Liquid-liquid extraction columns scale up and design requires accurately prediction of overall mass transfer coefficient Koc. Already many methods have been suggested by investigators to predict this coefficient. One of these methods is substitution of effective diffusion coefficient (Deff = RD) instead of diffusion coefficient (D) in Newman equation. We surveyed some correlations suggested for R, and compared their results with experimental data of water/acetone/toluene in a pulsed sieve-plate extraction column using axial dispersion model and finally a promising correlation has been developed by considering effect of pulse intensity and volumetric flow rate of phases by the average error of about 5% in Koca estimation. In this paper we solve nonlinear differential equations governing on this system analytically by AGM (Akbari-Ganji's Method). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration, the solution of the problem can be obtained very simply and easily, Which comparisons are made between AGM and Numerical Method (Runge-Kutte 4th). Finaly the results reveal that this method is very effective and simple, and can be applied for other nonlinear problems . And so in this manner enhance accuracy of problem solving , the Taylor expansion is not needed in most cases.

Keywords: Effective Diffusion Coefficient; Liquid Extraction; Overall Mass Transfer Coefficient; Pulsed Sieve Plate; Akbari-Ganji's Method (AGM).