Linear Mixtures in the Context of Equation of State Models

JUAN MILANESIO; MARTÍN CISMONDI; LIDIA QUINZANI; MARCELO ZABALOY

Cannes, Francia

Simposio; 23rd ESAT, European Symposium on Applied Thermodynamics; 2008

Models of the Equation of State (EOS) type, which are based on the van derWaals (vdW) EOS, are probably the only type of analytical models able to dealwith phase equilibrium properties of asymmetric systems over wide ranges ofpressure, composition and temperature. Nevertheless, conventional EOSs areunable to meet the ideal solution limit [1] [2], which has proven to be a usefulreference for modeling the thermodynamic properties of real systems. Incontrast, an unconventional treatment [1] [2] of the composition dependence forsystems where we model the constituent components at pure state using anEOS, does reproduce the ideal solution limit, if desired. However, suchunconventional treatment is unable to describe vapor-liquid critical points formixtures. This is because there is always a region in the Pressure-Temperaturespace where it is not possible to find, at given Temperature and Pressure, EOSroots (i.e., density values) of the same nature (e.g., liquid), for all purecompounds of the mixture. In such region the ideal solution system hasproperty values that are meaningless. Therefore, the ideal solution referencefinds limited applicability in the interpretation of the phase behavior of fluidsystems at liquid-vapor equilibrium in wide ranges of conditions. To improveour understanding of models of the EOS type, we study in this work a referencesystem which, opposite to the case of the ideal solution reference, hasproperties that should be meaningful at all conditions. Such reference system isthe linear system, i.e., a mixture whose parameters depend linearly oncomposition. In a linear system, the value for the partial molar parameter of agiven component within a multicomponent system equals the value for the purecompound parameter. This is analogous to the case of the partial molar volumein an ideal solution, which equals the pure compound molar volume. Thus, themixture volume. The linear system reference is at first sight appropriate forunderstanding EOS type models because, while satisfying the constraint ofequality between partial and pure compound parameters, the averagingprocedure to which it corresponds operates on properties (pure compoundparameters) that are independent from the phase nature (liquid or vapor). Thislast feature is lacking for the case of the conventional ideal solution limit and itmakes the properties of the reference (linear) system calculable at any conditionof temperature, composition and density, thus making linear systems able todescribe vapor-liquid critical points. In this work, we obtain a preliminaryanswer to the question of whether a linear system has a behavior analogous tothat 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 phaseequilibrium diagrams, which are defined by vapor-liquid and liquid-liquidcritical lines, by liquid-liquid-vapor lines and by pure compound vapor-liquidsaturation lines [3].