Excess Gibbs Free Energy Model Research Articles

Kirkwood-Buff Analysis of Binary and Ternary Systems Consisting of Alcohols (Methanol, Ethanol, 1-Propanol, and 2-Propanol), Water, and n-Hexane to Understand the Formation of Surfactant-Free Microemulsions.

Surfactant-free microemulsion (SFME) represents a class of fluid mixtures that can form microheterogeneous structures without detergents, offering an environmentally benign alternative to traditional microemulsions. However, the formation mechanism is still elusive. This work applies the Kirkwood-Buff theory to mixtures of alcohols, water, and n-hexane to elucidate the SFME formation mechanism. To ensure robust calculation of the Kirkwood-Buff integrals (KBIs), we construct a data set of densities and excess free energies of binary and ternary systems. Multiple excess Gibbs free energy models are assessed against this data set to select the most suitable model reproducing the experimental results. In addition, we introduce statistical methods to determine the optimal polynomial order of the Redlich-Kister correlation for the excess volume data. We first validate our methodology in binary systems. Then, we extend the calculation method to ternary mixtures. The KBI calculation results reveal that the alcohol-hexane and water-hexane interactions do not significantly affect SFME formation. In contrast, the interplay among water-water, water-alcohol, and alcohol-alcohol interactions critically influences the ability of a liquid mixture to form SFME structures. SFME systems exhibit the facile formation of water aggregates enveloped by alcohols, whereas non-SFME systems demonstrate homogeneous alcohol/water droplets dispersed in an oil continuous medium.

Thermodynamic study of imidazolium halide ionic liquid–water binary systems using excess Gibbs free energy models

In this work, the excess Gibbs free energy models, i.e., non-random two-liquid (NRTL) model and electrolyte NRTL model, including the original one and those with new strategies (association or hydration), were used to describe the macroscopic properties and interpret the microstructure of ionic liquid (IL) - H2O binary systems, clarifying the role of IL association and ion hydration in model development. To provide systematic data for model development, the enthalpy of mixing of three imidazolium-based IL-H2O systems containing the same cation but different sizes of anions, i.e., Cl−, Br−, and I−, were measured. The models were developed and evaluated based on the newly measured data and the osmotic coefficient from the literature. The results reveal that the model reflecting the intrinsic mechanism of dissociation and hydration gives the best modeling results; and the ionic strength and the degree of IL dissociation as a function of water content can be predicted using the newly established model. The study clarifies the significance of IL association and anion hydration in model development and quantitatively demonstrates how water content influences the microstructure and real species in IL-H2O systems.

An insight into the analogy between solute-solvent binding energy and solubility of acid gases in ionic liquids: Thermodynamic modeling versus molecular dynamic simulation

Ionic Liquids (ILs) have emerged as a promising generation of solvents for the absorption of acid gases (e.g., CO2 and H2S) due to their unparalleled physiochemical properties. This study focuses on thermodynamic modeling and molecular dynamic simulation approaches to estimate the solubility and interaction energies of CO2 and H2S gases in/with different frequently-used ILs. For thermodynamic modeling, the GE/EOS method was employed. This method allows for combining activity-coefficient models in the structure of the cubic equation of states. In the GE/EOS method, the modified Peng-Robinson equation of state (MPR2) together with the LCVM mixing rules was used. Excess Gibbs free energy models of Wilson, NRTL, and UNIQUAC were also applied for combination with the GE/EOS models. The prediction results of the combined models were compared with the experimental solubility data. The results demonstrated the capability of these models to predict the thermodynamic behavior of the acid gas-ILs systems. The results uncovered that the MPR2-LCVM-Wilson model can tabulate the highest correlation with the experimental data compared to the other model combinations. Results of the sensitivity analysis on the principal operational variables (temperature and pressure), showed superior effect of pressure on the gas solubility. In addition, the results of the molecular dynamic (MD) simulation disclosed an agreement between the trends of the solubility of acid gases in ILs with those of the released interaction energies of acid gases absorbed by the ILs. MD results also confirmed that the solubility of acid gases in ILs increases with an increase in the binding energy of the molecules with the ILs.

Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods

Combining COSMO-based excess Gibbs free energy models with the Peng-Robinson (PR) equation-of-state (EoS) via mixing rules has recently been shown as a promising method for satisfied VLE predictions on refrigerant systems by Mambo-Lomba and Paricaud. An extension is provided in this work for more systematic and dedicated evaluations focusing on a significantly larger refrigerant database and comparisons between different VLE modeling approaches. In particular, the COSMO-SAC-dsp model is combined with via the original Huron-Vidal (HVO), the modified Huron-Vidal (MHV1) and the Wong-Sandler (WS) mixing rules. Comprehensive model evaluation is performed on the basis of 447 vapor-liquid-equilibrium (VLE) experimental datasets for 233 refrigerant pairs. The results show that the combination of the COSMO-SAC-dsp with the PR yields satisfied and comparable prediction accuracy on the VLE in most cases comparing to the well-established group-contribution based Gex-EoS methods VTPR and PSRK. The performance of the three mixing rules on the studied database follows a decreasing order of MHV1 > HVO > WS but without qualitative difference. Large VLE prediction errors can appear between halogenated hydrocarbons and hydrocarbons. Moreover, errors become more significant and the VLE calculation cannot converge at all for mixtures involving R717 and R744 respectively. Improved predictive accuracy can be achieved by re-optimizing the atomic dispersion parameters of F and =O to 35.5 and 74.0 respectively.

Temperature Dependence of Solubility Predicted from Thermodynamic Data Measured at a Single Temperature: Application to α, β, and γ-Glycine.

Understanding of solid–liquid equilibria for polymorphic systems is crucial for rational design and efficient operation of crystallization processes. In this work, we present a framework to determine the temperature dependent solubility based on experimentally accessible thermodynamic data measured at a single temperature. Using this approach, we investigate aqueous solubility of α, β, and γ-glycine, which, despite numerous studies, have considerable quantitative uncertainty, in particular for the most stable (γ) and the least stable (β) solid forms. We benchmark our framework on α-glycine giving predictions in excellent agreement with direct solubility measurements between 273–340 K, using only thermodynamic data measured at the reference temperature (298.15 K). We analyze the sensitivity of solubility predictions with respect to underlying measurement uncertainty, as well as the excess Gibbs free energy models used to derive required thermodynamic quantities before providing solubility predictions for β and γ-glycine between 273–310 and 273–330 K, respectively. Crucially, this approach to predict solubility as a function of temperature does not rely on measurement of solute melting properties which will be particularly useful for compounds that undergo thermal decomposition or polymorph transition prior to melting.

Thermodynamics of solvent-driven water extraction from hypersaline brines using dimethyl ether

Solvent-driven water extraction (SDWE) has promising applications in hypersaline brine desalination, including zero-liquid discharge processing for industrial wastewaters, and resource recovery, such as the extraction of lithium and rare earth elements from solution mining leachates. In this study, we develop a computational thermodynamic framework to analyze the liquid–liquid extraction of water from hypersaline brines using dimethyl ether (DME), an aprotic solvent that is partially miscible with water. The high volatility of DME enables its rapid separation from water–DME mixtures after water absorption, while its low polarity minimizes the organic-phase solubility of electrolytes, such as sodium chloride (NaCl). We first build a thermodynamic model based on the LIQUAC excess Gibbs free energy model for water–DME–NaCl mixtures. Maximum likelihood estimators for water–DME–NaCl interaction parameters are calculated through the nonlinear regression of fluid phase equilibrium and osmotic coefficient data using metaheuristic global optimization techniques. A multistage counter-current liquid–liquid separator (LLS) model is then developed to explore the water recovery and brine concentration ratios achievable as a function of feed molality and DME to feed water flow rate ratio. For a saline feed with a molality of 2.0molkg−1 (over three times the salinity of seawater) our analysis demonstrates that a one-stage LLS can achieve a water recovery ratio of 0.51 with an initial DME to saline feed molar flow rate ratio of 4.0, rising to 0.63 with a second equilibrium stage. We conclude by quantifying the amount of DME required to reach zero-liquid discharge brine salinities and analyzing the impact of staging and temperature on separation performance. Our thermodynamic model enables the rapid evaluation of SDWE systems for emerging hypersaline brine desalination and valorization applications.

Energy and exergy analysis of parallel flow double effect H2O-[mmim][DMP] absorption refrigeration system for solar powered district cooling

Solar thermal energy-driven double effect absorption refrigeration system (DE-ARS) for district cooling in smart cities is an efficient, and sustainable alternative for centralized air conditioning and concurrently harnesses low-grade solar energy. This work investigates ionic liquid based H2O-[mmim][DMP] mixture as an alternative working fluid to overcome the drawback of H2O–LiBr driven DE-ARS. The thermodynamic properties of H2O-[mmim][DMP] mixture is evaluated using the excess Gibbs free energy model. Performance modeling and simulation of DE-ARS is based on both energy and exergy analysis by applying the first and second laws of thermodynamic. The performance, and solution circulation ratio of parallel flow DE-ARS is assessed and optimized under various temperatures and solution distribution ratios. In comparison to the conventional H2O–LiBr, the proposed H2O-[mmim][DMP] working fluid achieves 5.22% and 4.95% improvement in COP and ECOP, respectively at Th/Te/Ta/Tc of 140/5/30/30°C . An optimization of generator temperature to achieve maximum COP and ECOP is performed for a wide range of evaporation temperature from 5 to 20°C and Ta/Tc from 30 to 40°C. An optimization of H2O-[mmim][DMP] mixture driven DE-ARS reveals the uppermost COPmax and ECOPmax of 1.81 and 0.69 for Te of 20°C and TaTc=30°C.

Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K

The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations.

Experimental Data of Fluid Phase Equilibria- Correlation and Prediction Models: A Review

The examples of phase equilibria in binary systems, solid/liquid (SLE), liquid/liquid (LLE), vapor/liquid (VLE), as well as liquid/liquid equilibria in ternary systems mainly containing ionic liquids (ILs), or the infragrance materials, or pharmaceuticals with molecular organic solvents, such as an alcohol, or water, or hydrocarbons, are presented. The most popular correlation methods of the experimental phase equilibrium data are presented, related to the excess Gibbs free energy models such as Wilson, universal-quasichemical, UNIQUAC and non-random two-liquid model, NRTL as well as several popular theories for the modeling of the phase equilibria and excess molar enthalpy, HE in binary or ternary mixtures are presented: the group contribution method (Mod. UNIFAC) and modified UNIFAC model for pharmaceuticals and lattice theory based on non-random hydrogen bonding (NRHB). The SLE, LLE, or VLE and HE of these systems may be described by the Perturbed-Chain Polar Statistical Associating Fluid Theory (PC-SAFT), or a Conductor-like Screening Model for Real Solvents (COSMO-RS). The examples of the application of ILs as extractants for the separation of aromatic hydrocarbons from alkanes, sulfur compounds from alkanes, alkenes from alkanes, ethylbenzene from styrene, butan-1-ol from water phase, or 2-phenylethanol (PEA) from water are discussed on the basis of previously published data. The first information about the selectivity of extrahent for separation can be obtained from the measurements of the limiting activity coefficient measurements by the gas–liquid chromatography technique. This review outlines the main research work carried out over the last few years on direct measurements of phase equilibria, or HE and limiting activity coefficients, the possibility of thermodynamic modeling with emphasis on recent research achievements and potential for future research.

Predicting cyclohexane/water distribution coefficients for the SAMPL5 challenge using MOSCED and the SMD solvation model

We present blind predictions using the solubility parameter based method MOSCED submitted for the SAMPL5 challenge on calculating cyclohexane/water distribution coefficients at 298K. Reference data to parameterize MOSCED was generated with knowledge only of chemical structure by performing solvation free energy calculations using electronic structure calculations in the SMD continuum solvent. To maintain simplicity and use only a single method, we approximate the distribution coefficient with the partition coefficient of the neutral species. Over the final SAMPL5 set of 53 compounds, we achieved an average unsigned error of [Formula: see text] log units (ranking 15 out of 62 entries), the correlation coefficient (R) was [Formula: see text] (ranking 35), and [Formula: see text] of the predictions had the correct sign (ranking 30). While used here to predict cyclohexane/water distribution coefficients at 298K, MOSCED is broadly applicable, allowing one to predict temperature dependent infinite dilution activity coefficients in any solvent for which parameters exist, and provides a means by which an excess Gibbs free energy model may be parameterized to predict composition dependent phase-equilibrium.

Vapor-liquid equilibria for the binary mixtures of methanol+cyclopentyl methyl ether (CPME)

VLE data for binary systems of methanol (1)+cyclopentyl methyl ether (2) were measured at five equal-spaced temperatures between 313.15 and 353.15 K using a circulation-type equilibrium apparatus with on-line gas chromatography analysis. This binary system shows strong positive deviation from Raoult’s law and forms an azeotrope at each temperature. The experimental data were correlated with the Peng-Robinson equation of state using the Wong-Sandler mixing rule combined with the NRTL excess Gibbs free energy model. The overall average relative deviations of pressure (ARD-P (%)) and vapor phase compositions (ARD-y (%)) between experimental and calculated values through the temperature range from 313.15 to 353.15 K were 0.298 and 0.499%, respectively. In the range of experimental temperature, azeotropic compositions showed a linear relationship with temperature and were correlated by the empirical equation of x azeo =0.001 T/K+0.617.

Viscosity estimation of ternary mixtures containing ionic liquid from their binary subsystems: A comparison of three viscosity equations

Viscosity of the mixture containing ionic liquid (IL) is important for engineering design and application. The modeling of viscosity of the ternary mixtures containing IL is still in its infancy. The aim of this work is to evaluate the predictive ability of the semi-theoretical viscosity equations based on Eyring’s absolute rate theory and excess Gibbs free energy model for the ternary mixtures containing IL in terms of the viscosity of their binary subsystems. Three viscosity equations namely Eyring-UNIQUAC, Eyring-NRTL, and Eyring-Wilson equations are employed and extended to estimate the viscosity of ternary mixtures of IL with two molecular solvents using the interaction parameters obtained from their binary subsystems. The results were compared and discussed. The correlation results of the viscosity for 30 binary subsystems with 444 data points show that the Eyring-Wilson equation has more applicability and precision than those of the Eyring-UNIQUAC and Eyring-NRTL equations. Accordingly, the prediction results of the viscosity for 13 ternary mixtures containing IL with 813 data points indicate that the Eyring-Wilson equation has much better predictive ability than that of the Eyring-UNIQUAC and Eyring-NRTL equations. Moreover, the Eyring-Wilson equation can be used to predict the ternary viscosity at other temperature such as 313.15 K using the interaction parameters obtained from their binary subsystems at 298.15 K.

Measurement and correlation of the vapor–liquid equilibrium for methanol + acetonitrile + imidazolium-based ionic liquids at 101.3 kPa

Two imidazolium-based ionic liquids: 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) and 1-octyl-3-methylimidazolium tetrafluoroborate ([OMIM][BF4]) were studied as entrainer candidates for the separation of methanol+acetonitrile system. Isobaric vapor–liquid equilibrium (VLE) for the binary methanol+acetonitrile and the ternary mixtures containing imidazolium-based ionic liquids were determined at atmospheric pressure (101.3kPa). The experimental VLE results indicated ionic liquids (ILs) studied both showed a crossover salting effect for methanol. More importantly, when the amount of IL added increases, the azeotropic point of methanol+acetonitrile will disappear at one specific content. Meanwhile, the separation capacity of imidazolium-based ionic liquids follows the order: [OMIM][BF4]>[EMIM][BF4]. Finally, two different excess Gibbs free energy models were used to correlate the VLE data: the non-random two-liquid (NRTL), and the universal quasi-chemical (UNIQUAC).

Improving the Separation of n-Heptane + Ethanol Azeotropic Mixtures Combining Ionic Liquid 1-Ethyl-3-methylimidazolium Acetate with Different Inorganic Salts

In this work, the ionic liquid (IL) 1-ethyl-3-methylimidazolium acetate, [C2MIM][Ac], was combined with the inorganic salts (ISs) ammonium acetate, [NH4][Ac], ammonium chloride, [NH4]Cl, and ammonium thiocyanate, [NH4][SCN], and used as an extraction solvent for the separation of the azeotropic mixture of n-heptane + ethanol. The liquid–liquid equilibria (LLE) of the ternary mixtures of n-heptane + ethanol + IL or IL-IS was experimentally measured at 298.15 K and 0.1 MPa. The feasibility of the extraction solvents was assessed by the distribution coefficient and the selectivity. The results showed that the extraction solvents studied can be suitable candidates for the separation of ethanol from n-heptane. Additionally, we show that the solubilization of ISs in the IL can greatly increase the selectivity of the latter, while no significant impact on the distribution coefficient is verified. Moreover, the distribution coefficient values obtained for the [C2MIM][Ac] and its mixtures with ISs are the highest among neat ILs tested so far for the azeotropic mixture in study. The experimental liquid–liquid equilibrium data were correlated using the nonrandom two-liquid (NRTL) excess Gibbs free energy model.

Experimental Study and Modeling of Phase Equilibrium of the Methanol–Tripalmitin System: Application to Palm Oil Transesterification with Supercritical Methanol

The phase behavior of the methanol–palm oil system was first experimentally assessed in the temperature range of 363–393 K and pressure range of 1–4 MPa. Second, comparative modeling of the phase equilibrium of the methanol–tripalmitin system was performed using the Peng–Robinson equation of state (PR EoS) with second-order modified Huron–Vidal (MHV2) mixing rules, in combination with the universal functional activity coefficient model (UNIFAC) and the universal quasi-chemical (UNIQUAC) excess Gibbs free-energy model. The agreement between experimental and modeling results was found to be satisfactory when MHV2 mixing rules are used in combination with the UNIQUAC model. Finally, the thermodynamic model was applied to predict fluid phase equilibria of palm oil transesterification with supercritical methanol. From the isochoric method in the temperature range of 373–693 K and the pressure range of 1–16 MPa, the model was found to predict global mixture behavior.

On the application of nonelectrolyte UNIQUAC-NRF model for strong aqueous electrolyte solutions

An excess Gibbs free energy model composed of a short range term, expressed by the nonelectrolyte UNIQUAC-NRF model, and a long range contribution based on the Pitzer-Debye-Hückel equation is implemented for strong aqueous electrolyte solutions. The present model is applied for calculations of mean activity coefficient and osmotic coefficient of aqueous electrolyte solutions using two approaches: salt parameter model and ion specific parameter model. In salt parameter scheme, the present model has two adjustable parameters per each aqueous salt that are salt-water and water-salt energy parameters. In ion specific approach, the interaction energy parameters of each species with the other species are obtained. The experimental activity coefficients of aqueous electrolyte solutions are used to determine the energy parameters. The surface and volume parameters of ions are calculated using their radius. The results of the models are in good agreements with the experimental data. The extensions of the two approaches for prediction of solubility and osmotic coefficients of some mixed-salt systems have been carried out.

Numerical experiments with new metaheuristic algorithms in phase equilibrium problems

In this work, we presented some numerical experiments with two recently proposed metaheuristics (symbiotic organisms search and water wave optimisation) in the parameter estimation of an excess Gibbs free energy model (the Wilson model, using vapour-liquid equilibrium data) and in the calculation of azeotropes (non-reactive and reactive azeotropes). Both problems are characterised by nonlinear algebraic systems with multiple solutions, converted into optimisation problems with non-negative merit functions. The numerical results indicated that these new stochastic optimisation algorithms are capable to find the expected solutions in these real-world problems with robustness and accuracy. Moreover, fluid phase equilibrium problems can be viewed as challenging and useful tests for new metaheuristics.

An ion-based nonelectrolyte NRTL-NRF for aqueous electrolyte solutions

An excess Gibbs free energy model that is composed of the nonelectrolyte NRTL-NRF model as short range contribution and Pitzer–Deby–Huckel equation as long range part is applied to model strong aqueous electrolyte solutions. The ion specific interaction energy parameters appearing in the short range part of the model are obtained for water, various cations including Na+, Li+, K+, Cs+, Rb+, NH4+, H+, Ba2+, Ca2+, Mg2+, Al3+ and Cr3+ and several anions including Cl−, Br−, OH−, NO3−, Ac−, I− , F− and SO42-. The experimental data of activity coefficient of 62 binary aqueous electrolyte solutions at 298K are simultaneously used to achieve the parameters. The correlation results of the model are in good agreements with the experiment. Comparisons of the activity coefficient correlations with those of E-NRTL model show more accuracy of the present model; however the results of Pitzer model is better than present model. The osmotic coefficients of the binary electrolytes at 298K are calculated with good accuracy using the present model. Also some binary electrolytes have been taken in to account in temperature range of 273–373K to obtain temperature dependency of the interaction parameters. The model extension for ternary aqueous electrolytes is done using calculations of phase diagrams and osmotic coefficients of some mixed salt systems.

Vapor-liquid equilibria for the binary mixtures of dimethyl ether (DME)+ dimethyl carbonate (DMC)

Isothermal vapor-liquid equilibrium data for the binary system of dimethyl ether (DME)+dimethyl carbonate (DMC) were measured at 303.15, 313.15, 323.15, 333.15 and 343.15 K using a circulation-type equilibrium apparatus with on-line gas chromatography analysis. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the van der Waals one fluid mixing rule and the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rule combined with the NRTL excess Gibbs free energy model. This system showed negative deviation from Raoult’s law, and no azeotropic behavior was observed for all the temperature ranges studied here. Calculated results with PR-EoS using both two mixing rules showed good agreement with experimental data.

Ternary liquid–liquid equilibria and binary excess and deviation properties at constant temperature for mixtures of dimethyl carbonate, anisole, methanol, phenol and water

This study aims to determine the phase equilibria and mixture properties for the separation of reaction intermediates generated during the synthesis of non-phosgene diphenylcarbonate (DPC). The intermediates are based on dimethyl carbonate (DMC), phenol, methanol and anisole, etc. We analytically determined ternary liquid–liquid equilibria (LLE) for the following mixtures at atmospheric pressure and constant temperature: {water+DMC+anisole} at 313.15K, {water+methanol+anisole} at 308.15K and {water+methanol+phenol} at 328.15K. In addition, density, refractive indices, excess molar volumes (VE) and deviations in the molar refractivity (ΔR) of constituent binary systems at 298.15K were determined. The experimental LLE data correlated well with two excess Gibbs free energy models: Non-Random Two-Liquid (NRTL) and UNIversal QUAsiChemical (UNIQUAC). VE and ΔR data were correlated well with Redlich–Kister polynomial.