Techniques for computational fluid dynamics modelling of flow in membrane channels

Abstract Accurate modelling of the flow and concentration polarisation in pressure driven membrane processes is inhibited by the complex couplings in the flow equations along with any added effects of variable solution properties. A generic computational fluid dynamics (CFD) model has been developed which incorporates these effects and describes the flow across the membrane wall. The results have been validated against classical solutions available in the literature. Extended work indicates that overly simplified expressions for the dependence of viscosity and diffusivity on concentration produce velocity and concentration profiles that may grossly misrepresent reality.

[1]  Shoji Kimura,et al.  Concentration Polarization Effects in Reverse Osmosis Using Porous Cellulose Acetate Membranes , 1968 .

[2]  Mark M. Clark,et al.  A numerical model of steady-state permeate flux during cross-flow ultrafiltration , 1997 .

[3]  A. Acrivos On the solution of the convection equation in laminar boundary layer flows , 1962 .

[4]  Alan S. Michaels,et al.  SOLUTE POLARIZATION AND CAKE FORMATION IN MEMBRANE ULTRAFILTRATION: CAUSES, CONSEQUENCES, AND CONTROL TECHNIQUES , 1970 .

[5]  Robert L. Laurence,et al.  Influence of slip velocity at a membrane surface on ultrafiltration performance—I. Channel flow system , 1979 .

[6]  P. L. T. Brian,et al.  Concentration Polar zation in Reverse Osmosis Desalination with Variable Flux and Incomplete Salt Rejection , 1965 .

[8]  R. Probstein,et al.  ON The PREDICTION OF LIMITING FLUX IN LAMINAR ULTRAFILTRATION OF MACROMOLECULAR SOLUTIONS , 1977 .

[9]  A. S. Emanuel,et al.  High flux solid-liquid mass transfer , 1964 .

[10]  Leroy S. Fletcher,et al.  Investigation of Laminar Flow in a Porous Pipe with Variable Wall Suction , 1973 .

[11]  E. Lightfoot,et al.  Velocity Profiles in Porous-Walled Ducts , 1970 .

[12]  J. Gillis,et al.  Viscous Flow in a Pipe With Absorbing Walls , 1967 .

[13]  Viriato Semiao,et al.  Numerical modelling of mass transfer in slits with semi‐permeable membrane walls , 2000 .

[14]  Vítor Geraldes,et al.  Nanofiltration mass transfer at the entrance region of a slit laminar flow , 1998 .

[15]  A. S. Berman Laminar Flow in Channels with Porous Walls , 1953 .

[16]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[17]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[18]  E. Levy,et al.  Laminar Flow in a Porous Tube With Suction , 1975 .

[19]  R. M. Terrill Laminar Flow in a Porous Tube , 1983 .

[20]  H. Yeh,et al.  Analysis of the slip effect on the permeate flux in membrane ultrafiltration , 1999 .

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

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

[23]  D. Olander The influence of physical property variations on liquid-phase mass transfer for various laminar flows , 1962 .

[24]  E. Lightfoot,et al.  Ultrafiltration of proteins in stagnation flow , 1971 .

[25]  T. Wah Laminar Flow in a Uniformly Porous Channel , 1964 .

[26]  C. Tien,et al.  Analysis of continuous reverse osmosis systems for desalination , 1966 .

[27]  Chi Tien,et al.  Concentration Polarization Effects in a Reverse Osmosis System , 1965 .

[28]  William N. Gill,et al.  Mechanisms of brine-side mass transfer in a horizontal reverse osmosis tubular membrane , 1974 .

[29]  Clement Kleinstreuer,et al.  5 – Mathematical Modeling of Fluid Flow and Solute Distribution in Pressure-Driven Membrane Modules , 1984 .

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

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

[32]  Sandeep K. Karode,et al.  Flow visualization through spacer filled channels by computational fluid dynamics I. , 2001 .

[33]  P. Bhattacharya,et al.  Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration , 1997 .

[34]  T. Mizushina,et al.  STUDY OF FLOW IN A POROUS TUBE WITH RADIAL MASS FLUX , 1971 .

[35]  Anthony G. Fane,et al.  Effect of viscosity on concentration polarization in ultrafiltration , 1988 .

[36]  A. Michaels Effects of feed-side solute polarization on pervaporative stripping of volatile organic solutes from dilute aqueous solution: a generalized analytical treatment , 1995 .

[37]  Sudipta Bhattacharya,et al.  Concentration polarization, separation factor, and Peclet number in membrane processes , 1997 .

[38]  Y. Shah,et al.  Mass transport in reverse osmosis in case of variable diffusivity , 1971 .

[39]  S. W. Yuan,et al.  Laminar Pipe Flow With Injection and Suction Through a Porous Wall , 1955, Journal of Fluids Engineering.

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

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

[42]  R. G. Wylie The transfer coefficients of a laminar boundary layer with variable fluid properties , 1973 .

[43]  Dianne E. Wiley,et al.  Effects of natural convection instability on membrane performance in dead-end and cross-flow ultrafiltration , 1996 .