Parameter estimation in vapor-liquid equilibrium modeling of compounds related to biodiesel production using opposite point-based differential evolution algorithm.

Biodiesel stands out as the most favorable alternatives to fossil-derived diesel, offering a multitude of environmental benefits. At various stages of biodiesel production, the separation processes necessitate thermodynamic models with the capability to correlate and predict phase equilibria of mixtures. In this study, application of the classical differential evolution (DE) and its new enhanced version, the OPDE algorithm, for modeling vapor-liquid equilibrium (VLE) associated with components related to biodiesel production is presented. The algorithms were analysed and contrasted in terms of their performance, in estimating parameters for Wilson, NRTL and UNIFAC models. Additionally, classical least-squares (LS) and error-in-variable (EIV) approaches were examined and compared. Also, VLE datasets for a specific system have been merged, and parameters have been estimated. The findings suggest that parameters obtained through LS approach align with those reported in literature, indicating faster convergence in all problems. In contrast, the EIV approach achieved a higher objective function value compared to the LS approach, exhibiting low deviation. OPDE outperformed DE in terms of performance. The enhancement in RMSTD value has been found within range 91%-99% for EIV approach. Further, novel findings derived from some of the studied VLE datasets are presented.

Utilizing environment-friendly eugenol as a diluent with trioctylamine for the reactive extraction of aqueous levulinic acid.

This paper focuses on the reactive extraction of levulinic acid (LA) from aqueous solution by reactive extraction. This goal is achieved using eugenol, a green alternative in the industry, as a solvent in the liquid-liquid equilibrium (LLE) measurements for the ternary system of LA + Eugenol + H2O and quaternary systems of LA + Eugenol/ Methanol (MeOH) + H2O + Tri-n-octylamine (TOA) at T = 293.15 K. Additionally, the distribution coefficients (KD) were calculated for LA using the two diluents. Also, the ability of different diluents with TOA, in the extraction of LA were compared. The distribution coefficient of eugenol with TOA (KD = 9.44) is compared with other organic diluents which indicated that eugenol is a suitable option. MeOH, being the shortest chain alcohol, also turned out to be a diluent that could be utilized for extraction of LA with TOA. Furthermore, the Non-Random Two-Liquid (NRTL) excess Gibbs energy model was applied to correlate the measured phase equilibria. The obtained parameters were further validated using a decanter model.

Swelling kinetics of mixtures of soybean phosphatidylcholine and glycerol dioleate.

Lipid-based drug delivery systems offer the potential to enhance bioavailability, reduce dosing frequency, and improve patient adherence. In aqueous environment, initially dry lipid depots take up water and form liquid crystalline phases. Variation of lipid composition, depot size and hydration-induced phase transitions will plausibly affect the diffusion in and out of the depot. Lipid depots of soybean phosphatidylcholine (SPC) and glycerol dioleate (GDO) mixtures were hydrated for varying time durations in a phosphate-buffered saline (PBS) buffer and then analyzed with Karl Fischer titration, magnetic resonance imaging (MRI) and gravimetrically. Mathematical modeling of the swelling process using diffusion equations, was used to estimate the parameters of diffusion. Both composition of lipid mixture and depot size affect swelling kinetics… The diffusion parameters obtained in Karl Fischer titration and MRI (with temporal and spatial resolution respectively) are in good agreement. Remarkably, the MRI results show a gradient of water content within the depot even after the end of diffusion process. Apparently contradicting the first Fick's law in its classical form, these results find an explanation using the generalized Fick's law that considers the gradient of chemical potential rather than concentration as the driving force of diffusion.

Thermodynamic Modeling of the Au-Ge-X (X = In, Sb, Si, Zn) Ternary Systems.

In this study, the CALPHAD approach was employed to model the thermodynamics of the Au-Ge-X (X = In, Sb, Si, Zn) ternary systems, leveraging experimental phase equilibria data and previous assessments of related binary subsystems. The solution phases were modeled as substitutional solutions, and their excess Gibbs energies were expressed using the Redlich-Kister polynomial. Owing to the unavailability of experimental data, the solubility of the third elements in the Au-In, Au-Sb, and Au-Zn binary intermetallic compounds was excluded from consideration. Additionally, stable ternary intermetallic compounds were not reported in the literature and, thus, were not taken into account in the present thermodynamic calculations. Calculations of liquidus projections, isothermal sections, and vertical sections for these ternary systems have been performed, aligning with existing experimental findings. These thermodynamic parameters form a vital basis for creating a comprehensive thermodynamic database for Au-Ge-based alloys, which is essential for the design and development of new high-temperature Pb-free solders.

The Gd2O3 - GdSrFeO4 pseudo -binary phase diagram.

The Gd2O3 - GdSrFeO4 pseudo-binary phase diagram is presented for the first time. The liquidus and eutectic temperatures, metatectic points of the Gd2O3 transformations in the Gd2O3 - GdSrFeO4 section were defined using the Schröder-Le Chatelier equation, neglecting the effect of the isobaric heat capacity. The calculations were based on experimental data on the melting points of the end-members and the eutectic composition. From the results of phase relationships studies (subsolidus and high temperature region including literature data as well) and the above approach the Gd2O3-GdSrFeO4 pseudo-binary phase diagram in the temperature range 1400-2410 °C in air was constructed. It was shown that GdSrFeO4 of the K2NiF4- type is stable from 1100°Ð¡ to a congruent melting temperature of 1560°Ð¡ in air. The Gd2O3 - GdSrFeO4 system is eutectic with no intermediate compounds.

Freshwater Recovery and Removal of Cesium and Strontium from Radioactive Wastewater by Methane Hydrate Formation.

As human society has advanced, nuclear energy has provided energy security while also offering low carbon emissions and reduced dependence on fossil fuels, whereas nuclear power plants have produced large amounts of radioactive wastewater, which threatens human health and the sustainability of water resources. Here, we demonstrate a hydrate-based desalination (HBD) technology that uses methane as a hydrate former for freshwater recovery and for the removal of radioactive chemicals from wastewater, specifically from Cs- and Sr-containing wastewater. The complete exclusion of radioactive ions from solid methane hydrates was confirmed by a close examination using phase equilibria, spectroscopic investigations, thermal analyses, and theoretical calculations, enabling simultaneous freshwater recovery and the removal of radioactive chemicals from wastewater by the methane hydrate formation process described in this study. More importantly, the proposed HBD technology is applicable to radioactive wastewater containing Cs+ and Sr2+ across a broad concentration range of low percentages to hundreds of parts per million (ppm) and even subppm levels, with high removal efficiency of radioactive chemicals. This study highlights the potential of environmentally sustainable technologies to address the challenges posed by radioactive wastewater generated by nuclear technology, providing new insights for future research and development efforts.

Data on searching for synergy between alcohol and salt to produce more potent and environmentally benign gas hydrate inhibitors.

In order to systematically study the synergistic effect of gas hydrate inhibition with mixtures of methanol (MeOH) and magnesium chloride (MgCl2), the impact of these compounds on the thermodynamic stability of methane hydrate in the systems of CH4-MeOH-H2O, CH4-MgCl2-H2O, and CH4-MeOH-MgCl2-H2O was experimentally investigated. The pressure and temperature conditions of the three-phase vapor-aqueous solution-gas hydrate equilibrium were determined for these systems. The resulting dataset has 164 equilibrium points within the range of 234-289 K and 3-13 MPa. All equilibrium points were measured as the endpoint of methane hydrate dissociation during the heating stage. The phase boundaries of methane hydrate were identified for 8 systems with MeOH (up to 60 mass%), 5 MgCl2 solutions (up to 26.7 mass%), and 14 mixtures of both inhibitors. Most equilibrium points were measured using a ramp heating technique (0.1 K/h) under isochoric conditions when the fluids were stirred at 600 rpm. It was found that even a 0.5 K/h heating rate for the CH4-MgCl2-H2O system at low salt concentrations, along with all mixed aqueous solutions with methanol, gives results that do not differ from 0.1 K/h, considering the measurement uncertainties. Most measurements for the CH4-MgCl2-H2O system at high salt content were acquired using a step heating technique. The coefficients of the empirical equations approximating the equilibrium points for each inhibitor concentration were defined. The change in the slope parameter of the empirical equation was analyzed as a function of inhibitor content. Correlations that accurately describe the thermodynamic inhibition effect of methane hydrate with methanol and magnesium chloride on a mass% and mol% scale were obtained. The freezing temperatures of single and mixed aqueous solutions of methanol and magnesium chloride were determined experimentally to confirm the thermodynamic consistency of the methane hydrate equilibrium data.

Phase Equilibria Related to NiGa5 in the Binary Ni-Ga System.

The assembly of Ga alloys with Ni or Ni alloy has been widely developed for various low-temperature applications in recent years. In the constituent Ni-Ga binary system, however, the phase equilibrium with the phase "NiGa5" and its stability has scarcely been investigated. The present study used the diffusion couple technique combined with SEM-EPMA and XRD analysis to examine the phase stability and the homogeneity range of the phase. The results show that "NiGa5" is a stable phase in the binary system with little homogeneity range and suggest that the peritectic reaction L+Ni3Ga7→NiGa5 lies between 112.0 and 115.5 °C. This work provides new information for the modification of the Ga-rich low-T region of the Ni-Ga phase diagram.

Phase Equilibria of the V-Ti-Fe System and Its Applications in the Design of Novel Hydrogen Permeable Alloys.

The precise liquidus projection of the V-Ti-Fe system are crucial for designing high-performance hydrogen permeation alloys, but there are still many controversies in the research of this system. To this end, this article first uses the CALPHAD (CALculation of PHAse Diagrams) method to reconstruct the alloy phase diagram and compares and analyses existing experimental data, confirming that the newly constructed phase diagram in this article has good reliability and accuracy. Second, this obtained phase diagram was applied to the subsequent development process of hydrogen permeation alloys, and the (Ti65Fe35)100-xVx (x = 0, 2.5, 5, 10, 15, 25) alloys with dual-phase {bcc-(V, Ti) + TiFe} structure were successfully explored. In particular, the alloys with x values equal to 2.5 at.% and 5 at.% exhibit relatively high hydrogen permeability. Third, to further increase the H2 flux permeation through the alloys, a 500-mm-long tubular (Ti65Fe35)95V5 membrane for hydrogen permeation was prepared for the first time. Hydrogen permeation testing showed that this membrane had a very high H2 flux (4.06 mL min-1), which is ca. 6.7 times greater than the plate-like counterpart (0.61 mL min-1) under the same test conditions. This work not only indicates the reliability of the obtained V-Ti-Fe phase diagram in developing new hydrogen permeation alloys, but also demonstrates that preparing tubular membranes is one of the most important means of improving H2 flux.

Experimental Investigations of Ni-Ti-Ru System: Liquidus Surface Projection and 1150 °C Isothermal Section.

Ruthenium addition inhibits the formation of the topologically close-packed phases in Ni-based superalloys and improves the solid solution strength of Ni-Ti shape memory alloys. Therefore, the Ni-Ti-Ru phase stability is a very valuable indicator of the effects of Ru in Ni-based superalloys and Ni-Ti shape memory alloys. In this study, the isothermal section at 1150 °C and liquidus surface projection of the Ni-Ti-Ru ternary system were determined experimentally using the equilibrated alloy method and diffusion couple method, respectively. Alloys were prepared through the arc-melting of Ni, Ti, and Ru (all 99.99% purity), and then vacuum encapsulation in quartz tubes, followed by annealing at 1150 °C for 36 to 1080 h depending on the alloy composition. Diffusion couples were fabricated by joining one single-phase block (τ1) with one two-phase block (Ni3Ti + γ(Ni)), and the couples were annealed under vacuum at 1150 °C for 168 h. Reaction temperatures of as-cast alloys were determined by differential scanning calorimetry performed with heating and cooling rates of 10 °C/min. Scanning electron microscopy and X-ray diffraction were used to analyze the microstructure. Seven three-phase regions were found at the 1150 °C isothermal section. Seven primary solidification regions and five ternary invariant reactions were deduced in the liquidus surface projection. A new ternary compound τ1 was discovered in both the isothermal section at 1150 °C and liquidus surface projection. The results aid in thermodynamic modeling of the system and provide guidance for designing Ni-based superalloys and Ni-Ti shape memory alloys.

Experimental Investigation of Phase Equilibria of the Ho-Ir-O Ternary System at 1073 K.

An experimental study of the phase equilibria of the Ho-rich part of the Ho-Ir-O ternary system at 1073 K by means of x-ray diffraction, differential scanning calorimetry, and scanning electron microscopy has been carried out. Ho-hcp and four binary compounds, namely Ho3Ir, Ho5Ir2, Ho5Ir3, and Ho2O3, were identified in the Ho-Ir-O model alloys after long-term annealing (350-1220 h). No solubility of iridium in Ho2O3 oxide and Ho-hcp was observed. No ternary phase was found. Based on the experimental results, an isothermal section of the Ho-rich part of the Ho-Ir-O system at 1073 K was constructed. In addition, the microstructure of as-cast alloys was studied. An irregular eutectic consisting of faceted Ho-phase in Ho3Ir phase was observed in the alloys with Ho-hcp + Ho3Ir + Ho2O3 phase composition, and the temperature of the eutectic reaction Ho-hcp + Ho3Ir ↔ liquid was determined.

Role of site-site interaction on the phase equilibria of multiple-site associating fluids in a functionalized slit pore.

Vapor-liquid phase equilibria for multiple sites associating fluids with different associating strengths are investigated in a slit pore using grand-canonical transition matrix Monte Carlo method. The increase of critical temperature from two-site to four-site associating fluids at constant site strength is quite significant as compared to that of the one-site to two-site associating fluids, which is more pronounced at higher associating strength (ϵ* = 6). Monomer fraction and cluster size distribution are used to investigate the association of fluid particles in coexistence phases. The monomer fraction for both phases decreases with increased associating sites on the fluid particles due to more site-site interaction with neighboring fluid particles and forming a larger cluster. Therefore, the number of associating sites and their distribution play a vital role in the association of fluid particles. Moreover, the saturation chemical potential changes with the arrangement of the sites. For two-site associating fluids, we observe early vapor-liquid transition when the sites are oppositely placed, and when the sites are placed at 90°, the vapor-liquid transition is observed at the higher chemical potential. Moreover, four-site associating fluids with a square arrangement show early vapor-liquid phase transition, mainly because these arrangements of sites effectively interact with surface sites and the molecules in the next layer.

Mutual Solubilities between Ethylene Glycol and Organic Diluents: Gas Chromatography and NMR.

In this work, the mutual solubilities of sets of organic diluents (CHCl3, C6H6, C2H4Cl2, CCl4, C6H12, and n-hexane) with the organic compound ethylene glycol are investigated via gas chromatography (GC). The experimental data measured for these binary organic systems are used to adjust the future nonaqueous systems for the solvent extraction of various metals with ligands. The obtained results showed that the solubility of ethylene glycol decreased in the order CHCl3 > C6H6 > C2H4Cl2 > CCl4(0%) ≈ C6H12 ≈ n-hexane. On the other hand, the solubility of the tested traditional organic diluents in ethylene glycol decreased in the following order: C6H6 > CHCl3 > C2H4Cl2 > n-hexane > C6H12 > CCl4. 1H NMR was also used as an analytic method in order to compare the obtained results for the samples showing significant solubility only, including an additional study with 1,2- or 1,3-propanediol. The enhanced solubility of the C6H6 compound in ethylene glycol was identified here as critical due to the GC technique, which will be without future consequences in chemical technology. Therefore, it was found that the best molecular diluent for the recovery of metals among the tested ones is C6H12, with a green protocol as the new paradigm, replacing the aqueous phase with another nonaqueous phase, i.e., a second organic diluent.

Dataset for the phase equilibria and PXRD studies of urea as a green thermodynamic inhibitor of sII gas hydrates.

The equilibrium conditions of sII methane/propane hydrates have been experimentally determined for the C3H8/CH4-H2O-urea system. The equilibrium dissociation temperatures and pressures of sII hydrates span a wide P,T-range (266.7-293.9 K; 0.87-9.49 MPa) and were measured by varying the feed mass fraction of urea in solution from 0 to 50 mass%. The experimental points at feed urea concentration ≤ 40 mass% correspond to the V-Lw-H equilibrium (gas-aqueous urea solution-gas hydrate). A four-phase V-Lw-H-Su equilibrium (with an additional phase of solid urea) was observed because the solubility limit of urea in water was reached for all points at a feed mass fraction of 50 mass% and for one point at 40 mass% (266.93 K). Gas hydrate equilibria were measured using a high-pressure rig GHA350 under isochoric conditions with rapid fluid stirring and slow ramp heating of 0.1 K/h. Each measured point represents complete dissociation of the sII hydrate. The phase equilibrium data was compared with the literature reported for the C3H8/CH4-H2O and CH4-H2O-urea systems. A comprehensive analysis of the thermodynamic inhibition effect of urea to sII C3H8/CH4 hydrates on pressure and concentration of the inhibitor was carried out. The phase composition of the samples was analyzed by powder X-ray diffractometry at 173 K.

Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor-Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling.

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker's method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs-Helmholtz equation. Robinson-Mathias, and Peng-Robinson-Stryjek-Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.

Dataset for the experimental study of dimethyl sulfoxide as a thermodynamic inhibitor of methane hydrate formation.

To determine the ability of dimethyl sulfoxide (DMSO) to inhibit methane hydrate formation by the thermodynamic mechanism, we measured the pressures and temperatures of monovariant equilibrium of three phases: gaseous methane, aqueous DMSO solution, and methane hydrate. A total of 54 equilibrium points were obtained. Hydrate equilibrium conditions have been measured for eight different concentrations of dimethyl sulfoxide ranging from 0 to 55 mass%, at temperatures of 242-289 K and pressures of 3-13 MPa. Measurements were performed in an isochoric autoclave (volume of 600 cm3, inside diameter of 8.5 cm) at a heating rate of 0.1 K/h and intense fluid agitation (600 rpm) with four-blade impeller (diameter of 6.1 cm, blade height of 2 cm). The specified stirring speed for aqueous DMSO solutions at 273-293 K is equivalent to a range of Reynolds numbers of 5.3‧103-3.7‧104. The endpoint of methane hydrate dissociation at defined temperature and pressure values was taken as the equilibrium point. The anti-hydrate activity of DMSO was analyzed on a mass% and mol% scale. Precise correlations between the thermodynamic inhibition effect of dimethyl sulfoxide ΔTh and the influencing factors (DMSO concentration and pressure) were derived. Powder X-ray diffractometry was employed to examine the phase composition of the samples at 153 K. Measurement of ice freezing points in aqueous solutions of dimethyl sulfoxide (up to 50 mass%) at ambient pressure allowed us to clarify the location of the liquidus line in the DMSO-H2O system and to check the hydrate equilibrium data for thermodynamic consistency.

Direct Measurement of the Four-Phase Equilibrium Coexistence Vapor-Aqueous Solution-Ice-Gas Hydrate in Water-Carbon Dioxide System.

Precise data on the non-variant equilibrium of the four phases (vapor-aqueous solution-ice-gas hydrate) in P-T coordinates are highly desired for developing accurate thermodynamic models and can be used as reference points (similar to the triple point of water). Using the two-component hydrate-forming system CO2-H2O, we have proposed and validated a new express procedure for determining the temperature and pressure of the lower quadruple point Q1. The essence of the method is the direct measurement of these parameters after the successive formation of the gas hydrate and ice phases in the initial two-phase gas-water solution system under intense agitation of the fluids. After relaxation, the system occurs in the same equilibrium state (T = 271.60 K, P = 1.044 MPa), regardless of the initial parameters and the order of crystallization of the CO2 hydrate and ice phases. Considering the combined standard uncertainties (±0.023 K, ±0.021 MPa), the determined P and T values agree with the results of other authors obtained by a more sophisticated indirect method. Validating the developed approach for systems with other hydrate-forming gases is of great interest.

In Search of a Double Perovskite in the Phase Triangle of Bromides CsBr-CuBr-InBr3.

New bromide compounds A2BIBIIIBr6 with a double perovskite structure provide variety and flexibility of optoelectronic properties, and some of them are of poor toxicity in comparison with such popular lead halides. The promising compound with a double perovskite structure was proposed recently for the ternary system of CsBr-CuBr-InBr3. Analysis of phase equilibria in the CsBr-CuBr-InBr3 ternary system showed stability of the quasi-binary section of CsCu2Br3-Cs3In2Br9. Formation of the estimated phase Cs2CuInBr6 by melt crystallization or solid-state sintering was not observed, most likely, as a result of higher thermodynamic stability of binary bromides CsCu2Br3 and Cs3In2Br9. The existence of three quasi-binary sections was observed, while no ternary bromide compounds were found.

Phase Equilibria of the Fe-Cr-Er Ternary System in the Range 973-1273 K.

Phase relations of the Fe-Cr-Er system in the temperature range 973-1273 K were experimentally investigated using equilibrated alloys. The isothermal sections consisted of 9 single-phase regions, 16 two-phase regions, and 8 three-phase regions at 973 K and 1073 K. At 1273 K, the σ phase disappeared, and liquid appeared. All single phases had a solid solubility range that showed a downward trend with a decrease in temperature. The homogeneity range of the ErFe12-xCrx ternary compound was determined to be x = 1.8-4.5. The more accurate phase relations obtained in this work can better guide the preparation of Fe-Cr-Er alloys in actual production.