Mathematical analysis of the meso-scale flow field in spiral wound membrane modules, Ind. & Eng. Chemistry Research
Year : 2011
Author : Kostoglou M. and Karabelas A.J.
The use of flat-sheet, spiral-wound, membrane modules for reverse osmosis and nanofiltration applications is very extensive. Design and performance optimization of these modules requires sound mathematical modeling. This study focuses on the mathematical analysis of the mesoscale hydrodynamic equations for the narrow channels with spacers, of the entire membrane sheet, previously derived from the microscale momentum conservation laws14. The mathematical problem is enhanced by considering a spatial dependence of the retentate channel and membrane permeabilities to account for fouling/scaling, aiming at future use of the proposed techniques to simulate long time fouling dynamic behavior of the process. The formal mathematical treatment of the original problem leads to several levels of approximation (depending on the problem parameter values) which admit either analytical or numerical solutions with reduced dimensionality, or numerical solutions with reduced convergence difficulties. To confirm the validity of conclusions obtained by following these procedures, several results from simplified cases are compared with numerical solutions of the original problem. Furthermore, all possible simplifications and analytical solutions of the particular problem have been obtained, as well as the conditions under which they hold, thus forming the basis for more comprehensive modeling, including mass transfer and scaling/fouling phenomena. Specific criteria are also provided for selecting appropriate simplified solutions to specific cases, helpful in the development of flow and membrane fouling simulators.