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.

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.

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.

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.

Solubility, Density, Refractive Index, and Viscosity for the Polyhydric Alcohol + CsBr + H2O Ternary Systems at Different Temperatures

The solubility, density, refractive index, and viscosity data for the ethylene glycol + CsBr + H2O, 1,2-propanediol + CsBr + H2O, and glycerin + CsBr + H2O ternary systems have been determined at (288.15, 298.15, and 308.15) K. In all cases, the solubility of CsBr in aqueous solutions was decreased significantly due to the presence of polyhydric alcohol. The liquid–solid equilibrium experimental data were correlated using the NRTL (nonrandom two-liquid) activity coefficient model, considering nondissociation of the dissolved salt in the liquid phase, and new interaction parameters were estimated. The mean deviations between calculated and experimental compositions were low, showing the good descriptive quality and applicability of the NRTL model. The refractive indices, densities, and viscosities for the unsaturated solutions of the three ternary systems have also been measured at three temperatures. Values for all of the properties were correlated with the salt concentrations and proportions of polyhydric alcohol in the solutions.

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.

Disintegrability under composting conditions of plasticized PLA–PHB blends

The disintegration under composting conditions of films based on poly(lactic acid)–poly(hydroxybutyrate) (PLA–PHB) blends and intended for food packaging was studied. Two different plasticizers, poly(ethylene glycol) (PEG) and acetyl-tri-n-butyl citrate (ATBC), were used to limit the inherent brittleness of both biopolymers. Neat PLA, plasticized PLA and PLA–PHB films were processed by melt-blending and compression molding and they were further treated under composting conditions in a laboratory-scale test at 58 ± 2 °C. Disintegration levels were evaluated by monitoring their weight loss at different times: 0, 7, 14, 21 and 28 days. Morphological changes in all formulations were followed by optical and scanning electron microscopy (SEM). The influence of plasticizers on the disintegration of PLA and PLA–PHB blends was studied by evaluating their thermal and nanomechanical properties by thermogravimetric analysis (TGA) and the nanoindentation technique, respectively. Meanwhile, structural changes were followed by Fourier transformed infrared spectroscopy (FTIR). The ability of PHB to act as nucleating agent in PLA–PHB blends slowed down the PLA disintegration, while plasticizers speeded it up. The relationship between the mesolactide to lactide forms of PLA was calculated with a Pyrolysis–Gas Chromatography–Mass Spectrometry device (Py–GC/MS), revealing that the mesolactide form increased during composting.

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.

Processing and characterization of plasticized PLA/PHB blends for biodegradable multiphase systems

Blends of poly(lactic acid) (PLA) and poly(3-hydroxybutyrate) (PHB) plasticized with a lactic acid oligomer (OLA) added at three different concentrations (15, 20 and 30 wt% by weight), were prepared by an optimized extrusion process to improve the processability and mechanical properties of these biopolymers for flexible film manufacturing. Morphological, chemical, thermal, mechanical, barrier and migration properties were investigated and formulations with desired performance in eco-friendly films were selected. The efficiency of OLA as plasticizer for PLA_PHB blends was demonstrated by the significant decrease of their glass transition temperatures and a considerable improvement of their ductile properties. The measured improvements in the barrier properties are related to the higher crystallinity of the plasticized PLA_PHB blends, while the overall migration test underlined that all the proposed formulations maintained migration levels below admitted levels. The PLA_PHB blend with 30 wt% OLA was selected as the optimum formulation for food packaging, since it offered the best compromise between ductility and oxygen and water vapor barrier properties with practically no migration.

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.

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.

The combined effect of plastics and food waste accelerates the thermal decomposition of refuse-derived fuels and fuel blends

Mechanical treatments such as shredding or extrusion are applied to municipal solid wastes (MSW) to produce refuse-derived fuels (RDF). In this way, a waste fraction (mainly composed by food waste) is removed and the quality of the fuel is improved. In this research, simultaneous thermal analysis (STA) was used to investigate how different mechanical treatments applied to MSW influence the composition and combustion behaviour of fuel blends produced by combining MSW or RDF with wood in different ratios. Shredding and screening resulted in a more efficient mechanical treatment than extrusion to reduce the chlorine content in a fuel, which would improve its quality. This study revealed that when plastics and food waste are combined in the fuel matrix, the thermal decomposition of the fuels are accelerated. The combination of MSW or RDF and woody materials in a fuel blend has a positive impact on its decomposition.