An analytical model for spiral wound reverse osmosis membrane modules: Part I — Model development and parameter estimation

A mathematical model for spiral wound Reverse Osmosis membrane module is presented in this work. The model incorporates spatial variations of pressure, flow and solute concentration in the feed channel and uniform conditions of pressure in the permeate channel. Assuming solution–diffusion model to be valid, explicit analytical equations were derived for spatial variations of pressure, flow, solvent flux and solute concentration on the feed channel side of the module. Analytical procedures for estimation of model parameters were presented. Graphical linear fit methods were developed for estimation of parameters Aw (solvent transport coefficient), Bs (solute transport coefficient) and b (feed channel friction parameter). The mass transfer coefficient k was assumed to vary along the length of the feed channel with varying conditions of flow, solute concentration and pressure. Explicit analytical equations for estimation of mass transfer coefficient were presented. In this paper (Part I), theoretical studies on development of mathematical model and methods for estimation of model parameters are presented.In Part II of this paper series [1], Studies on validation of this model with experimental data are presented. The studies cover experimental work on a spiral wound RO module with an organic compound namely chlorophenol as a solute.

Research Highlights
► A new analytical model for spiral wound RO modules is developed.
► Validity of Solution diffusion model with concentration polarization is assumed.
► Model predicts spatial variations of Pressure, Flow and Concentration in feed channel.
► New graphical methods for estimation of membrane transport parameters are developed.
► Explicit equations for the estimation of mass transfer coefficient are derived.