Correlation of the liquid–liquid equilibrium data for specific ternary systems with one or two partially miscible binary subsystems

This paper presents the results of a liquid–liquid equilibrium data correlation for 11 ternary systems which have not been previously fitted using the NRTL model or, when they have, the results presented in the literature are inconsistent with the experimental behavior of the system. These ternary systems include mixtures with one or two partially miscible pairs. During the correlation process, new restrictions were imposed on the values for the NRTL binary parameters to ensure correct prediction of the total or partial miscibility for the binary pairs involved. In addition, topological concepts related to the Gibbs stability test have been applied in order to validate the results in the whole range of compositions.

Liquid–Liquid, Vapor–Liquid, and Vapor–Liquid–Liquid Equilibrium Data for the Water–n-Butanol–Cyclohexane System at Atmospheric Pressure: Experimental Determination and Correlation

The temperature and the composition of the vapor–liquid–liquid equilibrium (VLLE) and the vapor–liquid equilibrium (VLE) of a ternary mixture of water–n-butanol–cyclohexane were measured at atmospheric pressure (101.32 kPa) in a modified dynamic recirculating still. As found in the literature, the experimental data obtained reveal a ternary azeotrope at 341.86 K with a mole fraction composition of 0.281, 0.034, and 0.685 water, n-butanol, and cyclohexane, respectively. The liquid–liquid equilibrium (LLE) compositions were measured at a constant temperature of 313.15 K and compared with data in the literature collected at other temperatures. Thermodynamic consistency of all the experimental data was demonstrated. The universal quasichemical (UNIQUAC) and the nonrandom two-liquid (NRTL) thermodynamic models were used to correlate the VLE and LLE data, while the original universal functional (UNIFAC) model was used to compare the predicted data.

Modelling liquid–liquid equilibria for island type ternary systems

Closed miscibility gaps in ternary liquid mixtures, at constant temperature and pressure, are obtained if phase separations occur only in the ternary region, whilst all binary mixtures involved in the system are completely miscible. This type of behaviour, although not very frequent, has been observed for a certain number of systems. Nevertheless, we have found no information about the applicability of the common activity coefficient models, as NRTL and UNIQUAC, for these types of ternary systems. Moreover, any of the island type systems published in the most common liquid–liquid equilibrium data collections, are correlated with any model. In this paper, the applicability of the NRTL equation to model the LLE of island type systems is assessed using topological concepts related to the Gibbs stability test. A first attempt to correlate experimental LLE data for two island type ternary systems is also presented.

Phase equilibria of the water + 1-butanol + toluene ternary system at 101.3 kPa

Isobaric vapour–liquid and vapour–liquid–liquid equilibrium data for the water + 1-butanol + toluene ternary system were measured at 101.3 kPa with a modified VLE 602 Fischer apparatus. In addition, the liquid–liquid equilibrium data at 313.15 K were measured and compared with data from other authors at different temperatures. The system exhibits a ternary heterogeneous azeotrope whose temperature and composition have been determined by interpolation. The thermodynamic consistency of the experimental vapour–liquid and vapour–liquid–liquid data was checked by means of the Wisniak’s Li/Wi consistency test. Moreover, the vapour–liquid and the liquid–liquid equilibrium correlation for the ternary system with NRTL and UNIQUAC models, together with the prediction made with the UNIFAC model, were studied and discussed.

Liquid–Liquid Equilibria of Water + Ethanol + 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)imide Ternary System: Measurements and Correlation at Different Temperatures

In this work authors present the experimental liquid–liquid equilibria (LLE) data of water + ethanol + 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([bmim][Tf2N]) system at different temperatures. The LLE of the system was obtained in the temperature range from 283.2 to 323.2 K. The nonrandom two liquid (NRTL) and universal quasichemical (UNIQUAC) models were used to correlate ternary systems. The equilibrium compositions were successfully correlated by the interaction parameters from both models, however UNIQUAC gave a more accurate correlation. Finally, a study about the solvent capability of ionic liquid was made in order to evaluate the possibility of separating the mixture formed by ethanol and water using that ionic liquid.

Isobaric vapor–liquid–liquid–solid equilibrium of the water + NaCl + 1-butanol system at 101.3 kPa

A mixture of water + NaCl + 1-butanol at 101.3 kPa is studied in order to determine the influence of salt on its experimental vapor–liquid–liquid–solid equilibrium. A detailed analysis of the evolution with temperature of the different equilibrium regions is carried out. The study is conducted at a constant pressure of 101.3 kPa in a recirculating still that has been modified by our research group. The changes in the 1-butanol/water composition ratio in the vapor phase that are provoked by the salt are studied as a function of equilibrium region. In addition, the mutual solubility of 1-butanol and water is assessed in the liquid–liquid and solid–liquid regions.

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

Geometrical study of the three-dimensional temperature–composition diagrams. An important aid to understand the behavior of the liquid–vapour equilibrium in ternary systems

In this work the usefulness of qualitatively studying and drawing three-dimensional temperature–composition diagrams for ternary systems is pointed out to understand and interpret the particular behavior of the liquid–vapour equilibrium of non-ideal ternary systems. Several examples have been used in order to highlight the interest and the possibilities of this tool, which should be an interesting support not only for lecturers, but also for researchers interested in experimental equilibrium data determination.

Screen-printed electrode-based electrochemical detector coupled with in-situ ionic-liquid-assisted dispersive liquid–liquid microextraction for determination of 2,4,6-trinitrotoluene

A novel method is reported, whereby screen-printed electrodes (SPELs) are combined with dispersive liquid–liquid microextraction. In-situ ionic liquid (IL) formation was used as an extractant phase in the microextraction technique and proved to be a simple, fast and inexpensive analytical method. This approach uses miniaturized systems both in sample preparation and in the detection stage, helping to develop environmentally friendly analytical methods and portable devices to enable rapid and onsite measurement. The microextraction method is based on a simple metathesis reaction, in which a water-immiscible IL (1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, [Hmim][NTf2]) is formed from a water-miscible IL (1-hexyl-3-methylimidazolium chloride, [Hmim][Cl]) and an ion-exchange reagent (lithium bis[(trifluoromethyl)sulfonyl]imide, LiNTf2) in sample solutions. The explosive 2,4,6-trinitrotoluene (TNT) was used as a model analyte to develop the method. The electrochemical behavior of TNT in [Hmim][NTf2] has been studied in SPELs. The extraction method was first optimized by use of a two-step multivariate optimization strategy, using Plackett–Burman and central composite designs. The method was then evaluated under optimum conditions and a good level of linearity was obtained, with a correlation coefficient of 0.9990. Limits of detection and quantification were 7 μg L−1 and 9 μg L−1, respectively. The repeatability of the proposed method was evaluated at two different spiking levels (20 and 50 μg L−1), and coefficients of variation of 7 % and 5 % (n = 5) were obtained. Tap water and industrial wastewater were selected as real-world water samples to assess the applicability of the method.

Screen-printed electrode based electrochemical detector coupled with ionic liquid dispersive liquid–liquid microextraction and microvolume back-extraction for determination of mercury in water samples

A novel approach is presented, whereby gold nanostructured screen-printed carbon electrodes (SPCnAuEs) are combined with in-situ ionic liquid formation dispersive liquid–liquid microextraction (in-situ IL-DLLME) and microvolume back-extraction for the determination of mercury in water samples. In-situ IL-DLLME is based on a simple metathesis reaction between a water-miscible IL and a salt to form a water-immiscible IL into sample solution. Mercury complex with ammonium pyrrolidinedithiocarbamate is extracted from sample solution into the water-immiscible IL formed in-situ. Then, an ultrasound-assisted procedure is employed to back-extract the mercury into 10 µL of a 4 M HCl aqueous solution, which is finally analyzed using SPCnAuEs. Sample preparation methodology was optimized using a multivariate optimization strategy. Under optimized conditions, a linear range between 0.5 and 10 µg L−1 was obtained with a correlation coefficient of 0.997 for six calibration points. The limit of detection obtained was 0.2 µg L−1, which is lower than the threshold value established by the Environmental Protection Agency and European Union (i.e., 2 µg L−1 and 1 µg L−1, respectively). The repeatability of the proposed method was evaluated at two different spiking levels (3 and 10 µg L−1) and a coefficient of variation of 13% was obtained in both cases. The performance of the proposed methodology was evaluated in real-world water samples including tap water, bottled water, river water and industrial wastewater. Relative recoveries between 95% and 108% were obtained.

Isothermal (liquid + liquid) equilibrium data at T = 313.15 K and isobaric (vapor + liquid + liquid) equilibrium data at 101.3 kPa for the ternary system (water + 1-butanol + p-xylene)

The (vapor + liquid), (liquid + liquid) and (vapor + liquid + liquid) equilibria of the ternary system (water + 1-butanol + p-xylene) have been determined. (Water + 1-butanol + p-xylene) is a type 2 heterogeneous ternary system with partially miscible (water + 1-butanol) and (water + p-xylene) pairs. By contrast, (1-butanol + p-xylene) is totally miscible under atmospheric conditions. This paper examines the (vapor + liquid) equilibrium in both heterogeneous and homogeneous regions at 101.3 kPa of pressure. (Liquid + liquid) equilibrium data at T = 313.15 K have also been determined, and for comparison, the obtained experimental data have been calculated by means of several thermodynamic models: UNIQUAC, UNIFAC and NRTL. Some discrepancies were found between the (vapor + liquid + liquid) correlations; however, the models reproduced the (liquid + liquid) equilibrium data well. The obtained data reveal a ternary heterogeneous azeotrope with mole fraction composition: 0.686 water, 0.146 1-butanol and 0.168 p-xylene.

Tungsten coil atomic emission spectrometry combined with dispersive liquid–liquid microextraction: A synergistic association for chromium determination in water samples

A novel and environment friendly analytical method is reported for total chromium determination and chromium speciation in water samples, whereby tungsten coil atomic emission spectrometry (WCAES) is combined with in situ ionic liquid formation dispersive liquid–liquid microextraction (in situ IL-DLLME). A two stage multivariate optimization approach has been developed employing a Plackett–Burman design for screening and selection of the significant factor involved in the in situ IL-DLLME procedure, which was later optimized by means of a circumscribed central composite design. The optimum conditions were complexant concentration: 0.5% (or 0.1%); complexant type: DDTC; IL anion: View the MathML sourcePF6−; [Hmim][Cl] IL amount: 60 mg; ionic strength: 0% NaCl; pH: 5 (or 2); centrifugation time: 10 min; and centrifugation speed: 1000 rpm. Under the optimized experimental conditions the method was evaluated and proper linearity was obtained with a correlation coefficient of 0.991 (5 calibration standards). Limits of detection and quantification for both chromium species were 3 and 10 µg L−1, respectively. This is a 233-fold improvement when compared with chromium determination by WCAES without using preconcentration. The repeatability of the proposed method was evaluated at two different spiking levels (10 and 50 µg L−1) obtaining coefficients of variation of 11.4% and 3.6% (n=3), respectively. A certified reference material (SRM-1643e NIST) was analyzed in order to determine the accuracy of the method for total chromium determination and 112.3% and 2.5 µg L−1 were the recovery (trueness) and standard deviation values, respectively. Tap, bottled mineral and natural mineral water samples were analyzed at 60 µg L−1 spiking level of total Cr content at two Cr(VI)/Cr(III) ratios, and relative recovery values ranged between 88% and 112% showing that the matrix has a negligible effect. To our knowledge, this is the first time that combines in situ IL-DLLME and WCAES.

Influence of the Temperature on the Liquid–Liquid–Solid Equilibria of the Water + Ethanol + 1-Undecanol Ternary System

Liquid–liquid (L–L), solid–liquid (S–L), and solid–liquid–liquid (S–L–L) equilibrium data for the water–ethanol–1-undecanol ternary system have been determined experimentally at (275.15, 278.15, 281.15, 288.15, and 298.15) K and atmospheric pressure. Different shapes of the equilibrium diagrams have been observed depending on the temperature. A region with three phases (S–L–L) is present in the temperature range between (275.15 and 281.15) K. Above 288.15 K, only a L–L region is observed.

New methodology for describing the equilibrium beach profile applied to the Valencia's beaches

Mathematical models used for the understanding of coastal seabed morphology play a key role in beach nourishment projects. These projects have become the fundamental strategy for coastal maintenance during the last few years. Accordingly, the accuracy of these models is vital to optimize the costs of coastal regeneration projects. Planning of such interventions requires methodologies that do not generate uncertainties in their interpretation. A study and comparison of mathematical simulation models of the coastline is carried out in this paper, as well as elements that are part of the model that are a source of uncertainty. The equilibrium profile (EP) and the offshore limit corresponding to the depth of closure (DoC) have been analyzed taking into account different timescale ranges. The results have thus been compared using data sets from three different periods which are identified as present, past and future. Accuracy in data collection for the beach profiles and the definition of the median grain size calculation using collected samples are the two main factors that have been taken into account in this paper. These data can generate high uncertainties and can produce a lack of accuracy in nourishment projects. Together they can generate excessive costs due to possible excess or shortage of sand used for the nourishment. The main goal of this paper is the development of a new methodology to increase the accuracy of the existing equilibrium beach profile models, providing an improvement to the inputs used in such models and in the fitting of the formulae used to obtain seabed shape. This new methodology has been applied and tested on Valencia's beaches.