Comparative Analysis of Computational Prediction Methods for Liquid-Liquid Equilibria in Ternary Water-Ethanol-Benzene Mixtures

Ethanol (EtOH) purification is a pivotal research pursuit, with liquid-liquid extraction emerging as a significant purification methodology. This study focuses on utilizing benzene solvent for EtOH purification and investigates the liquid-liquid equilibrium (LLE) within three-component systems comprising EtOH, water, and benzene. Thermodynamic modeling of EtOH-benzene-water systems at temperatures of ۲۰ °C, ۳۰ °C, ۴۰ °C, and ۵۵ °C was conducted. In this paper, the equations used for predicting mole fraction include Non-Random Two-Liquid (NRTL), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Multilayer Perceptron Artificial Neural Network (MLP-ANN). First, the equation parameters were optimized using the particle swarm optimization (PSO) algorithm to employ the NRTL equation Experimental data was used to train the MLP-ANN and ANFIS methods, and the same experimental datasets were used for all models. These models estimated integral components across both phases, revealing effective system control across all methodologies. However, the comparative analysis indicated the superior performance of the MLP-ANN and ANFIS methods over the NRTL model. The Root Mean Square Deviation (RMSD) errors for the NRTL, MLP-ANN, and ANFIS models were ۰.۰۲۵۳, ۰.۰۰۳۵, and ۰.۰۰۱۷, respectively. These results indicate that despite the low prediction error of all three methods, the NRTL equation has the highest error, and the ANFIS method has the lowest mole fraction prediction error.

Keywords:

Liquid-liquid equilibria , Adaptive neuro-fuzzy inference system , artificial neural network , NRTL model , Partial Swarm Optimization Algorithm