مدل سازي ترموديناميكي تعادل مايع-مايع در مخلوط هاي متانول و مايعات يوني

In this study, thermodynamic modeling of the Liquid-Liquid Equilibrium (LLE) for the ternary system of n-hexane(1) + methanol(2) + [BMIM][NTf₂](3) was carried out at 298.15K an‎d atmospheric pressure using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. Experimental data comprising eleven tie-lines were taken from the literature. Methanol was modeled as an associating compound employing the 2B association scheme, while the ionic liquid was treated through a pseudo-association (ion-pair) approach. Three binary interaction parameters (k12, k13, an‎d k23) were regressed using a hybrid three-stage optimization strategy consisting of a Genetic Algorithm (GA) with a population size of 100 individuals over 50 generations, multi-start local optimization from 10 ran‎dom initial points, an‎d the Sequential Quadratic Programming (SQP) algorithm for final refinement. The objective function was defined as the sum of squared errors (SSE) between the experimental an‎d calculated mole fractions across both equilibrium phases. Out of 10 independent optimization runs, 7 converged to the same optimum, confirming the robustness an‎d reliability of the obtained solution. The final binary interaction parameters were determined as k12 = 0.0371 for the n-hexane–methanol pair, k13 = 0.0122 for the n-hexane–[BMIM][NTf₂] pair, an‎d k23 = -0.0275 for the methanol–[BMIM][NTf₂] pair. The negative value of k23 indicates an attractive interaction stronger than the geometric-mean prediction between methanol an‎d [BMIM][NTf₂], which is attributed to the formation of hydrogen bonds between the hydroxyl group of methanol an‎d the sulfonyl oxygen atoms of the [NTf₂]– anion. This strong cross-interaction constitutes the molecular basis for the selec‎tive extraction capability of the ionic liquid in separating methanol from its azeotropic mixture with n-hexane. Quantitative eva‎luation of the model performance was conducted using several statistical metrics. The root-mean-square deviation (RMSD) was found to be 0.0079, the coefficient of determination (R2) was 0.9995, the sum of squared errors (SSE) was 4.167×10-3, the average absolute deviation (AAD%) was 0.1493, an‎d the mean absolute error (MAE) was 0.0043. A comparison with the NRTL an‎d UNIQUAC models reported in the literature for the same system revealed that the PC-SAFT model, with an RMSD of 0.0079, provides approximately 46% an‎d 50% higher accuracy than the NRTL model (RMSD = 0.0147) an‎d the UNIQUAC model (RMSD = 0.0158), respectively. This superiority originates from the inherent capability of the PC-SAFT equation of state to explicitly account for association interactions through a dedicated association contribution term, thereby allowing for a separate treatment of dispersion forces an‎d hydrogen-bonding effects. Further validation was performed on a second ternary system, n-hexane + methanol + [BMIM][PF₆], which yielded comparable results with RMSD = 0.01135 an‎d R2 = 0.9989, confirming the effectiveness an‎d transferability of the proposed modeling approach.

محمدرضا احساني , ترانه جعفري بهبهاني

حميدرضا شاه وردي , علي اكبر دادخواه