nonrandom two-liquid model with differential evolution for experimental liquid-liquid equilibrium calculation

In this study, the nonrandom two-liquid (nrtl) model was used to calculate the isoactivity equations from the experimental liquid-liquid equilibrium (lle) data. additionally, the original differential evolution method (de_rand1) and its modifications involve the self-adaptive control parameters differential evolution (jde), the adaptive differential evolution with optional external archive (jade), and the composite differential evolution (code) have been used to estimate the binary interaction parameters. randomization of regression parameters has been used to minimize the fitting objective function. furthermore, the effectiveness of these optimization methods was tested in a quaternary system of water, acetic acid, 50 % dichloromethane (dcm), and 50 % methyl isobutyl ketone (mibk) at 301.15 k. moreover, the optimization process assessment was carried out by regression analysis using root mean square deviation (rmsd), mean, standard deviation, and the duration of execution time spent on both the activity and the fractional objective functions. root mean square deviation (rmsd) results that were less than or equal to 0.0107 demonstrated the effectiveness of differential evolution methods in estimating nrtl parameters for this specific system. finally, the original method (de_rand1) was found to be the most efficient approach among all its variations.