Predicting Permeate Fluxes and Rejection Rates in Reverse Osmosis and Tight‐Nanofiltration Processes

Abstract

International audienceThe performance of reverse osmosis and tight nanofiltration with flat-sheet membranes can be predicted accurately. The proposed numerical model solves the local momentum and mass conservation equations in the module's feed channel with solution-diffusion boundary conditions. Both qualitative and quantitative predictions of the permeate flux and of the rejection rate are obtained with an accuracy depending on the limitations of the solution-diffusion model for describing membrane mass transport and on the value of solute permeability. As an extension of the applications to plate-and-frame modules, the ability to describe the performance of processes carried out with spiral-wound modules is also tested with own desalination experiments and with data from the literature

Effects of Solute Permeability on Permeation and Solute Rejection in Membrane Filtration

“…This work follows the publication by Lopes et al , which demonstrated the adequacy of the numerical model developed by the authors for predicting permeate fluxes and solute rejection obtained experimentally in RO and tight NF in flat and spiral‐wound geometries. The current article begins with a summary of the model and a description of the simulations.…”

“…Let us first consider the behavior of the averaged permeate flux measured by experimentalists, U av , equivalent to the local permeate flux averaged along the membrane length . The classic influence of the inlet pressure on it is depicted in Fig.…”

“…A crossflow is not one‐dimensional by definition. While the previous paragraphs insisted on the role of U on the establishment of the polarization layer by advection of solute onto the membrane surface, the influence of the axial shearing generated upon this layer by W should not be neglected , . Consider: …”

“…As the model we used is described extensively in , , , only its main elements will be given here. The model considers a liquid solution of one solvent and one solute in laminar, steady, incompressible crossflow filtration (tangential filtration) along a 2D planar symmetric channel of axial and transverse coordinates Z and X , respectively, the channel walls being permeable to both solvent and solute.…”

“…The numerical solutions are calculated at each grid point in half of the channel via a second‐order finite difference scheme which solves the continuity equation, the 2D Navier‐Stokes equations, and the solute conservation equation simultaneously . The system is handled in dimensionless form under Prandtl's hypotheses , , whereby diffusion of momentum and mass in the longitudinal (axial) flow direction is negligible compared with that in the transverse direction. These equations are solved in the filtration channel only (flow domain), whereas membrane transport takes the form of boundary conditions (Eqs.…”