Application of a non-linear transformation to the surface fraction of the UNIQUAC model and the performance analysis of the subsequent model (FlexQUAC-Q).

Abstract

GE-model and equations of state are used to describe and predict phase equilibria. Current models have varying capabilities and some display selectivity for certain special mixtures. While many models are superior to others in their performance, all models share a common deficiency, the inability to simultaneously describe vapour-liquid (VLE) and liquid-liquid equilibria (LLE). Current models require separate parameters to describe the two equilibria. This formed the motivation for a non-linear transformation which was formulated by Rarey (2005). The transformation was applied to the concentration space. The clear advantage of such a transformation was that it could be easily applied to any model. The flexibility of the model was drastically increased. The effects were investigated on the local composition models, in particular the UNIQUAC model resulting in the FlexQUAC model. The model was used to regress a host of VLE and LLE data sets contained in the Dortmund Data Bank (DDB). The transformation had the desired effect on the flexibility of the model and the model was now able to describe VLE and LLE. However a symmetric transformation applied to the concentration space might not be effective in the description of systems exhibiting large difference in molecular size. This is a clear disadvantage of the proposed FlexQUAC model. In order to allow the model to cater to asymmetric systems, the transformation is now applied to the surface fraction of the residual contribution of the UNIQUAC model. The Guggenheim-Staverman expression in the combinatorial part was not transformed. Both the original combinatorial term and the more suitable modification of Weidlich and Gmehling (1987) were used. The newly formed model was called the FlexQUAC-Q model. The development of the FlexQUAC-Q model, derivation of activity coefficient expressions, model implementation and its performance analysis form the basis for this research study. The activity coefficient of the new model had to be re-derived due to the application of the transformation to the residual contribution of the UNIQUAC equation. The computation of the activity coefficient was programmed in FORTRAN and integrated into the regression tool (RECVAL) of the Dortmund Data Bank (DDB). The RECVAL tool was used to regress data sets contained in the DDB. Results obtained were comparable to those obtained using the GEQUAC model. The regression was also performed in EXCEL for the three models (UNIQUAC, FlexQUAC, FlexQUAC-Q). The regression in EXCEL was more rigorous and was used for the comparison of the objective functions and to obtain a set of unique model parameters for each data set. The performance of the FlexQUAC-Q model was assessed utilizing the same data sets used to analyse the performance of the FlexQUAC model. The model's performance was assessed in the regression of 4741 binary VLE data sets, 13 ternary VLE data sets and carefully select ternary LLE cases. The minor mean relative reduction of about 3% of the objective function using FlexQUAC-Q compared to FlexQUAC was observed compared to a reduction by about 53% relative to the UNIQUAC-results. It was necessary to illustrate that the new model does not degenerate the model's existing capabilities (e.g. ability to predict multi-component mixtures from binary data) and that the model performs as well as or superior to the UNIQUAC model. FlexQUAC-Q performed similarly to FlexQUAC. However the improvement in the qualitative description of data sets exhibiting asymmetry is apparent. Herein lies the justification of such a modification and this illustrates the preference of such a model when asymmetric systems are being considered. In addition, the FLEXQUAC-Q model can be adapted to be implemented into a group contribution method, a distinct advantage over the previous model FlexQUAC. The equations for the application of a non-linear transformation to a functional group activity coefficient model, UNIFAC are also explored in this study. The resulting model is referred to as FlexFaC.