On the Fluid Mechanics of Spiral-Wound Membrane Modules

Spiral-wound membrane (SWM) modules are comprised of several large-size membrane sheets with a net-type spacer at the retentate flow channel and a porous cloth/filler at the low-pressure permeate side; thus, two strongly interacting flow fields exist with spatially variable properties. Mathematical models of the SWM operation, based on an accurate description of transport phenomena taking place in those narrow flow passages, are necessary tools for optimizing both module design parameters and the entire membrane-based plant. Such integrated SWM models are not available at present. In this problem, the coexistence of several flow length scales, from the pores of the permeate side filler to the macroscopic dimensions of the module, renders the modeling task quite complicated. Typical modeling efforts vary between the extremes of detailed description of transport phenomena at small scale to macroscopic phenomenological-type simulation of the entire separation process in a module. The scope of this work is to describe the hydrodynamics of spiral-wound membranes, starting from first principles, to suggest and analyze some realistic approximations and their origin and to present an integrated model where linking phenomena at different length scales is an essential feature. This effort has resulted in an efficient numerical algorithm, allowing predictions of the spatial distribution of pressure, permeation, and cross-flow velocities throughout the membrane leaves. In this work, all possible analytical solutions have been derived which facilitate the development of the simulation algorithm. Typical examples of predicted flow and pressure distributions are presented.