An approximate analytical solution for the performance of reverse osmosis plants

✍ Scribed by A.E.S. Al-Zahrani; M.A. Soliman; I.S. Al-Mutaz

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 303 KB
• Volume: 75
• Category: Article
• ISSN: 0011-9164
• DOI: 10.1016/0011-9164(89)85002-7

✦ Synopsis

Recent developments in membrane technology and appropriate construction material made reverse osmosis plant attractive for large desalting capacity. Reserve osmosis showed a growing demand specially in sea water desalting. It can be considered the optimum process in areas where sufficient electric power is available at low cost. Due to these reasons, mathematical modeling of reverse osmosis plants became an important task in the design procedure. In this paper, the partial differential equations representing the material and momentum balances inside a hollow fine fiber reverse osmosis model are discretized by the method of orthogonal collocation. The approximate analytical solution is obtained by applying the one point collocation method in the radial and axial direction. This leads to simple expressions for the recovery and product concentration. The obtained expressions are compared by the more exact results obtained by using higher order collocation method. The applicability of these results to the design and operation of reserve osmosis plants will be disucssed. PREVIOUS WORK Dandavati et al(I) presented a model that assumes plug flow of the liquid in the the shell side in the radial direction. Experiments carried out by Soltanieh and Gill(2) suggested that the flow could be of the complete mixing type. The issue is settled by recent experiments of Gill et al who studied the dynamics of flow in radial flow hollow fiber membranes(2~31. Their study indicate with no doubt that the flow is mixed to a large extent. Since most of the previous analysis was based on Dandavatiet al work, we give special emphasis in this work on the effect of the mixing on the steady state behaviour of hollow fiber membranes and present approximate expressions for the recovery and product salt concentration.