Liquid Equilibria Of Mixtures Research Articles

Liquid–liquid equilibria in mixtures of formaldehyde, water, methanol, and isoprenol

Isoprenol (3-methyl-3-buten-1-ol) is an important intermediate in the chemical industry. It has to be separated from mixtures containing formaldehyde, water, and methanol in the production process. As water and isoprenol are only partially miscible in the liquid phase, these mixtures exhibit a liquid–liquid miscibility gap. Knowledge of this miscibility gap is essential for understanding the isoprenol process; however, only few experimental data and no models are presently available in the literature. Therefore, in the present work, liquid–liquid equilibria in the systems (water + isoprenol), (formaldehyde + water + isoprenol), and (water + methanol + isoprenol) were measured at 278, 293, and 313 K. The new experimental data were used to develop a model of the liquid–liquid equilibrium in mixtures of formaldehyde, water, methanol, and isoprenol, which can now be used in simulation studies of the isoprenol process.

Evaluation of association schemes in the CPA and PC-SAFT equations of state in modeling VLE of organic acids + water systems

The performance of various association schemes was evaluated in modeling isothermal and isobaric vapor–liquid equilibria of mixtures of organic acids and water with the CPA and the PC-SAFT equations of state. The organic acids considered were formic, acetic, propanoic and butanoic acid. Combinations of the 1A and 2B association schemes for the acids and the 2B, 3B, and 4C for water were tested. Polar contributions were also studied in PC-SAFT. The case in which no association contribution is included in the thermodynamic model was also assessed. It is concluded that the chosen association scheme greatly affects the performance of the equation of state. It was not possible to identify a single association scheme combination that would work well for all the systems and conditions studied. On average, PC-SAFT with the organic acid modeled as 1A and water as 4C showed the greatest accuracy. Interestingly, for some of the mixtures the nonassociation case gave considerably better representations than when the association term was used. When a binary interaction parameter is used the performance of the equations studied is comparable to the classic PR.

Solid–Liquid Equilibria and Characterization of the Reaction Mixture To Produce Sucrose Palmitate in Solvent-Free Media

This work deals with the characterization of the reactive mixtures involved in the production of sucrose palmitate from methyl palmitate and sucrose, through a solvent-free process. The solid–liquid equilibrium in mixtures of sucrose–methyl palmitate–sucrose palmitate (SE) at temperatures between 363 and 403 K and sucrose ester concentrations between 0 and 15 g SE/100 g methyl palmitate was measured. Solid and liquid heat capacities of sucrose palmitate and thermal properties useful in the equilibrium modeling were measured through differential scanning calorimetry and thermogravimetric analysis. The viscosity and surface tension of the reaction product were also measured. According to results sucrose palmitate melts at 315.82 K and decomposes at 510.67 K. The average solid and liquid heat capacities of sucrose ester in the evaluated ranges were 2010 J/kg·K and 2475 J/kg·K, respectively. The predictive modified UNIFAC method for sugars (mS-UNIFAC) and the nonrandom two-liquid equation were used to model t...

Modeling study of the phase behavior of mixtures containing non-ionic glycol ether surfactant

Abstract In this study, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) has been utilized for thermodynamic modeling of vapor–liquid and liquid–liquid equilibrium in mixtures containing glycol ether surfactant. Glycol ether surfactant molecules are modeled as associating components by considering two association sites per each molecule. The pure component parameters of the PC-SAFT EoS are adjusted to vapor pressure and liquid density experimental data with AARD of 0.861 and 0.379%, respectively. Using obtained parameters, the phase behavior of binary systems over wide range of thermodynamic conditions is studied. The average deviation between model calculations and experimental data for water + surfactant, alcohol + surfactant, hydrocarbon + surfactant and carbon dioxide + surfactant systems are about 2.18, 1.15, 2.67 and 14.55% respectively. Furthermore, the capability of the model has then been assessed by prediction of phase behavior for the ternary systems without any adjustable parameter. The results show that, the predicted and correlated results are in good agreement with experimental data.

Comparative Method of Calculating the Thermodynamic Parameters of Some Uranium Hexafluoride Solutions

It is shown that the thermodynamics characteristics of uranium hexafl uoride solutions with volatile hexaand pentafl uoride elements are a consequence of the strictly symmetric confi guration of their molecular structure in the gaseous and liquid states. Simple methods are proposed for evaluating the properties of binary mixtures of elemental penta- and hexafl uorides. These methods are based on a comparison of the element–fl uorine bond length in the constituent molecules of system and the known enthalpy of mixing of one solution with the potential energy in the formation of a pair of unlike molecules of a different solution. Researchers looking for a universal method of deep purifi cation of uranium hexafl uoride have turned their attention to a rectifi cation method, for which there are no limitations on the depth of purifi cation, and a list of impurities to be removed, including metal impurities which are diffi cult to remove by means of water-extraction conversions of uranium concentrates and give volatile fl uorides (molybdenum, tungsten, ruthenium, technetium, and others). Moreover, its specifi c productivity is high, the energy consumption is low, and the separation effi ciency is high. These advantages are due to the special properties of uranium hexafl uoride as a working substance for rectifi cation: high density of liquid (more than 3.5 times higher than the density of water) and gaseous uranium hexafl uoride, low viscosity comparable to that of water, good wettability of the metals which are corrosion resistant to fl uoride media, and low heat of evaporation of liquid uranium hexafl uoride (less than 1/10th that of water). Deep purifi cation of uranium hexafl uoride raw material by rectifi cation has been used in the Republic of South Africa for several decades now [1]. In our country, we have experience in prolonged operation of a large-tonnage rectifi cation process for purifying sublimate and high-enrichment uranium hexafl uoride [2–4]. In order to develop a rectifi cation process, it is necessary to have information on the phase equilibrium of mixtures based on uranium hexafl uoride and to predict the properties of systems with which it is diffi cult to experiment. Computer methods of calculating steam-water systems have now been developed and are being improved; examples are models of local compositions Wilson, NRTL, UNIQUAC, equations of state SRK, Peng Robinson, and the group model UNIFAC, TTA [5–7]. They are based on the equation of thermodynamic equilibrium between coexisting phases and are generalizations of the Van-der-Waals equation of phase equilibrium, expressed in terms of partial properties [8]. Some forms of this equation are identical to a previously used van-Laar equation expressing the dependence of the coeffi cient of activity of a component on the composition of the solution [9]. Such methods of calculating the liquid–vapor equilibrium in nonideal systems take account of the effect of variable temperature and are convenient for modeling mixtures with an appreciable difference of the boiling temperature of pure components, making it possible to obtain good agreement between the computed and experimental parameters for some solutions. The application of a comparative method for calculating the properties of pure substances and solutions and the characteristics of phase and chemical equilibria is illustrated in the monograph [10]. In the present work, a method is proposed for fi nding parameters that can be used to calculate the vapor–liquid equilibria of mixtures of elemental hexa- and pentafl uorides by means of a comparative method.

Liquid–Liquid Equilibrium in Mixtures Containing Propane-1,2,3-triol and Mixtures Containing Vegetable Oils at Atmospheric Pressure

Mutual solubility of propane-1,2,3-triol with pentane, hexane, heptane, or ethyl acetate and mutual solubility between different vegetable oils (sunflower oil, soybean oil, corn oil, and olive oil) with methanol or ethanol have been reported at temperatures ranging from (298.2 to 348.2) K and atmospheric pressure. Furthermore, the binodal curves for ethyl acetate + methanol or ethanol + propane-1,2,3-triol at (303.2, 313.2, and 323.2) K have been explored. A higher solubility has been found in the system containing ethanol than the system containing methanol. The GCA-EoS model has been used to represent these mixtures. The distribution coefficient of alcohol and the selectivity of propane-1,2,3-triol in the ternary mixture of ethyl acetate + methanol or ethanol + propane-1,2,3-triol have been evaluated by GCA-EoS model. These results indicate a more effective use of propane-1,2,3-triol as separation agent by liquid–liquid extraction in the binary mixture of ethyl acetate + methanol than ethyl acetate + ethanol. On the other hand, regarding the mixtures containing vegetable oil, the mutual solubility of alcohol in the phase rich in vegetable oil is bigger than the mutual solubility of vegetable oil in the phase rich in alcohol.

Vapor–liquid and liquid–liquid equilibrium calculations in mixtures containing non-ionic glycol ether surfactant using PHSC equation of state

In this study, vapor–liquid and liquid–liquid equilibrium in mixtures containing glycol ether surfactant, non-polar and polar compounds are calculated using Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). Pure liquid density and vapor pressure of surfactants are used for parameter estimation of glycol ether surfactants. The PHSC parameters are calculated for both ethylene glycol ether and propylene glycol ether surfactants. Glycol ether surfactant molecules are modeled as associating components by considering two association sites for each molecule. The results show that the PHSC model is capable of correlating thermodynamic behavior of binary (polar+surfactant) and (non-polar+surfactant) systems. Upper critical solution temperature (UCST) for hydrocarbon+surfactant and lower critical solution temperature (LCST) for water+surfactant systems are accurately calculated. The critical temperatures and the extent of immiscibility are in good agreement with the available experimental data.

Liquid + liquid equilibrium in mixtures of lithium fluoride with potassium and rubidium halides

The liquid+liquid phase equilibrium of molten mixtures of lithium fluoride with potassium and rubidium halides was investigated over an extended temperature range in the two-phase region along the saturation line by the electrical conductivity method. In the overwhelming majority of mixtures, the electrical conductivity for coexisting equilibrium phases increased when the temperature increased. For mixtures with only potassium bromide, it decreased because of the extensive solubility of potassium bromide in lithium fluoride. The electrical conductivity for the light phase was half the value of the conductivity of the pure lithium fluoride. The electrical conductivity of the heavy phase did not differ enough from the conductivity of the pure heavy alkali halides. At the same time, the solubility of the heavy component in LiF was many times less than the lithium fluoride solubility in the lower phase. This contradiction points to essential reorganisation of the structure of the light phase. The difference between the conductivities of the coexisting phases at equal temperatures increased as the radius of the halide anion or alkali cation grew. The temperature growth led to the increase in the conductivity difference along the saturation line for mixtures of LiF with RbI. For mixtures of LiF with lighter alkali halides, it decreased up to zero at the critical mixing point for LiF+KBr mixtures as the temperature increased. Between the coexisting equilibrium phases, a transient layer was revealed, where a conductivity gradient exists. The thickness of this layer decreased as the temperature decreased and the sum of the ionic radii of the mixtures increased.

Gas–liquid equilibrium modeling of mixtures containing supercritical carbon dioxide and an ionic liquid

Gas–liquid equilibrium in mixtures containing supercritical carbon dioxide and an ionic liquid has been modeled using the Peng–Robinson equation of state and the interesting modification proposed by Kwak and Mansoori. The proposal is based on statistical–mechanical arguments and on the fact that mixing rules are for constants of an equation of state and not for functions such as the alpha expression that makes the attractive term temperature dependent. Experimental data for mixtures containing carbon dioxide and ionic liquids were obtained from literature sources and the adjustable parameters of the mixing rules were found by minimizing the errors between predicted and experimental bubble pressure. Results were compared with experimental data and with results of other classical mixing rules, such as the proposal of Wong and Sandler. The deviations in correlating gas–liquid equilibrium found with the model Peng–Robinson/Kwak–Mansoori are lower in general than the results obtained with other models.

Application of Infinite Dilution Activity Coefficients for Determining Binary Equation of State Parameters

Infinite dilution activity coefficients can be determined relatively fast from several experimental techniques. Literature values for the infinite dilution activity coefficients are used to determine a binary interaction parameter of the perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state. The model is, subsequently, applied to the full concentration range of binary mixtures, and the results are compared to experimental data from literature. The applicability of the method is demonstrated for examples involving polar, associating, and polymeric components. It is confirmed that the parametrization allows for extrapolations in temperature. In combination with a group-contribution model for the estimation of infinite dilution activity coefficients (e.g., modified UNIFAC(Do)), the equation of state can be used to predict vapor−liquid equilibria of mixtures.

Study of vapor–liquid equilibrium of mixtures in the field of dilute solutions

Studies of phase equilibrium are performed for a series of binary mixtures including Kr-CF 4 , and the good reproducibility of experimental results is demonstrated with a change in concentration of micro-impurities in the end product.

Vapor–Liquid Equilibrium for Binary Mixtures of 1,4-Diazabicyclo[2.2.2]octane with Ethylenediamine, Ethanolamine, and Ethylene Glycol

Vapor–liquid equilibria of mixtures of 1,4-diazabicyclo[2.2.2]octane with ethylenediamine, ethanolamine, and ethylene glycol were studied. Ideal behavior in the ethylenediamine and 1,4-diazabicyclo[2.2.2]octane mixture was observed. Ethanolamine and 1,4-diazabicyclo[2.2.2]octane form an azeotrope with a minimum boiling point whereas ethylene glycol and 1,4-diazabicyclo[2.2.2]octane form an azeotrope with a maximum boiling point. Non-ideal behavior of the mixtures was described by the NRTL equation, and the corresponding constants were calculated.

Liquid−Liquid Equilibria in Binary Mixtures Containing Fluorinated Benzenes and Ionic Liquid 1-Ethyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide

Binary liquid−liquid equilibria in mixtures of fluorinated benzenes and ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N]), have been measured using the volumetric method over a temperature range from about (283 to 373) K. A general trend between the magnitude of the dipole moment (polarity) and the miscibility was found, although other intermolecular interactions (higher-order moments, π-electron effects, and hydrogen bonding) may also be playing a role for a more detailed trend. The fluorinated benzenes having the largest dipole moments (1,2-difluorobenzene, 1,2,3,4-tetrafluorobenzene, and 1,2,3-trifluorobenzene) were completely miscible in the [emim][Tf2N]. The binary systems (1,4-difluorobenzene, 1,3,5-trifluorobenzene, and 1,2,4,5-tetrafluorobenzene) with zero dipole moments, and the binary systems (1,2,4-trifluorobenzene, fluorobenzene, 1,3-difluorobenzene, pentafluorobenzene, and 1,2,3,5-tetrafluorobenzene) with dipole moments of about 1.4 D were only partial...

Vapor−Liquid Equilibrium of Mixtures Containing Adipic Acid, Glutaric Acid, Dimethyl Adipate, Dimethyl Glutarate, Methanol, and Water

Isothermal vapor−liquid equilibrium (VLE) data were measured, with a static-type apparatus, for the binary systems of methanol + dimethyl adipate, methanol + dimethyl glutarate, and dimethyl glutarate + glutaric acid at (353.15 to 453.15) K. These systems showed slightly positive deviations from the ideal solution behavior without any azeotrope formation. Additionally, the saturated pressures of dimthyl adipate, dimethyl glutarate, methanol + adipic acid, and methanol + water + adipic acid were also determined experimentally in a temperature range of (323.15 to 463.15) K. While the new binary VLE data were correlated with the NRTL-HOC and the UNIQUAC-HOC models, respectively, to determine the optimal values of the model parameters, the saturated pressure data of the ternary system were used to test the validity of the VLE prediction by using the parameters determined from solid−liquid equilibrium data.

Application of the Cubic-Plus-Association Equation of State to Mixtures with Polar Chemicals and High Pressures

The cubic-plus-association (CPA) equation of state has been previously applied to vapor−liquid, liquid−liquid, and solid−liquid equilibria of mixtures containing associating compounds (water, alcohols, glycols, acids, amines). Although some high-pressure applications have been presented, emphasis was given to low pressures and liquid−liquid equilibria. In this work, CPA is applied to two classes of mixtures containing polar chemicals for which high-pressure data are available: acetone-containing systems and dimethyl ether mixtures. They are of both scientific and industrial importance. Moreover, CPA is applied to high-pressure solid−liquid equilibria (SLE) for alcohol−alkane mixtures. In the case of acetone−hydrocarbon mixtures, satisfactory results are achieved if acetone is allowed to self-associate. Satisfactory high-pressure acetone−water vapor−liquid equilibrium (VLE) is obtained, comparable to conventional models such as MHV2. Very good results are also obtained for multicomponent vapor−liquid−liqu...

Prediction of Global Vapor−Liquid Equilibria for Mixtures Containing Polar and Associating Components with Improved Renormalization Group Theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.

Liquid−Liquid Equilibria for Mixtures of (Furfural + an Aromatic Hydrocarbon + an Alkane) at T = 298.15 K

Liquid−Liquid Equilibria for Mixtures of (Furfural + an Aromatic Hydrocarbon + an Alkane) at <i>T = </i>298.15 K

Supercritical hydrogenation processes: Experimental results on the fluid phase behavior of binary and ternary mixtures of hydrogen, propane and tripalmitin

The problems of low reaction rate and cis– trans isomerization encountered in the gas–liquid catalyzed hydrogenation of vegetable oils can be overcome by using a supercritical fluid to bring the reactive mixture into a homogeneous phase. For that purpose, experimental phase equilibrium data on mixtures of high molecular weight substrates with hydrogen and a supercritical fluid are needed in order to evaluate optimum process conditions. In this work vapor–liquid and liquid–liquid equilibria in mixtures of hydrogen+propane+tripalmitin have been measured. A temperature region between 323 and 453 K, and pressures up to 15 MPa were covered.

Phase equilibria in mixtures of fatty oils and derivatives with near critical fluids using the GC-EOS model

The Group Contribution Equation of State (GC-EOS) is applied to model high-pressure phase equilibria in mixtures of fatty oils and acid alkyl esters with supercritical fluids. The fatty oil is represented by a pseudo-triacylglyceride with the same molecular weight and degree of unsaturation of the natural oil. The critical hard sphere diameter of the oil, i.e. the size-related parameter, is determined from the correlation of infinite dilution activity coefficients of n-alkanes in high molecular weight triacylglicerides and hydrocarbons. Good predictions of vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria in mixtures of supercritical solvents (propane, ethane and CO 2) with pure triacylglycerides, natural vegetable oils and fatty acid alkyl esters are obtained. These results show the capability of the GC-EOS model to describe the phase equilibria of size-asymmetric mixtures and its potential for modeling supercritical processes involving oils and derivatives.

Solid–liquid equilibria in mixtures of molten salt hydrates for the design of heat storage materials

Abstract Enthalpy of melting can be used to store heat in a simple way for time periods of hours and days. Knowledge of the solid –liquid equilibria represents the most important presumption for systematic evaluations of the suitability of hydrated salt mixtures. In this paper, two approaches for predicting solid–liquid equilibria in ternary or higher component systems are discussed using the limited amount of thermodynamic data available for such systems. One method is based on the modified Brunauer–Emmett–Teller (BET) model as formulated by Ally and Braunstein. In cases of a strong tendency toward complex formation of salt components, the BET model is no longer applicable. Reaction chain models have been used to treat such systems. Thereby, the reaction chain represents a method to correlate step-wise hydration or complexation enthalpies and entropies and, thus, reduce the number of adjustable parameters. Results are discussed for systems containing MgCl2, CaCl2, ZnCl2, and alkali metal chlorides.