Linear Mixtures in the Context of Equation of State Models

J.M MILANESIO; M. CISMONDI; L.M. QUINZANI; M.S. ZABALOY

Cannes, France.

Simposio; 23rd European Symposium on Applied Thermodynamics (ESAT2008). May 29th to June 1st 2008; 2008

Laboratoire De Thermodynamique Des Separations - E.N.S.I.C.

Models of the Equation of State (EOS) type, which are based on the van der Waals (vdW) EOS, are probably the only type of analytical models able to deal with phase equilibrium properties of asymmetric systems over wide ranges of pressure, composition and temperature. Nevertheless, conventional EOSs are unable to meet the ideal solution limit [1] [2], which has proven to be a useful reference for modeling the thermodynamic properties of real systems. In contrast, an unconventional treatment [1] [2] of the composition dependence for systems where we model the constituent components at pure state using an EOS, does reproduce the ideal solution limit, if desired. However, such unconventional treatment is unable to describe vapor-liquid critical points for mixtures. This is because there is always a region in the Pressure-Temperature space where it is not possible to find, at given Temperature and Pressure, EOS roots (i.e., density values) of the same nature (e.g., liquid), for all pure compounds of the mixture. In such region the ideal solution system has property values that are meaningless. Therefore, the ideal solution reference finds limited applicability in the interpretation of the phase behavior of fluid systems at liquid-vapor equilibrium in wide ranges of conditions. To improve our understanding of models of the EOS type, we study in this work a reference system which, opposite to the case of the ideal solution reference, has properties that should be meaningful at all conditions. Such reference system is the linear system, i.e., a mixture whose parameters depend linearly on composition. In a linear system, the value for the partial molar parameter of a given component within a multicomponent system equals the value for the pure compound parameter. This is analogous to the case of the partial molar volume in an ideal solution, which equals the pure compound molar volume. Thus, the linear system could be seen as an “ideal” system where the property we consider when defining “ideality” is an EOS mixture parameter rather than the mixture volume. The linear system reference is at first sight appropriate for understanding EOS type models because, while satisfying the constraint of equality between partial and pure compound parameters, the averaging procedure to which it corresponds operates on properties (pure compound parameters) that are independent from the phase nature (liquid or vapor). This last feature is lacking for the case of the conventional ideal solution limit and it makes the properties of the reference (linear) system calculable at any condition of temperature, composition and density, thus making linear systems able to describe vapor-liquid critical points. In this work, we obtain a preliminary answer to the question of whether a linear system has a behavior analogous to that of the well-known ideal solution reference and in which ways. To this end, we study a series of binary systems for which we generate global phase equilibrium diagrams, which are defined by vapor-liquid and liquid-liquid critical lines, by liquid-liquid-vapor lines and by pure compound vapor-liquid saturation lines [3].