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Korean Journal of Chemical Engineering

, Volume 36, Issue 12, pp 2074–2084 | Cite as

Hydrodynamic modeling of the spiral-wound membrane module including the membrane curvature: reverse osmosis case study

  • Morteza Taherinejad
  • Mahdi MoghimiEmail author
  • Shahram Derakhshan
Separation Technology, Thermodynamics
  • 3 Downloads

Abstract

This study presents an integrated analytical model for the hydrodynamic behavior of the spiral-wound membrane element considering the curvature of the flow feed and permeate channels. The new model introduces a set of closed-form expressions for the output parameters of the permeate flow rate, fluid recovery fraction, and the permeation flux, which can be a necessary tool for optimization and evaluation of the parameters involved in the problem. Accordingly, the results were set forth for a reverse osmosis water treatment SWM element. The difference in the output parameters for the solutions with flat and curved membranes was investigated, and the consequences of the common assumption of the flat-sheet membrane were examined mathematically. It was found that neglecting the membrane curvature implements a significant impact/error on the prediction of the permeate channel pressure and membrane width with maximum permeation rate, whereas its impacts on feed channel pressure and output parameters are insignificant, especially for the considered reverse osmosis case study. Also, the curvature effect on the solution can be magnified by three parameters of the membrane width: permeate channel permeability, and membrane resistance.

Keywords

Hydrodynamics Curvature Spiral-wound Membrane Element Water Permeate Flow Rate Fluid Recovery Fraction 

Nomenclature

A, B, C

dimensionless parameters defined in the model

D

diameter of the feed spacer filament [m]

F

fluid recovery fraction

f1, f2

coefficients in pressure drop constitutive law (feed channel)

k

permeability [m2]

k1

permeate channel permeability parallel to the membrane [m2]

k2

permeate channel permeability perpendicular to the membrane [m2]

L

length of the feed spacer filament in a unit cell [m2]

Lpr

permeate channel height [m]

Lfr

feed channel height [m]

Lx

membrane sheet length [m]

Ly

membrane sheet width [m]

LMH

permeation flux [L/(m2 h)]

P

permeate channel pressure [Pa]

p

feed channel pressure [Pa]

Q

permeate flow rate [L/h]

R

curvature radius [m]

Rm

membrane resistance [m−1]

Re

Reynolds number (Re=ρUD/μ)

U

velocity in feed channel [m/s]

Uw

permeation velocity or permeation flux [m/s]

Greek Symbols

Θ

angle corresponds to the membrane width [Deg]

η

dimensionless curvature radius

ψ

percentage of difference [%]

α

dimensionless parameter defined in the solution

β

mesh angle (between the filaments of feed spacer) [Deg]

ΔP

pressure drop [Pa]

μ

fluid viscosity [Pa·s]

ρ

fluid density [kg/m3]

Subscripts

c

related to selected case study value

d

dimensionless

in

inlet

out

outlet

i

inner

o

outer

f

related to feed channel

p

related to permeate channel

r

index notation for cylindrical coordinates

θ

index notation for cylindrical coordinates

z

index notation for cylindrical coordinates

q

quantity (main output parameter)

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Copyright information

© The Korean Institute of Chemical Engineers 2019

Authors and Affiliations

  • Morteza Taherinejad
    • 1
  • Mahdi Moghimi
    • 1
    Email author
  • Shahram Derakhshan
    • 1
  1. 1.School of Mechanical EngineeringIran University of Science and TechnologyTehranIran

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