Equilibrium Tie-lines Research Articles

Separation of methanol and ethanol from azeotropic MTBE mixtures using choline chloride-based deep eutectic solvents

In this study, the performance of five different choline chloride – based deep eutectic solvents (DESs), including ChCl – urea, ChCl – ethylene glycol, ChCl – glycerol, ChCl – 1,2- propanediol, and ChCl – glucose, has been experimentally and computationally investigated for the purpose of liquid – liquid extraction at 298.15 K and 1 atm. In this regard, the effect of them on the extraction efficiency to separate methanol and ethanol from azeotropic systems, methyl tert-butyl ether (MTBE) + ethanol and MTBE + methanol, is studied. To synthesize these DESs, chlorine chloride as a hydrogen bond acceptor (HBA) is blended with urea, ethylene glycol, glycerol, 1,2- propanediol, and glucose as hydrogen bond donors (HBDs). Through the investigation, it is revealed that all the studied DESs deliver a distribution coefficient, β, that is higher than unity (β > 1). Similarly, the measured selectivities for these DESs have presented values that are far greater than unity (S ≫ 1). This is advantageous as it demonstrates their industrial applications. Furthermore, to have a better view of how effective they are in terms of the extraction capacity, the experimental data have been compared to the performance of ionic liquids used for the liquid – liquid extraction of MTBE + methanol. The reliability of the tie-line compositions was checked by applying the Othmer–Tobias equation. Additionally, to show the consistency, UNIQUAC Functional-group Activity Coefficients (UNIFAC) as a thermodynamic model has been employed to predict the equilibrium tie-lines. The predicted data is compared with the experimentally measured data through the calculation of the root-mean-square deviation (RMSD), showing that both predicted and experimental data are in a good agreement together.

The ternary system: Uranium – Zirconium – Silicon

Phase equilibria in the system U-Zr-Si were established at 1273 K by optical microscopy, X-ray micro analyses (XMA) and X-ray diffraction. One novel ternary compound was observed, U2-xZr3+xSi4 (x~1), extending at 1273 K from U8Zr47.6Si44.4 to U12Zr43.6Si44.4 (in at% from XMA). The crystal structure was elucidated by X-ray single crystal data refinement and found to be isotypic with the tetragonal Sc2−xRe3+xSi4-type (space group P41212). Uranium atoms partially and randomly occupy (~0.5 U+0.5 Zr) only the Zr-site 8b (~0, 0.35, 0.21) of the Sc2−xRe3+xSi4-type structure. UZr4Si4 is in equilibrium with all the many modifications of defect uranium disilicide (AlB2-type; U3Si5−x derivative structures) and forms a series of three-phase triangles, which characterize phase equilibria in the U-Zr-Si system at 1273 K: UZr4Si4 + (U1−xZrx)3Si2 (3 at% Zr, x~0.05) + L (~10 at% Si, 1 at% Zr), UZr4Si4 + (γU~90βZr~10) + (Zr1−xUx)3Si2 (3 at% U, x~0.05). Mutual solid solubilities are small and reside below about 3 at% for Zr in U3Si2 and U in Zr3Si2. Due to the equilibrium tie-lines, Zr3Si2 + (γU,βZr) and Zr2Si + (γU,βZr), no compatibility exists between the U-rich silicides U3Si or U3Si2 and zirconium metal.

Choline chloride-based deep eutectic solvents as green extractant for the efficient extraction of 1-butanol or 2-butanol from azeotropic n-heptane + butanol mixtures

In this study, choline chloride-based deep eutectic solvents are used as green extractant for the efficient extraction of 1-butanol or 2-butanol from azeotropic n-heptane + butanol mixtures at 298.15 K and atmospheric pressure. Choline chloride as hydrogen bond acceptor (HBA) is mixed with urea, ethylene glycol, glycerol, and 1,2-propanediol (propylene glycol) as hydrogen bond donors (HBDs) to study the effect of different choline chloride-based deep eutectic solvents on the extraction efficiency. The obtained results show that, although all the DESs provide solute distribution ratios smaller than unity (β < 1), the measured experimental selectivity values are much higher than unity (S> > 1), which is of interest for the economic feasibility of industrial extraction operations. The extraction capacity of the studied deep eutectic solvents for the separation of n-heptane +1-butanol mixture is compared with seven commonly used imidazolium-based ionic liquids. The experimental results are compared to UNIQUAC Functional-group Activity Coefficients (UNIFAC) model. It is visually observed that UNIFAC model predicts satisfactorily the equilibrium tie-lines, where the root-mean-square deviation (RMSD) for extraction of 1-butanol by ChCl-urea, ChCl-ethylene glycol, ChCl-glycerol and ChCl-1,2-propanediol are 2.99, 4.38, 1.12, and 1.56, respectively. In the case of 2-butanol extraction using the mentioned DESs, the RMSD is 0.69, 3.13, 1.47, and 1.11, respectively.

Measurement and Correlation of LLE Data for the Ternary System Water+Phosphoric Acid+1-Pentanol at 278.2 K and 288.2 K

In this study, experimental tie-line data analysis was conducted for the ternary system (water+phosphoric acid+1-pentanol) at 278.2 K and 288.2 K and atmospheric pressure. The compositions of equilibrium phases were determined using the acid-base and the Karl Fisher titration methods and mass balance calculations. Reliability of the experimental data was investigated using the Othmer–Tobias and Hand equations. The UNIQUAC thermodynamic model was applied for correlation of the equilibrium tie-line points. The experimental tie-lines were satisfactorily regressed using the thermodynamic model (%rmsd=2.48). Distribution coefficients and separation factors were determined over the biphasic area. Separation factors were greater than one in all the investigated feeds at the studied temperatures that guarantees the successful separation process. The Kamlet-Taft parameters were applied for the LSER modeling of the obtained distribution coefficients and separation factors. The effect of temperature on extraction process was investigated by adding a modification term in Kamlet-Taft equation. The ternary system revealed good fittings with the modified LSER model. The results showed that, the temperature decrement had positive effect on the extraction ability of the 1-pentanol for separating phosphoric acid from aqueous solution.

Measurement and Correlation of LLE Data for the Ternary System Water + Phosphoric Acid + 1-Undecanol at 303.2 K

Experimental solubility curve and tie-line data were obtained for the ternary system (water + phosphoric acid + 1-undecanol) at T = 303.2 K and ambient pressure. The cloud point method was employed to determine the binodal curve data. The mass fraction compositions of each layer were explored by acid-base and the Karl Fisher titration methods accompanied by mass balance calculations. For above mentioned ternary system, a type-1 LLE behavior was observed. The reliability of the experimental compositions was proved by using the Othmer–Tobias and Hand plots. The UNIQUAC and NRTL thermodynamic models were applied to correlate the equilibrium tie-line points. The experimental points were adequately regressed using the thermodynamic models. Distribution coefficients and separation factors were computed over the non-miscible region. For the separation process, separation factor should be greater than one and for the investigated system, this factor was suitable to apply separation treatment in all concentrations of phosphoric acid at the studied temperature. The Katritzky parameters were utilized for LSER modeling of distribution coefficients of the studied mixtures. The ternary system showed good fittings with the LSER model.

An analytical model with interaction between species for growth and dissolution of precipitates

An analytical model for growth in a semi-infinite matrix with cross-diffusion between species is presented. Application is given for precipitation of the γ′-phase in the γ-matrix during isothermal holding at 600 °C in the Ni - 7.56 at.% Al - 8.56 at.% Cr alloy. The exact time-dependent solutions for the solute profiles and the growth kinetics are validated with a numerical front-tracking simulation. The simulation of cross diffusion terms in a multicomponent alloy is thus demonstrated. Extension of the analytical solution is given for growth in a matrix of finite size. The driving force is then based on a mathematical estimation of the far-field composition. The Gibbs-Thomson effect is also accounted for to consider the effect of curvature on the equilibrium tie-lines. Comparison of analytical solution with the numerical front-tracking simulation shows excellent agreement. Results also point out the detrimental approximation of using the average composition of the matrix for computing the driving force as well as the limitation of the solution proposed by Chen et al. [Acta Mater. 56 (2008) 1890]. A detailed discussion is finally given on the origin of oscillations observed for the time evolution of the precipitate radius which alternates between growth and dissolution regimes, pointing out the combined role of solute fluxes and tie-lines compositions at the precipitate/matrix interface.

Liquid–Liquid Equilibrium Measurements for Model Systems Related to Catalytic Fast Pyrolysis of Biomass

We report liquid–liquid mutual solubilities for binary aqueous mixtures involving 2-, 3-, and 4-ethylphenol, 2-, 3-, and 4-methoxyphenol, benzofuran, and 1H-indene for the temperature range (300 < T/K < 360). Measurements in the water-rich phase for (2-ethylphenol + water) and (4-ethylphenol + water) were extended to T = 440 K and T = 380 K, respectively, to facilitate comparison with literature values. Liquid–liquid equilibrium tie-line determinations were made for four ternary systems involving (water + toluene) mixed with a third component: phenol, 3-ethylphenol, 4-methoxyphenol, or 2,4-dimethylphenol. Literature values at higher temperatures are available for the three (ethylphenol + water) systems, and in general, good agreement is seen. The ternary system (water + toluene + phenol) has been studied previously with inconsistent results reported in the literature, and one report is shown to be anomalous. All systems are modeled with the predictive methods NIST-modified-UNIFAC and NIST-COSMO-SAC, with ...

Erratum to: Determination of the Fe-Cr-Mo Phase Diagram at Intermediate Temperatures using Dual-Anneal Diffusion Multiples

A recently developed dual-anneal diffusion-multiple approach is employed to the determination of the Fe-Cr-Mo phase diagram at intermediate temperatures. Diffusion multiples of Fe-Cr-Ni-Co-Mo were first annealed at 1200 °C for 500 h to create wide ranges of solid solution compositions. Subsequent annealing of the diffusion multiples at individual intermediate temperatures induced various precipitate phases. Electron probe microanalysis (EPMA) across the interface between large precipitates and the matrix phase provided local equilibrium information for the establishment of equilibrium tie-lines which are utilized to construct the Fe-rich part of the Fe-Cr-Mo isothermal sections at 900 and 800 °C. The Mo-rich part of the isothermal sections at intermediate temperatures was not obtained due to the sluggish kinetics of precipitation and growth, resulting in too small precipitates for reliable EPMA composition evaluation. A complete 1200 °C isothermal section of the Fe-Cr-Mo system is also established from EPMA data on a water quenched diffusion multiple that was annealed at 1200 °C for 500 h only without a second anneal.

Critical nucleus composition in a multicomponent system.

The properties of a critical nucleus are derived using the capillarity theory in the framework of classical nucleation. An analytical solution for the composition of a critical nucleus is given for low supersaturation. The theory is valid for any multicomponent systems. It is found that the deviation in nucleus composition from the equilibrium tie-line is mainly due to the difference in the Hessian of the Gibbs energy of the phases and the magnitude of the deviation in composition from equilibrium is order of the supersaturation. Despite our analysis strictly holds for low supersaturation, this suggests strong deviations near the spinodal line.

Ostwald ripening in multicomponent alloys

A general theory of coarsening in a multicomponent alloy is developed, accounting for off-diagonal terms in the diffusion tensor. The analysis is valid for a non-ideal and non-dilute solution. The asymptotic analysis reveals that the temporal exponents for the average particle radius, number of particles per volume and both the precipitate and matrix compositions are identical to the binary limit. However, the amplitudes are different. It is found that the vector representing the matrix supersaturations coincides with the equilibrium tie-line, but in most alloys this is not the case with the precipitate compositions. It is also shown that considering only a low mobility species does not yield a description of the temporal evolution of the matrix and precipitate compositions, even though this can be the case for the average particle size and the number density of precipitates.

Liquid–liquid equilibrium tie-line compositions at elevated temperatures and pressures for the I2–H2O and HI–I2–H2O systems of the Sulfur–Iodine Cycle

Abstract Liquid–liquid equilibrium (LLE) tie-line compositions were measured for the binary system iodine–water and the ternary system hydrogen iodide–iodine–water (HI–I2–H2O) at 199.1 and 252.2 °C, at pressures of 60 bar, conditions of interest for the reactive distillation column of the Sulfur–Iodine Cycle. To keep the HI decomposition reaction negligible, a continuous-flow apparatus was used to minimize residence times at the elevated temperatures. Sixteen equilibrium tie lines were measured, using overall feed compositions ranging from 0.0 to 3.3 mol % HI, and the plait-point composition for 199.1 °C was estimated. Sample compositions for the lighter, water-rich phase and the heavier, I2-rich phase were both determined via titration of HI and I2, with water being obtained by difference. The phase behavior indicates that the selectivity of HI for the aqueous phase can be large, ranging from 10 to 100+ for tie lines removed from the critical region.

The ternary system: Silicon–tantalum–uranium

Phase equilibria in the ternary system Si–Ta–U have been established in an isothermal section at 1000 °C by optical microscopy, electron probe microanalysis and X-ray diffraction. Two novel ternary compounds were observed and were characterised by X-ray powder Rietveld refinement: stoichiometric τ 1-U 2Ta 3Si 4 (U 2Mo 3Si 4-type, P2 1/ c; a = 0.70011(1), b = 0.70046(1), c = 0.68584(1) nm, ß = 109.38(1); R F = 0.073, X-ray powder Rietveld refinement) and τ 2-U 2− x Ta 3+ x Si 4 at x ∼ 0.30 (Sc 2Re 3Si 4-type = partially ordered Zr 5Si 4-type, P4 12 12; a = b = 0.69717(3)(1), c = 1.28709(4) nm; R F = 0.056; X-ray single crystal data). Mutual solubility of U-silicides and Ta-silicides are found to be very small i.e. below about 1 at.%. Due to the equilibrium tie-line Ta 2Si–U(Ta), no compatibility exists between the U-rich silicides U 3Si or U 3Si 2 and tantalum metal. Single crystals obtained from alloys slowly cooled from liquid (2000 °C), yielded a fully ordered compound U 2Ta 2Si 3C (unique structure type; Pmna, a = 0.68860(1); b = 2.17837(4); c = 0.69707(1) nm; R F2 = 0.048).

Reactive interdiffusion: Deviation from local equilibrium in the Fe–NiTiO 3 couple

Deviation from local equilibrium between Fe–Ni alloy and (Fe,Ni)TiO 3 solid solution in the reaction–diffusion zone of the Fe–NiTiO 3 couple at 1273 K is evaluated by comparing the measured compositions in the zone with experimentally determined equilibrium tie-lines. The deviation is quantified by computing the Gibbs energy change for the reaction, Fe + NiTiO 3 → FeTiO 3 + Ni, from measured compositions in the zone and activity data available in the literature. Except near the extremities of the zone, the computed Gibbs energy change is constant, 8.2 kJ mol −1 higher than the standard Gibbs energy change for the reaction.

Development of a Simple Model for the Prediction of Tie-Lines for Ternary Systems

A novel, semi-analytic, and numerically convenient algorithm has been proposed for predicting the equilibrium tie-line composition with the given overall feed composition and binary interaction parameters of established models (UNIQUAC and modified UNIQUAC) for ternary liquid-liquid systems. The merit of the proposed model rests on the selection of the distribution coefficient of each component as unknown variables instead of the mole fraction. Moreover, the model relies on the analytical solution of the extract fraction instead of adopting any numerical schemes that are commonly practiced to solve the same. Its veracity has been successfully tested with the experimental results for standard ternary systems reported in literature. The calculation procedure renders a distinct advantage over the accepted existing methods from the utilitarian view point.

Effects of solute concentrations on kinetic pathways in Ni–Al–Cr alloys

The kinetic pathways resulting from the formation of coherent γ′-precipitates from the γ-matrix are studied for two Ni–Al–Cr alloys with similar γ′-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni–7.5Al–8.5Cr at.% and Ni–5.2Al–14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the γ′-precipitates of the alloys are similar, though the degrees of γ′-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the γ′-precipitate average radii and the γ-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the γ-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the γ′-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Measurements and Correlation of Liquid–Liquid Equilibria of (Water + Ethanol + Dimethyl Carbonate + 2,2,4-Trimethylpentane or n-Heptane) and (Water + Dimethyl Carbonate + n-Heptane + Toluene)

The experimental equilibrium tie-line compositions for the three quaternary mixtures of (water + ethanol + dimethyl carbonate + 2,2,4-trimethylpentane), (water + ethanol + dimethyl carbonate + n-heptane), and (water + dimethyl carbonate + n-heptane + toluene) and the five ternary mixtures of (water + ethanol + dimethyl carbonate), (water + dimethyl carbonate + n-heptane), (water + dimethyl carbonate + 2,2,4-trimethylpentane), (water + dimethyl carbonate + toluene), (water + n-heptane + toluene) have been measured at a temperature of 298.15 K and ambient pressure. The experimental ternary and quaternary (liquid + liquid) equilibrium data were correlated with the modified and extended UNIQUAC models including binary and multicomponent interaction parameters.

Using a Multiple-Mixing-Cell Model to Study Minimum Miscibility Pressure Controlled by Thermodynamic Equilibrium Tie Lines

In this work, we demonstrate that our simulation approach, referred to as the multiple-mixing-cell model, gives the same results as the analytical method for two-phase gas flooding. For a gas−oil system with nc components, the gas injection process leads to nc + 1 constant-composition zones, and the compositional path of the process, i.e., the path in composition space representing the total composition, is controlled by nc − 1 key thermodynamic equilibrium tie lines: the initial tie line, the injection tie line, and nc − 3 crossover tie lines. In addition, our approach clearly demonstrates that both the gas/oil ratio and fluid mobility do not affect tie-line compositional paths, i.e., compositional paths that lie on the thermodynamic equilibrium tie lines, but they do affect nc − 2 non-tie-line compositional paths. Therefore, neither the gas/oil ratio nor the fluid mobility affects the minimum miscibility pressure (MMP). In the context of the multiple-mixing-cell model, this fact has never been explicitly clarified before.

Ultrahigh-Temperature Metamorphism in the Palni Hills, South India: Insights from Feldspar Thermometry and Phase Equilibria

The Southern Indian shield is a classic terrain that may be regarded as a model for Precambrian crustal evolution. The Palni Hills represent a portion of the granulite-facies terrain of the Madurai block. Determination of ultrahigh temperature (UHT) in granulites requires re-integration of antiperthite, perthite, and mesoperthite to yield original hypersolvus feldspar compositions, which then yield peak metamorphic temperatures by feldspar solvus geothermometry. Backscattered electron images were used to calculate modal proportions of host and exsolved lamellae in feldspars. These data were combined with quantitative point chemical analyses of both host and lamellae to obtain re-integrated feldspar compositions, providing consistent ultrahigh temperatures in excess of 900°C. The feldspar compositions coexisting during closure of intercrystalline Al-Si exchange were calculated by reversing the K-Na exchange through shifts of Ab and Or contents of both feldspars at constant An contents until the equilibrium tie-line and the common isotherm on the ternary feldspar solvus were found. Besides, UHT metamorphic conditions were also obtained using the convergence method in exchange thermometers, suggesting peak metamorphism conditions at > 900°C at 9 kbar for the Palni granulites. Prevalence of UHT conditions in the many parts of the world could be useful in deducing Proterozoic tectonometamorphic processes along the deep crust-mantle interface.

Quaternary (liquid + liquid) equilibria for (water + 2-propanol + 1,1-dimethylethyl methyl ether + diisopropyl ether) at the temperature 298.15 K

(Liquid + liquid) equilibrium tie-lines were measured for one ternary system { x 1H 2O + x 2(CH 3) 2CHOH + (1 − x 1 − x 2)CH 3C(CH 3) 2OCH 3} and one quaternary system { x 1H 2O + x 2(CH 3) 2CHOH + x 3CH 3C(CH 3) 2OCH 3 + (1 − x 1 − x 2 − x 3)(CH 3) 2CHOCH(CH 3) 2} at T = 298.15 K and P ∘ = 101.3 kPa. The experimental (liquid + liquid) equilibrium results were satisfactorily correlated by modified and extended UNIQUAC models both with ternary and quaternary parameters in addition to binary ones.

Quaternary (liquid + liquid) equilibria for (methanol + 2,2,4-trimethylpentane + toluene + 1,1-dimethylpropyl methyl ether or 1,1-dimethylethyl methyl ether) at T = 298.15 K

The experimental equilibrium tie-lines of two quaternary mixtures for (methanol + 1,1-dimethylpropyl methyl ether + toluene + 2,2,4-trimethylpentane) and (methanol + 1,1-dimethylethyl methyl ether + toluene + 2,2,4-trimethylpentane) were measured at the temperature 298.15 K and ambient pressure. The quaternary experimental results and their constituent ternaries have been satisfactorily predicted using binary parameters alone obtained by an associated-solution model that takes into account association of methanol molecules and solvation between (methanol + polar molecules) with allowance for a non-polar interaction given by an extended form of the UNIQUAC model. The results are further compared with those correlated by modified and extended forms of the UNIQUAC models that include multi-body interaction parameters in addition to binary ones.