Abstract—In this work, Experimental tie-line results and solubility (binodal) curves were obtained for the ternary systems (water + acetic acid + methyl isobutyl ketone (MIBK)), (water + lactic acid+ methyl isobutyl ketone) at T = 294.15K and atmospheric pressure. The consistency of the values of the experimental tie-lines was determined through the Othmer-Tobias and Hands correlations. For the extraction effectiveness of solvents, the distribution and selectivity curves were plotted. In addition, these experimental tie- line data were also correlated with NRTL model. The interaction parameters for the NRTL model were retrieved from the obtained experimental results by means of a combination of the homotopy method and the genetic algorithms. Keywords—Liquid-liquid equilibria, homotopy methods, carboxylic acid, NRTL. I. INTRODUCTION ANY attempts have been made to describe the solvent extraction of carboxylic acids from aqueous fermentation solutions. The (liquid–liquid) equilibrium (LLE) measurements and phase behaviour of ternary systems including carboxylic acids has been the subject of much research in recent years [1]–[5]. LLE data of the related systems are not only needed for the design of an efficient and productive extraction system, but they are also indispensable in calibration and verification of analytical models. In the present work, liquid–liquid equilibrium data have been obtained for three different systems, namely, (water + acetic acid + methyl isobutyl ketone), (water + lactic acid+ methyl isobutyl ketone) at 294.15K and at atmospheric pressure. The distribution coefficients and separation factors were obtained from experimental results and are also reported. The tie lines were determined and were correlated by the methods of Othmer-Tobias and Hand on a mass-fraction basis. The experimental results are compared with values predicted by NRTL. D. Laiadi is with the Departement of industrial chemistry, University Mohamed Khider Biskra, Algeria (phone: +213-06-62006663,e-mail: ayadhi_jm@yahoo.com) A. Hasseine is with the Departement of industrial chemistry, University Mohamed Khider Biskra, Algeria (e-mail: hasEine@yahoo.fr) A. Merzougui is with the Departement of industrial chemistry, University Mohamed Khider Biskra, Algeria (,e-mail: merzouguikarim@yahoo.com) II. EXPERIMENTAL SECTION A. Chemicals Acetic acid, lactic acid, dichloromethane and methyl isobutyl ketone were purchased from Merck and were of 99, 99, 98, and 99% mass purity, respectively. The chemicals were used without further purification. Deionized and redistilled water was used throughout all experiments. B. Analytical Methods The Solubility curve was determined by the cloud point method [6] using a thermostated cell, equipped with a magnetic stirrer and isothermal fluid jacket. The cell was kept in a constant-temperature bath maintained at 21±0.1°C. The cell was filled with homogeneous water + carboxylic acid mixtures prepared by weighing, using a Nahita YP402N balance with a precision of 10 -2 g. The solvent was titrated into the cell from a microburet with an uncertainty of ±0.01cm 3 . The end point was determined by observing the transition from a homogeneous to a heterogeneous mixture. This pattern was convenient to provide the aqueous-rich side of the curves. The data for organic-rich side of the curves were therefore obtained by titrating homogeneous solvent + carboxylic acid binaries with water until the turbidity had appeared. The maximum error in the calculation of the compositions of the bimodal curve was estimated to be 10 -2 . Next, the refractive indexes of these ternary mixtures are measured by using a Nahita Modèle 690/1 refractometer. Each measurement was taken on three occasions. For the tie-line measurement, an equilibrium cell was immersed in a thermostat controlled at the desired temperature (±0.1 o C). The pure components were added, and the mixture was stirred for at least 3 h with a magnetic stirrer. The two- phase mixture was allowed to settle for at least 3. Samples were taken by syringe from the upper and lower mixtures. The refractive indexes of both phases at equilibrium were measured to later determine their compositions. III. MODELS THERMODYNAMIC The NRTL model was used to correlate the experimental data in this work, the NRTL model was expressed by: D. Laiadi, A. Hasseine, and A. Merzougui Liquid-Liquid Equilibria for Ternary Mixtures of (Water + Carboxylic Acid+ MIBK), Experimental, Simulation, and Optimization M World Academy of Science, Engineering and Technology International Journal of Chemical and Molecular Engineering Vol:7, No:6, 2013 384 International Scholarly and Scientific Research & Innovation 7(6) 2013 scholar.waset.org/1307-6892/4431 International Science Index, Chemical and Molecular Engineering Vol:7, No:6, 2013 waset.org/Publication/4431