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.

Pitfalls in the Evaluation of the Thermodynamic Consistency of Experimental VLE Data Sets

The thermodynamic consistency of almost 90 VLE data series, including isothermal and isobaric conditions for systems of both total and partial miscibility in the liquid phase, has been examined by means of the area and point-to-point tests. In addition, the Gibbs energy of mixing function calculated from these experimental data has been inspected, with some rather surprising results: certain data sets exhibiting high dispersion or leading to Gibbs energy of mixing curves inconsistent with the total or partial miscibility of the liquid phase, surprisingly, pass the tests. Several possible inconsistencies in the tests themselves or in their application are discussed. Related to this is a very interesting and ambitious initiative that arose within the NIST organization: the development of an algorithm to assess the quality of experimental VLE data. The present paper questions the applicability of two of the five tests that are combined in the algorithm. It further shows that the deviation of the experimental VLE data from the correlation obtained by a given model, the basis of some point-to-point tests, should not be used to evaluate the quality of these data.

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.

Improving some thermodynamic consistency tests for VLE data evaluation

Thermodynamics Conference 2013 (Statistical Mechanics and Thermodynamics Group of the Royal Society of Chemistry), The University of Manchester, 3-6 September 2013.

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.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.