Numerical study of concentration polarization in a rectangular reverse osmosis membrane channel: Permeate flux variation and hydrodynamic end effects

Abstract Concentration polarization in a rectangular reverse osmosis (RCRO) and a laboratory plate-and-frame RO (PAFRO) membrane channels were investigated using a finite-element numerical model consisting of the fully coupled governing equations for fluid dynamics and mass transfer. The model considers both the concentration dependence of model parameters and axial variation of permeate flux. In both the RCRO and PAFRO channel geometries the flux varies axially along the membrane commensurate with the coupled development of the concentration boundary layer. For the case of the RCRO channel, the effect of permeate flux was quantified via the computed feed-side mass transfer coefficient (commonly used in estimations of concentration polarization) in terms of a dimensionless correlation for the average Sherwood number, S h ¯ = A 1 ( 1 + A 2 R e A 3 S c A 4 ( H / L ) A 5 R e ¯ p ) [ R e S c ( H / L ) ] 1 / 3 , that reduces to the form of the classical Leveque solution in the limit of vanishing permeate flux. Simulations of desalting in a PAFRO channel demonstrated the importance of accounting for local permeate flux variability and coupling of the hydrodynamics and mass transfer model equations in order to predict local concentration variations and in particular local maxima of concentration polarization, especially in regions of flow recirculation where scaling by sparingly water soluble mineral salts could be first triggered should their concentrations exceed saturation.

[1]  Yoram Cohen,et al.  Morphometric characterization of calcium sulfate dihydrate (gypsum) scale on reverse osmosis membranes , 2005 .

[2]  Viriato Semiao,et al.  Integrated modeling of transport processes in fluid/nanofiltration membrane systems , 2002 .

[3]  R. Ranjan,et al.  Mass transfer coefficient with suction for turbulent non-Newtonian flow in application to membrane separations , 2004 .

[4]  David F. Fletcher,et al.  Computational fluid dynamics modelling of flow and permeation for pressure-driven membrane processes , 2002 .

[5]  Eric M.V. Hoek,et al.  Modeling concentration polarization in reverse osmosis processes , 2005 .

[6]  David F. Fletcher,et al.  Techniques for computational fluid dynamics modelling of flow in membrane channels , 2003 .

[7]  Thomas K. Sherwood,et al.  Salt Concentration at Phase Boundaries in Desalination by Reverse Osmosis , 1965 .

[8]  Tzvetan Kotzev,et al.  Numerical study of the fluid dynamics and mass transfer of an ultrafiltration performance in a tube membrane module , 1994 .

[9]  Michael K. Stenstrom,et al.  An unsteady-state model to predict concentration polarization in commercial spiral wound membranes , 1999 .

[10]  Lianfa Song,et al.  Concentration polarization in cross-flow reverse osmosis , 1999 .

[11]  P. Schmitz,et al.  Concentration polarisation in tubular membranes —a numerical approach , 2005 .

[12]  Eric M.V. Hoek,et al.  Pressure, flow, and concentration profiles in open and spacer-filled membrane channels , 2006 .

[13]  J. Miranda,et al.  Mass transport regimes in a laminar boundary layer with suction––parallel flow and high Peclet number , 2004 .

[14]  David F. Fletcher,et al.  Spiral wound modules and spacers - Review and analysis , 2004 .

[15]  Yoram Cohen,et al.  Diagnostic characterization of gypsum scale formation and control in RO membrane desalination of brackish water , 2006 .

[16]  R. I. Kermode,et al.  Prediction of concentration polarization and flux behavior in reverse osmosis by numerical analysis , 1990 .

[17]  Andrew L. Zydney,et al.  Stagnant film model for concentration polarization in membrane systems , 1997 .

[18]  Viriato Semiao,et al.  The effect on mass transfer of momentum and concentration boundary layers at the entrance region of a slit with a nanofiltration membrane wall , 2002 .

[19]  D. Hasson,et al.  Calcium sulphate fouling of reverse osmosis membranes: Flux decline mechanism , 1987 .

[20]  David Hasson,et al.  Flux decline due to gypsum precipitation on RO membranes , 1992 .

[21]  David F. Fletcher,et al.  A computational fluids dynamics study of buoyancy effects in reverse osmosis , 2004 .

[22]  M. C. Porter.  Concentration Polarization with Membrane Ultrafiltration , 1972 .

[23]  Lihan Huang,et al.  Finite element analysis as a tool for crossflow membrane filter simulation , 1999 .

[24]  A. Hasting,et al.  Concentration polarisation in reverse osmosis flow systems under laminar conditions. Effect of surface roughness and fouling , 1974 .

[25]  P. Guichardon,et al.  Transport phenomena in ultrafiltration: a new two-dimensional model compared with classical models , 2002 .

[26]  Yoram Cohen,et al.  High recovery membrane desalting of low-salinity brackish water: Integration of accelerated precipitation softening with membrane RO , 2007 .

[27]  Vivek V. Ranade,et al.  Fluid dynamics of spacer filled rectangular and curvilinear channels , 2006 .

[28]  Y. Cohen,et al.  Numerical model of non-isothermal pervaporation in a rectangular channel , 2005 .

[29]  T. Urase,et al.  The effect of suction velocity on concentration polarization in microfiltration membranes under turbulent flow conditions , 2000 .

[30]  Vítor Geraldes,et al.  Flow and mass transfer modelling of nanofiltration , 2001 .