A new approach for modeling of RO membranes using MD-SF-PF model and CFD technique Ali Moradi • Ali Farsi • Seyed Soheil Mansouri • Mehrnoosh Sarcheshmehpoor Received: 1 February 2011 / Accepted: 27 May 2011 Ó Springer Science+Business Media B.V. 2011 Abstract The modified surface force-pore flow (MD-SF-PF) model is a successful and powerful model for prediction of reverse osmosis (RO) membrane separation. In the MD-SF-PF model, a suitable mass and momentum balances were made through the cylindrical micro porous of the membranes. A one-dimensional potential function in radial direction was used to attain the velocity profile. The obtained nonlinear equations were solved by orthogonal collocation method. In our model, extended MD-SF-PF (Ex-MD-SF-PF) model, the potential function of the MD-SF-PF model was developed as both radial and axial directions. Both Ex-MD- SF-PF and MD-SF-PF models were solved by finite volume and finite difference methods based on a computational fluid dynamics (CFD) technique. The profiles of velocity and concentration were achieved and thereby the values of separation factors and fluxes for both models were obtained and were compared accordingly. This approach affected only at the end of pore, mainly on the concentration profile and slightly on the velocity profile. Keywords Membrane  MD-SF-PF  Potential function  CFD  Modeling List of symbols b Friction parameter defined in Eq. (31), dimensionless C Molar density of solution (kmol/m 3 ) C A (r,z) Concentration of solute inside a pore (kmol/m 3 ) A. Moradi (&)  A. Farsi  S. S. Mansouri  M. Sarcheshmehpoor Department of Chemical Engineering, Engineering Faculty, Shahid Bahonar University of Kerman, 76175-133, Kerman, Iran e-mail: amoradi@uk.ac.ir A. Farsi e-mail: ali.farsi@gmail.com A. Farsi  S. S. Mansouri Young Researcher Society, Shahid Bahonar University of Kerman, Kerman, Iran 123 Res Chem Intermed DOI 10.1007/s11164-011-0334-7