SEPARATION SCIENCE AND ENGINEERING Chinese Journal of Chemical Engineering, 17(3) 366 372 (2009) Prediction of Effective Diffusion Coefficient in Rotating Disc Columns and Application in Design Marzieh Amanabadi, Hossein Bahmanyar * , Zohreh Zarkeshan and Mohamad Ali Mousavian Engineering College, Chemical Engineering Faculty, University of Tehran, Iran Abstract A rotating disc column (RDC) with inner diameter 68 mm and 28 compartments is used in this study. Parameters including Sauter mean diameter, hold-up and mass transfer coefficient are measured experimentally un- der different operating conditions. The correlations in literature for molecular diffusion and enhancement factor equation including eddy diffusion, circulation and oscillation of drops are evaluated. A new equation for the effec- tive diffusion coefficient as a function of Reynolds number is proposed. The calculated values of mass transfer co- efficient and column height from the previous equations and present equation are compared with the experimental data. The results from the present equation are in very good agreement with the experimental results, which may be used in designing RDC columns. Keywords liquid-liquid extraction, rotating disc column, mass transfer coefficient, effective diffusion coefficient 1 INTRODUCTION Rotating disc column (RDC) is widely used for liquid-liquid extraction. The performance of these columns indicates that they are more efficient and possess better operational flexibility than the conven- tional sieve plate, packed and spray columns. An im- portant application of these contactors is in the petro- leum industry for furfural and sulfur dioxide extrac- tion, propane deasphalting, solfolane extraction and for caprolactum purification [1]. In order to obtain a suitable design for RDC columns, a number of hy- drodynamic parameters, axial mixing and mass trans- fer should be considered. In these columns, new drops are generated from breakage of bigger drops or coa- lescence of smaller drops [2, 3]. The variation of drop- let sizes and dispersed phase hold-up along the col- umn height due to droplet interactions have been studied by using the droplet population balance model [4 6]. Another most important parameter in design is the mass transfer coefficient. The fundamental process for the rate of mass transfer in extraction columns is still not sufficiently well understood nor adequately modeled [7]. Passage of drops from the continuous phase is under the influence of hydrodynamics and has a distinct effect on the mechanism and amount of mass transfer. With regard to the dispersion in the column, the inside of the drop may be stagnant, circu- lating, or oscillating [8, 9]. Therefore, the mass transfer mechanism inside the drop will be based on the exis- tence or non-existence of circular flows. In the following sections, by introducing a number of equations, the mass transfer coefficient will be calculated and the column height will be specified. A new equation for effective diffusivity is proposed for calculating the mass transfer coefficient and col- umn height, and the results are compared with the calculated values from other equations in literature and experimental data. 2 PREVIOUS WORK One of the oldest equations for the mass transfer coefficient, used for stagnant drops with molecular diffusion mechanism, is the Newman equation [10]. With the continuity equation and following initial and boundary conditions, Eq. (2) is obtained [11]. 2 d 2 2 C C C D t r r r ｧ ｷ w w w   ｨ ｸ w w w ｩ ｹ (1) I.C: C(r,0)  C 0 B.C.(1): C(r s ,t)  C * B.C.(2):   0 lim , r rt o is bounded.   2 2 2 d d 2 2 1 6 1 ln exp 4 / 6 n d K n Dtd t n f  ｪ ｺ    S ｫ ｻ S ｬ ｼ ｦ (2) where r s is the drop radius. In Eq. (2) the resistance of continuous phase is neglected. By applying the resistance in the continuous phase, Eq. (2) becomes [7]:   2 2 od d 2 1 6 ln exp 4 / 6 n n n d K C Dtd t O f  ｪ ｺ    ｫ ｻ S ｬ ｼ ｦ (3) where C n and O n are functions of K c d/D d . The equation, obtained by Kronig and Brink [12], for drops in which the mass transfer mechanism in- volves both molecular diffusion and composed inter- nal circulation, is presented as follows: 2 d od 2 1 3 64 ln exp 6 8 n n n d D t K C t d O f  ｪ ｺ  ｧ ｷ  ｫ ｻ ｨ ｸ ｩ ｹ ｬ ｼ ｦ (4) For the drops with toroidal internal circulation, Received 2008-08-25, accepted 2009-03-02. * To whom correspondence should be addressed. E-mail: hbahmany@ut.ac.ir