- Email: [email protected]
Modeling of reverse osmosis systems
DESALINATION ELSEVIER
Desalination 158 (2003) 323-329 www.elsevier.com/locate/desal
Modeling of reverse osmosis systems Abdul Sattar Kahdim”, Saleh Ismail, Alaa’ Abdulrazaq Jassimb* “National Committee for Technology Transfer, Baghdad Iraq ‘Department of Chemical Engineering, University of Basrah, Box 1458, Ashaar, Basrah, Iraq email: noor. b@uruklink net
Received 8 December 2002; accepted 27 February 2003
Abstract The BasrahUniversity reverse osmosis plant (BURO) is an experimental unit built to provide college laboratories with desalted water. The plant has a total capacity of 9 m% and is composed of three independent lines. The aim of this study is to develop a theoretical model to predict the performance of reverse osmosis (RO) systems and to compare the theoretical results with experimental values obtained from the pilot plant. The study was conducted using two types of membranes, viz. Saehane, type KE8040BE of South Korean origin and TFC-Koch system membranes model 8822XR of American origin to test the theoretical model that is predicted based on the generalized transport equation system involving solvent (water) and anynumberof ions (solute) that is dissolved inwater using the Kimura-Sourhajan analysis. The main objective of this work can be specified in three steps as follows: (1) develop a computer program as a general model for any type of RO system, (2) predict plant performance as a function of time (8 months of operation), and (3) perform comparative studies on the performance of the two types of membranes specified. The recovery of Saehane membranes is larger than Koch membranes due to the difference in the effective area for both types of membranes whereas the salt passage of Koch was always lower than Saehane membranes for brackish water having TDS larger than 550 ppm. There is agreement between theoretical and experimental results. Keywora!x Reverse osmosis; Kimura-Sourirajan analysis
1. Introduction Reverse osmosis (RO) is widely used for the
separation of dissolved salts and substances in solution. The process consists of passing aqueous *Correspondingauthor.
solution under pressure through an appropriate
porous membrane and withdrawing the membrane permeate at atmospheric pressure and ambient temperature. The product is enriched in one or more constituents of the mixture, leaving a solution of higher concentration on the highpressure side of the membrane. Fig. 1 shows the
Presented at the European Conference on Desalination and the Environment: Fresh Waterfor All, Malta, 4-8 May 2003. European Desalination Society, International Water Association.
001 l-9164/03/$- See front matter 8 2003 Elsevier Science B.V. All rights reserved PII:SOOll-9164(03)00471-S
A.S. Kahdim et al. /Desalination
324
158 (2003) 323-329
Fiber glass (FRP) outer wrapping
FEED ONCENTHATE
Fig. 1. Direction of flow through the membrane.
direction of flow through the membranes. The process does not require heating of the membranes, and no phase change in product recovery is involved compared with other processes for production of desalted water, e.g., multi-effect and multi-stage flash (MSF) evaporation systems or freezing processes. The main contribution factor to the fast growth of RO is its inherent efficiency and simplicity as compared to other processes like MSF evaporation as it is carried out at ambient temperature, involves no change in phase, and it has comparatively few scaling and corrosion problems. Water type is considered as the cornerstone in the design of an RO system. Natural waters are usually grouped under two types: brackish, having a salt content of 1000-15000 mg/l, and seawater, >15,000 mg/l, based on their total salinity [ 11. There are two types of RO membranes available commercially, namely BURO and SWRO, which are currently used for desalination of all waters regardless of the wide variation in their chemical nature. Generally speaking, the selection of an RO membrane is critically dependent on two main factors: the first is water type, and the second is the desired recovery. As water flows through the membrane and salts are rejected, a boundary layer is formed near the membrane surface in which the salt concentration exceeds its value in the bulk solution leading to higher osmotic pressure. This is known as concentration polarization (CP). The effects of CP are: increasing osmotic pressure, reducing net driving pressure differ-
ential across the membrane, reducing product flow rate, and increasing scale formation. In order to get the same recovery with time; greater pressure should be applied. Fouling is another factor that affects the performance of the membranes; the performance of RO systems is limited by fouling and CP. Various methods have been proposed to minimize or reduce the effect of these two phenomena. They include feed treatment, chemically modifying the membrane surface and the use of fluid instabilities and turbulence [2-6]. Many theoretical models have been developed over the past decades [7-121 for RO membranes. In developing a theoretical model to predict the performance of RO membranes, one of the first things to consider is the choice of the transfer model describing the flux of water and salt through the membrane. In this work a mathematical model based on the Kimura-Sourirajan analysis [ 131was used to describe the flux of water and salt through the membrane. This model depends on the values of the self-diffusion coefficient for different ions [ 141. A computer program using Quick-Basic language was written to describe the mass transfer. The model was tested for two types of membranes, namely Saehane membrane type RE8040BE and the TFC-Koch system membranes. The effect of different operation conditions on the performance of both types of membranes is discussed and the selection of the best type of membranes will be specified from different points of view.
325
AS. Kahdim et al. /Desalination 158 (2003) 323-329
2. The theoretical aspect The flux equations for both solvent (water) and ion transport for a RO system under steadystate operating conditions can be written using the Kimura-Sourirajan analysis [ 131 as follows. ??
Water transport:
NB =A[P-sc EX;,
+Cx;,) (1)
+JrE%+Z%)]
??
Cation transport:
Ni = (D,IK,
* 6) * c, *X, - (D,lK,, * “) i = 1,3,5 ,.... .
*c, *xi3 ??
(2)
Anion transport:
N,=(D,,l~~*8)*c,*~~-(D,,IIJ,*6) * Cj *X,3
j = 2,4,6 ,.....
(3)
In order to simplify the solution of the above transport equations, the following assumptions are necessary[ 131. LC,=C,=C,=C
2. N, > (ZNi + ml) 3. For evaluation of NBusing Eq. (l), we must have either the experimental osmotic pressure data for electrolyte mixtures or a method to estimate osmotic pressure data for such solution. 4* 4 = kNaC* (Di~DNaC1)m where ki and kNac,are the mass transfer coefficients for ion i and NaCl, respectively. The quantity kNa,-,is obtained from the Kimura-Sourirajan analysis [13] of the experimental data with the NaCl feed. The parameters Di and &,c, are the self-diffusion coefficients of ion i and NaCl in water, both at infinite dilution. Table 1 shows the values of the self-diffusion coefficients of various ions [ 141. With the above assumptions, the transport equations (l)-)8) can be simplified for representation of the flux equations of Na+ and Cl- as follows: (9)
where Ki = c *xi &*x&J
(4)
and
(10)
[(C’X,2)*(C*X,$% -(c*q*(c*43)%]
q. = c *J&*&)
(5)
The product mole fractions of cations and anions are given by: Xi, = NJr
for cations
(6)
X3 = Njlr
for anions
(7)
Table 1 Self-diffusion coefficient for various ions [ 141 Salt (i, j)
Cont.
DF 10.’ (cm*/s)
Dj*lO-’ (cm2/s)
NaCl CaCl
0.005-5 0.01-5.36
1.32-0.796 0.778-0.1
1.975-l .06 1.89-0.159
Ionic diffusion coeffkient
where r=N,+cN,+cN,
N2 = D2 /of2 *(DAM/K *8x2
(8)
Na’ Ion Diffusivity * 10m5 1.35
cl2.03
NO; 1.92
(cm*/s) SO;* 1.08
326
AS. Kahdim et al. /Desalination
158 (2003) 323-329
NW= (D&p* 8)* [(l-&J/&]
where
06) * c**xa2-c3*xa3 (
%
= k*C1
*(l-x,)
1
* q&2
and
(17)
(12) where the subscripts 1 and 2 refer to Na’ and Cl, respectively. The same analysis can be generalized to describe the flux equations for other ions as follows: . For anions = Di * DI’;i/o,; +‘) D~/~*a)~+zi)l(D~/~*~)~]
L
(13)
([(c*%y
* (c*Q(c*%y]
-[(c * !I!,,)“’* (c*xj3)/(c*x,,)z’]}
fori=3,
.
%)qT?l%)]
$7 ,......
For cations:
Z$ = Dj*(D~IK*8~~+~)ID,+2J’ [(C*q*(c*ql’Pf!!
(14)
- (C*&)” * (c*qYf$]
for j = 4, 6, 8,. . . The equations of overall mass transfer flux across the membranes can be written depending on the Kimura-Sourirajan analysis as follows: (15)
The main objective of the computer program developed in this work is to compute the membrane parameters and the flux of ions through the membrane in order to compare the experimental with the theoretical results. Also, the program is designed to predict the performance of the plant over time. 3. Results and discussion This paper presents the procedure used for performance evaluation of the BURO plant located in Basrah, one of the industrial cities in southern Iraq, which is considered a pilot plant for the production of desalinated water for drinking and industrial use. The RO pilot plant uses the Wafa Al-Kaeed River as a source for raw water due to its low salt content in the feed water that is fed to the membranes; accordingly, the surface lifetime of the membranes will be longer compared with other sources such as the Al-Arab River or the Arab Gulf. The plant has a capacity of 9 m3/h and is compared with two vessels, with a provision of adding a third vessel in order to increase the rate of production of the RO plant. In this work a mathematical model was tested to predict the performance of two types of membranes: Saehane, type RE8040BE-400 I?*of Korean origin and a Koch membrane, type 8822-XR-365 f? of US origin. The model is based on a generalized transport equation system involving solvent water and any number of completely ionized solutes with different valences. Table 2 shows a typical water analysis of the Wafa Al-Kaeed River.
AS. Kahdim et al. /Desalination 158 (2003) 323-329 Table 2 Analysis of typical brackish water Ion
Cont., ppm
Ca Mg SO, SiO, CaCO, Turbidity (NTU)
92 53 510 1.7 145 0.78
A computer program using the Quick-Basic language was written to describe the mass transfer and deliver different ionic concentration profiles and permeate flow rates for both types of membranes. The operating data of permeate and reject water were analyzed and compared with theoretical values; it was also used as a constraint for adjusted theoretical values of permeate flow rates and other parameters.
+ 0
Experimental +
2
4
The performance of any RO plant is usually expressed in terms of permeate flow rate and salt passage. Figs. 2 and 3 show the permeate flow rates for both types of membranes over a period of 8 months. As shown in these figures, there is good agreement between theoretical and experimental results. The main difference between them is the effect of scale formation and CP. Figs. 4 and 5 show the total dissolved solids (TDS) of permeate for both types of membranes as a function of operating period. It is clear that TDS of permeate increases rapidly with time. Cleaning therefore becomes necessary to improve the performance of the membrane after 7 months of operation. In general, there is a close resemblance between the experimental and predicted results, except at some points where the membrane had to be cleaned. Fig. 6 shows the differential pressure drop for both types of membranes as a function of the operating period. The increase in the differential
+
Theoretical
6
8
0
10
Experimental +
2
25 .O‘i $j $ 20 04 $3 15 Q i%p 5% I-
Theoretical
4 6 Time (months)
Time (months)
Fig. 2. Permeate flow rate for Saehame membranes.
327
8
10
Fig. 3. Permeate flow rate for Koch membranes. 12
--t
-W-
Experimental -m-Theoretical
‘Ei
10
5
a
gg
6
a 5 1 i g
5 0
Exiwimental
+-Theoretical
10
4 2 0
0
2
4 6 Time (months)
a
10
Fig. 4. Total dissolved solids of permeate for Saehane membranes.
0
2
4
6
8
10
Time (months)
Fig. 5. Total dissolved solids of permeate for Koch membrane.
328
AS. Kahdim et al. /Desalination 5r
I
+
0
12
3
Koch membranes
4
5
6
7
8
9
Time (months)
Fig. 6. Pressure drop for various membranes.
-3 -U-Koch 20
30
50
60
70
Percent recovery
Fig. 7. Effectof recovery on the qualityof permeate. h
b e
25 t
I
20
5 15 2 g 10 -+ Saehane membranes -t-Koch membranes
B 5 d
OJ
20
30
40 Percent
Fig. 7 shows the effect of applied pressure on the percent recovery for both types of membranes. As can be seen, the relationship between the applied pressure and percent recovery is linear. In addition, it can be seen that the percent recovery of the Saehane membrane is higher than the Koch membrane. This can be attributed to the difference in the effective area for both types of membranes. Fig. 8 shows the effect of percent recovery on the TDS of permeates for both types of membranes. The TDS of permeate through both membranes decreased with increasing recovery. The Koch membrane gave very good water quality compared to the Saehane membrane.
4. Conclusions
membranes 40
158 (2003) 323-329
50
60
70
recovery
Fig. 8. Effect of feed pressures on percent recovery.
pressure with operating time for both types of membranes may be attributed to the membrane blocking by scaling and fouling. Under high fouling conditions, the permeate flow rate is reduced and accordingly a higher feed pressure is required to produce the design flow permeate or percent recovery. Usually, there is a parallel increase in salt passage resulting in a higher salinity of permeates.
1. A mathematical model was developed to predict the performance of different types of RO membranes. The model is based on generalized transport equations systems involving solvent (water) and any number of completely ionized solute with different valences. There is agreement between theoretical and experimental results. 2. Percent salinity is inversely proportional to the percent recovery. Higher percent recovery increases the dilution of salt ions that passed through the membrane, and therefore lower permeate salinity. 3. The percent recovery of Saehane membranes is higher than Koch membranes. This is due to the difference in the effective area for both types of membranes. 4. The fouling process affects membrane performance leading to the reduction of permeate flow rate, and accordingly a higher feed pressure is required to attain the design flow. Usually, there is a parallel increase in salt passage resulting in a higher salinity of permeates.
AS. Kahdim et al. /Desalination 158 (2003) 323-329
5. Symbols -
-
-
-
KY
-
k kNsCl
-
NA
-
NB
-
Ni
-
4
-
NIV
-
P
-
x1,
x02,
x03,
&n
-
Pure water permeability Molar concentration of the solution Molar concentration in the feed, permeate and reject streams Molar concentration in membrane phase Diffusion coefficient of solute in water and membrane phases, respectively Diffusion coefficient of cation i in water and membrane phases, respectively Diffusion coefficient of anion] in water and membrane phases, respectively Diffusion coefficient of NaCl in water Solute transport parameter Solute transport parameter for salt Inter-facial equilibrium constant for a single solute Mass transfer coefficient Mass transfer coefficient as determined by the experiment Solute flux through the membrane Solvent flux through the membrane Ionic flux of cations i through the membrane Ionic flux of anionj through the membrane Water flux through the membrane Operating pressure Mole fraction of solute A in the feed, permeate, reject and membrane phases, respectively.
zi,
zj
-
329
Mole fraction of cation i in the feed, permeate, reject and membrane phases, respectively Mole fraction of anionj in the feed, permeate, reject and membrane phases, respectively Valence of cation i and anionj, respectively
Greek 6 x(;rxi2+&>MW3+&)
-
Effective thickness of membrane Osmotic pressure of the mixed electrolyte system in the permeate and reject phases, respectively
References VI S. El-Manharawy and A. Hafez, Desalination, 139 (2001) 97. PI R. Sheikholeslami, S. Al-Mu@, T. Koo and A. Young, Desalination, 139 (2001) 83. 131 S. Madaeni T. Mohamamdi and M. Moghadam, Desalination, 134 (2001). 141 R. Ning, Conference Proceedings, Qatar, 1999. PI A. Al-Rammah, Desalination, 132 (2000) 83. Fl S. Bahattacharjee, J. Chen and M. Elimelech, AICHE J., 47(12) (2001) 2733. 171 N. Al-Bastaki and A. Abbas, Desalination, 132 (2000) 181. PI A. Abbas and N. Al-Bastaki, Desalination, 136 (2001) 281. PI D. van Gauwbergen and J. Baeyens, Desalination, 139 (2001) 275. S. 1101 Hammad, M. Abdel-Jawad, M. Al-Tabtabaei and S. Al-Shmmari, 4th Gulf Water Conference, Oman, 1999, p. 521. [ 1 l] S. Ibrahim, S. Al-Mutaz and B. Al-Sultan, 4th Gulf Water Conference, Oman, 1999, p. 605. [12] N. Al-Bastaki and A. Abbas, Desalination, 126 (1999) 33. [13] S. Sourirajan, Reverse Osmosis, Logos Press, UK, 1971. [ 141 R. Parsons, Handbook of Electrochemical Constants, Butterworths, London, 1959.
Desalination 158 (2003) 323-329 www.elsevier.com/locate/desal
Modeling of reverse osmosis systems Abdul Sattar Kahdim”, Saleh Ismail, Alaa’ Abdulrazaq Jassimb* “National Committee for Technology Transfer, Baghdad Iraq ‘Department of Chemical Engineering, University of Basrah, Box 1458, Ashaar, Basrah, Iraq email: noor. b@uruklink net
Received 8 December 2002; accepted 27 February 2003
Abstract The BasrahUniversity reverse osmosis plant (BURO) is an experimental unit built to provide college laboratories with desalted water. The plant has a total capacity of 9 m% and is composed of three independent lines. The aim of this study is to develop a theoretical model to predict the performance of reverse osmosis (RO) systems and to compare the theoretical results with experimental values obtained from the pilot plant. The study was conducted using two types of membranes, viz. Saehane, type KE8040BE of South Korean origin and TFC-Koch system membranes model 8822XR of American origin to test the theoretical model that is predicted based on the generalized transport equation system involving solvent (water) and anynumberof ions (solute) that is dissolved inwater using the Kimura-Sourhajan analysis. The main objective of this work can be specified in three steps as follows: (1) develop a computer program as a general model for any type of RO system, (2) predict plant performance as a function of time (8 months of operation), and (3) perform comparative studies on the performance of the two types of membranes specified. The recovery of Saehane membranes is larger than Koch membranes due to the difference in the effective area for both types of membranes whereas the salt passage of Koch was always lower than Saehane membranes for brackish water having TDS larger than 550 ppm. There is agreement between theoretical and experimental results. Keywora!x Reverse osmosis; Kimura-Sourirajan analysis
1. Introduction Reverse osmosis (RO) is widely used for the
separation of dissolved salts and substances in solution. The process consists of passing aqueous *Correspondingauthor.
solution under pressure through an appropriate
porous membrane and withdrawing the membrane permeate at atmospheric pressure and ambient temperature. The product is enriched in one or more constituents of the mixture, leaving a solution of higher concentration on the highpressure side of the membrane. Fig. 1 shows the
Presented at the European Conference on Desalination and the Environment: Fresh Waterfor All, Malta, 4-8 May 2003. European Desalination Society, International Water Association.
001 l-9164/03/$- See front matter 8 2003 Elsevier Science B.V. All rights reserved PII:SOOll-9164(03)00471-S
A.S. Kahdim et al. /Desalination
324
158 (2003) 323-329
Fiber glass (FRP) outer wrapping
FEED ONCENTHATE
Fig. 1. Direction of flow through the membrane.
direction of flow through the membranes. The process does not require heating of the membranes, and no phase change in product recovery is involved compared with other processes for production of desalted water, e.g., multi-effect and multi-stage flash (MSF) evaporation systems or freezing processes. The main contribution factor to the fast growth of RO is its inherent efficiency and simplicity as compared to other processes like MSF evaporation as it is carried out at ambient temperature, involves no change in phase, and it has comparatively few scaling and corrosion problems. Water type is considered as the cornerstone in the design of an RO system. Natural waters are usually grouped under two types: brackish, having a salt content of 1000-15000 mg/l, and seawater, >15,000 mg/l, based on their total salinity [ 11. There are two types of RO membranes available commercially, namely BURO and SWRO, which are currently used for desalination of all waters regardless of the wide variation in their chemical nature. Generally speaking, the selection of an RO membrane is critically dependent on two main factors: the first is water type, and the second is the desired recovery. As water flows through the membrane and salts are rejected, a boundary layer is formed near the membrane surface in which the salt concentration exceeds its value in the bulk solution leading to higher osmotic pressure. This is known as concentration polarization (CP). The effects of CP are: increasing osmotic pressure, reducing net driving pressure differ-
ential across the membrane, reducing product flow rate, and increasing scale formation. In order to get the same recovery with time; greater pressure should be applied. Fouling is another factor that affects the performance of the membranes; the performance of RO systems is limited by fouling and CP. Various methods have been proposed to minimize or reduce the effect of these two phenomena. They include feed treatment, chemically modifying the membrane surface and the use of fluid instabilities and turbulence [2-6]. Many theoretical models have been developed over the past decades [7-121 for RO membranes. In developing a theoretical model to predict the performance of RO membranes, one of the first things to consider is the choice of the transfer model describing the flux of water and salt through the membrane. In this work a mathematical model based on the Kimura-Sourirajan analysis [ 131was used to describe the flux of water and salt through the membrane. This model depends on the values of the self-diffusion coefficient for different ions [ 141. A computer program using Quick-Basic language was written to describe the mass transfer. The model was tested for two types of membranes, namely Saehane membrane type RE8040BE and the TFC-Koch system membranes. The effect of different operation conditions on the performance of both types of membranes is discussed and the selection of the best type of membranes will be specified from different points of view.
325
AS. Kahdim et al. /Desalination 158 (2003) 323-329
2. The theoretical aspect The flux equations for both solvent (water) and ion transport for a RO system under steadystate operating conditions can be written using the Kimura-Sourirajan analysis [ 131 as follows. ??
Water transport:
NB =A[P-sc EX;,
+Cx;,) (1)
+JrE%+Z%)]
??
Cation transport:
Ni = (D,IK,
* 6) * c, *X, - (D,lK,, * “) i = 1,3,5 ,.... .
*c, *xi3 ??
(2)
Anion transport:
N,=(D,,l~~*8)*c,*~~-(D,,IIJ,*6) * Cj *X,3
j = 2,4,6 ,.....
(3)
In order to simplify the solution of the above transport equations, the following assumptions are necessary[ 131. LC,=C,=C,=C
2. N, > (ZNi + ml) 3. For evaluation of NBusing Eq. (l), we must have either the experimental osmotic pressure data for electrolyte mixtures or a method to estimate osmotic pressure data for such solution. 4* 4 = kNaC* (Di~DNaC1)m where ki and kNac,are the mass transfer coefficients for ion i and NaCl, respectively. The quantity kNa,-,is obtained from the Kimura-Sourirajan analysis [13] of the experimental data with the NaCl feed. The parameters Di and &,c, are the self-diffusion coefficients of ion i and NaCl in water, both at infinite dilution. Table 1 shows the values of the self-diffusion coefficients of various ions [ 141. With the above assumptions, the transport equations (l)-)8) can be simplified for representation of the flux equations of Na+ and Cl- as follows: (9)
where Ki = c *xi &*x&J
(4)
and
(10)
[(C’X,2)*(C*X,$% -(c*q*(c*43)%]
q. = c *J&*&)
(5)
The product mole fractions of cations and anions are given by: Xi, = NJr
for cations
(6)
X3 = Njlr
for anions
(7)
Table 1 Self-diffusion coefficient for various ions [ 141 Salt (i, j)
Cont.
DF 10.’ (cm*/s)
Dj*lO-’ (cm2/s)
NaCl CaCl
0.005-5 0.01-5.36
1.32-0.796 0.778-0.1
1.975-l .06 1.89-0.159
Ionic diffusion coeffkient
where r=N,+cN,+cN,
N2 = D2 /of2 *(DAM/K *8x2
(8)
Na’ Ion Diffusivity * 10m5 1.35
cl2.03
NO; 1.92
(cm*/s) SO;* 1.08
326
AS. Kahdim et al. /Desalination
158 (2003) 323-329
NW= (D&p* 8)* [(l-&J/&]
where
06) * c**xa2-c3*xa3 (
%
= k*C1
*(l-x,)
1
* q&2
and
(17)
(12) where the subscripts 1 and 2 refer to Na’ and Cl, respectively. The same analysis can be generalized to describe the flux equations for other ions as follows: . For anions = Di * DI’;i/o,; +‘) D~/~*a)~+zi)l(D~/~*~)~]
L
(13)
([(c*%y
* (c*Q(c*%y]
-[(c * !I!,,)“’* (c*xj3)/(c*x,,)z’]}
fori=3,
.
%)qT?l%)]
$7 ,......
For cations:
Z$ = Dj*(D~IK*8~~+~)ID,+2J’ [(C*q*(c*ql’Pf!!
(14)
- (C*&)” * (c*qYf$]
for j = 4, 6, 8,. . . The equations of overall mass transfer flux across the membranes can be written depending on the Kimura-Sourirajan analysis as follows: (15)
The main objective of the computer program developed in this work is to compute the membrane parameters and the flux of ions through the membrane in order to compare the experimental with the theoretical results. Also, the program is designed to predict the performance of the plant over time. 3. Results and discussion This paper presents the procedure used for performance evaluation of the BURO plant located in Basrah, one of the industrial cities in southern Iraq, which is considered a pilot plant for the production of desalinated water for drinking and industrial use. The RO pilot plant uses the Wafa Al-Kaeed River as a source for raw water due to its low salt content in the feed water that is fed to the membranes; accordingly, the surface lifetime of the membranes will be longer compared with other sources such as the Al-Arab River or the Arab Gulf. The plant has a capacity of 9 m3/h and is compared with two vessels, with a provision of adding a third vessel in order to increase the rate of production of the RO plant. In this work a mathematical model was tested to predict the performance of two types of membranes: Saehane, type RE8040BE-400 I?*of Korean origin and a Koch membrane, type 8822-XR-365 f? of US origin. The model is based on a generalized transport equation system involving solvent water and any number of completely ionized solutes with different valences. Table 2 shows a typical water analysis of the Wafa Al-Kaeed River.
AS. Kahdim et al. /Desalination 158 (2003) 323-329 Table 2 Analysis of typical brackish water Ion
Cont., ppm
Ca Mg SO, SiO, CaCO, Turbidity (NTU)
92 53 510 1.7 145 0.78
A computer program using the Quick-Basic language was written to describe the mass transfer and deliver different ionic concentration profiles and permeate flow rates for both types of membranes. The operating data of permeate and reject water were analyzed and compared with theoretical values; it was also used as a constraint for adjusted theoretical values of permeate flow rates and other parameters.
+ 0
Experimental +
2
4
The performance of any RO plant is usually expressed in terms of permeate flow rate and salt passage. Figs. 2 and 3 show the permeate flow rates for both types of membranes over a period of 8 months. As shown in these figures, there is good agreement between theoretical and experimental results. The main difference between them is the effect of scale formation and CP. Figs. 4 and 5 show the total dissolved solids (TDS) of permeate for both types of membranes as a function of operating period. It is clear that TDS of permeate increases rapidly with time. Cleaning therefore becomes necessary to improve the performance of the membrane after 7 months of operation. In general, there is a close resemblance between the experimental and predicted results, except at some points where the membrane had to be cleaned. Fig. 6 shows the differential pressure drop for both types of membranes as a function of the operating period. The increase in the differential
+
Theoretical
6
8
0
10
Experimental +
2
25 .O‘i $j $ 20 04 $3 15 Q i%p 5% I-
Theoretical
4 6 Time (months)
Time (months)
Fig. 2. Permeate flow rate for Saehame membranes.
327
8
10
Fig. 3. Permeate flow rate for Koch membranes. 12
--t
-W-
Experimental -m-Theoretical
‘Ei
10
5
a
gg
6
a 5 1 i g
5 0
Exiwimental
+-Theoretical
10
4 2 0
0
2
4 6 Time (months)
a
10
Fig. 4. Total dissolved solids of permeate for Saehane membranes.
0
2
4
6
8
10
Time (months)
Fig. 5. Total dissolved solids of permeate for Koch membrane.
328
AS. Kahdim et al. /Desalination 5r
I
+
0
12
3
Koch membranes
4
5
6
7
8
9
Time (months)
Fig. 6. Pressure drop for various membranes.
-3 -U-Koch 20
30
50
60
70
Percent recovery
Fig. 7. Effectof recovery on the qualityof permeate. h
b e
25 t
I
20
5 15 2 g 10 -+ Saehane membranes -t-Koch membranes
B 5 d
OJ
20
30
40 Percent
Fig. 7 shows the effect of applied pressure on the percent recovery for both types of membranes. As can be seen, the relationship between the applied pressure and percent recovery is linear. In addition, it can be seen that the percent recovery of the Saehane membrane is higher than the Koch membrane. This can be attributed to the difference in the effective area for both types of membranes. Fig. 8 shows the effect of percent recovery on the TDS of permeates for both types of membranes. The TDS of permeate through both membranes decreased with increasing recovery. The Koch membrane gave very good water quality compared to the Saehane membrane.
4. Conclusions
membranes 40
158 (2003) 323-329
50
60
70
recovery
Fig. 8. Effect of feed pressures on percent recovery.
pressure with operating time for both types of membranes may be attributed to the membrane blocking by scaling and fouling. Under high fouling conditions, the permeate flow rate is reduced and accordingly a higher feed pressure is required to produce the design flow permeate or percent recovery. Usually, there is a parallel increase in salt passage resulting in a higher salinity of permeates.
1. A mathematical model was developed to predict the performance of different types of RO membranes. The model is based on generalized transport equations systems involving solvent (water) and any number of completely ionized solute with different valences. There is agreement between theoretical and experimental results. 2. Percent salinity is inversely proportional to the percent recovery. Higher percent recovery increases the dilution of salt ions that passed through the membrane, and therefore lower permeate salinity. 3. The percent recovery of Saehane membranes is higher than Koch membranes. This is due to the difference in the effective area for both types of membranes. 4. The fouling process affects membrane performance leading to the reduction of permeate flow rate, and accordingly a higher feed pressure is required to attain the design flow. Usually, there is a parallel increase in salt passage resulting in a higher salinity of permeates.
AS. Kahdim et al. /Desalination 158 (2003) 323-329
5. Symbols -
-
-
-
KY
-
k kNsCl
-
NA
-
NB
-
Ni
-
4
-
NIV
-
P
-
x1,
x02,
x03,
&n
-
Pure water permeability Molar concentration of the solution Molar concentration in the feed, permeate and reject streams Molar concentration in membrane phase Diffusion coefficient of solute in water and membrane phases, respectively Diffusion coefficient of cation i in water and membrane phases, respectively Diffusion coefficient of anion] in water and membrane phases, respectively Diffusion coefficient of NaCl in water Solute transport parameter Solute transport parameter for salt Inter-facial equilibrium constant for a single solute Mass transfer coefficient Mass transfer coefficient as determined by the experiment Solute flux through the membrane Solvent flux through the membrane Ionic flux of cations i through the membrane Ionic flux of anionj through the membrane Water flux through the membrane Operating pressure Mole fraction of solute A in the feed, permeate, reject and membrane phases, respectively.
zi,
zj
-
329
Mole fraction of cation i in the feed, permeate, reject and membrane phases, respectively Mole fraction of anionj in the feed, permeate, reject and membrane phases, respectively Valence of cation i and anionj, respectively
Greek 6 x(;rxi2+&>MW3+&)
-
Effective thickness of membrane Osmotic pressure of the mixed electrolyte system in the permeate and reject phases, respectively
References VI S. El-Manharawy and A. Hafez, Desalination, 139 (2001) 97. PI R. Sheikholeslami, S. Al-Mu@, T. Koo and A. Young, Desalination, 139 (2001) 83. 131 S. Madaeni T. Mohamamdi and M. Moghadam, Desalination, 134 (2001). 141 R. Ning, Conference Proceedings, Qatar, 1999. PI A. Al-Rammah, Desalination, 132 (2000) 83. Fl S. Bahattacharjee, J. Chen and M. Elimelech, AICHE J., 47(12) (2001) 2733. 171 N. Al-Bastaki and A. Abbas, Desalination, 132 (2000) 181. PI A. Abbas and N. Al-Bastaki, Desalination, 136 (2001) 281. PI D. van Gauwbergen and J. Baeyens, Desalination, 139 (2001) 275. S. 1101 Hammad, M. Abdel-Jawad, M. Al-Tabtabaei and S. Al-Shmmari, 4th Gulf Water Conference, Oman, 1999, p. 521. [ 1 l] S. Ibrahim, S. Al-Mutaz and B. Al-Sultan, 4th Gulf Water Conference, Oman, 1999, p. 605. [12] N. Al-Bastaki and A. Abbas, Desalination, 126 (1999) 33. [13] S. Sourirajan, Reverse Osmosis, Logos Press, UK, 1971. [ 141 R. Parsons, Handbook of Electrochemical Constants, Butterworths, London, 1959.