Liquid Equilibrium Research Articles

A Geometric Approach for the Calculation of the Nonrandomness Factor Using Computational Chemistry.

The nonrandomness factor (α) is a parameter related to the polarity (and consequent randomness of spatial orientation) of the molecules and is generally fixed between 0.20 and 0.47 since no technique has been developed so far for its accurate estimation. However, the consideration of a constant nonrandomness factor for mixtures is known to harden azeotrope description and to cause convergence issues in both the Nonrandom Two-Liquid (NRTL) and Universal Quasi-chemical (UNIQUAC) models, which have been widely applied in the correlation of phase equilibria. In this work, a novel geometric methodology, named Porto's approach, was applied in the calculation of the nonrandomness factors for 50 pure components (mainly alkanes, alcohols, and ketones) at 298.15 K and 0.1 MPa. This methodology relied on computational chemistry (Density Functional Theory, DFT) to minimize the energy of molecules in a cavity within a solvent composed of molecules of their own (applying the Polarizable Continuum Model, PCM), and thereafter define the most stable chemical configuration in the pure liquid state. Then, the nonrandomness factor of each component was determined based on its molecular dipole moment, which was calculated after a population analysis of the optimized partial electrical charges with the Natural Bond Orbital (NBO) function. This innovative approach was applied in the correlation of liquid-liquid equilibria (LLE) data for 15 ternary systems comprising only neutral molecules with NRTL and UNIQUAC. The classical methods (α = 0.2 or 0.3 for NRTL and α = 0.2 for UNIQUAC) were compared against the usage of a component-specific nonrandomness factor, and similar standard deviations were obtained. Hence, this work is considered a strong advance in the application of these excess free Gibbs energy models to phase equilibria estimation and opens the door to more accurate thermodynamic modeling of nonideal mixtures (such as the ones containing electrolytes) by providing enhanced physical meaning to the nonrandomness factors.

Clean and efficient recovery of gallium–indium alloy from gallium-based liquid metal waste using a two-stage vacuum distillation method

Gallium (Ga) and indium (In) are rare metals widely used in the high-tech industry. Gallium-based liquid metal (G-LM) waste is produced during the preparation of liquid metal and related products. G-LM waste is a potential source of gallium and indium. In this study, the saturated vapor pressure, separation coefficient, and gas–liquid equilibrium phase diagram were determined using the simplified molecular interaction volume model. A two-stage vacuum distillation method was used to recover Ga–In alloy from G-LM waste. First, low-temperature vacuum distillation was used to recover 98.23 % of Zn under optimal conditions (1–5 Pa; 773 K; 60 min). Then, the Ga–In alloy was recovered through high-temperature vacuum distillation. Under the optimal conditions (1–5 Pa; 1523 K; 120 min), the recovery rates of gallium and indium were 85.14 and 95.23 %, and the content of Ga–In alloy in the product was 99.46 %. Compared with the traditional hydrometallurgical process for recovering gallium and indium, this process generates no exhaust gas or waste. In addition, this new method is simple, efficient, clean, and pollution-free. Overall, this new method for recovering Ga–In alloy provides a new avenue for comprehensively utilizing G-LM waste.

Experimental determination of liquid-liquid equilibrium and interaction insights for ternary mixtures 2,2,2-trifluoroethanol + water + pyridinium-based ionic liquids

Background2,2,2-Trifluoroethanol (TFE) as an important fluorinated alcohol has been widely applied in industry. An aqueous solution containing TFE can be obtained during its production and applications. Because TFE and water can form an azeotrope, it is difficult to recover TFE by conventional distillation. MethodsTo separate TFE and water by liquid-liquid extraction, three pyridyl ionic liquids (ILs), n-ethylpyridinium bis(trifluoromethyl sulfonyl)imide ([Epy][NTf2]), n-butylpyridinium bis(trifluoromethyl sulfonyl)imide ([Bpy][NTf2]) and n-hexylpyridinium bis(trifluoromethyl sulfonyl)imide ([Hpy][NTf2]) were adopted as the extraction reagents. The liquid-liquid equilibrium data for (ILs + TFE + water) were measured at 101.3 kPa and 298.15 K. The separation ability of the three extractants was assessed by distribution coefficient and selectivity. The experimental data were regressed using the NRTL model. Significant findingsThe results showed that IL [Epy][NTf2] had a better ability to recover TFE from its aqueous solution compared to the other two ILs. The correlated results by the NRTL model agreed with the experimental data. Besides, the calculated values of bond length, interaction energy, electrostatic potential and reduced density gradient between the molecules of the ILs and TFE revealed the relation between the IL structures and their extraction performance, which can provide a route for designing a rational IL for separating the mixture of water and TFE.

Thermodynamics of antimony—selenium alloys formation and evaporation

The thermodynamic functions of alloy formation and evaporation were considered for two particular systems — Sb – Sb2Se3 and Sb2Se3 – Se in connection with the presence of congruently melting compound Sb2Se3 in the antimony—selenium system. The calculations are based on the partial vapor pressure values of the components forming the particular systems. The thermodynamic activity of antimony selenide and selenium as the most volatile components in the systems was calculated based on the saturated vapor pressure values of antimony selenide over the Sb – Sb2Se3 and selenium melts over Sb2Se3 – Se liquid alloys determined by the boiling point method (isothermal variant). Similar functions of the low volatile components in the above systems: Sb in the first system and Sb2Se3 in the latter one was calculated by numerical integration of the Gibbs—Duhem equation using the substitution proposed by Darken. The partial pressures of antimony selenide and antimony over Sb – Sb2Se3 and Sb2Se3 – Se melts were approximated by temperature—concentration relationships. The system is distinguished with a positive deviation from ideality due to the presence of a delamination region in the first system. The partial and integral entropies and enthalpies of the formation of liquid alloys were calculated based on the values of component activities found as the ratio of the partial vapor pressure of an element or compound above the solution to the saturated vapor pressure of a pure element or compound. The partial and integral functions of alloy formation are presented in the form of graphical dependences on the selenium amount in the melt. The obtained thermodynamic constants will replenish the physical and chemical data base and will be used to calculate the boundaries of the vapor— liquid equilibrium fields on the diagram of state, allowing to determine the possibility and completeness of distillation separation of molten systems.

Liquid–Liquid Equilibrium Data of Ternary Mixture of Polymer, Sodium Thiosulfate, and Water: Effect of Type and Molar Mass of Macromolecule

Liquid–Liquid Equilibrium Data of Ternary Mixture of Polymer, Sodium Thiosulfate, and Water: Effect of Type and Molar Mass of Macromolecule

Thermodynamic and molecular insights into the separation of ethanol/ethyl propionate by extraction using low transition temperature mixtures

Low-transition temperature mixtures (LTTMs) have been proposed as green solvents for the separation of ethanol (EtOH)/ethyl propionate (EtPa) azeotropes. COSMO-SAC model was used to screen LTTMs, and ammonium acetate, ethylammonium chloride, and choline chloride were selected as hydrogen bond acceptors to form LTTMs with ethylene glycol. Liquid-liquid phase equilibrium experiments were carried out for the screened LTTMs and the separation system to confirm the validity of the selected solvents. And the distribution coefficients of EtOH in the three LTTMs were all greater than 1.2, and the selectivity for EtOH ranged from 6 to 50. The separation mechanism at the molecular level was revealed through quantum chemical calculations and wave function analysis. The thermodynamic behavior of the EtOH/EtPa/LTTMs system and the role of hydrogen bonding interactions were systematically investigated. The results indicated that electrostatic forces are the main molecular interactions, and the stronger interaction of LTTMs with ethanol is the basis for achieving the azeotropic separation.

Solid-liquid phase equilibrium and thermodynamic model of ternary system (NH4+ //SO42−, H2PO4−–H2O) from 313.15 to 343.15 K

A tremendous amount of wastewater containing ammonium salts, mainly NH4H2PO4 and (NH4)2SO4, has been produced in the production of cathode material of lithium iron phosphate (LFP). However, as an important basis for salt separation, the solid–liquid phase equilibrium (SLPE) of these two salts has been investigated by few studies. In this study, SLPE of the ternary system (NH4+ //SO42−, H2PO4−–H2O) from 313.15 K to 343.15 K at 101.2 kPa were investigated by isothermal dissolution method, and the corresponding physicochemical properties (density, viscosity, and pH) of saturated solution were measured. The phase diagram is composed of one invariant point, two univariant curves, and two single-salt crystallization fields for NH4H2PO4 and (NH4)2SO4. Comparing the phase diagrams from 263.15 K to 343.15 K, it is obvious that two single-salt crystallization fields shrink with increasing temperature. And the area reduction of NH4H2PO4 in two salts is more significant. When the temperature drops below 268.15 K, the ice crystallization field would appear. Neither single-salt solid solution, hydrous salt nor double salt was found in the whole temperature range. Furthermore, Pitzer model was successfully applied to describe the SLPE of the ternary system at temperatures from 273.15 K to 343.15 K. The lacking Pitzer-model parameters of mixed electrolytes (θSO4-H2PO4 and ψNH4-SO4-H2PO4) were calculated, and the temperature coefficients of model parameters and dissolution equilibrium constant were obtained. The importance of this study is that it supplies basic data and theoretical references for the separation and resource utilization of two ammonium salts from wastewater in the LFP batteries industry.

Solid–Liquid Equilibrium Modeling and Analysis of Acetylcysteine in 12 Pure Solvents

Solid–Liquid Equilibrium Modeling and Analysis of Acetylcysteine in 12 Pure Solvents

Studies on solubility measurement of codeine phosphate (pain reliever drug) in supercritical carbon dioxide and modeling

In this study, the solubilities of codeine phosphate, a widely used pain reliever, in supercritical carbon dioxide (SC-CO2) were measured under various pressures and temperature conditions. The lowest determined mole fraction of codeine phosphate in SC-CO2 was 1.297 × 10−5 at 308 K and 12 MPa, while the highest was 6.502 × 10−5 at 338 K and 27 MPa. These measured solubilities were then modeled using the equation of state model, specifically the Peng-Robinson model. A selection of density models, including the Chrastil model, Mendez-Santiago and Teja model, Bartle et al. model, Sodeifian et al. model, and Reddy-Garlapati model, were also employed. Additionally, three forms of solid–liquid equilibrium models, commonly called expanded liquid models (ELMs), were used. The average solvation enthalpy associated with the solubility of codeine phosphate in SC-CO2 was calculated to be − 16.97 kJ/mol. The three forms of the ELMs provided a satisfactory correlation to the solubility data, with the corresponding average absolute relative deviation percent (AARD%) under 12.63%. The most accurate ELM model recorded AARD% and AICc values of 8.89% and − 589.79, respectively.

Flowsheets for hydroxyacetone–phenol binary mixture separation: The use of special distillation methods

Objectives. To study the possibility of hydroxyacetone–phenol binary mixture (a constituent of a mixture of phenol production by the cumene method) separation in flowsheets based on the use of distillation special methods. This is the addition of separating agents to increase the relative volatility of the components of the original mixture, and the variation of pressure in the columns.Methods. A computational simulation in Aspen Plus® was used as the research method. Mathematical modeling of the vapor–liquid equilibrium was carried out using a local compositions model Non-Random Two Liquid. The viability of the latter was confirmed by comparing experimental and calculated on phase equilibrium data, and azeotropic data. The average relative error does not exceed 3%.Results. The dependence of the composition and boiling point of the hydroxyacetone–phenol azeotrope on pressure was determined in a computational experiment (as the pressure increases, the azeotrope is enriched with phenol). The possibility of using a complex of columns operating under different pressures to separate the mixture was shown (the shift of the azeotrope is about 9%). The change in the relative volatility of components of the original mixture in the presence of a high(diethylene glycol) and a low-boiling (acetone) separating agent was investigated. Both solvents are selective agents used in extractive and re-extractive distillation processes. Three technological separation flowsheets containing two distillation columns were proposed.Conclusions. The study established the operation parameters of the columns (number of theoretical stages, feed stages of the original mixture and separating agent, and reflux ratio) and energy consumption (total heat supplied to the columns boiler) of three separation flowsheets ensuring the production of products of a given quality (not less than 0.99 mol fractions). The flowsheet with diethylene glycol is characterized by the lowest energy consumption. It is recommended that complexes of extractive and re-extractive distillation be further optimized. This enables the second product of cumulus production—acetone—to be involved in the technological cycle.

Vapor-liquid-liquid equilibrium (VLLE), density, and viscosity of the ternary mixtures of normal hexane, water and bitumen at T=185–210°C and at P= 2.5 MPa

This paper presents a study on the vapor-liquid-liquid equilibrium (VLLE) of a ternary system consisting of normal-hexane (n-C6) as a solvent, water (H2O), and Mackay River bitumen. The study was conducted at temperatures ranging from 185 to 210 °C and a pressure of 2.5 MPa. The solvent/steam and solvent/bitumen ratios were varied to understand the effect of solvent (n-C6) on the phase behavior and the thermophysical properties of the associated phases. The co-injected solvent with steam is often reported as the concentration of solvent in the solvent/steam mixture. Two concentrations of n-C6 in n-C6/water mixture, including mole fractions of 0.01 and 0.05 (i.e., 6.85 and 27.70 vol.%), were considered to examine the effect of the co-injected solvent with steam. Also, two different mole fractions of n-C6 in the mixture of bitumen/n-C6 at 0.7 and 0.4 (37.45 and 14.61 vol.%), respectively, were considered to examine the effect of solvent solubility in bitumen. In addition to the VLLE study, the viscosity and density of the two distinct liquid phases, hydrocarbon-rich oleic and water-rich aqueous phases, were measured and reported. The results from the experiment infer that the concentration of n-C6 co-injected with steam does not significantly affect the equilibrium phase concentrations and thermophysical properties. However, the mixture showed liquid-liquid equilibria (LLE) instead of the vapor-liquid-liquid equilibria (VLLE) when the concentration of n-C6 in bitumen/solvent mixture was less than the equilibrium solubility of n-C6 in the hydrocarbon-rich phase at that operating condition. Furthermore, the results suggest that the presence of bitumen in equilibrium with n-C6 and H2O has no significant effect on the concentration of n-C6 in the vapor phase when compared with the n-C6/H2O binary mixture. Thermodynamic modelling of the VLLE data was performed using the cubic plus association equation of state (CPA EoS). The matching parameters were obtained by tuning the two-phase data, and those parameters were used in predicting the VLLE data. The model was also used to construct the phase regions of the solvent/bitumen/water system on the ternary diagram at different temperatures and pressures. Different phase regions were determined by phase stability analysis. The findings provide insight into steam/solvent condensation behavior with applications to the solvent-aided thermal recovery of bitumen from oil sands.

Recovery of 1,4-butanediol from aqueous solutions through aqueous two-phase systems with K2CO3

1,4-butanediol (BDO) can be produced by the biotechnological route; however, the process of separating BDO from fermentation broths is energy-intensive due to its high boiling point and complete miscibility with water, which motivates to propose separation routes that involve energy savings. Therefore, an aqueous two-phase system was proposed for the recovery of BDO from aqueous solutions using K2CO3 as a phase-forming agent, without the need for additional solvent. The liquid-liquid equilibrium of the system K2CO3 + BDO + H2O was determined at 25 °C and the ENRTL-RK thermodynamic model was used to correlate the experimental data and perform the process simulation in Aspen Plus. Applying this technique, it was possible to concentrate a BDO solution from 12.5% w/w to 84.58% w/w in a liquid-liquid extraction stage with a recovery of 99.59%. Therefore, K2CO3 is a dehydrating agent that could be used for the recovery of BDO obtained by fermentation.

Experimental data driven thermodynamic modelling and process simulation for biogas upgrading

Data driven thermodynamic models has a great potential to add value to the accuracy of simulation processes. In this study experimental data driven e-NRTL activity coefficient model is used to evaluate the behavior of MEA/AMP and MDEA/AMP aqueous systems for biogas upgrading. The vapor liquid equilibrium (VLE) experimental data is used for regression of the electrolyte pair parameters of e-NRTL activity coefficient model, which were then used to design the process for biogas upgrading by using Aspen Plus in combination with MATLAB. Experiments have been carried out for CO2 solubility as a function of CO2 partial pressure (PCO2) at different amine blending ratios such as 9/21/70, 15/15/70, and 21/9/70 (w/w/w percent) for each MEA/AMP/H2O and MDEA/AMP/H2O systems at a wide temperature range of 323.15–383.15 K. The importance of regressed parameters was confirmed through global sensitivity analysis (GSA) using Monte Carlo simulation. The local sensitivity analysis (LSA) and GSA for biogas upgrading process based on data driven thermodynamic modeling have been carried out in terms of the biomethane purity, reboiler heat duty, and methane slip. Finally, the optimal process parameters were found through multi-objective optimization (MOO) for developed biogas upgrading process.

Study on drug separation in Two-Phase aqueous systems using deep eutectic solvent consisting of choline chloride and 1,2 propanediol

Biphasic-aqueous systems have been the subject of extensive research due to their strength to simultaneously separate and purify active pharmaceutical molecules with high efficiency and purity. Aqueous Two-Phase Systems (ATPS) have been used to extract and purify cells, nucleic acids, proteins, antibodies, and tiny molecules due to their intermolecular interaction and chemical makeup. We used a deep eutectic solvent containing (choline chloride and 1,2 propanediol), K2HPO4, and water in the initial investigation of the biphasic curve of this system at the temperature of 298.15 K and atmospheric pressure. Furthermore, we used the ATPSs to study the separation of the selected pharmaceuticals. As new findings, we examined the partition coefficient and the impact of variables such as salt and the deep eutectic solvent concentration on the partitioning of the drugs. Based on the present finding, the pharmaceuticals have the propensity to be extracted in the top phase, which is rich in deep eutectic solvents. Finally, we conducted thermodynamic modeling of the present aqueous two-phase system (ATPS) using experimental liquid–liquid equilibrium data employing the nonrandom two-liquid nonrandom factor (NRTL-NRF) and NRTL models. The NRTL-NRF model can accurately correlate the aqueous two-phase system's thermodynamic behavior with the average relative deviation percent of 4.22.

Temperature stability of a Joule–Thomson microcooler operating with pure and mixed gases

Benefiting from the developments in micromachining technologies, Joule–Thomson (JT) cryogenic coolers have been miniaturized for cooling cold electronics based either on semiconductor, superconductor, or a combination of the two. The performance of these electronics is affected not only by temperature but also by temperature stability; however, many problems related to the temperature stability of JT microcoolers have not been solved. In this study, we investigate experimentally the performance of a JT microcooler operating with pure nitrogen gas, nitrogen/methane mixture, and nitrogen/ethylene mixture. The cool-down curves and the cooling powers of the microcooler operating with the three types of working fluids between 0.1 MPa and 6.0 MPa are presented. Based on the cooling power measurements, the effect of heat load on the temperature stability of the microcooler is discussed. The microcooler operating with nitrogen/ethylene mixture demonstrates the best temperature stability due to its characteristics of vapor–liquid–liquid equilibrium. Besides the properties of the working fluids, the degree of change in mass-flow rate of the microcooler also affects the temperature stability. This study is conducted to promote the widespread use of cryogenic electronics that are sensitive to the temperature fluctuation.

Enhancing aromatics extraction by double salt ionic liquids: Rational screening‐validation and mechanistic insights

AbstractDespite offering remarkable advantages as solvents, double salt ionic liquids (DSILs) have been scarcely studied for extractive dearomatization from hydrocarbons as well as many other applications, thus urging a theoretical guidance method. In this work, a systematic framework combining the rational screening validation and mechanistic analysis is proposed for tailoring DSILs for the o‐xylene/n‐octane separation. From an initial pool of commercially available ionic liquids (ILs), key thermodynamic properties of paired DSILs are predicted by COSMO‐RS while their important physical properties are estimated from those of corresponding parent ILs (retrieved from experimental database or predicted by a deep learning model). Promising DSILs are tested by liquid–liquid equilibrium experiments, wherein the effect of ion ratio is also evaluated. The mechanism underlying the tunability of DSIL thermodynamic properties is disclosed by quantum chemistry calculation and molecular dynamics simulation. This work can be a valuable reference for guiding the design of DSILs for diverse applications.

Dynamical correlations in simple disorder and complex disorder liquids

Liquids in equilibrium exhibit two types of disorder, simple and complex. Typical simple disorder liquid is liquid nitrogen, or weakly polar liquids. Complex liquids concern those who can form long lived local assemblies, and cover a large range from water to some soft matter and biological liquids. The existence of such structures leaves characteric features upon the atom-atom correlation functions, concerning both atoms which directly participate to these structures and those who do not. The question we ask here is: do these features have also characteristic dynamical aspects, which could be tracked through dynamical correlation functions? Herein, we compare the van Hove function, intermediate scattering function and the dynamical structure factor, for both types of liquids, using force field models and computer simulations. The calculations reveal the paradoxical fact that neighbouring atom correlations for simple disorder liquids relax slower than that for complex disorder liquids, while prepeak features typical of complex disorder liquids relax even slower. This is an indication of the existence of fast kinetic self-assembly processes in complex disorder liquids, while the lifetime of such assemblies itself is quite slow. This is further confirmed by the existence of a very low-k dynamical pre-peak uncovered in the case of water and ethanol.

Entrainer assisted production of high purity 2-phenyl ethyl acetate by reactive distillation

Reactive distillation (RD) is a promising alternative for the processes involving reversible reactions. In this work, we examine its potential for the esterification of a heavy alcohol (2-phenyl ethyl alcohol) with acetic acid in the presence of an ion exchange resin (Amberlyst-15) as the catalyst. The proposed RD process facilitates separation of the desired product, 2-phenyl ethyl acetate, in the pure form and provides a cost-effective and compact alternative to the conventional batch process. We determine the feasibility of this approach by conducting experiments in a laboratory-scale hybrid reactive distillation column having structured packings filled with Amberlyst-15. The experimental results are compared with the predicted values from an equilibrium-staged RD model. The model uses reaction kinetics developed in our earlier studies and the vapor–liquid equilibrium model is based on the experimental data generated in the present work and data available in literature. The experimentally validated model is further used to identify the best possible operating and design parameters to achieve high purity, high conversion and longer catalyst life. All in all, entrainer-based reactive distillation was found to be feasible in this case. The methodology followed here can be easily extended to similar reactions of heavy alcohols with lower carboxylic acids like acetic acid.

Trace elements in IVA iron meteorites explained by limited solid–liquid equilibration during inward solidification

Iron meteorites are windows into the formation and evolution of planetesimal cores. The trace element compositions of IVA iron meteorites are enigmatic; specifically, to explain the fractionations of different elements requires various sulfur contents of the parent liquid. Here, we propose a possible solution to this problem. IVA irons are thought to sample an exposed core that underwent inward solidification. In an inward solidifying core, sulfur-rich liquids expelled by crystallization are buoyant and stably stratified in the interstices of the mushy solidification front, until they eventually solidify at the eutectic point. Solidification proceeds through in-situ dendritic crystallization of mushy parcels of identical compositions, with the absence of chemical fractionation. In order for fractionation to take place, “pristine” liquids must flow into the mushy front and react with solids, which would be possible if circulation is driven by external forcing, for example, collisions. In this picture, the fluid exchange (which enables fractionation) is driven by occasional events, and each incremental solid can react with only a limited amount of liquid during solidification. We develop a simple model to describe the fractionation associated with this limited solid–liquid equilibration. With this model, we can explain the concentrations of different elements satisfactorily with a single sulfur content (∼5wt%) of the IVA iron parent liquid. Assuming that the stirring is caused by collisions to the solidifying body, we combine the new model for element fractionation with a model for solidification (as a Stefan problem) to suggest a frequency on the order of once per few thousand years for collisions that are large enough to cause the required stirring.

Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column

This study focuses on separating a mixture consisting of 1,2-ethanediol (1,2-ED), 1,3-propanediol (1,3-PD), and 1,4-butanediol (1,4-BD). Vapor–liquid equilibrium (VLE) data for 1,2-ED + 1,4-BD and 1,3-PD + 1,4-BD are determined at 101.3 kPa using a modified Rose equilibrium still. The consistency of the VLE data is checked with both Redlich–Kister and Fredenslund tests. The VLE data are fitted by the Wilson, NRTL, and UNIQUAC activity coefficient models. All three models can effectively correlate the VLE data. Then, the separation of the mixture is designed with the NRTL model and its correlated binary interaction parameters. A liquid-only transfer dividing wall column (LDWC) is investigated on the basis of a direct conventional distillation sequence (DCDS). For a fair comparison, both DCDS and LDWC are optimized to minimize total annual cost using sequential iterative optimization procedures. After optimization, LDWC exhibits a 16.87% reduction in total annual cost, while cooling and heating utility consumptions are reduced by 28.40% and 19.24% compared to DCDS.