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An improved resistance model for gas permeation in composite membranes
j o u r n a l of MEMBRANE SCIENCE ELSEVIER
Journal of Membrane Science 118 (1996) 1-7
An improved resistance model for gas permeation in composite membranes Gaohong He a,*, Xiangyang Huang b, Renxian Xu b, Baolin Zhu b a Dalian University of Technology, Department of Chemical Engineering, Dalian 116012, PR China b Dalian Institute of Chemical Physics, Chinese Academy of Sciences, P.O. Box 110, Dalian 116012, PR China
Received 9 October 1995; accepted 4 January 1996
Abstract An improved resistance model based on Henis-Tripodi's model for gas permeation in composite membranes has been established, in which the degree of penetration of the coating material into the defects or pores of the effective dense layer has been taken into account. The influences of the degree of penetration, the thickness of the coating layer and surface porosity of the dense layer on gas permeation resistance throughout the composite membrane and separation factor of the composite membrane have been calculated and analysed. Some experimental results have also been explained with this model. The model together with its corresponding coating method is useful for the improvement of membrane separation properties. Keywords: Gas permeation; Resistance model; Composite membrane; Degree of penetration; Permeation mechanism
1. Introduction A major breakthrough in the history of gas membrane separation was made by Henis and Tripodi [1,2] who developed composite membranes with acceptable permeability and very high permselectivity [3,4]. These found commercial applications in H 2 purification and recovery in ammonia production. Henis and Tripodi have also established a resistance model to explain the behavior of composite gas separation membranes [2]. The membrane consists of a porous asymmetric substrate of one polymer with a dense layer and a coating of another polymer - a second layer that is very thin and made by a nonselective and highly permeable material. The influ-
* Corresponding author.
ences of surface porosity of the dense layer and coating thickness on membrane separation properties have been studied by Henis and Tripodi with their model. In their work, Henis and Tripodi have drawn a further conclusion. They believed that when the coating material does not penetrate to the full depth of the pores, but penetrates to only 0.1 or 0.01% of that depth, the results are much the same [2]. This means that the composite membrane will have very high separation factor with a very low degree of penetration. This point is open to discussion. Kimmerle [5] and Ashworth [6] have done additional research work but they assumed that the coating materials penetrate and fill the pores of the dense layer. In our early research work, it was realized that the degree of penetration of the coating material into the defects or pores of the dense layer greatly influences the membrane separation properties [7].
0376-7388/96/$15.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved. P11S0376-7388(96)00023-3
2
G. He et al./Journal of Membrane Science 118 (1996) 1-7
In this paper, we have made a small modification to Henis and Tripodi's resistance model considering the degree of penetration and found an improved resistance model. We have calculated hydrogen and nitrogen separation properties with different degrees of penetration using the model developed.
2. Theory: the improved resistance model
2.1. Simplified description of the composite membrane The well-known Henis and Tripodi's electrical circuit analog [2] divide the composite membrane into three regions: the coating layer, the dense layer in substrate and the pores or defects in the dense layer filled with coating material. In our improved resistance model, the composite membrane is divided into five regions with the consideration of the degree of penetration. As shown in Fig. 1, these five regions are: 1. the coating layer; 2. the non-porous part of the dense layer without pores or defects; 3. the highly porous substrate region; 4. the part of defects or pores in the dense layer which is close to the coating layer and filled with the coating material; 5. the remaining part of defects or pores in the dense layer that is close to the porous substrate region and not filled with the coating material. These regions are labelled as 1, 2, 3, 4 and 5 in the corresponding order to Fig. 1. The average thickness and gas permeation resistance of each region are L 1, L2, L3, L4, Ls, RI, R2, R3, R 4 and R 5, respectively.
2.2. Assumptions The following assumptions were made for the mathematical analysis of the gas permeation in the composite membranes described above: 1. the coating layer is homogeneous and non-porous; 2. there are only one dimensional diffusion or flow in the composite membrane; 3. the pores and defects in the dense layer are circular and have uniform radius and length, the length of the pores is equal to the thickness of the dense layer; 4. the radius of the pores in the dense layer is small so that the gas flow through the 5th region is Knudsen flow; 5. the highly porous substrate region has no resistance for gases so that R 3 = 0.
2.3. Definition of the degree of penetration The average thickness L 4 represents the part in the pores in the dense layer which is filled with coating material, while the average thickness L 2 represents the length of the pores in the dense layer. Thus, the degree of penetration of the coating material into the dense layer is defined as:
s=
L4
where L a < L 2 , L 2 = L * + L 5 a n d O < f < l .
2.4. Gas permeation properties According to the mechanism of gas flow through each region, the resistance to permeate flow for each region can be expressed as follows [7]: L1 R, = P, A
f Lz
_t: T
Fig. 1. Schematic representation of a composite membrane and the corresponding electrical circuit analogue.
(1)
R2
L2 P2A( 1 _ e2 )
(2)
(3)
fL2 R4-- P,A~-----~
(4)
3(1 - f ) Lzp o R5 = 4r2T° AEz~/ZR,/rrTM
(5)
G. He et al. / Journal of Membrane Science 118 (1996) 1-7
Thus, the total gas permeation resistance, according to the improved resistance model (shown in Fig. 1) is defined as: Rt = R1 +
1
1 + - R2 R4 + R5
(6)
The gas permeation flux throughout the membrane can be calculated by equation: Ap Q -
Rt
(7)
where Ap is the pressure drop across the membrane. The gas permeability throughout the membrane can also be calculated by equation:
3
fibers for at least 5 min. The other was carried out using a solution of 0 . 4 - 0 . 5 wt% silicone rubber and 0.04-0.05 wt% curing agent supplied in gasoline, and the bundles were first immersed into the 0 . 4 - 0 . 5 wt% coating solution for about 40 h, then a vacuum was applied inside the fibers for at least 5 min. All the coated bundles were then cured in air for 24 h at room temperature before use.
3.2. Apparatus and permeability measurement The apparatus consists of a gas cylinder, a pressure regulator, a separation module, pressure meters and a bubble flowmeter [8]. Bundles of hollow fibers were potted into the separator module and the permeate flows from the open end were measured at 25°C.
1 J = --
RtA
(8)
4. Results
The separation factor for components i and j in the gas mixture is:
4.1. Mathematical analysis of the improved resistance model
Rtj
a -
(9) Rti
Using Eq. (6) and Eq. (9), the influences of the degree of penetration, the thickness of coating layer and the porosity of the dense layer on the membrane separation properties can be calculated and analyzed.
3. Experimental
3.1. Membranes The asymmetric hollow fibers were spun by a d r y - w e t spinning procedure on a laboratory spinning apparatus. A spinning solution of 32 wt% polysulfone in complex solvents was used. After washing and drying, fibers of typical dimensions ( 5 2 0 / 3 1 0 /xm o . d . / i . d . ) were obtained. Bundles of 4 0 - 5 0 fibers each with a length of 25 cm were sealed by epoxy resin at one end. The bundles were then coated to form composite gas separation membranes by the vacuum method. Two kinds of coating procedure were performed. One kind o f coating was carried out using a solution of 4 wt% silicone rubber and 0.4 wt% curing agent supplied in gasoline outside the fibers of the bundle and vacuum inside the
The properties of PDMS coated polysulfone composite membranes via the degree of penetration have been calculated for the separation of binary H2/N 2 system using the improved resistance model. The following data were used for the calculation: PI(H2) = 3.9 × 10 - s cm 3 c r n / c m 2 s cmHg Pj(N 2) = 1.81 × 10 - s cm 3 c m / c m 2 s cmHg P2(H2)=1.3×10 9 cm 3 c m / c m 2 s c m H g P2(N2) = 1.8 × 10 -11 c m 3 c m / c m 2 s cmHg L 1 = 1 × 10 -4 ~ 1 × 1 0 -3 cm L 2 -- 1 × 10 -5 cm r 2 = 1.5 × 10 - 6 c m ~2 = 1 X 10 - 6 ~ 1 × 10 - 4 Po = 76 cmHg TO = 273.15 K A = 18.096 cm 2 Where Px indicates the permeability coefficient of gas H 2 or N 2 in PDMS material, P2 indicates the permeability coefficient of gas H 2 or N 2 in polysulfone. Permeability coefficients were obtained from the literature [9].
4.1.1. Effect of the degree of penetration f A ratio w is defined as:
O~f
w= - af-1
(10)
4
G. He et al./Journal of Membrane Science 118 (1996) 1-7
when f < 0.03, the total gas permeation resistance increases very rapidly; when 0.03 < f < 0.1, the total gas permeation resistance increases very slowly; when f > 0.1, the total gas permeation resistance tends to be a constant. In the case of slow moving gas N2: when f < 0.1, the total gas permeation resistance increases very rapidly; when 0.1 < f < 0.4, the total gas permeation resistance increases very slowly; when f > 0.4, the total gas permeation resistance also tends to be a constant. That is to say, when f < 0.4 the influence of f on the movement of slow gas is larger than that on the movement of fast gas, and when f is large enough the difference of the influences becomes small. The conclusion is therefore that only when f > 0.4 can separation factor c~ reach a high value, and a greater f value is beneficial to higher separation factor a and will not decrease the permeation flux of the composite membrane.
Table 1 Comparison c~y with af= 1 at different degrees of penetration Degree of penetration f
f = 0.01
f = 0.1
f = 1
Separation factor a~zz Ratio w (%)
7.04 14
28.28 57
48.87 100
where c~f is the separation factor when the degree of penetration is f (0 < f < 1), and ~/= ~ is the separation factor when the degree of penetration is 1, respectively. The defects or pores in the dense layer are completely filled with coating materials when f is equal to 1 as assumed by Henis and Tripodi. We have calculated c~/ when f = 0.01 and f = 0.1 and compared them with c~f=I. The results are shown in Table 1. It can be seen from Table 1 that the degree of penetration f plays a very important role in affecting the membrane separation properties. If f is very small, the separation factor cannot reach the maximum value c~f=1, which is given by Henis and Tripodi's resistance model. The influences of the degree penetration f on the total gas permeation resistance to H 2 and N 2 throughout the membrane and on the membrane separation factor a are shown in Fig. 2. It is shown that in the case of the permeation of the fast moving gas H2:
4.1.2. Effect of the thickness (L 1) of the coating layer at uarious degrees of penetration The effect of the thickness of the coating layer on the membrane separation factor at various degrees of
IE+5
_-
_--
_-
_--
,
60 50
""L~
...,.""
40 30
0[,~
IE+3 20
i':
,
,
o.z
o.4
IE+2
o.o
the de~r~ of
t 10 '
~
o.~
o.s
0
~.o
pcnclrafionf
Fig. 2. Effect of the degree of penetration on the separation factor and the total gas permeation resistance of composite membrane for the separation of hydrogen and nitrogen, L 1 = 1 × 10 -~ cm, e 2 = 1 X 10 -4.
G. He et al. / Journal of Membrane Science 118 (1996) 1 - 7
5
:~0 ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
\
@
f~0 0 .
50 ~
• \
50 ~ ':i?\.
!
40 i ~ ~r2
s 2 = I x l O -6
........fffio.4
:)\
..... ,~i
:':"}:.. 5 : . ".._
~.5
.... )I(, f'~-l.0
3O 2O
10 0E+0
2E-4
4E-4
6E-4
8E-4
1E-3
the thickness o f the coating layer (cm)
0 0.0 O.2 O.4 O.6 0.8
Fig. 3. Effect of the thickness (L 1) of the coating layer at various degrees of penetration on the separation factor of composite membrane, for the separation of hydrogen and nitrogen, L2 = 1 × 10 -5 cm, if2 = 1 X 10 -4.
1.0
the degree of penetrationf Fig. 4. Effects of surface porosity (E 2) on the separation factor of a composite membrane at various degrees of penetration, L~ = 1 × 10 -4 cm, L2 = 1 × 10 -5 cm.
penetration is s h o w n in Fig. 3. It is seen that the influence of L 1 on m e m b r a n e separation factor is great and w h e n f ! s ' l a r g e r than 0.4, the separation factor decreases fast as L~ increases. The m e m b r a n e separation factor remains almost constant w h e n f = 0, h o w e v e r , very low and very close to the intrinsic separation factor o f P D M S material for H 2 / N 2 sepa-
ration. So it is important to control the degree o f penetration and the thickness o f the coating layer to obtain a high p e r f o r m a n c e m e m b r a n e . The deeper the coating material penetrates into the pores, the higher the m e m b r a n e separation factor is. M o r e o v e r
IE+5 o
J
o ~t~ m+4
- " i ~ t t y a ' o l ~ S2 -_.l x l 0 a +Nitro$m sa = I x l 0 "4 .~: N i t n n ~
s2 = Ix I0 "6
:.:. Hydrol~
s2 = Ix I0 -e
IE+3
O IE+2 0.0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
the degree of penetration f Fig. 5. Effects of surface porosity ( E 2 ) o n the total gas permeation resistance of a composite membrane at various degrees of penetration, L l = 1 X 10 -4 cm, L 2 = 1 X 10 -5 cm.
6
G. He et al./Journal of Membrane Science 118 (1996) 1-7
Table 2 Gas permeation properties with different concentration of the coating solution Concentration of coating
Permeability J (cm3/cm 2 s cmHg)
Separation factor
solution (%)
H2
N2
o~H~
4 0.5 4 0.4
1.12X10 -4 1.93 X 10 -4 8.87× 10 -5 1.07X 10 -4
1.95X 2.84X 1.79× 1.60X
10 -6 10 -6 10 -6 10 -6
57.4 68.0 49.6 66.9
centration of a coating solution is lower, the coating material penetrates the pores of the dense layer more easily and more deeply thus obtaining a larger f value, and the thickness of the coating layer becomes thinner. As a result, the membrane permeation flux and the membrane separation factor will be raised according to the previous analysis of the improved resistance model.
5. Conclusions the thinner the thickness of the coating layer is, higher the membrane separation factor is and higher the gas permeation flux is, because the permeation flux is inversely proportional to membrane thickness.
the the gas the
4.1.3. Effects of porosity of the dense layer at various degrees of penetration The effects of porosity (E 2) of the dense layer at various degrees of penetration on the membrane separation factor and total gas permeation resistance are shown in Figs. 4 and 5, respectively. It is found that when E2 is small, for example E2 1 X 10 - 6 , the effects of f on ce and the total gas permeation resistance are relatively small; when 62 is larger, a cannot reach a high value until f > 0.4. When f is great enough, for example f > 0.4, there is a very limited difference in total gas permeation resistance between a large e2 and a small e 2. A membrane with a smaller E2 value is therefore preferable; if E2 is large, f should be large enough to ensure a high separation factor for the membrane.
The improved resistance model describing the gas permeation process in composite membranes shows that the degree of penetration is the most important factor which influences the membrane separation properties. It is suggested that making the degree of penetration greater than 0.4 will provide high selective composite membranes. In the coating processes, "deep penetration with a thin coating" appears to be most favorable to ensure obtaining a membrane with both higher permeation flux and higher separation factor.
:
4.2. Experimental results Some experimental results are listed in Table 2 which show that coating with very lean coating solutions leads to higher membrane separation performances than coating with 4 wt% coating solutions. These phenomena are very promising. It is well known that increases in permeability are usually accompanied by a decrease in the membrane separation factor, however in our experiments, both the membrane permeabilities and the membrane separation factors were raised after coating with very lean coating solutions. We suggested that when the con-
6. List of symbols P
J
Q Rt
a
f A L r E2
R' M T
the intrinsic permeability coefficient of the polymeric material (cm 3 c m / c m z s cmHg) permeability of the composite membrane (cm3/cm 2 s cmHg) gas permeation flux throughout the composite membrane (cm3/s) the total gas permeation resistance throughout the composite membrane (cmHg s / c m 3) the membrane separation factor the degree of penetration membrane area (cm 2) the average thickness average radius of the pores in the dense layer (cm) porosity of the dense layer universal gas constant gas molecular weight temperature (K)
G. He et a l . / Journal of Membrane Science 118 (1996) 1 - 7
ro
temperature at standard state (K),
Po Pl Pp
pressure at standard state (cmHg) pressure of the feed side (cmHg) pressure of the permeate side (cmHg), p* = (pf+pp)/2po pressure drop between the feed and the permeate side (cmHg)
r* = ~ / L
Ap 6.1. Subscripts i,j 1 .....
5
gas component i or j represent reference regions defined in this paper to describe the structure of the composite membrane
References [1] J.M.S. Henis and M.K. Tripodi, Multicomponent membranes for gas separations, US Pat., 4, 230, 463, 1977.
7
[2] J.M.S. Henis and M.K. Tripodi, Composite hollow fiber membranes for gas permeation: The resistance model approach, J. Membrane Sci., 8 (1981) 233-246. [3] H.K. Lonsdale, The growth of membrane technology, J. Membrane Sci., l0 (1982) 81. [4] R.W. Baker, Membrane Separation System, Noyes Data Corporation, 1991. [5] K.K. Kimmerle, Analysis of gas permeation through composite membranes, J. Membrane Sci., 61 (1991) 1. [6] A.J. Ashworth, Relation between gas permselectivity and permeability in a bilayer composite membrane, J. Membrane Sci., 71 (1992) 169. [7] G. He, Polym. Mater. Sci. Eng. (in Chinese), 9(4) (1993) 97. [8] W. Dongliang Wang, Determination of surface dense layer structure parameters of the asymmetric membrane by gas permeation method, J. Membrane Sci., 52 (1990) 97. [9] T. Nakagawa, Gas separation technology and the industrial applications of membranes, in Fuji Technological System (in Japanese), Fuji, Tokyo, 1983.
Journal of Membrane Science 118 (1996) 1-7
An improved resistance model for gas permeation in composite membranes Gaohong He a,*, Xiangyang Huang b, Renxian Xu b, Baolin Zhu b a Dalian University of Technology, Department of Chemical Engineering, Dalian 116012, PR China b Dalian Institute of Chemical Physics, Chinese Academy of Sciences, P.O. Box 110, Dalian 116012, PR China
Received 9 October 1995; accepted 4 January 1996
Abstract An improved resistance model based on Henis-Tripodi's model for gas permeation in composite membranes has been established, in which the degree of penetration of the coating material into the defects or pores of the effective dense layer has been taken into account. The influences of the degree of penetration, the thickness of the coating layer and surface porosity of the dense layer on gas permeation resistance throughout the composite membrane and separation factor of the composite membrane have been calculated and analysed. Some experimental results have also been explained with this model. The model together with its corresponding coating method is useful for the improvement of membrane separation properties. Keywords: Gas permeation; Resistance model; Composite membrane; Degree of penetration; Permeation mechanism
1. Introduction A major breakthrough in the history of gas membrane separation was made by Henis and Tripodi [1,2] who developed composite membranes with acceptable permeability and very high permselectivity [3,4]. These found commercial applications in H 2 purification and recovery in ammonia production. Henis and Tripodi have also established a resistance model to explain the behavior of composite gas separation membranes [2]. The membrane consists of a porous asymmetric substrate of one polymer with a dense layer and a coating of another polymer - a second layer that is very thin and made by a nonselective and highly permeable material. The influ-
* Corresponding author.
ences of surface porosity of the dense layer and coating thickness on membrane separation properties have been studied by Henis and Tripodi with their model. In their work, Henis and Tripodi have drawn a further conclusion. They believed that when the coating material does not penetrate to the full depth of the pores, but penetrates to only 0.1 or 0.01% of that depth, the results are much the same [2]. This means that the composite membrane will have very high separation factor with a very low degree of penetration. This point is open to discussion. Kimmerle [5] and Ashworth [6] have done additional research work but they assumed that the coating materials penetrate and fill the pores of the dense layer. In our early research work, it was realized that the degree of penetration of the coating material into the defects or pores of the dense layer greatly influences the membrane separation properties [7].
0376-7388/96/$15.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved. P11S0376-7388(96)00023-3
2
G. He et al./Journal of Membrane Science 118 (1996) 1-7
In this paper, we have made a small modification to Henis and Tripodi's resistance model considering the degree of penetration and found an improved resistance model. We have calculated hydrogen and nitrogen separation properties with different degrees of penetration using the model developed.
2. Theory: the improved resistance model
2.1. Simplified description of the composite membrane The well-known Henis and Tripodi's electrical circuit analog [2] divide the composite membrane into three regions: the coating layer, the dense layer in substrate and the pores or defects in the dense layer filled with coating material. In our improved resistance model, the composite membrane is divided into five regions with the consideration of the degree of penetration. As shown in Fig. 1, these five regions are: 1. the coating layer; 2. the non-porous part of the dense layer without pores or defects; 3. the highly porous substrate region; 4. the part of defects or pores in the dense layer which is close to the coating layer and filled with the coating material; 5. the remaining part of defects or pores in the dense layer that is close to the porous substrate region and not filled with the coating material. These regions are labelled as 1, 2, 3, 4 and 5 in the corresponding order to Fig. 1. The average thickness and gas permeation resistance of each region are L 1, L2, L3, L4, Ls, RI, R2, R3, R 4 and R 5, respectively.
2.2. Assumptions The following assumptions were made for the mathematical analysis of the gas permeation in the composite membranes described above: 1. the coating layer is homogeneous and non-porous; 2. there are only one dimensional diffusion or flow in the composite membrane; 3. the pores and defects in the dense layer are circular and have uniform radius and length, the length of the pores is equal to the thickness of the dense layer; 4. the radius of the pores in the dense layer is small so that the gas flow through the 5th region is Knudsen flow; 5. the highly porous substrate region has no resistance for gases so that R 3 = 0.
2.3. Definition of the degree of penetration The average thickness L 4 represents the part in the pores in the dense layer which is filled with coating material, while the average thickness L 2 represents the length of the pores in the dense layer. Thus, the degree of penetration of the coating material into the dense layer is defined as:
s=
L4
where L a < L 2 , L 2 = L * + L 5 a n d O < f < l .
2.4. Gas permeation properties According to the mechanism of gas flow through each region, the resistance to permeate flow for each region can be expressed as follows [7]: L1 R, = P, A
f Lz
_t: T
Fig. 1. Schematic representation of a composite membrane and the corresponding electrical circuit analogue.
(1)
R2
L2 P2A( 1 _ e2 )
(2)
(3)
fL2 R4-- P,A~-----~
(4)
3(1 - f ) Lzp o R5 = 4r2T° AEz~/ZR,/rrTM
(5)
G. He et al. / Journal of Membrane Science 118 (1996) 1-7
Thus, the total gas permeation resistance, according to the improved resistance model (shown in Fig. 1) is defined as: Rt = R1 +
1
1 + - R2 R4 + R5
(6)
The gas permeation flux throughout the membrane can be calculated by equation: Ap Q -
Rt
(7)
where Ap is the pressure drop across the membrane. The gas permeability throughout the membrane can also be calculated by equation:
3
fibers for at least 5 min. The other was carried out using a solution of 0 . 4 - 0 . 5 wt% silicone rubber and 0.04-0.05 wt% curing agent supplied in gasoline, and the bundles were first immersed into the 0 . 4 - 0 . 5 wt% coating solution for about 40 h, then a vacuum was applied inside the fibers for at least 5 min. All the coated bundles were then cured in air for 24 h at room temperature before use.
3.2. Apparatus and permeability measurement The apparatus consists of a gas cylinder, a pressure regulator, a separation module, pressure meters and a bubble flowmeter [8]. Bundles of hollow fibers were potted into the separator module and the permeate flows from the open end were measured at 25°C.
1 J = --
RtA
(8)
4. Results
The separation factor for components i and j in the gas mixture is:
4.1. Mathematical analysis of the improved resistance model
Rtj
a -
(9) Rti
Using Eq. (6) and Eq. (9), the influences of the degree of penetration, the thickness of coating layer and the porosity of the dense layer on the membrane separation properties can be calculated and analyzed.
3. Experimental
3.1. Membranes The asymmetric hollow fibers were spun by a d r y - w e t spinning procedure on a laboratory spinning apparatus. A spinning solution of 32 wt% polysulfone in complex solvents was used. After washing and drying, fibers of typical dimensions ( 5 2 0 / 3 1 0 /xm o . d . / i . d . ) were obtained. Bundles of 4 0 - 5 0 fibers each with a length of 25 cm were sealed by epoxy resin at one end. The bundles were then coated to form composite gas separation membranes by the vacuum method. Two kinds of coating procedure were performed. One kind o f coating was carried out using a solution of 4 wt% silicone rubber and 0.4 wt% curing agent supplied in gasoline outside the fibers of the bundle and vacuum inside the
The properties of PDMS coated polysulfone composite membranes via the degree of penetration have been calculated for the separation of binary H2/N 2 system using the improved resistance model. The following data were used for the calculation: PI(H2) = 3.9 × 10 - s cm 3 c r n / c m 2 s cmHg Pj(N 2) = 1.81 × 10 - s cm 3 c m / c m 2 s cmHg P2(H2)=1.3×10 9 cm 3 c m / c m 2 s c m H g P2(N2) = 1.8 × 10 -11 c m 3 c m / c m 2 s cmHg L 1 = 1 × 10 -4 ~ 1 × 1 0 -3 cm L 2 -- 1 × 10 -5 cm r 2 = 1.5 × 10 - 6 c m ~2 = 1 X 10 - 6 ~ 1 × 10 - 4 Po = 76 cmHg TO = 273.15 K A = 18.096 cm 2 Where Px indicates the permeability coefficient of gas H 2 or N 2 in PDMS material, P2 indicates the permeability coefficient of gas H 2 or N 2 in polysulfone. Permeability coefficients were obtained from the literature [9].
4.1.1. Effect of the degree of penetration f A ratio w is defined as:
O~f
w= - af-1
(10)
4
G. He et al./Journal of Membrane Science 118 (1996) 1-7
when f < 0.03, the total gas permeation resistance increases very rapidly; when 0.03 < f < 0.1, the total gas permeation resistance increases very slowly; when f > 0.1, the total gas permeation resistance tends to be a constant. In the case of slow moving gas N2: when f < 0.1, the total gas permeation resistance increases very rapidly; when 0.1 < f < 0.4, the total gas permeation resistance increases very slowly; when f > 0.4, the total gas permeation resistance also tends to be a constant. That is to say, when f < 0.4 the influence of f on the movement of slow gas is larger than that on the movement of fast gas, and when f is large enough the difference of the influences becomes small. The conclusion is therefore that only when f > 0.4 can separation factor c~ reach a high value, and a greater f value is beneficial to higher separation factor a and will not decrease the permeation flux of the composite membrane.
Table 1 Comparison c~y with af= 1 at different degrees of penetration Degree of penetration f
f = 0.01
f = 0.1
f = 1
Separation factor a~zz Ratio w (%)
7.04 14
28.28 57
48.87 100
where c~f is the separation factor when the degree of penetration is f (0 < f < 1), and ~/= ~ is the separation factor when the degree of penetration is 1, respectively. The defects or pores in the dense layer are completely filled with coating materials when f is equal to 1 as assumed by Henis and Tripodi. We have calculated c~/ when f = 0.01 and f = 0.1 and compared them with c~f=I. The results are shown in Table 1. It can be seen from Table 1 that the degree of penetration f plays a very important role in affecting the membrane separation properties. If f is very small, the separation factor cannot reach the maximum value c~f=1, which is given by Henis and Tripodi's resistance model. The influences of the degree penetration f on the total gas permeation resistance to H 2 and N 2 throughout the membrane and on the membrane separation factor a are shown in Fig. 2. It is shown that in the case of the permeation of the fast moving gas H2:
4.1.2. Effect of the thickness (L 1) of the coating layer at uarious degrees of penetration The effect of the thickness of the coating layer on the membrane separation factor at various degrees of
IE+5
_-
_--
_-
_--
,
60 50
""L~
...,.""
40 30
0[,~
IE+3 20
i':
,
,
o.z
o.4
IE+2
o.o
the de~r~ of
t 10 '
~
o.~
o.s
0
~.o
pcnclrafionf
Fig. 2. Effect of the degree of penetration on the separation factor and the total gas permeation resistance of composite membrane for the separation of hydrogen and nitrogen, L 1 = 1 × 10 -~ cm, e 2 = 1 X 10 -4.
G. He et al. / Journal of Membrane Science 118 (1996) 1 - 7
5
:~0 ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
\
@
f~0 0 .
50 ~
• \
50 ~ ':i?\.
!
40 i ~ ~r2
s 2 = I x l O -6
........fffio.4
:)\
..... ,~i
:':"}:.. 5 : . ".._
~.5
.... )I(, f'~-l.0
3O 2O
10 0E+0
2E-4
4E-4
6E-4
8E-4
1E-3
the thickness o f the coating layer (cm)
0 0.0 O.2 O.4 O.6 0.8
Fig. 3. Effect of the thickness (L 1) of the coating layer at various degrees of penetration on the separation factor of composite membrane, for the separation of hydrogen and nitrogen, L2 = 1 × 10 -5 cm, if2 = 1 X 10 -4.
1.0
the degree of penetrationf Fig. 4. Effects of surface porosity (E 2) on the separation factor of a composite membrane at various degrees of penetration, L~ = 1 × 10 -4 cm, L2 = 1 × 10 -5 cm.
penetration is s h o w n in Fig. 3. It is seen that the influence of L 1 on m e m b r a n e separation factor is great and w h e n f ! s ' l a r g e r than 0.4, the separation factor decreases fast as L~ increases. The m e m b r a n e separation factor remains almost constant w h e n f = 0, h o w e v e r , very low and very close to the intrinsic separation factor o f P D M S material for H 2 / N 2 sepa-
ration. So it is important to control the degree o f penetration and the thickness o f the coating layer to obtain a high p e r f o r m a n c e m e m b r a n e . The deeper the coating material penetrates into the pores, the higher the m e m b r a n e separation factor is. M o r e o v e r
IE+5 o
J
o ~t~ m+4
- " i ~ t t y a ' o l ~ S2 -_.l x l 0 a +Nitro$m sa = I x l 0 "4 .~: N i t n n ~
s2 = Ix I0 "6
:.:. Hydrol~
s2 = Ix I0 -e
IE+3
O IE+2 0.0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
the degree of penetration f Fig. 5. Effects of surface porosity ( E 2 ) o n the total gas permeation resistance of a composite membrane at various degrees of penetration, L l = 1 X 10 -4 cm, L 2 = 1 X 10 -5 cm.
6
G. He et al./Journal of Membrane Science 118 (1996) 1-7
Table 2 Gas permeation properties with different concentration of the coating solution Concentration of coating
Permeability J (cm3/cm 2 s cmHg)
Separation factor
solution (%)
H2
N2
o~H~
4 0.5 4 0.4
1.12X10 -4 1.93 X 10 -4 8.87× 10 -5 1.07X 10 -4
1.95X 2.84X 1.79× 1.60X
10 -6 10 -6 10 -6 10 -6
57.4 68.0 49.6 66.9
centration of a coating solution is lower, the coating material penetrates the pores of the dense layer more easily and more deeply thus obtaining a larger f value, and the thickness of the coating layer becomes thinner. As a result, the membrane permeation flux and the membrane separation factor will be raised according to the previous analysis of the improved resistance model.
5. Conclusions the thinner the thickness of the coating layer is, higher the membrane separation factor is and higher the gas permeation flux is, because the permeation flux is inversely proportional to membrane thickness.
the the gas the
4.1.3. Effects of porosity of the dense layer at various degrees of penetration The effects of porosity (E 2) of the dense layer at various degrees of penetration on the membrane separation factor and total gas permeation resistance are shown in Figs. 4 and 5, respectively. It is found that when E2 is small, for example E2 1 X 10 - 6 , the effects of f on ce and the total gas permeation resistance are relatively small; when 62 is larger, a cannot reach a high value until f > 0.4. When f is great enough, for example f > 0.4, there is a very limited difference in total gas permeation resistance between a large e2 and a small e 2. A membrane with a smaller E2 value is therefore preferable; if E2 is large, f should be large enough to ensure a high separation factor for the membrane.
The improved resistance model describing the gas permeation process in composite membranes shows that the degree of penetration is the most important factor which influences the membrane separation properties. It is suggested that making the degree of penetration greater than 0.4 will provide high selective composite membranes. In the coating processes, "deep penetration with a thin coating" appears to be most favorable to ensure obtaining a membrane with both higher permeation flux and higher separation factor.
:
4.2. Experimental results Some experimental results are listed in Table 2 which show that coating with very lean coating solutions leads to higher membrane separation performances than coating with 4 wt% coating solutions. These phenomena are very promising. It is well known that increases in permeability are usually accompanied by a decrease in the membrane separation factor, however in our experiments, both the membrane permeabilities and the membrane separation factors were raised after coating with very lean coating solutions. We suggested that when the con-
6. List of symbols P
J
Q Rt
a
f A L r E2
R' M T
the intrinsic permeability coefficient of the polymeric material (cm 3 c m / c m z s cmHg) permeability of the composite membrane (cm3/cm 2 s cmHg) gas permeation flux throughout the composite membrane (cm3/s) the total gas permeation resistance throughout the composite membrane (cmHg s / c m 3) the membrane separation factor the degree of penetration membrane area (cm 2) the average thickness average radius of the pores in the dense layer (cm) porosity of the dense layer universal gas constant gas molecular weight temperature (K)
G. He et a l . / Journal of Membrane Science 118 (1996) 1 - 7
ro
temperature at standard state (K),
Po Pl Pp
pressure at standard state (cmHg) pressure of the feed side (cmHg) pressure of the permeate side (cmHg), p* = (pf+pp)/2po pressure drop between the feed and the permeate side (cmHg)
r* = ~ / L
Ap 6.1. Subscripts i,j 1 .....
5
gas component i or j represent reference regions defined in this paper to describe the structure of the composite membrane
References [1] J.M.S. Henis and M.K. Tripodi, Multicomponent membranes for gas separations, US Pat., 4, 230, 463, 1977.
7
[2] J.M.S. Henis and M.K. Tripodi, Composite hollow fiber membranes for gas permeation: The resistance model approach, J. Membrane Sci., 8 (1981) 233-246. [3] H.K. Lonsdale, The growth of membrane technology, J. Membrane Sci., l0 (1982) 81. [4] R.W. Baker, Membrane Separation System, Noyes Data Corporation, 1991. [5] K.K. Kimmerle, Analysis of gas permeation through composite membranes, J. Membrane Sci., 61 (1991) 1. [6] A.J. Ashworth, Relation between gas permselectivity and permeability in a bilayer composite membrane, J. Membrane Sci., 71 (1992) 169. [7] G. He, Polym. Mater. Sci. Eng. (in Chinese), 9(4) (1993) 97. [8] W. Dongliang Wang, Determination of surface dense layer structure parameters of the asymmetric membrane by gas permeation method, J. Membrane Sci., 52 (1990) 97. [9] T. Nakagawa, Gas separation technology and the industrial applications of membranes, in Fuji Technological System (in Japanese), Fuji, Tokyo, 1983.