1. Introduction

The pioneering work of Van Konynenburg and Scott [1] demonstrated that the van der Waals one-fluid model has wide possibilities of qualitative reproducing the main types of phase diagrams of binary mixtures. The thermodynamic equilibrium mapping onto the space of parameters of an equation of state gives the possibility to obtain the criteria for the phase behavior of binary mixtures. The functions of temperature T, pressure p, chemical potential μ, and component concentration x are determined as the "field" variables that are the same for all phases coexisting in equilibrium of a substance i. The molar fraction is the "density" that is in principle of liquid (l) and gas (g) phases. Global phase diagrams (GPD) of binary mixtures

represent boundaries between types of phase behavior in a dimensionless space of EOS parameters.

and other physicochemical properties. A great role in the IL applications plays

Azeotrope-Breaking Potential of Binary Mixtures in Phase Equilibria Modeling

Considering a huge number of the "off the shelf" mixtures scheduled for destroying or recycling, it becomes key importance to develop the theoretically sound methods for reliable assessment of thermodynamic and phase behavior. Experimental retrieval of the azeotrope properties is time-consuming and a costly process. Availability of theoretical predictions for azeotropic phenomena would not only reduce this cost but also make efficient required experimental investigations. The objective of this study is to present novel approach which encompasses global phase diagram technique and Pareto-optimal EoS parameter estimation for azeotropic and double azeotropic criteria evaluation in terms of critical parameters of pure components for the binary mixtures of refrigerants and ionic liquids.

This paper is organized as follows. In Section 2, the phase diagram classification

and the one-fluid model of the equation of state for global phase diagrams are presented. Section 3 provides approach to sustainable property calculation based on a fuzzy set methodology providing a trade-off solution among different sources of data required for regression of model parameters. Section 4 discusses the results of azeotrope-breaking criteria for IL-refrigerant mixtures based at the approaches

Mapping of the global equilibrium surface into the parameter space of the equation of state model provides the most comprehensive set of criteria for predic-

The impact of critical parameters of components on phase topology is provided via global phase diagrams. The diagrams are depicted in the space of the equation of state parameters, e.g., van der Waals a and b parameters. The specific points and lines of global phase diagrams, including tricritical points, double critical endpoints, azeotropic lines, etc., create the boundaries at the diagram and divide the model parameter space into the regions corresponding to the various types of the phase behavior. Generally, global phase diagram is expressed in dimensionless parameters which depend on the equation of state model. The global phase diagrams of such different models as the one-fluid EoS of binary Lennard-Jones fluid [6, 7] and the Redlich-Kwong model [5, 8, 9] are almost identical, in particular for the case of

2. Phase diagram classes and global phase diagram

the azeotropic phenomena.

DOI: http://dx.doi.org/10.5772/intechopen.83769

provided in previous sections.

equal-sized molecules.

molecules:

as follows [13]:

73

tion phase behavior of the binary mixture.

We consider here the cubic-type models:

a ¼ ∑ 2 i¼1 ∑ 2 j¼1 <sup>p</sup> <sup>¼</sup> RT

where R is the universal gas constant and the EoS parameters a and b of mixture depend on the mole fractions xi and xj of the components i and j and on the corresponding parameters aij and bij for different pairs of interacting

<sup>v</sup> � <sup>b</sup> � a Tð Þ

xixjaij <sup>1</sup> � <sup>k</sup>ij , b <sup>¼</sup> <sup>∑</sup>

The convenient set of dimensionless parameters for the Redlich-Kwong model is

2 i¼1 ∑ 2 j¼1

v vð Þ <sup>þ</sup> <sup>b</sup> (1)

xixjbij (2)

GPD also provides good visualization of the impact of model parameters of mixture components to the topology of phase behavior. The proposed types of phase behavior classification [1] are generally used to characterize the different types of phase behavior in binary mixtures.

Varchenko [2] has provided a more rigorous classification for conventional features of equilibrium surface and phase diagrams for binary mixtures with strict determination of the eight topologically different rearrangements.

Current topological analysis of equilibrium surfaces of binary fluid systems provides 26 singularities and 56 scenarios of phase behavior evolution depicted in p–T diagrams [3].

The various phase diagram classes and p–T projections of the main types of phase diagrams have been described in literature [1–3]. Global phase diagrams are a technique which can be used for the prediction of different phase behavior in the mixtures without vapor–liquid equilibrium calculations [4–11].

Patel and Sunol [12] developed a robust automated routine for global phase diagram generation in binary systems. The approach uses any equation of state models, takes into account solid-phase existence, and provides type VI phase diagram generation. The generated data set includes calculations of the critical endpoints, quadruple points, critical azeotrope points, azeotrope endpoints, pure azeotrope points, critical line, liquid–liquid–vapor line, and azeotrope line.

Azeotrope-breaking is important for the successful distilling of industrially important mixtures. To simulate the mixture phase behavior, models based on the equation of state (EoS) presentation for thermodynamic properties are more preferable. The conventional methods of parameter identification use the statistical paradigm, which is based on maximum likelihood or a posteriori probability criteria and does not take into account uncertainties of vague nature. Decision-making process under various uncertainties requires mathematical methods, which include uncertainty evaluation a priori. Statistical methods interpret all variety of uncertainty types in the framework of the randomness concept. Nevertheless, there are ill-structured situations, which have not any strictly defined boundaries and cannot be accurately formulated.

The main challenge is to deal with such kind of expressions like "neighborhood" or "best fit," which do not have strict boundaries, separating one class of objects from others. Generally, there are ambiguous verbal models, which can be treated as fuzzy formulated targets, depending on biased assessment of boundaries for approximations used. As a case study, we provide estimation of the optimal parameters of the Redlich-Kwong equation of state [13], retrieved from the different conflicting data sets resulting from the inconsistency problems arising in the modeling of phase equilibria. Such process reflects different types of uncertainties, including uncertainties of nonstatistical origin. The parameters of phase equilibria models are considered as alternatives, i.e., they allow meeting the targets and prescribed constraints. The parameter estimation problem of phase equilibrium modeling multicriteria approach is applied. To describe the uncertainties of such type, the "fuzzy set" approach introduced by L.A. Zadeh [14] is used.

The problem of optimum parameter estimation of thermodynamic and phase behavior under the uncertainty is a search of the Pareto set. The diverse computational methods of the Pareto-optimum parameter convolution crisp and fuzzy schemes to reduce a vector criterion into the scalar are provided.

Ionic liquids can be treated as "adjustable" working fluids given the fact that variations of different "R – " groups and cation/anion ratio selection ensure meeting preferred trade-off solution between density, viscosity, melting point,
