Advanced Materials Research Vols 734-737 (2013) pp 2210-2213
© (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.734-737.2210
Online: 2013-08-16
Effect of porous-jump model parameters on membrane flux prediction
Honghai LI1,*, Yangyang CHENG
1
College of Chemical Engineering, Qingdao University of Science & Technology,
53 Zhengzhou Road, Qingdao 266042, China
*Email address: lhhtju@126.com
Keywords: membrane separation; porous-jump model; face permeability; pressure-jump
coefficient
Abstract: A three-dimensional computational fluid dynamics (CFD) simulation was performed to
study the velocity distribution on membrane surface in membrane separation process, and the effect
of face permeability, porous medium thickness, and pressure-jump coefficient of porous-jump
model on membrane flux. The study shows that all the three factors have important impact on
membrane flux. Membrane flux increases linearly with the increase of face permeability. When the
membrane thickness is between 0.04~0.1mm, the membrane flux decreases with the increase of
membrane thickness. The membrane flux decreases with the increase of pressure-jump coefficient.
So that there must be a complex relationship between membrane flux and face permeability, porous
medium thickness, and pressure-jump coefficient.
Introduction
Compared with other separation technologies, membrane separation technologies have been widely
used in the fields of pharmaceutical, environmental protection, chemical industry, energy, water
treatment, et. al., due to their functions of molecular level separation and purification, and their
features of high efficiency, energy-saving, and environmental protection. Membrane separation
technologies have generated huge economic and social benefits and become one of the most
important means of separation sciences [1,2].
In recent years, computational fluid dynamics (CFD) simulation have become popular in
membrane separation simulation. Scholars have done a lot of research work on the flow field in
membrane separation process. Schwinge et al [3,4] have studied the changes of flow field in the
flow channel of spiral-wound membrane module. Their study shows that geometric parameters of
spacer in spiral-wound membrane module and Reynold number of the fluid have an important
impact on the generation of circulation region in the flow channel. Ahmad et al [5,6] have studied
the effect of different shapes of spacer filaments on velocity distribution in flow channel in the
membrane separation process. Their study shows that for high flowrate filtration system, the usage
of circular filament is recommended for energy minimization; and for low flowrate filtration system,
the employment of triangular and square filament can offer better concentration polarization
reduction while compensating moderate amount of energy due to the minor increase in head losses
as compared to the gain from the concentration reduction. Till now, most of the research work was
focused on the effect of geometric parameters of spacer on flow field changes in flow channel of the
membrane module. However, the characteristic of porous membrane medium was also important
for membrane flux.
This work mainly focuses on the effect of face permeability, porous medium thickness,
pressure-jump coefficient of porous-jump model on membrane flux. And a three-dimensional CFD
simulation was performed to study the velocity distribution in flow channel of the membrane
module, and the effect of face permeability, porous medium thickness, and pressure-jump
coefficient of porous-jump model on membrane flux.
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Advanced Materials Research Vols. 734-737
2211
Methods
1. Model establishment
Fig.1 The established physical model cell diagram
A three-dimensional CFD physical model was established, as shown in Fig.1, the top and bottom
part of the model are membranes, and the middle part of the model is spacer cell. The spacer is
constituted of two filament layers, the upper layer and the lower layer, respectively, each layer
filaments are parallel and the cross section of the filaments are circular.
Water containing fine particles was used as working fluid, and the fluid density and viscosity are
998.2 kg·m−3 and 0.001003 kg·(m·s)-1, respectively. The raw working liquid flows into the channel
from the left side of the middle part along the positive direction of X-axis, the concentrated liquid
flows out of the model from the right side of the middle part, and the filtrate flows out of the model
from top and bottom layers of membrane. As the model shows that the flow attack angle is 0°, the
angle between crossing filaments is 90°, then the top layer spacer filaments are all parallel to X-axis,
the bottom layer spacer filaments are all parallel to Y-axis. In addition, diameter of the spacer
filaments is 0.3 mm, and the distance of the parallel filaments is 4 mm. Both the width and length of
the membrane are 5 mm, pore size of membrane is 0.02 µm, porosity of membrane ε is 0.038.
2. Membrane parameters setting
Fluent software was used to CFD for the simulation of the velocity distribution in flow channel of
the membrane module, and the effect of face permeability, porous medium thickness, and
pressure-jump coefficient of porous-jump model on membrane flux were investigated. Porous-jump
model [7] is used to solve the membrane permeability. Three parameters of the porous-jump model
are needed to set, face permeability α, porous medium thickness h and pressure-jump coefficient C.
The face permeability α of porous-jump model can be calculated by Eq.(1) :
D p2
ε2
α =
(1)
1 5 0 (1 − ε ) 2
and the pressure-jump coefficient C of porous-jump model can be calculated by Eq.(2) :
3 . 5 (1 − ε )
(2)
C =
D p
ε 2
where Dp is diameter of spherical particles or volume-equivalent diameter of non-spherical
particles; ε is porosity. When Dp is 2µm, and ε is 0.038, the face permeability α is 4.16×10-17 m2,
pressure-jump coefficient C is 1.2×109 m-1. In addition, Dp is 2~10µm, porous medium thickness h
is 0.04~0.1mm.
3. Boundary conditions setting
The inlet velocity of the working fluid is 1m·s−1, the outlet pressure of the concentrated liquid is
-10000Pa, the outlet pressure of the filtrate is -100000Pa, the filament is set as wall, and the
membrane is set as porous jump.
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Resources and Sustainable Development
Results and discussion
1. Velocity distribution in the membrane flow channel unit
(a)
(b)
(c)
Fig.2. The velocity distribution on (a) tangent plane of the bottom layer membrane, (b) middle plane
between bottom and top layer filaments, and (c) tangent plane of the top layer membrane
respectively as Dp is 2µm.
Fig.2 shows that there are many irregularly shaped speckles on the bottom layer membrane, tangent
plane of bottom and top layer filaments, and top layer membrane. In the area where speckles exist,
velocity magnitude decreases from inside to outward. The velocity distribution on bottom layer
membrane and top layer membrane is almost the same because of the symmetry of the model.
2. Effect of face permeability α, porous medium thickness h, pressure-jump coefficient C of
porous-jump model on membrane flux
1.8
3.5
2 -1
membrane flux /kg*(m *s)
2 -1
membrane flux /kg*(m *s)
1.7
1.6
1.5
1.4
1.3
1.2
bottom layer membrane flux
top layer membrane flux
bottom layer membrane flux
top layer membrane flux
3.0
2.5
2.0
1.5
1.1
1.0
0.04
1.0
0.06
0.08
0.10
0
2
4
6
8
10
12
membrane thickness h /mm
face permeability a *1016
Fig.3 Effect of membrane thickness h on
membrane flux
Fig.4 Effect of face permeability α on
membrane flux
Fig.3 shows that when the membrane thickness h is between 0.04~0.1mm, the membrane flux
decreases with the increase in membrane thickness. Fig.4 shows that both the bottom and the top
layer membrane fluxes increase with the increase in face permeability α linearly overall. The
change trend of two curves is almost the same because of the symmetry of the model.
Advanced Materials Research Vols. 734-737
2213
2 -1
membrane flux/kg*(m *s)
3.0
bottom layer membrane flux
top layer membrane flux
2.5
2.0
1.5
1.0
2
4
6
8
10
8
pressure-jump coefficient/ c*10
12
Fig.5 Effect of pressure-jump coefficient C on membrane flux
Fig.5 shows that the membrane flux reduces with the increase in pressure-jump coefficient C
overall. When the pressure-jump coefficient C is between 2×108~3×108, the membrane flux is
reduced with the increase in pressure-jump coefficient rapidly, and when the pressure-jump
coefficient C is between 3×108~12×108, the membrane flux is reduced with the increase in
pressure-jump coefficient slowly. The change trend of two curves is also almost the same because
of the symmetry of the model.
Conclusions
(1) There are many irregularly shaped speckles on the bottom layer membrane, tangent plane of
bottom and top layer filaments, and top layer membrane all. In the area where speckles exist,
velocity magnitude decreases from inside to outward.
(2) Face permeability, porous medium thickness, pressure-jump coefficient of porous-jump model
all have important impact on membrane flux. Firstly, membrane flux is increased with the increase
in face permeability linearly. Secondly, when the membrane thickness is between 0.04~0.1mm, the
membrane flux is decreased with the increase in membrane thickness. Thirdly, the membrane flux is
reduced with the increase in pressure-jump coefficient.
(3) There must be a complex relationship between membrane flux and face permeability, porous
medium thickness, and pressure-jump coefficient.
References
[1] XS. Wang. Membrane separation technology and its application. M. Beijing: Chemical industry
press.2002. In Chinese.
[2] Z. Wang,. Basic principles of membrane separation technology. M. Beijing: Chemical industry
press.2000. In Chinese.
[3] J. Schwinge, DE. Wiley, D. Ffletcher. A CFD study of unsteady flow in narrow spacer-filled
channels for spiral-wound membrane modules. J. Desalination. 146 (2002), p.195.
[4] YL. Li, KL. Tung. CFD simulation of fluid flow through spacer-filled membrane Module:
selecting suitable cell types for periodic boundary conditions. J. Desalination, 233(2008), p.351.
[5] AL. Ahmad, KK. Lau, ZZ. Abu Bakar. Impact of different spacer filament geometries on
concentration polarization control in narrow membrane channel. J. Journal of Membrane Science.
262(2005), p.138.
[6] M. Shakaib, S.M.F. Hasani, M. Mahmood. Study on the effects of spacer geometry in
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[7] H. Mirsaeedghazi, Z. Emam-Djomeh, SM. Mousavi et al. Modeling the membrane clarification
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Resources and Sustainable Development
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Effect of Porous-Jump Model Parameters on Membrane Flux Prediction
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