Reverse osmosis desalination in tubular membrane duct

Abstract

A mathematical analysis, based on boundary layer theory, is presented for the case of a tubular reverse osmosis duct whose walls are made of a semi-permeable membrane. The analysis considers the simultaneous development of velocity and concentration profiles. The momentum and diffusion equations, coupled through both the boundary conditions and the convective terms in the diffusion equation, are solved by the integral method which also takes into account the non-linear effects created by the varying water flux produced. The analysis assumes flat velocity and concentration profiles at the entrance, two dimensional, steady-state laminar flow and constant physical properties. The analysis is applicable to both the entrance region and the fully developed region. Typical results are presented for the concentration build up at the membrane wall, the flux of water produced and the productive capacity of the system. Since the concentration profile at any value of 2 + is given as a simple polynomial, the results can be used to study the relaxation of concentration polarization as a Graetz type of problem. No experimental data were available with which the results of the present work could be compared.