and as the variation of activity coefficients with mixture composition. Quality of the VLE data fitting was assessed based on root mean square deviations and mean deviations in temperature. Some experimental binary t–x data sets were compared to those available in literature (measured in much narrower concentration range) or predicted from ternary VLE data. The selection of ILs in this study was related to the separation of ethanol−water mixture by extractive distillation. Principal IL selection criterium was its ability to affect the ethanol–water relative volatility. Thermodynamic description of the VLE data of IL-containing systems within a wide concentration range is an essential building block of the mathematical model of separation devices, especially in case of regeneration equipment where concentrated IL is present.

Solubility and thermodynamic parameters of nicotinic acid in different solvents

Nicotinic acid is an important compound needed for the body to keep proper functioning and stay healthy. The determination of solubility parameters in different solvents can be useful for operations such as crystallization or encapsulation of nicotinic acid. In this study, we critically evaluated the solubility of nicotinic acid in nine solvents: water, methanol, ethanol, propanol, propan-2ol, butanol, acetone, ethyl acetone and dimethyl sulfoxide (DMSO). Solubility data are provided as mole fractions of solvent versus temperature. Results showed that DMSO afforded the highest nicotinic acid solubility, greater than the ideal solubility values. Thermodynamic parameters such as the activity coefficient, melting temperature and enthalpy of fusion were determined by differential scanning calorimetry. Non-predictive activity coefficient models were obtained to represent the experimental data through Margules, van Laar, Wilson, NRTL, and UNIQUAC equations. The van Laar, Wilson, and NRTL models showed broadly similar performance. The UNIQUAC model showed an optimum performance for six of the nine solvents.

Extraction of methylcyclohexane−toluene mixture using imidazolium ionic liquids

Separation of aromatics from non-aromatic hydrocarbons was exemplified assuming the liquid-phase extraction process for methylcyclohexane−toluene model mixture separation using the newly tested 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMim][NTf2]) ionic liquid (IL). For this process a separation unit was proposed consisting of separation part represented by a counter-current extraction column and regeneration part including a vacuum evaporator and a vacuum distillation column. Separation of feed composed of 10 mole% of toluene in methylcyclohexane was considered in the designed separation unit. Designed separation efficiency of the unit was based on the following specifications: minimum methylcyclohexane and toluene content in the product streams of 99.5 mole% and the purity of regenerated extraction solvent recycled to the extraction column above 99 mole%.Mathematical model of a counter-current extractor was compiled and its operation was simulated in the Matlab environment. In extractor simulations, proprietary phase equilibrium data were employed. Ternary liquid–liquid equilibrium (LLE) of the methylcyclohexane−toluene−[EMim][NTf2] system was estimated experimentally, from which the model parameters of the original NRTL equation were evauated and used for the ternary phase equilibrium description.Aspen Plus was used to design a separation unit for the title hydrocarbons mixture separation, including the extraction solvent regeneration. Simulation of the proposed separation unit operation was focused not only on its separation efficiency but also on the evaluation of the unit energetic requirements.Results of the unit design calculations (parameters of individual equipment, heat duties) obtained for the tested ionic liquid [EMim][NTf2] were confronted with the simulation results obtained for two ILs recommended in the literature for the non-aromatic–aromatic hydrocarbon mixture separation, namely 1‑butyl‑3-methylimidazolium tetracyanoborate [BMim][TCB] and 1-hexyl-3-methylimidazolium tetracyanoborate [HMim][TCB]. Based on the energetic analysis, the heat integration of the suggested separation unit was carried out for ionic liquid [HMim][TCB], which appeared to be the most efficient extraction solvent among those tested in this study, The heat integration resulted in about 71% reduction of the heat demand of the proposed separation unit.

Vapor-liquid equilibrium for dimethyl ether and three imidazolium ionic liquids as working pairs in absorption-refrigeration cycle

To overcome the shortcomings of traditional working pairs of H2O/LiBr and NH3/H2O, the combination of dimethyl ether (DME) and ionic liquids (ILs) have been studied recently. The solubilities of DME in [HMIM][BF4], [HMIM][PF6] and [HMIM][Tf2N] were firstly measured and correlated using NRTL equation. The thermodynamic performance of absorption refrigeration system (ARS) using those working pairs are compared with R152a/[HMIM][Tf2N], R1234ze(E)/[HMIM][Tf2N] and other DME/IL pairs which include [BMIM][BF4], [BMIM][PF6] and [BMIM][Tf2N]. Under the studied condition Tg/Ta/Tc/Te = 325–370 K/300 K/300 K/278 K, the maximum COPs of DME/[HMIM][Tf2N], DME/[BMIM][PF6] and R152a/[HMIM][Tf2N] in ARS are 0.592, 0.531 and 0.648, respectively, while that of R1234ze(E)/[HMIM][Tf2N] is only 0.345. DME/[BMIM][PF6] performs best at Tg = 350 K, but at Tg = 340 K, DME/[HMIM][Tf2N] shows better performance. The difference of optimal Tg between them is about 10 K. It shows that ARS of using DME/[HMIM][Tf2N] can utilize lower-grade waste heat. Our studies prove that DME/ILs are good choices to balance the environmental protection property and energy efficiency improve.

Solubility, Correlation, Dissolution Properties, and Molecular Simulations of an Explosive Intermediate in Twelve Pure Solvents

The solubility and thermodynamic properties of N-nitropyrazole (N-NP) in different pure solvents are crucial for crystallization, purification, and further theoretical research. The solid–liquid equilibrium solubility of N-NP in the range of 293.15–323.15 K was determined in 12 pure solvents of water, mesitylene, n-hexane, cyclohexane, ethanol, chlorobenzene, benzonitrile, propylene glycol, anisole, dimethyl sulfoxide, N,N-dimethylformamide, and o-dichlorobenzene by the laser dynamic method at an atmospheric pressure of 0.1 MPa. In the temperature range of 293.15–323.15 K, the solubility of N-NP in water, mesitylene, n-hexane, cyclohexane, ethanol, chlorobenzene, benzonitrile, propylene glycol, anisole, dimethyl sulfoxide, N,N-dimethylformamide, and o-dichlorobenzene displayed the mole fraction solubility of 0.001271–0.003540, 0.033858–0.139782, 0.001966–0.009268, 0.002621–0.013898, 0.013601–0.058669, 0.097849–0.310726, 0.170722–0.387823, 0.017647–0.065427, 0.069507–0.379656, 0.225911–0.457260, 0.210072–0.415353, and 0.017651–0.172345, respectively. The measured solubility data of N-NP had a good correlation with the modified Apelblat equation, the NRTL equation, the Wilson equation, as well as the λh equation. Through the comparison of the minor average of the root-mean-square deviation (103RMSD) and the coefficient of determination (R2), the Wilson equation yielded a more satisfactory correlation result. Thermodynamic parameters of mixing enthalpy (ΔmixH), mixing entropy (ΔmixS), and mixing Gibbs energy (ΔmixG) were calculated and analyzed based on the experimental data. The positive ΔmixH and ΔmixS implied that the dissolution process of N-NP in the selected solvents was endothermic and entropy-driven. The relative contributions of enthalpy and entropy demonstrated that enthalpy was the main contributor to the Gibbs free energy in the dissolution process. In addition, the solute–solvent interaction was calculated to elaborate the solubility of N-NP in selected solvents deeply. In addition, the solid–liquid surface tension and the surface entropy factor of N-NP were discussed on the basis of the experimental solubility data.

Heterogeneous phase diagram and residue curve map for ethanol-water-ethyl acetate and ethanol-water-ethyl acrylate system

Heterogeneous phase diagram and residue curve map data are simulated using NRTL equation which are useful for design of heterogeneous Azeotropic distillation column. Simulated data are compared with experimental data.

Modeling on the phase equilibrium of gas hydrate in electrolytes containing system

The phase equilibrium of gas hydrate is fundamental for flow assurance, energy exploitation, and hydrate concerning technique. In this study, the electrolyte NRTL equation coupled with the two-step hydrate model of Chen and Guo was successfully applied to predict the phase equilibrium of gas hydrate in the presence of single and binary mixed electrolytes. The predicted results were in good agreement with the available experimental data over a wide range of electrolyte concentrations when taking into account the contributions of long-range and short-range interactions in saline solution. Validated with 943 hydrate experimental data of pure gas and gas mixture formed in single and mixed electrolytes, the average absolute deviations in pressure are 5.42 % and 4.71 %, respectively. More importantly, it is further investigated that the proposed model shows a better performance for the high-concentration saline solution with concentration up to the near-saturation, with an average deviation of 0.59 K for methane hydrate. Therefore, the proposed model in this work is significant for comprehending gas hydrate phase behavior in saline solution, and provides better guidance for hydrate exploitation and industrial applications.

Solubility measurement, thermodynamic modeling and solubility parameters of Clarithromycin（form ӀӀ）in aqueous ethanolic solution

ABSTRACT To develop and optimise the crystallisation process of clarithromycin, the solid–liquid equilibrium solubility and solvent effect of clarithromycin form ӀӀ in aqueous ethanol mixtures was experimentally determined at the temperature range from 273.15 K to 333.15 K under atmospheric pressure of 0.1 MPa. Experimental results confirmed that the crystal form did not change during the determination of solubility. The results indicated that the solubility of clarithromycin is dependent on the composition of the mixed solvent, and it reaches its maximum value when the mole fraction of ethanol in the mixture solvent is equal to 0.61. In addition, the solubility of clarithromycin was positively related to the temperature in the ethanol-water mixed solvent. Furthermore, solubility parameter was used to elucidate the relation between the solubility and the mixed solvent. The modified Apelblat equation, van’t Hoff equation, λh equation, CNIBS/R–K model and Jouyban–Acree model were employed to correlate the solubility data. The correlation results showed good agreement with the experimental data, the modified Apelblat equation provides the best correlation results. The NRTL equation was utilised to calculate the thermodynamic properties of the dissolution process of clarithromycin, and the dissolution process of clarithromycin was estimated to be endothermic and entropy-driven.

Investigation of solid–liquid equilibrium and thermodynamic models of D-Tagatose in mono-solvents and binary solvents

As a rare sugar, D-Tagatose is regarded as an excellent low-energy food sweetener. It is especially beneficial for physical health, such as inhibiting hyperglycemia, improving intestinal flora, and avoiding caries. It is broadly employed in food, medicine, cosmetics, and other fields. Acquiring D-Tagatose solubility is vital to develop D-Tagatose crystallization process to obtain high-quality D-Tagatose production. In this study, the solubility of D-Tagatose in seven pure solvents (methanol, ethanol, n-propanol, water, N, N-dimethylformamide, dimethyl sulfoxide, N-methylpyrrolidone), three binary solvents (ethanol-water mixtures, ethanol-methanol mixtures, and n-propanol-water mixtures) was determined by HPLC method at temperatures from 293.15 K to 323.15 K. Then, the Van't Hoff equation, Apelblat equation, λh equation, NRTL equation, CNIBS/Redlich-Kister model and modified Jouyban-Acree-van't Hoff model were used to correlate the solubility. The correlated solubility accounted for suitable compatibility with the experimental results (ARD <10%). Furthermore, we investigated the intermolecular interactions in the crystal structure through Hirshfeld surface analysis and estimated the overall charge distribution of molecules by molecular electrostatic potential surface (MEPs). Then, we analyzed the solvent effects and solvation free energy to explain the solubility behaviors. The results indicated that hydrogen bonds play a decisive role in determining the solubility of D-Tagatose.

Influence of high pressure on the solubility of ribavirin in six pure solvents from 283.15 to 323.15 K

The solubility of ribavirin in six pure solvents was measured at 9.0 MPa and 0.1 MPa to evaluate the influence of high pressure on solubility at the temperature range from 283.15 K to 323.15 K. The results indicated that all the solubilities of ribavirin decreased slightly at 9.0 MPa compared with those at 0.1 MPa. Solvation free energy of ribavirin in six solvents under two pressures was calculated to explain the decrease of solubility under high pressure. Besides, the solubility of ribavirin increased with the rising temperature under both 0.1 MPa and 9.0 MPa. Furthermore, the experimental solubility data under two pressures were correlated by the modified Apelblat equation and NRTL model. The average relative deviation (ARD%) value of the modified Apelblat equation is less than 3 %, which can give better correlation results. Finally, the thermodynamic properties of mixing and dissolution of ribavirin in six pure solvents under two pressures were also calculated based on the solubility experimental data and the NRTL equation.

Effects of intermolecular interactions and solvent properties on the solid-liquid phase equilibrium of isosorbide 5-mononitrate

Isosorbide 5-mononitrate (5-SIMN) is an organic nitrate pharmaceutical for the treatment of angina pectoris. In this work, first, the solubility of 5-ISMN in ten organic solvents was determined by the laser dynamic method at temperatures ranging from 278.15 K to 318.15 K. The results showed that the equilibrium solubility of 5-ISMN was temperature-dependent and increased monotonically with temperature. In addition, the effect of solvent properties on the dissolution behavior of 5-ISMN was also investigated, in which the “like dissolves like” principle played a critical role in the equilibrium solubility of 5-ISMN in different solvents. Next, four models (Apelblat equation, Van't Hoff equation, λh equation, and NRTL equation) were used to verify and correlate the experimental solubility data. The Apelblat equation fits the data well, and the maximum ARD% was less than 3%. Furthermore, molecular dynamics simulations were explored to reveal the effect of solute-solvent interactions on the dissolution behavior. Finally, the mixing thermodynamic properties of 5-ISMN were derived, and the results demonstrated that the mixing process was entropy-driven and spontaneous.

Solubility measurement and correlation of 2-chlorothioxanthone (CTX) in twelve mono organic solvents

• Solubility of 2-chlorothioxanthone in twelve pure solvents was determined. • Solubility was correlated by Apelblat, λh , Wilson and NRTL model. • Thermodynamic properties of mixing process were also discussed. 2-Chlorothioxanthone (CTX) is one of the most widely used commercial photoinitiators for pharmaceutical preparations as well as for preparations of synthetic resins. The solubility of CTX in twelve pure organic solvents was measured using the gravimetric method from 287.55 to 335.95 K at normal pressure. The results shows that the solubility of CTX in all the solvents increases as temperature rising. The melting point and fusion enthalpy of CTX were measured with differential scanning calorimeter. The experimental solubility data were correlated with four thermodynamic models, including modified Apelblat equation, λh equation, Wilson equation and NRTL equation. The best correlation results were found with modified Apelblat equation and NRTL equation. The mixing thermodynamic functions (Gibbs free energy, enthalpy and entropy) were calculated based on the Wilson equation. The results showed that the entire mixing process is spontaneous.

Performance of Some Novel Mixed Solvents as Entrainers for Separation of Water and Acetonitrile

Performance of some novel mixed solvents as entrainers was tested for acetonitrile dehydration by extractive distillation. The mixed solvents are composed of ethylene glycol (EG) and choline chloride (ChCl) (EG + ChCl 8:1, EG + ChCl 4:1, EG + ChCl 2:1, and EG + ChCl 4:3), ethylene glycol (EG) and glycerol (EG + glycerol 1:1, EG + glycerol 1:2, EG + glycerol 1:4, and EG + glycerol 1:6), and dimethyl sulfoxide (DMSO) and ChCl (DMSO + ChCl 14:1). Isobaric vapor–liquid equilibrium (VLE) data were measured at 101.3 kPa and at a solvent-free acetonitrile mole fraction of 0.95 for the quaternary systems of water + acetonitrile + EG + ChCl, water + acetonitrile + EG + glycerol, and water + acetonitrile + DMSO + ChCl and for the ternary system of water + acetonitrile + DMSO. The NRTL equation was used for the correlation of the experimental VLE data. For all the three quaternary systems and one ternary system, the mean absolute deviations of equilibrium temperature were no more than 0.33 K, and the mean absolute deviations of water and acetonitrile vapor phase mole fractions were no more than 0.0026 and 0.0047, respectively. The mixed solvent EG + ChCl 4:3, which is also a deep eutectic solvent, showed favorable solvent performance. The azeotrope of water + acetonitrile can be removed at a solvent mass fraction of 0.212 or a solvent mole fraction of 0.104. This amount is less than that of EG (0.367 in mass fraction and 0.227 in mole fraction), EG + glycerol 1:6 (0.341 in mass fraction and 0.195 in mole fraction), and DMSO + ChCl 14:1 (0.266 in mass fraction and 0.153 in mole fraction).

Assessment of the simultaneous regression of liquid-liquid and vapor-liquid equilibria data of binary systems using NRTL and artificial neural networks

A numerical analysis on the phase equilibrium modeling performance of the NRTL equation in binary mixtures using different data regression strategies was carried out. Several formulations for the binary interaction parameter estimation were studied including a novel approach using an artificial neural network model for the simultaneous correlation of liquid-liquid and vapor-liquid equilibria data. The artificial neural network strategy substantially improved the estimation of the liquid-liquid equilibrium data in comparison with the traditional parameter estimation strategies utilized for the thermodynamic models. A detailed analysis on the performance of the model in terms of the calculation of homogeneous and heterogeneous azeotropes was also performed. This study showed that the application of artificial intelligence tools is an interesting alternative to improve the capabilities of local composition models for the liquid-liquid and vapor-liquid equilibria calculations.