Ilya Polishuk

Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state II. Carbon dioxide-heavy n-alkanes

In the present study we present the final development of the Global Phase Diagram-based semi-predictive approach (GPDA), which requires only 2–3 key data points of one homologue to predict the complete phase behavior of the whole homologues series. The ability of GPDA to predict phase equilibria in CO2–heavy n-alkanes is compared with the equations of state LCVM and PSRK. It is demonstrated that both LCVM and PSRK are more correlative rather than predictive because their parameters are evaluated by the local fit of a considerable amount of VLE experimental data. In addition, these models fail to predict accurately the VLE of systems, which have not been considered in the evaluation of their parameters. They are also particularly inaccurate in predicting LLE and critical lines. In contrast, GPDA is reliable in the entire temperature range and for all types of phase equilibria. It yields an accurate prediction of the global phase behavior in the homologues series and their critical lines. Moreover, increasing asymmetry does not affect the reliability of GPDA; it predicts very accurately even the data of the heaviest homologues of the series.

Prediction of the critical locus in binary mixtures using equation of state: II. Investigation of van der Waals-type and Carnahan–Starling-type equations of state

Abstract The ability to predict critical lines of members of the methane–, perfluoromethane– and water–alkanes homologous series is compared for van der Waals (vdW)-type and Carnahan–Starling (CS)-type equations of state. A temperature dependent combining rule for the binary attraction parameter is discussed and employed. It is found that the appropriate choice of the adjustable parameters yields quite accurate results for both equations. A new application of global phase diagrams is proposed for the quantitative description of real mixtures. In this diagram, the boundaries of the different types of phase behavior are presented in the k12–l12 plane. Analysis of this diagram has allowed us to reach conclusions that cannot be obtained by a simple fit of data points. In particular, it is demonstrated that the global phase diagrams shape defines the correlative ability of the equations. It is found that CS-type equations tend to predict a larger region of liquid–liquid immiscibility, the accuracy of the result depends on the particular experimental system. Changes in the density dependence of the attraction term of the two-parameter equations influence mostly the predicted critical volumes and not their qualitative performance. In addition, the development of a CS-type equation suitable for engineering calculations is discussed.

Prediction of the critical locus in binary mixtures using equation of state. I. Cubic equations of state, classical mixing rules, mixtures of methane-alkanes

Abstract This work compares the critical lines predicted by six cubic equations of state (EOS) and classical mixing rules with the experimental data available for the mixtures of methane–alkanes up to and including octane. A simple method for calculating the critical line is proposed. The influence of the values of the unlike pair parameter k 12 is followed and analyzed from the point of view of the global phase diagram. It is shown that different cubic EOS can yield similar semi-quantitative and even quantitative predictions with the optimized values of this parameter. The results are compared with the information available in the literature.

The numerical challenges of SAFT EoS models

Abstract This study reviews various numerical challenges that should be addressed by further development of SAFT models, such as the fictitious phase equilibria, artificial co-volumes and lacking of capability to describe the critical and the subcritical data simultaneously.

Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state III. Methane–n-alkanes

Abstract The present study compares the ability of three semi-predictive approaches, namely, the Global Phase Diagram-based semi-predictive approach (GPDA), the Predictive Soave-Redlich-Kwong (PSRK) and the Linear Combination of the Vidal and Mixing rules (LCVM), to describe the phase equilibrium data in the homologous series methane–n-alkanes. The results obtained for the series under consideration demonstrate, similarly as shown before for the homologue series carbon dioxide–n-alkanes, that GPDA predicts the data more accurately than the GE-based models correlate them. In particular, GPDA predicts the critical points very accurately and yields a qualitatively correct picture of the global phase behavior in the series. In contrast, both PSRK and LCVM overestimate the critical pressures and generate false liquid–liquid split in the system methane–n-pentane. Although, the GE-based models yield more accurate results for dew-point data at high temperatures, GPDA predicts these data better at the moderated and low temperatures. In addition, it is clearly better in predicting the bubble-point data. PSRK is more accurate than LCVM in description of the homologues lighter than methane–n-decane, however it fails to predict the data of the heavier ones.

A novel approach for defining parameters in a four-parameter EOS

Abstract In the present study we propose an approach that can be used as a shortcut method for defining the parameters of a four-parameter equation of state (EOS). The value of the covolume of an accurate EOS is shown to be close to that of the saturated molar volume of the liquid phase at low pressures. Hence, it is proposed that the covolume be taken as the value of the liquid molar volume at the triple point. Use of experimental values of the critical compressibility factor is also recommended. The approach suggested has been applied to the simplest form of a van der Waals-type four-parameter EOS (C4EOS) and the results compared to those of the best cubic EOS (Peng–Robinson and Trebble–Bishnoi–Salim) available. The C4EOS is more accurate than the Peng–Robinson EOS. Although the Trebble–Bishnoi–Salim EOS is more precise for describing pure compounds, the C4EOS has a clear advantage in predicting the global phase behavior in non-polar homologous series for which experimental data are available. It is recommended to apply the present approach to EOSs that include theoretically based repulsive terms.

Association and molecular chain length effects on interfacial behavior

The scope of this work is to analyze the influence of the molecular chain length and association effects on the properties of vapor–liquid interfaces. Calculations are based on the gradient theory applied to the Statistical Associated Fluid Theory (SAFT) equation of state (EOS), yielding thus an approach that predicts both phase equilibrium and interfacial properties. In addition, the theoretical structure of the SAFT-EOS includes the specific effects under consideration. The approach proposed here is coherent with the density functional theory, although it is more direct to apply, and predictions are in good agreement with experimental data. Results show that the interface thickness decreases, while the interfacial tension increases, as the molecular chain length and/or the association degree increases at isothermal conditions. Such a trend may be explained in terms of the distortion of the cohesion energy. Detailed examples are discussed for subcritical binary mixtures and predictions are confronted with experimental data. §Partial results of this paper were presented at the 17th iupac conference on chemical thermodynamics, Rostock, Germany on July 28 – August 2, 2002.

Phase behavior of Dieterici fluids

This study presents an analysis of the Dieterici equation of state using the global phase diagram methodology. The main difference between the EOS of Dieterici and equations of state of the van der Waals type is that Dieterici isotherms do not give negative pressures. It is shown that this feature results in the inability of the Dieterici EOS to describe liquid properties at very low pressures and temperatures and it limits the possibility to generate transitional mechanisms with negative pressure critical lines. Common behavior, such as liquid–liquid immiscibility in real fluids at very low temperatures, cannot be described with this EOS. Thus, without major modifications, the Dieterici EOS cannot be expected to replace EOS of van der Waals type for the correlation and prediction of data of mixtures. The most important conclusion of the present study is that in order to be useful in practice, an EOS should be able to generate isotherms that present negative pressures.

Closed loops of liquid–liquid immiscibility predicted by semi-empirical cubic equations of state and classical mixing rules

The present study demonstrates that semi-empirical cubic EOSs, which include temperature functionalities such as that of Soave and van der Waals classical mixing rules, predict the behavior around the mathematical double points of the second kind. For the first time these results allow one to fit Type VI behavior in real water solutions, that include both first and second hypercritical points, or the absence of each of these points. Although the predicted data match the experimental data, their genesis is explained by fundamental numerical pitfalls, namely non-physical and non-differentiable breaking points that are characteristic for several empirical temperature functionalities. Hence, such results cannot represent the physical nature of the real systems. Although these pitfalls may take place outside the range of practical significance for pure compounds, they may strongly affect the predictions of the mixtures even at ordinary conditions. Therefore it is shown once again that all parts of the thermodynamic phase space predicted by the EOSs are closely inter-related.

Phase Stability Analysis in Binary Systems

Abstract Stability analysis should be a standard practice for testing the physical validity of phase equilibrium states predicted by thermodynamic models however, it is seldom used in routine work of experimental data modeling. Lack of stability analysis may result in potential modeling pitfalls or in an inadequate prediction of data. In this contribution the concept of stability is reviewed from a general viewpoint, showing how it applies to completely general cases of binary phase equilibrium, from low to high-pressure ranges. Graphical examples are given using excess Gibbs energy models and equations of state.