Correlating bubble points of ternary systems involving nine solvents and two ionic liquids using artificial neural network

The use of ionic liquids is being increasingly investigated in separation technologies, for example, in special distillation processes such as azeotropic or close-boiling mixtures. Such applications require accurate knowledge of the physical properties of the mixtures involved. In this respect, the correlation or estimation of the bubble points might be difficult due to the complex nature of some ternary systems, especially in the presence of ionic liquids. In the present study, the bubble points of several ternary mixtures containing an ionic liquid were correlated using an artificial neural network modeling approach. The solvents investigated consisted of 1-propanol, 2-propanol, ethyl ethanoate, methyl ethanoate, chloroform, propanone, ethanol, methanol and water and the ionic liquids considered were 1-ethyl-3-methylimidazolium trifluoromethane-sulfonate ([emim][CF3SO3]) and 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]). For this purpose, a total of 529 experimental data points from previously published literature were collected to aid in finding the best network architecture and the optimum parameters. To do this, the collected data were divided into two subsets, namely the training and testing subsets. Using the training data set, and based on a trial and error procedure, the optimum network parameters were determined to be three layers including one input, one hidden and one output layer, nine neurons in the hidden layer, the logarithmic-sigmoid transfer function for the hidden layer, and the purline function for the output layer. The optimized weights and biases were also obtained and presented. The feasibility of the proposed network for the correlation of ternary bubble point was then examined using data that were not used in optimizing the network. The overall average absolute relative deviation (AARD %), mean square error (MSE), maximum deviation (Emax), minimum deviation (Emin) and correlation coefficient (R2) were calculated to be 0.20%, 0.9953, −0.97, 0.87 and 0.95, respectively.