Improvements of a hollow fiber reverse osmosis desalination model: Analysis of numerical results

Abstract

In this work, a rigorous model describing the processes taking place in hollow fiber modules for reverse osmosis desalination is analyzed. The Kimura-Sourirajan model is used for describing transport phenomena through the membrane. The concentration polarization phenomenon is mathematically described using the film theory, while the Hagen-Poiseuille and Ergun equations describe the pressure drop in the fiber bore and on the shell side of the fiber bundle, respectively. Improving the previous model, in this work the salt concentration of the permeate accumulated along the fiber is calculated from appropriate mass balances. Hence, the osmotic pressure and the water and salt fluxes through the membrane that depend on this concentration change through the module; and it also influences indirectly the calculation of other process parameters. The solutions of all the differential equations involved in the model are accurately approximated by the finite differences method applied over an appropriate discretization. The value of the output variables changes less than 1% when the finite difference mesh is increased from 6 to 7 grid points in the range of each domain, axial and radial. The flow rates and salt concentrations profiles obtained by the proposed model are analyzed. The influences of the transmembrane and osmotic pressures over the permeate flow rates and salt concentrations are studied. The effect of incorporating the accumulated permeate salinity is showed. It is proved that errors committed by ignoring the permeate accumulated salinity can be significant. Sensitivity analysis for the permeate flow rate and permeate salt concentration is performed by studying the influence of different kind of data: input variables, physical coefficients and design variables.