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.

Identification of the local productive systems in Spain: a new approach

Paper submitted to the 44th European Congress of the European Regional Science Association, Porto, 25-29 August 2004.

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.

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.

Pitfalls on computing liquid-liquid phase equilibria using the k-value method

Poster presented in the 11th Mediterranean Congress of Chemical Engineering, Barcelona, October 21-24, 2008.

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.

Gibbs Energy of Mixing Function: Topological Analysis in Azeotropic Systems

ESAT 2014. 27th European Symposium on Applied Thermodynamics, Eindhoven University of Technology, July 6-9, 2014.

Quantum spin Hall phase in multilayer graphene

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

Edge states in graphene-like systems

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non-dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional quantum Hall effect, the quantum anomalous Hall (QAH) and the quantum spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin–orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.