高分子概論報告
題目名稱: membrane contactor
姓名:江育豪
學號:49940088
一.原理
薄膜反應器( m e m b r a n e r e a c t o r )這個觀念，基本上，薄膜反應器的構造是將傳統反應器設計上加了薄膜，使得反
應器同時具有反應和分離的功能。
近年來，因為無機材料(金屬和陶瓷)在薄膜的研製上有更進一步的發展，使得薄膜在高溫觸媒反應的應用，相當令人矚
目並受到廣泛的討論。由於無機薄膜的耐熱性質和機械性質的提昇，使得許多必須在高溫下才能進行的反應，例如：脫氫、
氧化脫氫和熱裂解反應， 現在皆可藉由薄膜反應器來進行。
一雙套管構造， 以內管中心軸為對稱的薄膜反應器示意圖。反應物從進料層( f e e d - s i d e )的進端( f e e d ) 進入， 一
部份的物質會從進料層的出口端( r e j e c t ) 流出；而另一部份的物質，則會從進料層經由薄膜層擴散到滲透層( p e r m e a
t e - s i d e ) 的出口端 p e r m e a t e ) 流出。由於進料物質從進料層向滲透層擴散時，必須經過薄膜層，而此薄膜層具有
選擇性，即利用各物質在薄膜層中擴散速度的不一樣，進而造成物質的分離。依據勒沙特列原理( L e C h â t e l i e r p r i n
c i p l e )可知，當可逆反應的系統中有物質被移出或移入，則會改變其平衡狀態。因此選擇性地移出產物，則可增加反應
的轉化率。由此觀點來看，最能夠發揮薄膜反應器效果的應用情況有下列幾類反應：1 )可逆反應為熱力學平衡( t h e r m o
d y n a m i c e q u i l i b r i u m ) 限制的反應； ( 2 )平行式反應( p a r a l l e l r e a c t i o n s ) ； ( 3 ) 串連式反應( s e r i e
s r e a c t i o n s )。它們的原理都是藉由選擇性地移出部份產物， 而使得反應的轉化率得以增加。
薄膜有選擇性，要注意其適用範圍
二.應用/用途
薄膜交換苦應用於燃料電池的質子交換模、醫療用途上的中空纖維膜、RO 你滲透的滲透模、汙水處理
等等等
薄膜交換的應用範圍很廣，可是薄膜有選擇性，要注意適不適用，以免造成薄膜損壞
三.參考文獻(兩篇)
一.
Journal of Membrane Science 427 (2013) 270–275
Contents lists available at SciVerse ScienceDirect
Journal of Membrane Science
journal
homepage: www.elsevier.com/locate/memsci
Carbon dioxide stripping from diethanolamine solution through porous surface modified PVDF hollow fiber membrane
contactor
M. Rahbari-Sisakht
a,b,c
a,b,n
d
d
, A.F. Ismail
, D. Rana , T. Matsuura
a Advanced Membrane Technology Research Center (AMTEC), Universiti Teknologi Malaysia, 81310, Skudai, Johor, Malaysia
b Gas Engineering Department, Faculty of Petroleum and Renewable Energy Engineering, Universiti Teknologi Malaysia, 81310, Skudai,
Johor, Malaysia
c Department of Chemical Engineering, Gachsaran Branch, Islamic Azad University, Gachsaran, Iran
d Department of Chemical and Biological Engineering, University of Ottawa, 161 Louis Pasteur St., Ontario K1N 6N5, Canada
ar ti c l e
i n f o
Article history:
Received 15 June
2012 Received in
revised form 14
September 2012
Accepted 29 September 2012
Available online 11 October
2012
Keywords:
Polyvinylidene fluoride (PVDF)
Surface Modifying
macromolecules (SMM) Hollow
fiber membrane contactor
CO2
stripping
Diethanolamine
(DEA)
abstr act
Porous asymmetric polyvinylidene fluoride (PVDF) hollow fiber membrane were fabricated via
a phase-inversion method using surface modifying macromolecules (SMM) (1 wt%) as the
additive in the spinning dope. Distilled water and tap water were used as internal and external
coagulation bath, respectively. The membranes were characterized in terms of gas permeation,
wetting resistance, overall porosity, contact angle and collapsing pressure. CO2 stripping from
diethanolamine (DEA) solutions was conducted through the gas–liquid membrane contactor.
The effect of some operating conditions such as gas and liquid velocities, DEA concentration
and rich solution temperature on the CO2 stripping flux and
efficiency were investigated. By increasing liquid flow rate to 200 ml.min 1, the maximum
CO2 stripping
efficiency of almost 82% was achieved. In addition, an increase in the liquid flow rate resulted
in a
1
significant increase of CO2 stripping flux. By increasing the liquid flow rate from 50 to , the
200 ml min
CO2 flux increased by 900%. By increasing the gas velocity the CO2 desorption flux
increased but this
changing was negligible. The effect of rich solution temperature was investigated and the results
showed that the CO2 desorption
flux increased with
increasing the
solution
temperature from 80 to 90 1C. The results of DEA concentration enhancement on the
CO2 desorption flux showed that the CO2 stripping flux increased drastically with enrichment
of the DEA concentration from 1.0 to 3.0 (mol l 1). Therefore, the higher stripping efficiency
can be achieved by applying the higher liquid flow rate, temperature and DEA concentration
in the absorbent liquid in the membrane contactor module.
& 2012 Elsevier B.V. All rights
reserved.
1. Introduction
Fossil fuels such as oil, gas and coal are the major source of the
energy for industries and domestic usages. Carbon dioxide (CO2),
a major greenhouse gas, is emitted by the combustion of fossil
fuels, which consequently causes air pollution. Therefore, it
should be removed from industrial and domestic flue gas streams.
Recently, many methods have resorted to CO2 absorption into
aqueous solution of alkanolamines. The use of aqueous alkanolamine solutions allows regeneration of the liquid absorbents by
simple heating. Hence, a typical process for CO2 capture consists
of two major units, absorption and desorption. Desorption is
generally performed by using conventional columns that have
operational problems such as flooding, channeling, and entrainment. Usually, the stripper unit operates at slightly above normal
n Corresponding author at: Universiti Teknologi Malaysia,
Advanced Membrane Technology Research Center (AMTEC),
Skudai, 81310 Johor Bahru, Johor, Malaysia. Tel.: þ 60 7
5535592; fax: þ 60 7 5535925.
E-mail addresses: afauzi@utm.my, fauzi.ismail@gmail.com
(A.F. Ismail).
pressure and high temperature [1]. One of the methods that has
been used for CO2 absorption is employing hollow fiber
membrane contactors. In membrane contactors gas and liquid
contact together via a porous membrane without dispersion of gas
in liquid, which provides higher interfacial area, independent
control of the liquid and gas flow rates, and a small equipment
size. The membrane contactor is made modular and hence it is
easy to scale up or down. By using a suitable membrane such as a
hollow fiber, fluids can be contacted on opposite sides of the
membrane and the gas–liquid interface is formed at the mouth of
each membrane pore. Mass transfer occurs by diffusion across the
0376-7388/$ - see front matter & 2012 Elsevier B.V. All
rights reserved.
http://dx.doi.org/10.1016/j.memsci.2012.09.060
interface similar to tradi- tional contacting equipment. In addition,
using the membrane contactors presents greater performance
compared to the conven- tional equipment. Since the membrane
contactors offer high inter- facial area per volume, membrane
contactors are a compact device. This leads to reduced capital cost
and less energy consumption [2].
Besides, the membrane contactors can also be appropriate for
desorption or regeneration of liquid absorbents. The CO2
stripping mechanism from the liquid phase is shown
schematically in Fig. 1. CO2 is desorbed at the liquid/gas
interface at one end of the
membrane pore, diffuses through the pore before being carried
away by the stripping gas (N2) at the other end of the membrane
pore. Although the stripping units are highly energy-consuming,
the majority of the researches have emphasized on CO2 absorption using gas–liquid membrane contactors [3–9]. In reality, the
investigations on CO2 stripping through membrane contactors
are rare.
Khaisri et al. [1] developed a membrane contactor based
regeneration unit to strip CO2 gas from CO2 loaded monoethanolamine (MEA) solution. They employed PTFE hollow fiber membranes
to test the desorption performance. The experimental results
showed that the CO2 desorption flux increased with an increase in
the liquid velocity, operating temperature, and MEA concentration. They found that excessive increase of MEA concentration
resulted in the decrease of the overall mass transfer coefficient due
to the effect of viscosity. The maximum MEA concentration that
gave the highest CO2 desorption performance in their work was
5 k mol m 3. They also found that the gas phase mass transfer
resistance in gas stripping membranes has a minor effect
on the CO2 desorption flux as generally found in a gas absorption
membrane. They showed that the desorption rate increased by a
factor of two when the available membrane surface was doubled. It
indicated that the gas stripping membrane contactor can be linearly
scaled-up. Membrane porosity affected the CO2 desorption flux as
well as the membrane wetting. Their experimental results also
showed that high membrane porosity resulted in high desorption
performance, but the long term performance dropped due to the
membrane wetting.
Koonaphapdeelert et al. [10] fabricated ceramic hollow fiber
membrane contactors for CO2 stripping from a monoethanolamine (MEA) solution at high temperature. They found that
the membrane contactors could be operated very well even in the
region of an ordinary column showing flooding or loading. The
maximum capacity factor tested in the experiment was at least
2–10 times higher than the flooding line without any sign of
flooding.
A study of CO2
desorption from CO2
loaded
2-amino-2-methyl- 1-propanol (AMP) solution using the
membrane contactor was carried out by Kumazawa [11].
Polytetrafluoroethylene (PTFE) hollow fiber membranes were
used in the experiments. It was found that the desorption process
was controlled by diffusion and chemical reaction in the liquid
film. Their results showed that the overall mass transfer
coefficient increased with an increase in AMP solution
concentration and CO2 loading in the solution.
Naim et al. [12] prepared microporous PVDF hollow fiber
membranes via wet spinning process for CO2 stripping from
aqueous diethanolamine (DEA) solution. They studied the effects
of LiCl concentration in the polymer dope on the membrane
properties and the stripping performance of the membranes. Their
results demonstrated a linear increase of stripping flux and
stripping efficiency as the LiCl concentration increased in the
polymer dope. As a result, the stripping flux was found the
highest when a combination of finger-like and sponge-like structures was formed at 5 wt% LiCl. The maximum stripping efficiency
thus achieved was 62% at 5 wt% LiCl and 0.45 m s 1 of liquid
velocity. Finally, they concluded that an enhanced CO2 stripping
flux and efficiency could be achieved by improving the structure
of the PVDF hollow fiber membranes.
The porous surface modified polyvinylidene fluoride (PVDF)
hollow fiber membranes using surface modifying macromolecules
(SMMs) as additive in the spinning dope were prepared and
characterized for CO2 absorption experiment, which presented high
performance in our previous work [4]. To the best of our knowledge
no research has been done on the PVDF hollow fiber membrane
with surface modification by SMM for stripping applications. In this
work, the surface modified PVDF hollow fiber membrane contactor
was used for CO2 stripping from diethanolamine (DEA) solutions.
The effect of some operating conditions such as gas and liquid
velocities, DEA concentration and solution temperature on the CO2
stripping flux and efficiency were investigated.
2. Theory
In order to describe a resistance in series model in gas–liquid
contactor system, film theory has been used. The concentration
profile of gas moving from the liquid phase to the gas phase in gas
stripping membrane contactor systems is shown in Fig. 2. As in
Fig. 2, three resistances exist in the resistance in series model:
1- Gas film resistance
2- Liquid film resistance
3- Membrane resistance
For the non-wetted mode of operation for the hollow fiber
module with liquid feed in the lumen side and gas flow in the shell
side, the resistance in series model can be written as follows [13].
1
K L di
Fig. 1. Schematic of CO2
stripping mechanism
through gas–liquid membrane contactor.
¼
1
EkL di
þ
1
HkM dln
1
þ
HkG do
1Þ
ð
Fig. 2. Mass transfer resistance in resistance-in-series model
for desorption in membrane contactors.
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
Where KL is the overall liquid-phase mass transfer coefficient,
kL, kM, and kG are the liquid, membrane, and gas mass transfer
coefficient, respectively. H represents Henry’s constant, and do, di,
and dln are the outer, inner and logarithmic mean diameters of the
membrane. E is the enhancement factor which is included to
account for the effect of the reaction. The mass transfer coefficients can be calculated by using correlation equations. The
correlation
to
calculate
the
individual
mass
transfer
coefficients
for membrane contactor depends on whether it is for tube side
mass transfer coefficient or shell side mass transfer coefficient.
Yang and Cussler [14] suggested correlations to determine both
tube and shell side mass transfer coefficients. The tube side mass
transfer coefficient can be generally depicted by the Leveque’s
correlation:
0:33
kL
di
di
¼ 1:62
ð2Þ
Sh ¼
ReSc
L
DL
This equation is valid for Gz 4 20 to calculate the liquid mass
transfer coefficient on the tube side. For the gas mass transfer
coefficient on the shell side, they also reported the correlation as
follows:
0:93
kG d h
0:3
dh
ð3Þ
Sh ¼
Re
Sc 3
DG ¼ 1:25
L
where dh and L are the hydraulic diameter and membrane length,
respectively. Eq. (3) is valid for 0.5 o Re o 500. The membrane
mass transfer coefficient depends on the mode of operation such
as non-wetted, wetted or partially wetted. The membrane mass
transfer coefficient in the non-wetted mode of operation can be
calculated by [15]:
DG,ef f e
kM
ð4Þ
td
¼
where DG,eff is the effective diffusion coefficient of gas in the
gas filled membrane pores, and e, tand d are the porosity,
tortuosity, and thickness of the membrane, respectively.
3. Experimental
Fabrication and characterization of porous hollow fiber
membranes
Commercial PVDF polymer pellets (Kynars740) were
supplied
by
Arkema
Inc.,
Philadelphia,
USA.
1-Methyl-2-pyrrolidone (N-Methyl-2-pyrrolidone, NMP, 4
99.5%) was used as solvent without further purification.
Methylene bis(p-phenyl isocyanate)
(diphenylmethane diisocyanate; MDI), a,o-aminopropyl
poly
TM
(dimethyl siloxane) (PDMS) and Zonyl
(low
BA-L
fraction
2-(perfluoroalkyl) ethanol) were used for synthesis of SMM. The
details of SMM synthesis were reported earlier [16]. The structure
of SMM so synthesized is shown elsewhere [4]. Tap water was
used as the coagulant or a part of the coagulant.
The PVDF polymer in pellet form was dried at 70 7 2 1C in a
vacuum oven for 24 h to remove the moisture. The spinning dope
of 18 wt% PVDF, 1 wt% SMM in NMP was prepared by stirring the
solution at room temperature until the solution became homogeneous. The resulting solution was degassed for 24 h at room
temperature before spinning. The hollow fiber spinning process
by the dry/wet phase inversion was described earlier [17]. Table 1
lists the detailed spinning parameters. The spun fibers were
immersed in water for 3 days to remove the residual NMP and the
additive. Then, they were dried at room temperature.
272
Table 1
Hollow fiber spinning conditions.
Dope extrusion rate (ml/min)
Bore fluid composition
Bore fluid rate (ml/min)
External coagulant
Air gap distance (cm)
Spinneret o.d./i.d. (mm)
Coagulation temperature (1C)
4.50
Distilled water
2.00
Tap water
5.0
1.0/0.50
25
to a stainless steel tubing with a length of 10 cm. The latter end
was cut using a sharp knife after the epoxy resin was hardened to
open the hollow fibers [18]. The feed gas (N2) was supplied to the
shell side of the module and the pressure was controlled by a
pressure regulator to 1–2.5 bar (absolute). The permeation rate of
the gas coming out from the other (lumen) side was measured by
a soap-bubble flow meter. The theory and equations used for the
calculation of the mean pore size and the effective surface porosity
are given elsewhere [19]. By assuming cylindrical pores in the skin
layer of the asymmetric membranes, the gas permeance, mean pore
size and effective surface porosity can be calculated. The flow
diagram of the experimental setup for gas permeation test was
shown elsewhere [5,6].
The critical water entry pressure (CEPw) is the minimum
pressure required to drive water through the membrane pore. For
CEPw measurement, the same modules as those used in the gas
permeation test were used. Distilled water was pumped into the
lumen side of the hollow fibers. The pressure was gradually
increased at 0.2 105 Pa (0.2 bar) interval. At each pressure, the
membrane module was kept constant for 30 min to check if any
water droplet appeared at the outer surface of the fiber. The CEPw
is the pressure at which the first water droplet appears on the
outer surface of the hollow fiber.
The membrane overall porosity, em, was determined by gravimetric method. It is defined as the volume of the pores divided by
the total volume of the membrane. The calculation method is
available in the literature [20]:
ðw1
w2 Þ=rw
ð5Þ
e m ¼ ðw
þ w =r
w
Þ=r
1
2 w
2
p
where w1 is the weight of the wet membrane, w2 the weight of
the dry membrane, rw water density and rp is the polymer
density. In order to prepare the wet membranes, five spun hollow
fibers were selected after the solvent was exchanged by tap water
for 3 days. The fibers were immersed in distilled water for another
24 h and the remaining water on the inner surface was blown by
air stream, before measuring the wet weight of the membrane.
Then the membranes were further dried in a vacuum oven for 2 h
at 120 1C, before measuring the dry weight.
Gas permeation tests were done to measure the mean pore size
and the effective surface porosity. Two hollow fibers were glued
with epoxy resin at one end and the other end was potted
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
In order to assess the mechanical stability of the hollow
fiber membranes, a collapsing pressure test was performed. During
the gas permeation test, the upstream pressure on the shell side
was increased at 0.5 105 Pa intervals. Collapsing pressure is the
pressure at which a sudden change, either decrease or increase, in
the permeate flow on the lumen side is observed. The characteristics
of the prepared PVDF hollow fiber membrane are given in Table 2.
CO2 stripping experiment
The CO2 stripping efficiency of the fabricated membranes
was measured using a membrane contactor module. A total of
30 hollow fibers were packed randomly in a stainless steel
mem- brane module. The details of the membrane contactor
module are given in Table 3.
In order to prepare the liquid feed stream for the CO2 stripper
membrane contactor module, diethanolamine (DEA) solutions
273
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
274
were preloaded with pure CO2
in the gas–liquid
membrane
contactor and used as the liquid feed stream in the CO2 stripping
on the inner surface of the hollow fibers as:
module. Pure nitrogen as a sweep gas was made to flow through
the module shell side while, preloaded DEA solution was made to
flow inside the lumen side of the hollow fibers. A counter-current
flow mode was used for the gas and liquid phases. The gas was
introduced into the module before the liquid stream in order to
prevent wetting problems. The pressure and flow rates of gas and
liquid phases were controlled by the control valves. A pressure
difference of 0.2 105 Pa was applied on the liquid stream and gas
JCO2 ¼
C l, o
C
100
1
ð6Þ
l,i
where Cl,o and Cl,i are the liquid phase CO2 concentrations
(mol/m3) at outlet and inlet of the membrane module, respectively. The experimental CO2 stripping flux was calculated based
Table
2
Properties of fabricated PVDF hollow
fiber membranes.
Average pore size (nm)
1)
Fig. 4 shows the effect of liquid velocity on the CO2 stripping
flux and CO2 concentration in the outlet liquid. Also, the effect of
liquid velocity on the stripping efficiency is shown in Fig. 5. As can
be seen, stripping flux and stripping efficiency increased by
increasing liquid velocity. The highest stripping flux of 1.2
10
3 (mol m 2 s 1) and the lowest CO concentration in outlet liquid
2
of 5 10 4 (mol l 1) were achieved at the liquid flow rate of 200
(ml min 1) ( ¼ 0.7 m s 1), respectively. Naim et al. [12]
reported stripping efficiency of 38.83% for plain PVDF membrane
(prepared without adding LiCl in the dope) at liquid velocity of
1
0.45 m s . At the same liquid velocity, the stripping efficiency of
almost 66% was achieved in this work due, most likely, to the high
wetting resistance of the fiber in the presence of SMM in the
membrane.
The highest stripping efficiency of almost 82% was also
achieved. This is due to the reduction in liquid boundary layer
resistance and the increase in CO2 mass transfer coefficient at the
105 Pa)
N2 permeance at 300 k Pa (
0.34
Contact angle, outer surface
256
3
85 7 0.75
Overall porosity (%)
Collapsing pressure (
4. Results and discussion
385
Effective surface porosity (e/Lp) (m
CEPw (
105 Pa)
7
10 6 mol/m2 s Pa) 6.85 7
92 7 1.25
ð7Þ
Ai
2
where JCO2
is the CO2 stripping flux (mol/m s), Ql is liquid
flow
rate (m3/s), and Ai is inner surface of the hollow fiber membranes.
Strippingflux (mol/m2.s)
Zð%Þ ¼
Ql
l,
o
1.60E03
1.20E-03
1.40E03
1.00E-03
8.00E-04
1.20E03
6.00E-04
1.00E03
8.00E04
6.00E-04
Table 3
Specifics of the gas–liquid
membrane contactor.
Module i.d. (mm)
Module length (mm)
Fiber o.d. (mm)
Fiber i.d. (mm)
CO2concentration in outlet liquid (mol/l)
side to avoid the formation of bubbles on the liquid side. The CO2
concentration of the liquid stream at the inlet and outlet of the
stripper module was measured to determine stripping flux and
efficiency by using double chemical titration method [21]. Before
taking the samples, all the experiments were carried out for 30
min to achieve a steady state condition. Fig. 3 shows the flow
diagram of the experimental stripping membrane contactor
system schematically. The CO2
stripping efficiency (Z)
of the
module was calculated as:
C l,i
C
4.00E-04
4.00E-04
2.00E-04
2.00E-04
14
270
0.7–0.9
0.00E+00
0.45–0.
50
Effective fiber length (mm) 150
Number of fibers
30
Contact area (inner, mm2)
0
0.2
0.4
0.8
Liquid velocity (m/s)
0.6
0.00E+00
Fig. 4. Effect of the liquid velocity on CO2 stripping flux and
CO2 concentration in
outlet liquid (T ¼ 80 1C, MDEA ¼ 1 mol/l).
6358.5
To vent
T
P
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
P
Membrane
stripper
275
F
F
N2
cylinerd
Heater
CO2
analyzer
(Titration
)
Diaphragm
pump
Preloade
d
DEA solution
Fig. 3.
Flow diagram of experimental stripping membrane contactor system.
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
276
5.00E-05
90
Stripping flux (mol/m2.s)
Stripping efficiency (%)
80
70
60
50
40
30
20
4.00E-05
3.00E-05
2.00E-05
1.00E-0
5
10
0
0.2
0.8
0.4
0.6
Liquid velocity (m/s)
Fig. 5. Effect of liquid velocity on stripping efficiency (T ¼ 80 1C,
MDEA ¼ 1 mol/l).
0.005
0.01
0.015
0.02
0.025
Gas velocity (m/s)
Fig. 6. Effect of the gas velocity on CO2 stripping flux (T ¼ 80 1C,
MDEA ¼ 1 mol/l).
3.50E-03
Stripping flux (mol/m2.s)
higher liquid flow rates [22]. On the other hand, Khaisri et al. [23]
reported that the gas phase mass transfer resistance has a minor
effect on the desorption performance of a CO2 stripping membrane
contactor system. According to them, the contribution of the gas
phase mass transfer resistance to the overall mass transfer resistance
is approximately 5–10%. Kumazawa [11] and Koonaphapdeelert et
al. [10] found that the mass transfer in gas stripping membrane
contactors was mainly controlled by the liquid film mass transfer
coefficient. It can be therefore reasonably concluded that the
liquid phase controls the overall mass transfer resistance of
desorption processes by the membrane contactor. This trend was
also similar to most gas absorption studies in membrane contactor
applications [4–6].
As shown in Fig. 4, the CO2 concentration in the liquid outlet
0
0.00E+0
0
0
o
80 C
85 oC
90 oC
3.00E-0
3
2.50E-0
3
2.00E-0
3
1.50E-0
3
1.00E-0
0
3
0.2
0.4
0.6
Liquid velocity (m/s)
0.8
5.00E-0
4
0.00E+0
0
increase in the gas velocity increased the CO2 desorption flux
slightly the change was almost negligible. The results confirmed
the previous conclusion that the liquid phase mass transfer
resistance is the controlling resistance in the system.
The effect of rich solution temperature is also shown in Fig. 7. As
it is clear the CO2 desorption flux increased with an increase of the
solution temperature. The temperature directly affects the CO2
equilibrium partial pressure, chemical reaction equilibrium constant,
and diffusion coefficient [1]. The equilibrium partial pressure of
CO2 increases by the factors of 5–8 for a 10 1C increase of
temperature [24]. This is the result of decrease in the chemical
reaction equilibrium constant (see Eq. (8) below). Thus, increasing
the operating temperature leads to an increase in the driving
force for stripping of CO2 from the DEA solution.
Fig. 7. Effect of rich solution temperature on CO2 stripping flux
(MDEA ¼ 1 mol/l).
7.00E-03
6.00E-0
3
Strippingflux (mol/m2.s)
decreased considerably with an increase in liquid velocity. Therefore, higher stripping flux and efficiency were achieved at higher
liquid velocity (Figs. 4 and 5).
The effect of gas velocity was examined at 80 1C
solution temperature. Fig. 6 shows that the enhancement of CO2
stripping
flux with gas velocity was not significant. The CO2 desorption
flux
increased from 1.05
10 5
to 1.57
10 5
(mol
2
1
m
s ) by
increasing gas flow rate from 50 to 200 (ml min 1). Although an
1.0 M
2.0 M
5.00E-0
3
3.0 M
4.00E-0
3
3.00E-0
3
2.00E-0
3
1.00E-0
3
0
0.2
0.4
0.6
0.8
Liquid velocity (m/s)
0.00E+0
0
DEA solution concentration
influences the stripping perfor- Fig. 8. Effect of DEA
concentration on CO2
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
mance in the membrane contactor. Fig. 8 shows that CO2 stripping flux increased with an increase in the concentration of DEA
solution from 1.0 to 3.0 (mol l 1). This result can be explained by
the following overall reaction between CO2 and DEA [25].
CO2 þ 2 R2NH2R2NHþ2 þ
R2NCOO
(8)
When DEA concentration is increased, more CO2 is absorbed
during the CO2 preloading, forming a larger amount of carbamate
277
stripping flux (T ¼ 90 1C).
(R2NCOO ), according to Eq. (4). When the solution enters the
membrane stripper, more CO2 is released, leading to the higher
CO2 partial pressure at the interface. This results in an increase in
the driving force [1].
It should be noted, however, that an increase in DEA concentration increases the solution viscosity, which results
in a
decrease in liquid side mass transfer coefficient [1]. Operation at a
high DEA concentration can also increase the corrosion rate in
steel vessel and steel piping. This factor needs to be considered.
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
5. Conclusion
Porous surface modified PVDF hollow fiber membranes were
fabricated via a wet spinning process for CO2 stripping applications.
The membranes were characterized in terms of gas permeation,
wetting resistance, collapsing pressure, contact angle and overall
porosity. CO2 stripping from diethanolamine (DEA) solutions by
nitrogen gas was studied using a gas–liquid membrane contactor.
The effects of the operating conditions such as gas and liquid
velocities, DEA concentration and rich solution temperature on the
CO2 stripping flux and efficiency were investigated. It was found that
the liquid flow rate, rich solution temperature and DEA concentration were the key parameters for the gas stripping operation. The
results showed that by increasing liquid flow rate to 200 ml min 1,
the maximum CO2 stripping efficiency of almost 82% was achieved.
In addition, an increase in the liquid flow rate resulted in a significant
increase of CO2 stripping flux. By increasing the liquid flow rate from
50 to 200 ml min 1, the CO2 flux increased about 900%. The CO2
desorption flux increased insignificantly by increasing the gas velocity.
The CO2 desorption flux increased by increasing the solution
temperature from 80 to 90 1C. The CO2 stripping flux increased
drastically with an increase in the DEA concentration from 1.0 to
3.0 (mol l 1). Therefore, the higher stripping efficiency
can be
achieved by applying the higher liquid flow rate, temperature and
DEA concentration in the absorbent liquid in the membrane contactor module.
Nomenclature
A
(m2)
Cl,o
(mol m
Cl,i
(mol m
dh
(m),
mass transfer area
3)
3)
hydraulic
CO2 concentration in the outlet liquid
CO2 concentration in the inlet liquid
diameter
ð4
cross-sectional
2
2 areaÞ=
wetted perimeter ¼ ds
ndo =ds þ ndo
di
inside diameter of membrane (m)
dln
logarithmic mean diameter of membrane (m),
do
di =ln do =di
do
outside diameter of membrane (m) E
enhancement factor
(dimensionless) GZ
Graetz number
(dimensionless)
H
Henry’s constant (dimensionless)
278
[2] J.L. Li, B.H. Chen, Review of CO2 absorption using
chemical solvents in hollow fiber membrane contactors,
Sep. Purif. Technol. 41 (2005) 109–122.
[3] S.A.M. Marzouk, M.H. Al-Marzouqi, M.H. El-Naas, N.
Abdullatif, Z.M. Ismail, Removal of carbon dioxide from
pressurized CO2–CH4 gas mixture using hollow fiber
membrane contactors, J. Membr. Sci. 351 (2010) 20–27.
[4] M. Rahbari-Sisakht, A.F. Ismail, D. Rana, T. Matsuura, A novel
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for CO2 absorption, J. Membr. Sci. 415–416 (2012)
221–228.
[5] M. Rahbari-Sisakht, A.F. Ismail, T. Matsuura,
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membrane contactor for CO2 absorption, Sep. Purif.
Technol. 86 (2012) 215–220.
[6] M. Rahbari-Sisakht, A.F. Ismail, T. Matsuura, Effect of bore
fluid composition
on structure and performance of asymmetric
polysulfone hollow fiber
membrane contactor absorption, Sep. Purif. Technol.
88 (2012)
for CO2 99–106.
[7] D. deMontigny, P. Tontiwachwuthikul, A. Chakma, Using
polypropylene and polytetrafluoroethylene membranes in
a membrane contactor for CO2 absorption, J. Membr. Sci.
277 (2006) 99–107.
[8] M. Rahbari-Sisakht, A.F. Ismail, D. Rana, T.
Matsuura, Effect of different
additives on the physical and chemical CO2 absorption in
polyetherimide hollow fiber membrane contactor system,
Sep.
Purif.
Technol.
http://dx.doi.
org/10.1016/j.seppur.2012.06.033.
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internal coagulant on effectiveness of polyvinylidene
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[10] S. Koonaphapdeelert, Z. Wu, K. Li, Carbon dioxide stripping
in ceramic hollow
fiber membrane contactors, Chem. Eng. Sci.
64 (2009) 1–8.
[11] H. Kumazawa, Absorption and desorption of CO2 by
aqueous
solutions
of
sterically
hindered
2-amino-2-methyl-1-propanol in hydrophobic microporous hollow fiber contained contactors, Chem. Eng.
Commun. 182 (2000) 163–179.
[12] R. Naim, A.F. Ismail, A. Mansourizadeh, Preparation of
microporous PVDF
hollow fiber membrane contactors for CO2 stripping from
diethanolamine solution, J. Membr. Sci. 392–393 (2012)
29–37.
[13] K.K. Sirkar, Other new membrane processes, in: W.S.W. Ho,
K.K. Sirkar (Eds.), Membrane Handbook, Chapman & Hall,
New York, 1992, pp. 885–899.
[14] M.C. Yang, E.L. Cussler, Designing hollow-fiber contactors,
AIChE J. 32 (1986)
1910–19
16.
[15] H. Kreulen, C.A. Smolders, G.F. Versteeg, W.P.M. Van Swaaij,
Determination of
mass transfer rates in wetted and non-wetted microporous
membranes,
Chem. Eng. Sci. 48 (1993) 2093–2102.
[16] (a) D.E. Suk, T. Matsuura, H.B. Park, Y.M. Lee, Synthesis
of a new type of surface modifying macromolecules
(nSMM) and characterization and testing of
nSMM
blended
membranes
for
membrane
distillation, J. Membr. Sci. 277 (2006) 177–185;
(b) M. Qtaishat, D. Rana, T. Matsuura, M. Khayet, Effect of
surface modifying macromolecules stoichiometric ratio
on composite hydrophobic/hydro- philic membranes
characteristics and performance in direct contact
membrane distillation, AIChE J. 55 (2009) 3145–3151;
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
M. Qtaishat, D. Rana, T. Matsuura, M. Khayet,
s
JCO2
CO2 desorption flux (mol m
2
1)
(c)
Preparation and characterization
of
novel
hydrophobic/hydrophilic
polyetherimide
composite
membranes
for desalination by direct contact
membrane distillation,
279
M. Rahbari-Sisakht et al. / Journal of Membrane Science 427 (2013) 270–275
kG
gas-phase mass transfer coefficient (ms 1)
kL
physical liquid-phase mass transfer coefficient (ms 1)
kM
membrane mass transfer coefficient (ms 1)
1)
KL
overall liquid-phase mass transfer coefficient (ms
L
effective membrane length (m) Re Reynolds number
(dimensionless)
Sh
Sherwood number (dimensionless)
T
Temperature
(K)
(dimensionless) Sc
Schmidt
280
number
Greek letters
d
e
Z
t
membrane thickness (m)
membrane porosity (dimensionless)
Stripping efficiency
membrane tortuosity (dimensionless)
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二.
Journal of Environmental Management 92 (2011) 121e130
Contents lists available at ScienceDirect
Journal of Environmental Management
journal h om epag e : w w w . el s ev i er .c o m / loc a t e /j env ma n
Simulation studies of ammonia removal from water in a membrane contactor under liquideliquid extraction mode
1
Amish Mandowara , Prashant K. Bhattacharya*
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
a r t i c l e
i n f o
Article history:
Received 5
February 2010
Received in revised
form 12 July 2010
Accepted 20 August 2010
Available online 16
September 2010
Keywords:
Ammonia-water
Hollow fibre membrane
contactor Diffusion
Modelling & numerical
simulation Liquideliquid
extraction
ab s t r a c t
Simulation studies were carried out, in an unsteady state, for the removal of ammonia from
water via a membrane contactor. The contactor had an aqueous solution of NH3 in the lumen
and sulphuric acid in the shell side. The model equations were developed considering radial
and axial diffusion and convection in the lumen. The partial differential equations were
converted by the finite difference technique into a series of stiff ordinary differential
equations w.r.t. time and solved using MATLAB. Excellent agreement was observed between
the simulation results and experimental data (from the literature) for a contactor of 75 fibres.
Excellent agreement was also observed between the simulation results and laboratorygenerated data from a contactor containing 10,200 fibres. Our model is more suitable than the
plug-flow model for designing the operation of the membrane contactor. The plug-flow
model over-predicts the fractional removal of ammonia and was observed to be limited when
designing longer contactors.
2010 Elsevier Ltd. All rights
reserved.
1. Introduction
Some industries face the problem of releasing wastewater
containing dissolved gases in low concentrations. The problem is
aggravated if the dissolved gases are toxic. For example, fertilizer
industries manufacturing urea have dissolved ammonia
(500e2000 ppm) in their wastewater. The ammonia is present in
low concentrations and the quantity of discharge may be low.
However, ammonia-containing wastewater can not be drained
because the gas escapes and creates serious environmental
problems.
In the dissolved state, ammonia exists in two forms. One is toxic
ammonia (NH3) and the other is less harmful ammonium ions
(NH4þ). The composition of these constituents depends on pH and
temperature. Toxic ammonia is harmful to aquatic life (concentrations as low as 0.01 ppm have negative effects on fish; while
0.1 ppm can be deadly to some other species). It is therefore
imperative for industries to remove the dissolved gases and to
recycle the water for further use.
Various techniques are available for the removal of dissolved
ammonia, such as air stripping, break-point chlorination, selective
ion exchange, biological nitrification, and denitrification (Sarioglu,
* Corresponding author. Tel.: þ91 512 2597093; fax: þ91 512
2590104.
E-mail address: pkbhatta@iitk.ac.in (P.K. Bhattacharya).
1 Presently at R&D unit, Engineers India Limited, Gurgaon,
Haryana, India.
2005). Removal by conventional extraction or stripping
processes may not be suitable for low-concentration wastewater.
Break-point chlorination suffers from several disadvantages
including large treatment volume, associated risk, difficulty of pH
control, and high chemical costs. The ion-exchange process
requires expensive organic resins and large quantities of
regenerant (Sarioglu, 2005). Biological nitrification and
denitrification are slow processes and require large treatment
vessels. Therefore, most of the available treatment processes are
not particularly effective. Some of the advances made in
membrane processes may solve this problem.
In recent years, membrane contactors have proved to be useful
for removing low-concentration solutes from wastewater and
they may prove to be an attractive alternative for the present
work. Hollow fibre-encased membrane contactors, usually in a
shell-and- tube configuration, offer many advantages over
traditional contact operations (Drioli et al., 2006). Membrane
contactors provide a large and stable interfacial area. Two fluids
flowing across the hollow fibre allow mass transfer to occur
between the fluids. The hydrophobic microporous polymeric
membrane provides the transfer area and restricts the permeation
of water. The transfer takes place at the pore opening, inside the
pore, or at the pore exit (Kiani et al., 1984; Qi and Cussler, 1985a,
1985b; Reed et al., 1995). For gases in water, poly- propylene (PP),
polytetrafluoroethylene (PTFE), and polyvinylidene fluoride
(PVDF) are normally used (Norddahl et al., 2006; Keshavarz et al.,
2008a) as hydrophobic polymers.
The present work is an attempt to develop a model to design
membrane contactors and to describe the fundamental aspects of
mass transfer and fluid flow behaviour. Several researchers have
carried out simulation studies of the degasification of water via
convective diffusion using membrane contactors (Mandowara and
Bhattacharya, 2009; Kieffer et al., 2008; Al-Marzouqi et al., 2008;
Lee et al., 2001). Mandowara and Bhattacharya (2009) simulated
ammonia removal by a vacuum application on the shell side and
obtained concentration profiles. Kieffer et al. (2008) used computational fluid dynamics to numerically study mass transfer in a
liquid-liquid-phase
membrane
contactor,
and
they
observed a clear separation between the reaction and mixing
zones. Al- Marzouqi et al. (2008) modelled the chemical
absorption of CO2
in MEA solvent using PP membrane contactors; they considered
both radial and axial diffusion under the condition of complete
wetting. Lee et al. (2001) studied the removal of CO2 in a hollowfibre membrane contactor using aqueous potassium carbonate;
they derived and numerically solved coupled nonlinear partial
differential equations and also reported the optimal absorbent flow
rate. Keshavarz et al. (2008a) developed and solved a mathematical
model
for
membrane
contactors
operated
under
non-wet or
partially wetted conditions during the simultaneous absorption of
carbon dioxide and hydrogen sulphide in diethanolamine (DEA)
solution.
Bottino et al. (2008) experimentally and numerically studied
CO2 removal from a gas stream using aqueous monoethanolamine
as an extract phase. The work used different numbers of commercial polypropylene capillary membranes in a membrane contactor
and found the CO2 removal efficiency. The experimental results
were in good agreement with the predicted results. Malek et al.
(1996) experimentally and numerically studied microporous
hollow-fibre membrane modules operated under partially wetted
conditions. The nonlinear partial differential equations were solved
using an orthogonal collocation technique. The experimental
results were found to be in good agreement with the modelling
results.
McDermott et
al.
(2007)
studied
the
vacuum-assisted
removal of volatile and semi-volatile organic contaminants from
water using hollow-fibre-based membrane contactors. They used a
hybrid numerical-analytical approach and investigated the main
factors controlling the removal characteristics, e.g., the Henry’s law
coefficient, gas-side diffusion resistance, and aqueous diffusion
limitation.
The objective of the present study is to model membrane contactor operated in a liquideliquid extraction mode. Tan et al. (2006)
have developed a model for the liquideliquid extraction mode and
could predict the percentage of ammonia removal based on plugflow behaviour. Further, their model uses an empirically estimated
overall mass transfer coefficient assuming average concentration
and average velocity at any cross-section of the lumen.
The present work includes fundamental aspects of mass transfer
and fluid flow phenomena to better design and describes
the
contactor process. The model is based on radial diffusion, axial
diffusion, and convection in the tube (lumen) side. Transport inside
the membrane pores is considered through Knudsen and bulk
diffusion, whereas instantaneous reaction is assumed at the pore
exit of the membrane (shell-side) interface. Finally, the study
presents an unsteady-state numerical simulation of the model
equations of the membrane contactor, operated in liquideliquid
extraction mode, with ammonia solution flowing in the lumen side
and sulphuric acid flowing in the shell side.
2. Theory and model development
Fig. 1 shows a schematic of membrane contactor operation in
the liquideliquid extraction mode. The model equations were
developed by considering aqueous ammonium chloride solution in
Fig. 1. Membrane contactor operated under liquideliquid
extraction mode for removal of dissolved ammonia.
Agitators are used in both tanks to ensure uniform mixing. Both
solutions are circulated in loops as shown in Fig. 1.
In the aqueous solution, ammonia exists as both unprotonated
and protonated ammonia. This is an unsteady-state process in
which the transport of ammonia and ammonium ions is governed
by axial diffusion, radial diffusion, and convection in the lumen
side. A three-step transport may be considered to occur sequentially during the ammonia removal. The first step is radial diffusion
of both unprotonated ammonia and ammonium ions to the internal
surface of the hollow fibre. The second step is the diffusion of
ammonia inside the pore. Finally, ammonia in gaseous form reaches the interface (located at the pore exit of the hydrophobic
membrane) and instantaneously reacts with the extract phase
(sulphuric acid present at the shell side). Because ammonia is
highly soluble in sulphuric acid, no reaction zone is formed; it
reacts only at the interface. Given the above considerations, the
numerical model is based on the following assumptions:
i)
ii)
iii)
iv)
Isothermal operation;
Fully developed parabolic profile in the lumen side;
No pore blockages and pores are filled with air;
Feed and extract volumes (and hence tank volumes) are large
compared to that of the hollow-fibre module;
v) Flow rates of both feed and extract (ammonia solution and
sulphuric acid, respectively) are constant because the feed is
dilute.
Hydrophobi
c
Membrane
Lumen side:
Ammoni
a
solution
C j ,b
Boundary
Layer
p
Shell side:
Sulfuric
acid
g
a,in
t
C a ,int
Gas
filled
pore
pa,m
0
Liquid –Ga
s interface
the lumen side and aqueous sulphuric acid in the shell side.
Fig. 2. Concentration profile for the species j at a particular time
when it moves from lumen side towards shell side through a
microporous hydrophobic membrane.
123
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
Mass balance inside the lumen
The transport of both ammonia and ammonium ions in the lumen
is expressed through a convective-diffusive equation (Mandowara
and Bhattacharya, 2009):
v Cj ~
þ
vt
(1)
2
U$VCj
¼
V
Dj
Cj
þ
Rj
where Cj denotes the local combined concentration of ammonia and
ammonium ions (component j), D is the diffusivity of the
component in water, R is the rate of generation due to the chemical
reaction, and
is the velocity vector. As there is no chemical
~
U
reaction in the lumen side, symmetry is assumed inside the lumen
(cylindrical):
The above assumption is justified because the bulk movement
(convection) of ammonia is more pronounced at the exit of the lumen
(Lee et al., 2001; Bottino et al., 2008; Kreulen et al., 1993; Zhang et al.,
2006, 2008; Keshavarz et al., 2008b; Drioli et al., 2006). Accordingly,
at the exit of the lumen, vCj=vZis a function of r only; and hence its
variation w.r.t. Z is assumed to be negligible (Treybal, 1981).
2.2.4. Fig. 2 shows the concentration profile
At the inner surface of the hollow fibre, the flux of the ammonia in
aqueous phase equals the flux of the gaseous ammonia diffused
through the pore. Therefore, at r ¼ R, the boundary condition is
described by
¼
(9)
r¼ kg;pore
R
In this equation, the concentration of ammonia at the pore exit
is assumed to be negligible. This is because an instantaneous
reaction between acid and ammonia takes place at the pore exit.
Further, as described earlier, Cj is the combined concentration of
ammonia and ammonium ions:
Dj
vCj
¼ 0
vq
(2)
Only diffusion and convection of ammonia are assumed to occur
and hence Rj ¼ 0. Further, Ur (the radial velocity), which is due to
the diffusion of ammonia in the radial direction, also becomes zero.
This is because the rate of diffusion of ammonia in water is negligible and the bulk flow is in the Z direction (Mandowara and
Bhattacharya, 2009). Equation (1) can now be written as
(
vCj
1v
v2 )
vCj
vCj
Cj
r
þ
(3)
2
vZ
þ UZ
¼ Dj r vr
vr
vt
vZ
The velocity distribution in the lumen side under laminar flow
conditions can be written (Kreulen et al., 1993) as
2
1.
(4)
R
r
Defining U to be the average velocity of the fluid inside the
lumen:
Q
U ¼
(5)
NpR2
UZ ðrÞ ¼ 2U
g !
a;int
Rg T
p
vCj
vr
¼ Ca þ Cam:
Cj
(10)
At the liquidegas interface (located at the pore entrance, Fig. 2),
Henry’s law may be applicable:
pg
a;int
g
or
¼ HaCa;int
*
Ca;int
¼ Ha Ca;int
(11)
Further, in the aqueous solution, the following equilibrium is
observed:
Kb
NH3 þ H2 O % NH4þ þ OH
where
CamCOH
¼
Ca
Kb
(12)
Since the pH is maintained (using a buffer) during the process,
the concentration of the base is kept constant in the lumen and is
given by
Boundary conditions
Symmetry inside the fibre: at r ¼ 0; all Z and t
¼ 10pH
COH
vCj
vr
¼ 0
r¼0
(6)
At Z ¼ 0; all r and t
The model is based on an unsteady-state situation considering
radial and axial diffusion in the lumen; however, at the entrance,
both types of diffusion are neglected. Wehner and Wilhelm (1956)
also stated accordingly. Hence,
Cj;Z¼0
(7)
¼
14
(13)
The mass transfer coefficient inside the pore, Ka,g,pore can be
estimated using the following correlation (Mandowara and
Bhattacharya, 2009):
3
o
ka;g;pore
¼
(14)
n
sb
Da;c;pore
where the tortuosity (Bottino et al., 2008) is given by
1
s ¼
Ctank
At Z ¼ L; all r and t
Assuming the diffusion of ammonia at the exit of the lumen (in
the Z-direction) to be negligible in comparison to its movement in
the same direction due to bulk flow, one may obtain the boundary
condition at the exit of the lumen as
(15)
32
Assuming the pores to be sufficiently small, Knudsen and bulk
diffusions may co-exist. Thus, the combined diffusivity (Mandowara
and Bhattacharya, 2009) Da,c,pore is expressed by
1
Da;c;pore
¼
1
1
þ
Dk;a;pore Da;air
Further, the Knudsen diffusion Dk,a,pore is given by
(16)
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
Dj
!
v2 Cj
¼ 0
vZ 2
Z¼L
(8)
Dk;a;pore
¼
dpor 8Rg T
e 1=2
pMa
3
124
(17)
125
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
Membrane mass transfer coefficient depends on the pore
diameter, porosity to tortuosity ratio and thickness of the
membrane. The main aim of any membrane contactor design is to
reduce the resistance offered by the membrane (this is the additional resistance developed as compared to any traditional contacting equipment). Larger membrane pore, larger porosity to
tortuosity ratio and lesser thickness of the membrane will result in
increased mass transfer coefficient of the membrane and hence
results in lesser resistance to the mass transfer of ammonia.
2.3. Mass balance over ammonia tank
Under the assumption of uniform mixing, the mass balance
equation can be written
Table 2
Specifications of various parameters used for simulation.
Hydrophobic membrane specifications and other
Specifications
Pore diameter, dpore (m)
10 8
Thickness of the membrane, b (m)
Porosity, 3
Tortuosity of pore, s
Inner diameter of the lumen, di (m)
4
Outer diameter of the lumen, do(m)
Length of the fibre, L (m)
Kinematic viscosity of water at T ¼ 298 K, n (m2/s)
Initial concentration C0 (mol/m3)
Flow rate of ammonia solution, Q (m3/s)
5
Volume of feed tank, V (m3)
pH
Number of fibres, N
V
dCt ¼ QCj;z¼L
ank
dt
QCtank
¼ C0
(19)
Fractional removal b of ammonia at time t in the tank:
CtankðtÞ
b ¼ 1
C0
(20)
Values of parameters
10
5
10
3
10 4
0.2
10 6
50
1.67
10
5
10
11
10,200
3.1.1. Comparison of simulated results with experimental results
obtained for 75 hollow fibres (Tan et al., 2006)
Fig. 3 shows the residual fraction of ammonia in the tank at
different operating conditions over time. The fraction of ammonia
decreases exponentially as a function of time; hence, the rate of
removal is much higher during the initial period.
Fig. 3 further presents the validation of the model
using
experimental results (Tan et al., 2006) for 75 hollow fibres. Obviously, to compare the simulation results with the results of Tan et
al. (2006), the same design parameters were used for
the
Properties
Values
Henry’s law constant, Ha (Pa.m3/mol)
The physical properties of ammonia at T ¼ 298 K were taken
from Tan et al. (2006) and are given in Table 1.
Other parameters are given in Table 2.
Solution technique
The Z/L and r/R axes were converted into 20 mesh points each,
and the second-order finite difference technique was used at each
grid point (i, j) to convert the PDE into a series of stiff ODEs w.r.t.
time. Here i correspond to the axial point and j corresponds to the
radial point. The stiff ODEs were solved using MATLAB’s built-in
solver ode23s. The relative error tolerance was taken as 1
10 3.
3. Results and discussion
Validation of results
The main objective of the present work is to make the membrane
contactor operate as a degasser. The basic function of a degasser is
to remove gas from a feed fluid across a hollow fibre through either
LLE or vacuum mode. The present objective is to observe the rate
of gas removal in an unsteady state under the LLE mode. The
removal results (simulated data as predicted from model) are
presented as a fraction of the residual gas in the feed tank (as per
the scheme shown in Fig. 1) as a function of time.
Table 1
Properties of ammonia at T ¼ 298 K (Tan et al., 2006).
4
0.54
3.43
2.2
(18)
Initial Condition: at t ¼ 0
Ctank
Values
3
1.62
3
A. Mandowara,
Bhattacharya
Journal
membrane contactor. The marker symbols
in theP.K.
plot
indicate /the
experimental data-points and the solid line represents the simulated data. As is evident, there is excellent agreement between the
simulated and experimental data.
3.1.2. Comparison of simulated results with experimental results
generated for 10,200 hollow fibres (Shukla, 2008)
Dimensionless Henry’s law a
6.54
10
constant,H*
2
Dj (m /s)
1.76
Diffusivity in
10 5 9
water,
(m2/s)
1.89
10
Diffusivity in
air,
Da,air
1.744
Dissociation constant of Kb
ammonia,
10 5
of Environmental
Managementthe
92 (2011)
121e130and
Fig. 4 compares
simulated
4
experimental results; there is126
good agreement between the two.
The experimental data were generated in the laboratory
(Shukla, 2008) from a Liqui-Cel membrane contactor (X50 fibre
model) with 10,200 fibres. The experimental runs were taken with a
lumen side feed at pH ¼ 10.5, V ¼ 5 l, L ¼ 0.2 m. The other
operating conditions are given in Fig. 4. The agreement is quite
Fig. 3. Fraction of residual ammonia in the tank vs.
time: comparison between
experimental results (Tan et al., 2006) and simulated values.
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
127
Fig. 4. Fraction of residual ammonia in the tank vs.
time: comparison between simulated values and experimental
data through Liqui-Cel
contactor.
close; the small difference is probably due to the evaporation of
ammonia from the feed tank during the experimentation.
Analysis of simulated results: concentration profiles
Concentration profiles were observed in terms of variations at
different radial and axial positions.
Concentration variation at different radial positions over time at
varying Z/L
Fig. 5(aec) shows the variation in concentration over time at
different radial positions with Z/L fixed at 0.2, 0.6,
and 0.8, respectively.
In Fig. 5(a), the uppermost curve corresponds to the point
r/R ¼ 0, Z/L ¼ 0.2; the lowermost curve corresponds to r/R ¼ 1, Z/L
¼ 0.2. Radial positions were taken at intervals of 0.2. The plot
shows that at time t ¼ 0þ the concentration shoots up and then it
exponentially declines over time at different radial positions. This is
because at time t ¼ 0, the lumen was empty and the ammonia
solution takes some time to fill it. Once the lumen is full, diffusions
start in the radial and axial directions together with convective mass
transfer. Simultaneously, desorption of ammonia is achieved through
instantaneous acidegas reaction at the shell side. Accordingly, there
is an exponential decline in concentration. The curves at points (0,
0.2) and (0.2, 0.2) almost coincide. This is because the
concentration boundary layer is located near the wall, and hence the
bulk concentration remains almost constant near the axis of the fibre.
Also, as r/R increases, there is a more rapid decrease in concentration
because of the radial diffusion of ammonia. Similar behaviour can
be observed in Fig. 5(b) and (c).
Concentration variation at different axial points over time at
varying r/R
Fig. 6(aec) shows the variation in concentration over time at
different axial positions with r/R fixed at 0.2, 0.6,
and 0.8, respectively.
In Fig. 6(a) the uppermost curve corresponds to the point (r/ R
¼ 0.2, Z/L ¼ 0); the lowermost curve corresponds to (0.2, 1). Axial
positions are taken at intervals of 0.2. The top curve corresponds to
the lumen entrance. At time t ¼ 0, the solution is uniformly
distributed across the lumen entrance (i.e., at all r/R and Z/L ¼ 0)
Fig. 5. (a) Concentration variation at different radial points with
time at Z/L ¼ 0.2. (b) Concentration variation at different radial
points with time at Z/L ¼ 0.6. (c) Concen- tration variation at
different radial points with time at Z/L ¼ 0.8.
and elsewhere in the lumen the concentration is zero. As time
passes, there is an exponential decline in concentration at different
axial positions due to radial diffusion, axial diffusion, and convection inside the lumen. Similar behaviour can be observed in Fig. 6
(b) and (c).
Radial and axial profiles of concentration at time t ¼ 108 s
For the radial concentration profile, it was decided to identify a
time period at which the effect of the fractional removal of the
ammonia, b, is significant. A period of 108 contact seconds was
chosen. Fig. 7 shows a plot of the radial concentration profile at t
¼ 108 s at different axial locations.
Near the axis of the fibre, the bulk-phase concentration remains
almost constant to a certain radial distance and then reduces
128
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
0.86
0.76
Increasing Z/L (intervals:
0.2) Range: 0-1; at t=108
s
0.66
Cj / C0
0.56
0.46
0.36
0.26
0.16
0.06
0
0.1
0.2
0.3
0.4
0.5
r/R
0.6
0.7
0.8
0.9
1
Fig. 7. Plot of radial profile of concentration vs. r/R for different
axial points at time
t ¼ 108 s.
Analysis of simulated results of diffusion: effect of axial
diffusion
Earlier authors (Lee et al., 2001; Bottino et al., 2008; Kreulen
et al., 1993; Zhang et al., 2006, 2008; Keshavarz et al., 2008b;
Drioli et al., 2006) have consistently considered axial diffusion to
be negligible inside the lumen. This is possible, but in our model the
influence of axial diffusion was included. Fig. 9 depicts this and
indeed axial diffusion is observed to have little effect on the
removal process.
Obviously, the diffusion of ammonia in the Z direction is
observed to be almost negligible in comparison to the bulk movement in the same direction because in the axial direction convection dominates. Thus, the axial diffusion is negligibly small
compared to the diffusion in the radial direction.
Influence of process variables on fractional removal of
ammonia
Feed: flow rate
Fig. 10 exhibits the exponential increase in the fractional
removal of ammonia (b) over time. It also illustrates the influence of
the feed flow rate on the fractional ammonia removal. It is evident
that removal increases as volumetric feed flow rate increases.
0.9
0.
8
Fig. 6. (a) Concentration variation at different axial points with time
at r/R ¼ 0.2. (b) Concentration variation at different axial points
with time at r/R ¼ 0.6. (c) Concen- tration variation at different
axial points with time at r/R ¼ 0.8.
0.
7
0.
6
Cj / C0
gradually because of the formation of the boundary layer near the
fibre wall. Further, the ammonia solution is uniformly distributed at
Z/L ¼ 0, i.e., at the lumen entrance; hence the concentration profile
remains flat.
Fig. 8 shows the axial profile at different radial locations. The
concentration decreases rapidly as Z/L increases and this decrease is
significantly affected by the increase of r/R. As r/R increases, the
Increasing r/R (intervals: 0.2)
Range: 0-1; at t=108 s
0.
5
ax
ial
co
nc
en
tr
ati
on
pr
ofiles decrease from almost-linear to expo-
129
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Z/
L
nential patterns. This may be due to the formation of a liquid
boundary layer near the lumen wall.
Fig. 8. Plot of axial profile of concentration vs. Z/Lfor different radial
points at time
t ¼ 108 s.
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
Fig. 9. Plot of fractional removal vs. time: effect of axial
diffusion.
This is due to the increased convection in the lumen resulting in
decreased viscous layer resistance near the lumen wall of the fibre.
Further, a negligible variation in b is observed beyond a flow rate of
6.00
10 5 m3/s; it was observed that the top two curves
corresponding to feed flow rates, 6.00
10 5 m3/s and 6.16
10 5
m3/s, merged with each other. This is because beyond 6.00
10
5 m3/s,
the diffusion resistance in the membrane becomes the
mass transfer controlling step. Hence, any further increase in feed
flow
rate may have a negligible effect on the fractional removal.
Feed: pH
Fig. 11 shows the influence of the feed solution pH on the variation in fractional removal over time.
The pH was varied from 8 to 12. It is evident that the fractional
ammonia removal increases as pH increases. Beyond pH 10.5, any
further increase would have negligible effect on the fractional
removal as the total dissolved ammonia exists only in the form of
unprotonated ammonia. Mathematically, i.e., from Eqs. (10) to (13),
one can observe that the concentration of unprotonated ammonia is
a strong function of pH and can be specifically represented as
130
Fig. 11. Fractional removal of ammonia vs. time: varying
pH.
(21) and the temperature dependency of the dissociation constant
Kb of ammonia is given by the van’t Hoff equation as
dlnKb
dT
DH
¼ RT 2
(22)
Feed: initial concentration
Fig. 12 shows the variation in fractional removal as a function of
time with initial feed concentration varying from 10 to 120 mol/m3.
It is clear that the variation in the initial concentration does not
influence the fractional removal. This is because the diffusivity
coefficient is a weak function of ammonia concentration, especially
in the dilute range. Hence, the overall mass transfer coefficient
which incorporates both liquid side mass transfer coefficient as
well as membrane mass transfer coefficient becomes independent
of the initial concentration of the ammonia. In other words, the
resistance offered by the overall process to the ammonia removal
becomes independent of the initial ammonia concentration.
(21)
Membrane contactor: number of fibres
Fig. 13 shows the variation in fractional ammonia removal (b)
over time. It also depicts the influence of the number of fibres,
At pH above 10.5, the factor ðKbÞ=ð10pH 14Þ becomes negligible.
Hence, the dissolved ammonia is all in the unprotonated form. The
concentration of toxic ammonia (free ammonia) is thus given by Eq.
Fig. 10. Fractional removal of ammonia vs. time: varying
flow rate.
Ca
¼
Cj
1 þ Kb=10pH
14
A. Mandowara, P.K. Bhattacharya / Journal
ranging from 1000 to 30,000.
It is evident that b increases as the number of fibres in the
module increases. In other words, there is an increase in the
available interfacial area facilitating a higher mass transfer. Further,
one may observe that for merging curves (8e10, i.e., from 20,000 to
Fig. 12. Fractional removal of ammonia vs. time: varying
initial concentration.
of Environmental Management 92 (2011) 121e130
131
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
Fig. 13. Fractional removal of ammonia vs. time: varying
number of fibres.
30,000) there is a negligible influence on b as the number of fibres
increases above 20,000; however, the present work deals with the
dilute range of the ammonia solution. Hence, around 20,000 fibres
are sufficient to provide the required interfacial area for the chosen
concentration range.
Membrane contactor: lumen radius
Fig. 14 shows the variation in fractional removal (b) with time;
superimposed on this figure is the variation of the lumen radius,
from 30 to 600 mm. Rest all other parameters like number of fibres,
length of the fibre etc. were kept constant, as mentioned in Table 2.
It is clear that as the radius of the lumen increases the fractional
removal increases. This is because for a constant flow rate, as R
increases U decreases, as per Eq. (5). Hence, the bulk movement of
ammonia at a particular time gets reduced in the Z direction. At the
same time, the radial diffusion zone of ammonia increases as R
increases. This results in an increasing number of moles of ammonia
reaching the shell side by radial diffusion phenomena; and thus
instantaneously reacting with the sulphuric acid present in the shell
side. It may also be observed that beyond 300 mm increasing the
fibre radius has a negligible influence on the frac- tional ammonia
removal, particularly because of the dilute concentrations
considered.
Fig. 14. Fractional removal of ammonia vs. time: varying
radius of fibre.
132
Fig. 15. Fractional removal of ammonia vs. time: varying
length of fibre.
Membrane contactor: fibre (lumen) length
Fig. 15 shows the variation in fractional removal as a function of
time with varying length from 0.1 to 1.0 m.
The figure clearly shows that as the length of the fibre increases
the fractional removal increases. This is because of the increase in
the radial diffusion of ammonia to the shell side as it moves along
the lumen, i.e., a longer lumen provides a larger zone of radial
diffusion. Further, beyond 0.4 m, the length has a negligible effect
on the fractional removal. This is obviously due to the dilute
concentration (in Fig. 15, the initial concentration chosen was
50 mol/m3).
Model adequacy
To assess the adequacy of the model, which considers both
diffusions (radial and axial) as well as convection in the tube
(lumen) side, it was compared with an earlier model based on plugflow behaviour (Tan et al., 2006).
Varying lumen length
It is clearly seen from Fig. 16 that as the length of the lumen
increases, the error between the plug-flow model and our model
widens. Hence, a higher contactor length may induce a larger error.
Fig. 16. Comparison between developed model and plug-flow
model: variation of lumen length.
A. Mandowara, P.K. Bhattacharya / Journal of Environmental Management 92 (2011) 121e130
d
D
H
Fig. 17. Comparison between developed model and plug-flow
model: variation of lumen length and radius.
A small lab-scale contactor has negligible error (see curves 1 and 2
of Fig. 16; for comparison, the radius is fixed at 2
10 4 m).
Varying lumen radius and length
Here the lumen length was kept constant (L ¼ 0.8 m) and the
lumen radius was varied. In Fig. 17, curves 3 to 6 depict this variation. Larger errors are observed between the two approaches (plugflow and our model) as the radius increases. The plug-flow model
over-predicts the fractional removal. As can be observed from curves
1 and 2, a shorter lumen length (L ¼ 0.3 m) leads to much less error.
4. Conclusions
An unsteady-state numerical simulation of mass transfer and
momentum transfer under laminar flow conditions was carried out,
and the results were analyzed. Model equations were developed
with ammonia solution in the lumen and extract phase (sulphuric
acid solution) in the shell side. The reaction was assumed to be
instantaneous and at the interface only because ammonia is highly
soluble in sulphuric acid; hence, there is no reaction zone.
Accordingly, the axial and radial profiles of concentration are presented at a particular time. The results show a decrease in
concentration along the radial and axial directions. Radial diffusion
and convection in the lumen side may have caused this effect.
Confirming earlier work, the axial diffusion was found to be
negligible compared to the radial diffusion. An increase in the feed
flow rate gave higher fractional removal up to 6.00
10 5 m3/s,
beyond which there was little effect. Similarly, pH up to 10.5
increased the fractional removal; beyond this value there was little
effect. A larger lumen radius, length, and number of fibres resulted
in a higher fractional removal. A comparison with a plug-flow
model demonstrated the usefulness of our model. The plug-flow
model over-predicts the fractional removal of ammonia and was
found to be inadequate for designing long contactors.
Notations
b
membrane
thickness (m)
C
concentration (mol/m3)
133
diameter (m)
diffusivity (m2/s)
Henry’s constant (Pa m3/mol)
H*
dimensionless Henry’s
constant DH
enthalpy change of
the reaction k
mass
transfer
coefficient (m/s)
Kb
ionization equilibrium constant of ammonia
L
length of the module (m)
M
molecular weight (g/mol)
N
number of fibres
p
partial pressure (Pa)
Q
feed flow rate (m3/s)
r
radial coordinate (m)
R
radius of the lumen (m)
Rg
universal gas constant (J/mol. K)
Rj
rate of generation of component j due to chemical
reaction (mol/s.m3)
t
time (s)
T
temperature (K)
U
velocity inside the fibre (m/s)
V
volume of feed tank (m3)
Z
axial coordinate (m)
Subscript
0
a
am
air
c
g
i
int
j
k
m
o
pore
Z
initial
unprotonated ammonia
protonated ammonia
air
combined
gas
inner
liquid-gas interface
combined unprotonated ammonia & protonated
ammonia
Knudsen diffusion
membrane
outer
membrane pore
axial direction
Superscript
averaged
w
vector
g
gas
Greek letters
v
kinematic viscosity of water (m2/s)
3
porosity of the membrane
s
tortuosity of the pore
b
fractional removal of ammonia
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