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Hydraulic permeation of NaCl solution through sulfonated polysulfone-polyvinyl alcohol polysulfone composite reverse osmosis membrane
Polymer Testing 14 (1995) 415-424 0 1995 Elsevier Science Limited Printed in Malta. All rights reserved 0142-9418(94)00032-3
0142-9418/95/$9.x)
DATA INTERPRETATION Hydraulic Permeation of NaCl Solution Tbrou b Sulfonated Polysulfone-Pol vinyl Alcohol olysuptone Composite Reverse B smosis Mem %rane Mu-Hoe
Yang
Department of Chemical Engineering, Kao Yuan Junior College of Technology & Commerce, Kaohsiung County, Taiwan 82101, Republic of China (Received 27 October 1994; accepted 14 November 1994)
ABSTRACT The hydraulic permeation of NaCl solution through sulfonated polysulfone-polyvinyl alcohol/poly&one
composite reverse osmosis membrane was systematically
investigated. It was found that the transport of water in a sulfonated polysulfonepolyvinyl alcohol/polysulfone composite reverse osmosis membrane follows the modified solution d@iion
equation developed by Yang and Chu. Moreover, the
equation between salt rejection and applied pressure was proposed for describing the hydraulic permeation of salt solution through a sulfonated polysulfone-polyvinyl alcohol/polysulfone composite membrane. The salt rejection was found to fit the greater part of separation transport mechanism. The experimental data and the salt
rejection equation appear to be in excellent agreement.
INTRODUCTION Membrane separation provides a simple, energy-efficient way to remove undesirable components from feed and product streams in many chemical engineering processes l 4 Since the development of the Loeb-Sourirajan7 type membrane at UCLA, USA, many polymer materials have emerged as potential materials for reverse osmosis membranes. The transport properties of sulfonated polysulfone-polyvinyl alcohol composite reverse osmosis membrane were investigated and reported in an earlier study.’ In our earlier papers, ‘-lo the modified solution diffusion equation was proposed for describing the relationship between water flux and applied pressure. However, it lacked the related equation between salt 415
Mu- Hoe Yang
416
rejection and applied pressure for the swollen membrane separation process. The aim of this study is two-fold: firstly, to understand what the rejection characteristics are for various applied pressures and to find a salt rejection equation to describe the relationship between salt rejection and applied pressure of the swollen membrane. Secondly, it will be useful to test the salt rejection equation to see how NaCl presence in the solution can be separated by this composite membrane. Hopefully this study will give more understanding of the swollen membrane property and in turn, help to find the transport parameters for a desired membrane separation purpose.
EXPERIMENTAL The materials, preparation of membranes and permeation experimental procedure, were the same as those employed in our previous paper.* The heat-treatment conditions employed in this study are listed in Table 1. The testing apparatus shown in Fig. 1. The experiment was designed to run two experiments at different pressure and flow rates simultaneously.
THEORY The modified solution was employed in the membrane. According given by the following
Preparation Membrane no.
M-l M-2 M-3 M-4 M-5
diffusion equation developed by Yang and Chug,” analysis of the water transport through a swollen to the model, the water flux (J,,,) of a membrane is equations:
Conditions SPSf/PVA ratio
4i2 313 214 115 O/6
TABLE 1 of Different SPSf-PVA/PSf Overall polymer concentration
6.0 wt% 6.0 wt% 6.0 wt% 60 wt% 6.0 wt%
Composite Membranes Heat-treatment Temperature
Time
120°C 120°C 120°C 120°C 120°C
4h 4h 4h 4h 4h
of NaCl solution
Hydraulic permeation
417
1 I
Fig. 1. The flow chart of permeation
constant-pressure
testing. (1) Feed tank; (2) constant-flow pump; (3) pump; (4) pressure gauge; (5) test cell; (6) conductivity detector; (7) permeate; (8) needle valve; (9) concentrate out.
b&wKvJP AX,,,V;,‘:(l+
bAP)
--
Ea
RT
(2)
(3)
Vw,l= Lo/U + bAP)
(4)
where J, is water flux, litres/m’h; D, is mutual diffusion coefficient, cm2/s; AP is PO- PI, Pa; b is compressive coefficient, l/MPa; AX,,, is dry thickness of the membrane, cm; V,,, is the volume of dry membrane material, cm3/cm3. The salt flux (JJ of a membrane is given by the following equation:4
(5) where J, is flux of salt, litres/m2h; D, is diffusivity of salt, cm2/s; K, is partition coefficient of salt, cm3/cm 3; AC,= Cg-Cl; AX1 is the thickness of the membrane, cm; P, (= D,K,) is the permeation coefficient of salt on
Mu-Hoe
418
Yang
the membrane, cm2/s; Ci is the concentration of the salt at the upstream, g/cm3; Cgl is the concentration of the salt at the downstream, g/cm3. The salt rejection (RJ of the membrane is defined by”
For the swollen membrane AP=O, then” VJ
v,jry= u(:* a;*a;
= wp.0 =
v-
113. P.0
j,J- 113. P.0
jr,“3
(7)
where V, is the volume of dry membrane and water; Vdry is the volume of dry membrane; a:, I.$, cc; represent the linear deformation factor in X-axis Y-axis and Z-axis; a: = AXx.o/AXx.xd,,,, aE!= AXY.o/AXY.~dry, ct;= AXz.o/AXz.Xdty . AP is applied pressure on the swollen membrane as Fig. 2. Because the swollen membrane in Y-axis and Z-axis are fixed, the change of the swollen membrane is only in the X-axis direction. Therefore
v,/v,,,=a;~a;v.; = l/1/,, 1 =c(,
1 . j,r l/3 ’ VP;;/3 P.0
(8)
where V, is the volume of dry membrane and water at AP condition. Substitution of eqn (8) into eqn (7) gives
cc; = v;,‘o”/vP.1 Because a,’ = AXI/AXdry
(9)
Hydraulic
permeation
of NaCi solution
419
AP
;;o+(-prgg X
dry state, V&
swollen state, VO
swollen state, Vf
Fig. 2. The changes
of swollen membrane
at various conditions.
Hence
AX I = (Vi!: VP,1 )AX,ry Substitution
(10)
of eqn (10) into eqn (7) gives
(11) Hence, according to eqn. (1 I), the reciprocal of salt rejection is proportional to the reciprocal of applied pressure across the swollen membrane.
RESULTS
AND DISCUSSION
Test of the modified solution diffusion equation
The effects of the applied pressure, l/(AP- An), on the water flux, l/J,,,, through different sulfonated polysulfone-polyvinyl alcohol/polysulfone (SPSf-PVA/PSf) composite membranes at 3O”C, prepared by heat-treatment at 120°C for 4 h, is shown in Fig. 3. According to eqn (3) a straight line should result between the reciprocal of the water flux and the reciprocal of the applied pressure. The l/JW dependence of the l/(AP- An) for different SPSf-PVA/PSf membranes is given in Fig. 3, which illustrates for those cases that a straight line exists between reciprocal of the water flux and the reciprocal of the applied pressure, where the slope is
Mu-Hoe Yang
420 80r
1 /(A
P-An)
@Pa-')
Fig. 3. Reciprocal relationship water flux and applied pressure in the composite membrane at 30°C. Overall polymer concentration, 6.0wt%; heat-treatment, 120°C for 4h, feed solution, 0.35 % NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (0) l/S, (A) O/6.
AX,,, V~!~/(bDW/VW,,)and the intercept is AXdryVz!,"/(D, VW,,). From this dependence D, and b were evaluated by linear regression analysis of the data points and are listed in Table 2. As shown in Table 2, the value of D, increased with increase in the ratio of SPSf-PVA/PSf. The diffusivity of water increased with increase in the ratio of SPSfPVA/PSf. TABLE 2
The Transport
Membrane no.
Parameters Determined by Using the Modified Solution Diffusion Equation and the Salt Rejection Equation
(lIMPa)
M-l M-2 M-3 M-4 M-5
Water
b value x Id
7.96 8.21 64.9 46.7 40.0
D, x 1OR (cm’/s)
8.50 5.98 4.64 4.30 3.03
Salt Ea (kJ/mol)
P, x IO’”
21.6 22.1 25.0 25.3 25.6
1.50 1.87 6.64 9.42 36.6
(cm’ls)
Ea (ldjmol)
26.2 29.2 37.4 37.9 42.7
Hydraulic permeation
-3 c
of NaCI solution
421
-11.
S 8
-12.
ri z
-13.
3 -14
t
_,S----J-3.0
3.1
3.2
1
HO3
3.3
3.4
a
3.5
(K-‘)
r Fig.4. Temperature dependence of the ln(J,) for water through the composite membranes. Overall polymer concentration, 6.0wt%; heat-treatment, 120°C for 4 h; feed solution, 0.35% NaCl aqueous solution; SPSfjPVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (0) l/5, (A) O/6.
The mutual diffusion Arrhenius equation
coefficient D, is expressed
D, = D,, exp( - Ea/RT)
by the following
u-3
where D,, represents pre-exponential factor; Ea represents apparent activation energy, kJ/mol; and R represents the gas constant, 8.314 J/g mol K. The temperature dependence of the h&I.,,) for different swollen SPSfPVA/PSf membranes is given in Fig. 4. As shown in Fig. 4, an Arrheniustype dependence of ln(.I,) on temperature is observed. From this dependence apparent activation energies were evaluated by linear regression analysis of the data points and are shown in Table 2. The data in Table 2 are calculated from the slope of the straight lines in Fig. 4. As shown in Table 2, the apparent activation energy of the water diffusivity decreased with increasing ratio of SPSf-PVA/PSf. Test of the salt rejection equation
The effects of the applied pressure, l/(AP-AZ), on the salt rejection, l/Rs, through different SPSf-PVA/PSf membranes at 30°C prepared by heat-
422
Mu-Hoe Yang
treatment at 120°C for 4 h, are shown in Fig. 4. According to eqn (ll), a straight line should give between the reciprocal of the salt rejection and the reciprocal of the applied pressure. The l/k dependence of the l/(AP- An) for different SPSf-PVA/PSf membranes is given in Fig. 5 which illustrates for those cases that a straight line exists between the reciprocal of the water flux and the reciprocal of the applied pressure, where the slope is D,K,V,,J(bD,I/,,J and the intercept is 1 +D,K,/(D,V,,,). From this dependence D,K, was evaluated by linear regression analysis of the data points and values are listed in Table 2. As shown in Table 2, the permeability of salt decreased with increasing ratio of SPSf-PVA/PSf. The permeation coefficient P,( =D,K,) is expressed by the following Arrhenius equation P, = P,, exp( - Eu/R T)
(13)
where P,, represents pre-exponential factor. The temperature dependence of the ln(P,) (=ln(D,K,)) for different swollen SPSf-PVA/PSf membranes is given in Fig. 6. As shown in Fig. 6, an Arrhenius-type dependence of ln(Ps) on temperature is observed. From this, dependence of the apparent activation energies were evaluated by linear regression analysis of the data points and are shown in Table 2. The data in Table 2 were calculated from
0.0’ a ’ * ’ ’ ’ ’ ’ * ’ * 1 ! 0.0 0.2 0.4 0.6 0.8- 1.0 I /(A
P-&n)
(ifPa_‘)
Fig. 5. Reciprocal relationship salt rejection and applied pressure in the composite membrane at 30°C. Overall polymer concentration, 6.0 wt%; heat-treatment, 120°C for 4 h, feed solution, 0.35% NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (n) l/5, (A) O/6.
Hydraulic permeation of NaCl solution
423
\
$
-20
*
-21
.
-22
-
e 4 i
-2J-----.O
3.1
3.2
3.3
ixrd
3.4
3 i
(K-‘)
Fig. 6. Temperature
dependence of the In(D,K,) for NaCl through the composite membrane. Overall polymer concentration, 6*0wt%; heat-treatment, 120°C for 4 h; feed solution, 0.35% NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (a) l/5, (A) 016.
the slope of the straight lines in Fig. 5. The apparent activation energy decreased with increasing ratio of SPSf-PVA/PSf.
CONCLUSION A composite membrane for reverse osmosis was prepared from sulfonated polysulfone and polyvinyl alcohol with polysulfone as the substrate. The equation between salt rejection and applied pressure was proposed to describe the salt rejection in terms of the applied pressure on the SPSf-PVA/PSf composite membrane. The data and the salt rejection equation appear to be in excellent agreement, indicating very good utility of the salt rejection equation in analysis data for the swollen membranewater system. The diffusivity for water, calculated by these experimental conditions, increased with increasing ratio of SPSf/PVA. The permeability for salt decreased with increasing ratio of SPSf/PVA. The apparent activation energy for water diffusivity and salt permeability decreased with increasing ratio of SPSf/PVA. The salt rejection equation employed in this paper was reasonable for the purpose of describing the relationship between the salt rejection and
the applied pressure. It was found that a linear relationship exists between the reciprocal of salt rejection and the reciprocal of applied pressure. Its use makes it convenient to calculate transport parameters for the hydraulic permeation of NaCl solution through the SPSf-PVA/SPSf membrane.
ACKNOWLEDGEMENTS The author would like to acknowledge financial support of this study by the National Science Council of the Republic of China. The author extends special thanks to Professor T. J. Chu, Professor J. H. Wang, and Professor J. F. Kuo for their helpful discussions and constructive criticism.
REFERENCES 1. 2, 3. 4. 5.
Applegate, L. E., Chem. Eng. Jun., 11 (1984) 64. Soltanieh, M. & Gill, W. N., Chem. Eny. Commun., 12 ( 198 1) 279. Chang, H. N., Desalination, 42 (1982) 63. Peter, S., Hese, N. & Stefan, R., Desalination, 19 (1976) 161. Mulder, M. H. V., Hendrikman, J. O., Wijmans, J. G. & Smolders, C. C., J.
Appl. Polym. Sci., 30 (1985) 805. 6. Reinhart, C. T. & Peppas, N. A., J. Mrmbr. Sci., 18 (1984) 805. 7. Loeb, S. & Sourirajan, S., Adv. Chem. Ser., 38 (1962) 117.
8. 9. 10. 11.
Yang, M. Yang, M. Yang, M. Eisenberg,
H. & Chu, T. J., Sep. Sci. Tech., 28(6) (1993) 1315. H. & Chu, T. J., Polym. Test., 12( 1) (1993) 3. H. & Chu, T. J., Polym. Test., 12(2) (1993) 97. T. N. & Joe Middlebrooks E., In Reverse Osmosis Treatment qf Drinking Water, Butterworth Publishers Press, Stoneham, MA, 1986, Ch. I, p. 6. 12. Flory, P. J., In Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York, 1953, Ch. XIII, p. 578.
0142-9418/95/$9.x)
DATA INTERPRETATION Hydraulic Permeation of NaCl Solution Tbrou b Sulfonated Polysulfone-Pol vinyl Alcohol olysuptone Composite Reverse B smosis Mem %rane Mu-Hoe
Yang
Department of Chemical Engineering, Kao Yuan Junior College of Technology & Commerce, Kaohsiung County, Taiwan 82101, Republic of China (Received 27 October 1994; accepted 14 November 1994)
ABSTRACT The hydraulic permeation of NaCl solution through sulfonated polysulfone-polyvinyl alcohol/poly&one
composite reverse osmosis membrane was systematically
investigated. It was found that the transport of water in a sulfonated polysulfonepolyvinyl alcohol/polysulfone composite reverse osmosis membrane follows the modified solution d@iion
equation developed by Yang and Chu. Moreover, the
equation between salt rejection and applied pressure was proposed for describing the hydraulic permeation of salt solution through a sulfonated polysulfone-polyvinyl alcohol/polysulfone composite membrane. The salt rejection was found to fit the greater part of separation transport mechanism. The experimental data and the salt
rejection equation appear to be in excellent agreement.
INTRODUCTION Membrane separation provides a simple, energy-efficient way to remove undesirable components from feed and product streams in many chemical engineering processes l 4 Since the development of the Loeb-Sourirajan7 type membrane at UCLA, USA, many polymer materials have emerged as potential materials for reverse osmosis membranes. The transport properties of sulfonated polysulfone-polyvinyl alcohol composite reverse osmosis membrane were investigated and reported in an earlier study.’ In our earlier papers, ‘-lo the modified solution diffusion equation was proposed for describing the relationship between water flux and applied pressure. However, it lacked the related equation between salt 415
Mu- Hoe Yang
416
rejection and applied pressure for the swollen membrane separation process. The aim of this study is two-fold: firstly, to understand what the rejection characteristics are for various applied pressures and to find a salt rejection equation to describe the relationship between salt rejection and applied pressure of the swollen membrane. Secondly, it will be useful to test the salt rejection equation to see how NaCl presence in the solution can be separated by this composite membrane. Hopefully this study will give more understanding of the swollen membrane property and in turn, help to find the transport parameters for a desired membrane separation purpose.
EXPERIMENTAL The materials, preparation of membranes and permeation experimental procedure, were the same as those employed in our previous paper.* The heat-treatment conditions employed in this study are listed in Table 1. The testing apparatus shown in Fig. 1. The experiment was designed to run two experiments at different pressure and flow rates simultaneously.
THEORY The modified solution was employed in the membrane. According given by the following
Preparation Membrane no.
M-l M-2 M-3 M-4 M-5
diffusion equation developed by Yang and Chug,” analysis of the water transport through a swollen to the model, the water flux (J,,,) of a membrane is equations:
Conditions SPSf/PVA ratio
4i2 313 214 115 O/6
TABLE 1 of Different SPSf-PVA/PSf Overall polymer concentration
6.0 wt% 6.0 wt% 6.0 wt% 60 wt% 6.0 wt%
Composite Membranes Heat-treatment Temperature
Time
120°C 120°C 120°C 120°C 120°C
4h 4h 4h 4h 4h
of NaCl solution
Hydraulic permeation
417
1 I
Fig. 1. The flow chart of permeation
constant-pressure
testing. (1) Feed tank; (2) constant-flow pump; (3) pump; (4) pressure gauge; (5) test cell; (6) conductivity detector; (7) permeate; (8) needle valve; (9) concentrate out.
b&wKvJP AX,,,V;,‘:(l+
bAP)
--
Ea
RT
(2)
(3)
Vw,l= Lo/U + bAP)
(4)
where J, is water flux, litres/m’h; D, is mutual diffusion coefficient, cm2/s; AP is PO- PI, Pa; b is compressive coefficient, l/MPa; AX,,, is dry thickness of the membrane, cm; V,,, is the volume of dry membrane material, cm3/cm3. The salt flux (JJ of a membrane is given by the following equation:4
(5) where J, is flux of salt, litres/m2h; D, is diffusivity of salt, cm2/s; K, is partition coefficient of salt, cm3/cm 3; AC,= Cg-Cl; AX1 is the thickness of the membrane, cm; P, (= D,K,) is the permeation coefficient of salt on
Mu-Hoe
418
Yang
the membrane, cm2/s; Ci is the concentration of the salt at the upstream, g/cm3; Cgl is the concentration of the salt at the downstream, g/cm3. The salt rejection (RJ of the membrane is defined by”
For the swollen membrane AP=O, then” VJ
v,jry= u(:* a;*a;
= wp.0 =
v-
113. P.0
j,J- 113. P.0
jr,“3
(7)
where V, is the volume of dry membrane and water; Vdry is the volume of dry membrane; a:, I.$, cc; represent the linear deformation factor in X-axis Y-axis and Z-axis; a: = AXx.o/AXx.xd,,,, aE!= AXY.o/AXY.~dry, ct;= AXz.o/AXz.Xdty . AP is applied pressure on the swollen membrane as Fig. 2. Because the swollen membrane in Y-axis and Z-axis are fixed, the change of the swollen membrane is only in the X-axis direction. Therefore
v,/v,,,=a;~a;v.; = l/1/,, 1 =c(,
1 . j,r l/3 ’ VP;;/3 P.0
(8)
where V, is the volume of dry membrane and water at AP condition. Substitution of eqn (8) into eqn (7) gives
cc; = v;,‘o”/vP.1 Because a,’ = AXI/AXdry
(9)
Hydraulic
permeation
of NaCi solution
419
AP
;;o+(-prgg X
dry state, V&
swollen state, VO
swollen state, Vf
Fig. 2. The changes
of swollen membrane
at various conditions.
Hence
AX I = (Vi!: VP,1 )AX,ry Substitution
(10)
of eqn (10) into eqn (7) gives
(11) Hence, according to eqn. (1 I), the reciprocal of salt rejection is proportional to the reciprocal of applied pressure across the swollen membrane.
RESULTS
AND DISCUSSION
Test of the modified solution diffusion equation
The effects of the applied pressure, l/(AP- An), on the water flux, l/J,,,, through different sulfonated polysulfone-polyvinyl alcohol/polysulfone (SPSf-PVA/PSf) composite membranes at 3O”C, prepared by heat-treatment at 120°C for 4 h, is shown in Fig. 3. According to eqn (3) a straight line should result between the reciprocal of the water flux and the reciprocal of the applied pressure. The l/JW dependence of the l/(AP- An) for different SPSf-PVA/PSf membranes is given in Fig. 3, which illustrates for those cases that a straight line exists between reciprocal of the water flux and the reciprocal of the applied pressure, where the slope is
Mu-Hoe Yang
420 80r
1 /(A
P-An)
@Pa-')
Fig. 3. Reciprocal relationship water flux and applied pressure in the composite membrane at 30°C. Overall polymer concentration, 6.0wt%; heat-treatment, 120°C for 4h, feed solution, 0.35 % NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (0) l/S, (A) O/6.
AX,,, V~!~/(bDW/VW,,)and the intercept is AXdryVz!,"/(D, VW,,). From this dependence D, and b were evaluated by linear regression analysis of the data points and are listed in Table 2. As shown in Table 2, the value of D, increased with increase in the ratio of SPSf-PVA/PSf. The diffusivity of water increased with increase in the ratio of SPSfPVA/PSf. TABLE 2
The Transport
Membrane no.
Parameters Determined by Using the Modified Solution Diffusion Equation and the Salt Rejection Equation
(lIMPa)
M-l M-2 M-3 M-4 M-5
Water
b value x Id
7.96 8.21 64.9 46.7 40.0
D, x 1OR (cm’/s)
8.50 5.98 4.64 4.30 3.03
Salt Ea (kJ/mol)
P, x IO’”
21.6 22.1 25.0 25.3 25.6
1.50 1.87 6.64 9.42 36.6
(cm’ls)
Ea (ldjmol)
26.2 29.2 37.4 37.9 42.7
Hydraulic permeation
-3 c
of NaCI solution
421
-11.
S 8
-12.
ri z
-13.
3 -14
t
_,S----J-3.0
3.1
3.2
1
HO3
3.3
3.4
a
3.5
(K-‘)
r Fig.4. Temperature dependence of the ln(J,) for water through the composite membranes. Overall polymer concentration, 6.0wt%; heat-treatment, 120°C for 4 h; feed solution, 0.35% NaCl aqueous solution; SPSfjPVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (0) l/5, (A) O/6.
The mutual diffusion Arrhenius equation
coefficient D, is expressed
D, = D,, exp( - Ea/RT)
by the following
u-3
where D,, represents pre-exponential factor; Ea represents apparent activation energy, kJ/mol; and R represents the gas constant, 8.314 J/g mol K. The temperature dependence of the h&I.,,) for different swollen SPSfPVA/PSf membranes is given in Fig. 4. As shown in Fig. 4, an Arrheniustype dependence of ln(.I,) on temperature is observed. From this dependence apparent activation energies were evaluated by linear regression analysis of the data points and are shown in Table 2. The data in Table 2 are calculated from the slope of the straight lines in Fig. 4. As shown in Table 2, the apparent activation energy of the water diffusivity decreased with increasing ratio of SPSf-PVA/PSf. Test of the salt rejection equation
The effects of the applied pressure, l/(AP-AZ), on the salt rejection, l/Rs, through different SPSf-PVA/PSf membranes at 30°C prepared by heat-
422
Mu-Hoe Yang
treatment at 120°C for 4 h, are shown in Fig. 4. According to eqn (ll), a straight line should give between the reciprocal of the salt rejection and the reciprocal of the applied pressure. The l/k dependence of the l/(AP- An) for different SPSf-PVA/PSf membranes is given in Fig. 5 which illustrates for those cases that a straight line exists between the reciprocal of the water flux and the reciprocal of the applied pressure, where the slope is D,K,V,,J(bD,I/,,J and the intercept is 1 +D,K,/(D,V,,,). From this dependence D,K, was evaluated by linear regression analysis of the data points and values are listed in Table 2. As shown in Table 2, the permeability of salt decreased with increasing ratio of SPSf-PVA/PSf. The permeation coefficient P,( =D,K,) is expressed by the following Arrhenius equation P, = P,, exp( - Eu/R T)
(13)
where P,, represents pre-exponential factor. The temperature dependence of the ln(P,) (=ln(D,K,)) for different swollen SPSf-PVA/PSf membranes is given in Fig. 6. As shown in Fig. 6, an Arrhenius-type dependence of ln(Ps) on temperature is observed. From this, dependence of the apparent activation energies were evaluated by linear regression analysis of the data points and are shown in Table 2. The data in Table 2 were calculated from
0.0’ a ’ * ’ ’ ’ ’ ’ * ’ * 1 ! 0.0 0.2 0.4 0.6 0.8- 1.0 I /(A
P-&n)
(ifPa_‘)
Fig. 5. Reciprocal relationship salt rejection and applied pressure in the composite membrane at 30°C. Overall polymer concentration, 6.0 wt%; heat-treatment, 120°C for 4 h, feed solution, 0.35% NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (n) l/5, (A) O/6.
Hydraulic permeation of NaCl solution
423
\
$
-20
*
-21
.
-22
-
e 4 i
-2J-----.O
3.1
3.2
3.3
ixrd
3.4
3 i
(K-‘)
Fig. 6. Temperature
dependence of the In(D,K,) for NaCl through the composite membrane. Overall polymer concentration, 6*0wt%; heat-treatment, 120°C for 4 h; feed solution, 0.35% NaCl aqueous solution; SPSf/PVA ratio: (m) 4/2, (0) 3/3, (0) 2/4, (a) l/5, (A) 016.
the slope of the straight lines in Fig. 5. The apparent activation energy decreased with increasing ratio of SPSf-PVA/PSf.
CONCLUSION A composite membrane for reverse osmosis was prepared from sulfonated polysulfone and polyvinyl alcohol with polysulfone as the substrate. The equation between salt rejection and applied pressure was proposed to describe the salt rejection in terms of the applied pressure on the SPSf-PVA/PSf composite membrane. The data and the salt rejection equation appear to be in excellent agreement, indicating very good utility of the salt rejection equation in analysis data for the swollen membranewater system. The diffusivity for water, calculated by these experimental conditions, increased with increasing ratio of SPSf/PVA. The permeability for salt decreased with increasing ratio of SPSf/PVA. The apparent activation energy for water diffusivity and salt permeability decreased with increasing ratio of SPSf/PVA. The salt rejection equation employed in this paper was reasonable for the purpose of describing the relationship between the salt rejection and
the applied pressure. It was found that a linear relationship exists between the reciprocal of salt rejection and the reciprocal of applied pressure. Its use makes it convenient to calculate transport parameters for the hydraulic permeation of NaCl solution through the SPSf-PVA/SPSf membrane.
ACKNOWLEDGEMENTS The author would like to acknowledge financial support of this study by the National Science Council of the Republic of China. The author extends special thanks to Professor T. J. Chu, Professor J. H. Wang, and Professor J. F. Kuo for their helpful discussions and constructive criticism.
REFERENCES 1. 2, 3. 4. 5.
Applegate, L. E., Chem. Eng. Jun., 11 (1984) 64. Soltanieh, M. & Gill, W. N., Chem. Eny. Commun., 12 ( 198 1) 279. Chang, H. N., Desalination, 42 (1982) 63. Peter, S., Hese, N. & Stefan, R., Desalination, 19 (1976) 161. Mulder, M. H. V., Hendrikman, J. O., Wijmans, J. G. & Smolders, C. C., J.
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