Liquid-liquid extraction operation is important in chemistry for separating useful chemicals and pollutants. The design and optimization of such processes require accurate representation and prediction of ternary liquid-liquid equilibrium behavior, which relies on thermodynamic models such as NRTL and UNIQUAC. The model's parameters are estimated using optimization methods such as the Bat Algorithm and the Improved Differential Evolution algorithm (DE_New), which minimize an objective function by solving isoactivity equations numerically. To evaluate the accuracy of both models' predictions, a comparative study of RMSD, AAD, and AARD was conducted using the differences between experimental and predicted data.
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