Phase Stability Analysis: A Consistent Guide for Drawing Maps for Safe Traveling through the World of Azeotropy and Miscibility

Phase equilibria for systems that present different types of azeotropy have been analyzed by using the dimensionless Gibbs energy of mixing (gM) for the liquid and vapor phases along with both the common tangent criterion and the phase stability test. First, the gM,L function for the liquid phase and its derivatives have been analyzed to obtain the boundary function between the homogeneous (L) and heterogeneous (LLE) regions as a function of the parameters for different activity coefficient models. Next, the excess Gibbs free energies and their first derivatives for the liquid and vapor phases have been analyzed to determine the mathematical conditions and the limits of different types of azeotropy (VLE and VLLE) and the possible combinations of two azeotropes in the same binary system. Finally, as a result of the combination of all this information, azeotropy and miscibility maps have been obtained as a function of the parameter values for Margules, van Laar, Wilson, and NRTL activity coefficient models

New Empirical Model for the Excess Gibbs Free Energy: Correlation of Liquid–Liquid Equilibrium for Island-Type Ternary Systems

Island-type ternary systems, at constant temperature and pressure, present a closed liquid–liquid miscibility gap in the ternary region while the three binary subsystems are completely miscible. Correlation of this type of phase equilibrium behavior is a challenge. Accordingly, correlation results using classical activity coefficient models (as NRTL or UNIQUAC) are not usually reported in the literature for this type of system. In this paper, the limitations of the NRTL model to correlate LLE data sets for island-type ternary systems are discussed. The lack of flexibility and the uncertainty in the equilibrium solution are the main problems. A new expression for the excess Gibbs free energy is proposed to overcome these limitations with a practical aim. The empirical model proposed has two contributions: a Gaussian-like function and a non-ideal homogeneous term. Both are combined to fulfill the topological requirements of the Gibbs energy of mixing surfaces for island-type ternary systems according to the Gibbs common tangent plane criterion along with the phase stability analysis. The model proposed avoids the uncertainty problems of classical activity models for island-type ternary systems. Additionally, in this model, the relations between the parameter values and the calculated LLE are easily interpreted, which allows generating good initial values and guiding the correlation algorithm when convergence problems occur. Some island-type ternary systems have been selected to illustrate this subject.The authors would like to thank “Generalitat Valenciana: Consellería de Educación, Investigación, Cultura y Deporte” for the PhD grant (ACIF/2019/040)

Analysis of Vapor–Liquid Equilibrium in Ternary Systems for an Adequate Planning of Their Experimental Determination and Correlation

Experimental vapor–liquid equilibrium (VLE) data, and the activity coefficient model parameters obtained by their correlation, are frequently used in separation processes design. The inspection of this information for ternary systems has revealed some problems that are not widely known and could lead to serious mistakes. A small sampling of ten ternary systems, with VLE data sets at constant pressure, arbitrarily selected has been considered to illustrate these problems. The experimental VLE data and the NRTL model parameters for these systems have been taken from different sources, one database and two commercial simulation packages. A MATLAB code has been developed to prepare 3D graphs where the T/x and T/y surfaces calculated by the activity coefficient model (NRTL) are represented along with the experimental VLE data. The results of the analysis of this small sample are very worrying. In fact, half of the selected systems present severe inconsistences between the experimental VLE data and the T/x,y surfaces calculated using the correlation results published or implemented in the simulation software. These inconsistences are of different natures, but the most notable is the existence of parameter sets that do not correlate at all the VLE behavior of the system that they supposedly represent. These irregularities may occur only in the ternary region, only in the binary subsystems, or, in some cases, in both. These problems go frequently unnoticed for different reasons. As discussed in this work, the typical 2D graphs and deviations in T or P and vapor composition are not enough in some cases so as to have an adequate idea of both the quality of the data and the suitability of the model to represent them. This is particularly true when considering, as is strongly advisible, the complete set of data, i.e. the ternary and binary VLE data simultaneously. Some recommendations are presented in this work to overcome the problems detected both when planning the experimental design to determine VLE data and to correlate them with a model.The authors would like to thank “Ministerio de Ciencia e Innovación” for financial support through Project PID2020-119320GB-I00

Aqueous Two-Phase Systems: A Correlation Analysis

Aqueous two-phase systems involve a limited region of a complicated phase diagram usually containing solid phases. Studies regarding these systems generally focus on the liquid–liquid region because it provides a suitable medium for liquid extraction of biomolecules and metal ions. In this work, the whole phase diagram was determined for ternary mixtures of water, dipotassium tartrate, and ethanol or 1-propanol at several temperatures and atmospheric pressure. In addition, density and refractive index of a diluted region of the mixtures were measured for compositional analysis of samples. Different regions were found involving solid and liquid phases, or the anhydrous and hemihydrated salt. The correlation of equilibrium data within the different regions was carried out with the nonrandom two-liquid model. To that aim, some restrictions were required to ensure the miscibility of the binary subsystem with water and alcohol. Individual correlation at each temperature and simultaneous correlation of data at all temperatures led to adequate phase diagram representation and low deviations. Despite the use of temperature-dependent parameters, results were slightly worse in the latter case (around or below 1%). The liquid–liquid equilibrium (LLE) data alone were also correlated, obtaining similar deviations to those obtained considering all equilibrium data. In all cases deviations found with 1-propanol are higher (in the range of 3–4%) due to the proximity of the LLE region to the miscible water + 1-propanol binary subsystem. The correlation of exclusive LLE data is easier from the point of view of computation but leads to model parameters with limited utility.The authors are grateful to Xunta de Galicia for support through Project ED431B 2017/023 and the Galician Network of Ionic Liquids (ED431D 2017/06) and the CRETUS Strategic Partnership (ED431E 2018/01), cofunded by the European Regional Development Fund

Procedure for the correlation of normal appearance VLE data, where the classical models dramatically fail with no apparent reason

The necessity of using a pressure (P) or temperature (T) dependence in the Gibbs energy of mixing of the liquid phase (gM,L) for some isothermal (or isobaric) VLE data sets, respectively, is discussed in this paper. A graphical representation, directly obtained from the experimental data, is proposed as a method to clearly classify the behaviour of the systems and select the adequate model (i.e. including when appropriate the T or P dependence) to correlate them. The result is that many of the poorly fitted systems in the literature could be precisely modelled using the correct procedure with adequate functions of P or T. Some suitable examples are used to illustrate the validity of these ideas, providing satisfactory correlation results for those systems in the literature. The ideas presented in this paper reveal important aspects related to the inappropriate application of some thermodynamic consistency (TC) tests to evaluate the quality of VLE data sets

Necessity of imposing total miscibility for certain binary pairs in LLE data correlations

Liquid-liquid equilibrium (LLE) data correlation of multicomponent mixtures is frequently carried out without using any procedure to ensure that the model parameters obtained for the totally miscible binary mixtures are consistent with such behavior (i.e. they do not lead to two liquid phases in equilibrium). In other words, the behavior of the model beyond the LLE region fitted (experimental tie-lines) is not usually considered in LLE correlations. It seems to be wrongly assumed that the mere absence of tie-lines data in totally miscible regions should guarantee that the parameters resulting from the LLE correlation lead to total miscibility in such homogeneous regions. We have checked that for the correlation of certain type 1 ternary systems (Treybal classification) a high probability exists of obtaining inconsistent model parameters, which lead to type 2 instead type 1 ternary behavior, unless specific restrictions for such parameters are imposed during the correlation. Commercial tools to carry out this type of data fitting, which are frequently included in process simulation packages such as Aspen Plus, do not include the possibility of applying such restrictions and consequently they could provide this type of misleading correlation results with serious consequences in equipment design. In the present paper, LLE data correlation for certain type 1 ternary systems has been carried out using Aspen Plus resulting in inconsistent type 2 results. These same systems have been satisfactorily correlated using our own correlation tools including restrictions to ensure the required miscibility behavior, and thus obtaining consistent parameters. A similar problem could occur in the correlation of the less frequent island (or zero) type ternary systems. Some examples are also presented for such type of systems.The authors would like to thank “Generalitat Valencia: Consellería de Educación, Investigación, Cultura y Deporte” for the PhD grant (ACIF/2019/040)

Equilibria and correlation of systems involving 1-hexyl-3-methylpyridinium trifluoromethanesulfonate

Ionic liquids are being proposed for the improvement of many refinery-related applications where water and oil coexist. However, the lack of relevant thermodynamic data on equilibrium processes involving water, oil and an ionic liquid is a stumbling block. Phase diagrams of these systems are complex, with many different regions, especially when the ionic liquid is solid at room conditions. This greatly complicates modelling, which is usually neglected or carried out only partially. In this work, for the first time, the simultaneous correlation not only of liquid–liquid and liquid–liquid–liquid but also solid–liquid equilibrium data for ternary systems involving ionic liquids has been carried out. To that end, the ionic liquid 1-hexyl-3-methylpyridinium trifluoromethanesulfonate, with an alkyl chain length that favours nano-segregation, was selected. Phase diagrams with water and different representative oils (octane, toluene and cyclohexane) have been determined at various temperatures and atmospheric pressure. The great capacity of the NRTL model, a powerful tool used in all chemical process simulators, was shown by simultaneously correlating data from all the equilibrium regions. However, adequate equilibrium equations and pivotal strategies were required. Low deviations and a good representation of phase diagrams was achieved. A topological analysis based on the Gibbs common tangent criterion and a stability test allowed validation of the proposed correlation parameters.The authors acknowledge the Ministry of Science, Innovation and Universities (Spain) for financial support throughout project PGC2018-097342-B-I00 (including European Regional Development Fund advanced funding)

Liquid–Liquid Equilibrium Data Correlation Using NRTL Model for Different Types of Binary Systems: Upper Critical Solution Temperature, Lower Critical Solution Temperature, and Closed Miscibility Loops

In this work, liquid–liquid equilibrium (LLE) data at different temperatures have been correlated for 30 binary systems that presented different miscibility behaviors: 15 upper critical solution temperature (UCST), 5 lower critical solution temperature (LCST), and 10 closed loop LLE region systems. The NRTL model along with an expression frequently used in the literature for the temperature dependence in the binary interaction has allowed an acceptable fitting of all the systems. The parameters obtained have been validated by the inspection of the Gibbs energy of mixing function regarding the fulfillment of the Gibbs common tangent equilibrium condition, and also by the stability of the solution to avoid possible metastable equilibrium solutions. The critical solution temperatures have been calculated by extrapolation using the NRTL parameters obtained for all selected binary systems. Moreover, the NRTL parameter values have been analyzed using some proposed representations that also include the boundary curve between miscible (L) and partially miscible (LLE) regions. These graphical representations are useful because they show the parameter value requirements to reproduce UCST, LCST, or closed loop behaviors.The authors would like to thank “Generalitat Valenciana: Conselleria de Educación. Investigación, Cultura y Deporte” for the Ph.D. grant (ACIF/2019/040)

Analysis of Vapor–Liquid Equilibrium in Ternary Systems for an Adequate Planning of Their Experimental Determination and Correlation

Experimental vapor–liquid equilibrium (VLE) data, and the activity coefficient model parameters obtained by their correlation, are frequently used in separation processes design. The inspection of this information for ternary systems has revealed some problems that are not widely known and could lead to serious mistakes. A small sampling of ten ternary systems, with VLE data sets at constant pressure, arbitrarily selected has been considered to illustrate these problems. The experimental VLE data and the NRTL model parameters for these systems have been taken from different sources, one database and two commercial simulation packages. A MATLAB code has been developed to prepare 3D graphs where the T/x and T/y surfaces calculated by the activity coefficient model (NRTL) are represented along with the experimental VLE data. The results of the analysis of this small sample are very worrying. In fact, half of the selected systems present severe inconsistences between the experimental VLE data and the T/x,y surfaces calculated using the correlation results published or implemented in the simulation software. These inconsistences are of different natures, but the most notable is the existence of parameter sets that do not correlate at all the VLE behavior of the system that they supposedly represent. These irregularities may occur only in the ternary region, only in the binary subsystems, or, in some cases, in both. These problems go frequently unnoticed for different reasons. As discussed in this work, the typical 2D graphs and deviations in T or P and vapor composition are not enough in some cases so as to have an adequate idea of both the quality of the data and the suitability of the model to represent them. This is particularly true when considering, as is strongly advisible, the complete set of data, i.e. the ternary and binary VLE data simultaneously. Some recommendations are presented in this work to overcome the problems detected both when planning the experimental design to determine VLE data and to correlate them with a model

Acetone + 1-ethyl-3-methylimidazolium acetate phase diagram: A correlation challenge

Several physical properties and the isobaric vapour-liquid equilibria at 101.32, 50, and 30 kPa were measured for the binary system consisting of acetone and the ionic liquid 1-ethyl-3-methyl-imidazolium acetate. Liquid-liquid equilibrium data were also measured at temperatures from 298.15 up to 328.35 K and atmospheric pressure. An hourglass-shaped miscibility gap was found. The simultaneous correlation of both VLE and LLE regions at 101.32 kPa was addressed. The NRTL model, considering different options to formulate the temperature dependence of the parameters, was tested and found unable to correlate the whole set of equilibrium data. A detailed analysis of the excess Gibbs energy demonstrated the limitations of the classical equation and allowed the definition of a new model with a correction term. A unique set of parameters were used to simultaneously correlate both sets of equilibrium data with very low deviations from experimental data. Moreover, the corrected NRTL function overcomes some uncertainty problems that may occur in liquid-liquid equilibrium calculations.The authors would like to thank “Generalitat Valencia: Consellería de Educación, Investigación, Cultura y Deporte” for the PhD grant (ACIF/2019/040) and Xunta de Galicia for support through project ED431B 2020/021. M.K.W. is grateful to the Erasmus + programme of the European Union for the award of a mobility traineeship