ABSTRACT
Modeling and prediction of phase equilibrium data are very important for simulation, design, and optimize of separation operations. A large amount of investigation has been carried out in recent years on the liquid-liquid equilibrium (LLE) measurements of ternary systems, in order to understand and provide further information about the phase behavior of such systems. Usually, the thermodynamic models have been successfully applied for the correlation of several LLE systems but these conventional methods for LLE data prediction of complex systems are tedious and involve a certain amount of empiricism. To avoid these limitations, new correlation methods were developed by using artificial neural networks (ANNs) which have been recently applied to many prediction tasks. The ANNs are non linear and highly flexible models that used to model complex non-linear relationships. The ANNs offer the potential to overcome the limitations of the traditional thermodynamic models and polynomial correlation method for the complicated systems, especially in estimating the LLE and vapor-liquid equilibrium (VLE) (Ganguly, 2003; Guimaraes and McGreavy, 1995; Mohanty, 2005; Sharma et al., 1999, Urata et al., 2002). The ANNs are able to determine the relationship between a set of input data and the corresponding output data without the need for predefined mathematical equations between these data but the inherent complexity in the design of neural networks in terms of understanding the most appropriate topology and coefficients has a great impact on their performance (Nariman-zadeh and Jamali, 2007). Conversely, the group method of data handling (GMDH) (Ivakhnenko, 1971) is aimed to identify the functional structure of a model hidden in the empirical data. The GMDH creates adaptively models from data in form of networks of optimized transfer functions in a repetitive generation of layers. Neither, the number of nodes (neurons) and layers in the network, nor the transfer functions of neurons are predefined. All these are adjusted during the process of selforganization by the process itself. As a result, an explicit analytical model representing relevant relationships between input and output variables is available immediately after modeling (Onwubolu, 2007). The GMDH uses a feed-forward network structure based on short-term polynomial transfer function whose coefficients are obtained using regression technique (Farlow, 1984). The GMDH was developed for complex systems modeling, prediction, identification and approximation of multivariate processes, diagnostics, pattern recognition, and clusterization of data sample. It was proved that for inaccurate, noisy, or small, data can be found best optimal simplified model, accuracy of which is higher and structure is simpler than structure of usual full physical model. In this work, an LLE prediction method was developed by using GMDH algorithm to predict LLE data of a ternary system (water + 1-propanol+ diisopropyl). Using existing data from (Ghanadzadeh and Haghi, 2006), the proposed model was trained and then used to predicting of LLE data in aqueous and organic phases. Then, the predicted data from the GMDH model compared with the experimental data. Also, mean deviations obtained by UNIFAC and proposed model have been compared. The phase diagrams for the studied ternary system including both the experimental and predicted tie-lines are presented.
