New Parametric Model to Correlate the Gibbs Excess Function and Other Thermodynamic Properties of Multicomponent Systems. Application to Binary Systems

Abstract

A new empirical mathematical model for the Gibbs excess function, g E ) ψ(p,T,x), is presented for a multicomponent system. Dependence on the composition is achieved through the so-called active fraction, z i , which, in turn, is related to the molar fraction x i of the components of a solution and a parameter k ij , the determination of which is also indicated. The efficacy of the model in relation to its extension of application is discussed, considering various cases and three possible ways to calculate the parameter k ij . This produces different versions of the model for data correlation the advantages of which are discussed. The model proposed for the Gibbs excess function adopts the following generic expression, g E (P,T,x) ) z(x)[1z(x)]∑ i)0 g i (P,T)z i where g i (P,T) ) g i1 + g i2 P 2 + g i3 PT + g i4 /T + g i5 T 2 , which can be applied to a general case of vapor-liquid equilibrium with variation of the three main variables x i , p, and T, or by considering the experimental values for two important situations, isobaric and isothermal, which are also studied here. Other mixing properties are obtained via mathematical derivation, and a simultaneous correlation is carried out on several of them. The model has been applied to various binary systems for which experimental data are available in the literature and over a wide range of p and T. The results obtained can be considered acceptable.

Liquid–Liquid Equilibria in Binary Solutions Formed by [Pyridinium-Derived][F4B] Ionic Liquids and Alkanols: New Experimental Data and Validation of a Multiparametric Model for Correlating LLE Data

“…. The database generated was used together with data published previously 4À7 to achieve one of the objectives of this work, to treat and correlate them using two models: the NRTL model 8 and a parametric model proposed by the authors in previous works 9,10 (detailed in the following section). The graphs in Figures 1aÀe show the results for the set of compounds studied, with the distribution of experimental points obtained for each of the ILs.…”

“…Two correlation models were used for the Gibbs function: one previously employed by the authors to correlate vaporÀliquid equilibrium (VLE) data 9,10 and derived thermodynamic quantities, and an extended version of the local composition model (Non-Random Two Liquids, NRTL), for comparative purposes. A correlation method was applied (the same for both models) using a genetic algorithm (GA) 36 as a correlation tool and the appropriate objective functions for this procedure.…”

“…The characteristics of these global algorithms are similar to those of others constructed for the joint correlation of different thermodynamic properties, and some of their applications to other cases, which have been presented in previous works. 9,10 The detailed stages of this procedure are as follows: (1) Initial values are calculated for the model parameters obtained by optimizing an objective function (OF) γ , based on the isoactivity criterion and expressed as…”

“…In recent studies, 9,10 we have discussed the utility of a parametric model, of the type G E = G E (p, T, x), for the Gibbs excess function in multicomponent systems, of the form…”

“…8 However, because of the irregular distribution of the LLE data, there is some difficulty fitting the systems studied, and extended versions of the original model must be used to obtain acceptable correlations. Previous works 9,10 have presented the development and application of a polynomial model for Gibbs excess function G E = ψ{p, T, z(x)}, which gave good results for the correlation of vaporÀliquid equilibrium (VLE) data and other properties of solutions. This model will be Industrial & Engineering Chemistry Research ARTICLE used in this work for the first time to study its efficacy in the treatment of liquidÀliquid equilibrium (LLE) data, comparing the goodness of fit of the correlation obtained with that obtained via the NRTL model.…”