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acid aqueous solutions using hollow fiber reverse osmosis
Journal of Membrane Science, 54 (1990) 175-189 Elsevier Science Publishers B.V., Amsterdam
175
Separation of ternary salt/acid aqueous solutions using hollow fiber reverse osmosis Frank J. Sapienza Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260 (U.S.A.)
William N. Gill and Mohammad Soltanieh* Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 (U.S.A.) (Received February
12,199O; accepted in revised form June 4,199O)
Abstract A hollow fiber reverse osmosis system was used to separate ternary mixtures of sodium chloride and acetic acid aqueous solutions to investigate interactions between an inorganic salt and a weak organic acid which does not ionize extensively. Acetic acid rejection is enhanced and permeability is decreased by adding NaCl to the solution. Conversely, the separation of NaCl is decreased and permeability increased as the concentration of acetic acid in the mixture is increased. Furthermore, the permeability of acetic acid in the polyamide hollow fiber membrane is approximately one order of magnitude larger than that of the salt. The results suggest that it may be possible to purify etching solutions of weak acids by passing water and unionized acid through the membrane and rejecting ionized and particulate constituents. The linear relationship between the inverse of salt rejection and the inverse of solvent flux, as developed by Pusch (1977) for flat membranes and later applied by Soltanieh and Gill (1981,1982,1984) to hollow fiber systems on the basis of the completely-mixed model, also is valid in this case which involves ternary solutions. The coupling between the components of mixtures shown in this study may be useful in understanding better applications as diverse as treatment by the reverse osmosis of etching solutions of microelectronic industries to wastewaters from oil shale retorting, metal finishing industries and other wastes streams involving organic/inorganic mixtures.
Introduction Membrane processes now are used in many applications including metal and metal finishing, pulp and paper, textile, electronic, pharmaceutical, petroleum production, power plants, food, medicine, and biotechnology industries [l-6]. Although most practical applications involve the separation of complex mixtures of inorganic and organic solutions, there have been only a few fundamen*On leave from Department 11365-8639, Tehran, Iran.
of Chemical Engineering,
0376-1388/90/$03.50
0 1990 -
Sharif University
Elsevier Science Publishers
B.V.
of Technology,
P.O. Box
176
ta1 studies dealing with mixtures of more than two components. Sourirajan and Matsuura [ 41 have presented a general method to predict the membrane performance (i.e. the solute separation with respect to each component and the product flow rate) in aqueous solutions of various organics or inorganic solutes. Lee [ 71 studied the separation of multicomponent inorganic mixtures by reverse osmosis. However, many industrial waste streams contain both organic and inorganic components and some, such as etching solutions, involve weak acid solutions which are not highly ionized. Examples of these types of wastes include wastes from electroless plating baths, photographic wastes, wood preservative wastes, landfill leachates, microelectronic etches which may include either strong (H&30,) or weak (HF, H3P04, CH,COOH) etching solutions as described by Kern and Deckert [ 81, and oil shale (synfuel) retorting wastewater. Recently, McNeil [9] has reviewed various applications of the membrane separation techniques for treatment of hazardous wastes. Siler and Bhattacharyya [lo] have performed extensive experiments in treating hazardous wastes by using low pressure composite reverse osmosis membranes. They have used oil shale (synfuel) wastes which contained organic and inorganic components. They also conducted experiments to treat phenolic wastes, organic acid wastes, and pesticides wastes. Despite its industrial importance, there are few reports regarding the interaction of inorganic solutes with organic components, a very good example of which is the treatment by reverse osmosis of wastewater from the oil shale retorting process. Sapienza [ 111studied separation of a ternary solution containing sodium chloride, acetic acid, and water by using a hollow fiber reverse osmosis system. Although the actual wastewater from the oil shale retorting process is far more complex than the ternary system considered here [ 10,121 it is the objective of this study to investigate the possible interactions that an inorganic solute might have with the separation of an organic solute or vise versa; this can be done best with solutions which are well defined. It is hoped that our work on well defined relatively simple mixtures will give some insight into the more complicated cases. Theoretical background Membrane transport models Basically there are two approaches for modeling mass transfer across membranes. The first is based on irreversible thermodynamics in which the membrane is treated as a black box where slow processes take place near equilibrium. The second approach assumes some mechanism of solute and solvent transport across the membrane. In the latter, one needs physicochemical data for the solute, solvent, and membrane, as well as knowledge about interactions among them.
177
The first model from irreversible thermodynamics [ 131 was derived by Kedem and Katchalsky [ 141 based on the linear relationships between fluxes (of solutes and solvent) and forces (gradients of pressure, concentrations, etc. ) . Spiegler and Kedem [ 151 have extended the model of Kedem-Katchalsky to account for the nonlinear relationship between fluxes and forces across the membrane. Starting with the Kedem-Katchalsky model for the volume flux (J,) and solute flux (J, ) : J” =Lp(dP-od7r)
(1)
and:
J,= (C,),,(l-a)J,+cLldn
(2)
Pusch [ 161 has derived the following relationship between the inverse of solute rejection, l/R = (1 - C,/C,) -l, and the inverse of the volume flux (l/J,):
or simply:
$A+B
$ 0 ”
(4)
This equation was found to be valid for a wide range of experimental data [17,18]. The second group of membrane transport models includes the solution-diffusion model [ 191, solution-diffusion-imperfection-model [ 201, preferential sorption-capillary flow model [ 51, frictional model [ 151. These models have been reviewed and critically compared with each other by Soltanieh and Gill [ 181. They showed that the linear relationship shown above also is valid when one uses the solution-diffusion model, solution-diffusion-imperfection model, or any other similar linear models. The difference would be in the interpretation of coefficients A and B. For example, if one uses the solution-diffusion model, A will be equal to unity and B will be equal to the solute permeability coefficient, K,, i.e.:
According to the solution-diffusion model, the solute permeability coefficient, K,, is defined by:
J,=K,AC
(6a)
where AC is the concentration difference across the membrane, and the volume
178
flux (J,) is related to the effective pressure difference across the membrane by the relationship: J, =A,(dP-h)
(6b)
where A,, is the hydraulic or solvent permeability of the membrane. Hollow fiber (HF) module design Several investigators have attempted to derive mathematical models that describe the hydrodynamic and mass transport in HF modules. To predict the productivity (the ratio of product or permeate flow rate to the feed flow rate) and the product concentration of the module under specified operating conditions for a given module, two approaches have been used. The first approach assumes plug flow in the shell side of the module [21-241 and proposes the idea that the fibers be considered continuously distributed sinks and develops this concept together with Happel’s mobile cell idea [ 25-28,341. More recently Bruining [ 351 and Rautenbach and Dahm [291, have discussed these mathematical models and based their approach on that of Dandavati et al. [26], Doshi et al. [ 271 and Kabadi et al. [ 281. In the second approach, it is assumed that the fluid in the shell side of the module is completely mixed, as in a CSTR, and the concentrations is uniform in the shell [ 301. The validity of this assumption has been tested independently by measuring the flow patterns in hollow fiber modules by using tracerresponse curves [ 311. Since the complete mixing model is very simple, it is used in the present study of ternary solutions. The complete mathematical model has been described by Soltanieh and Gill [ 321. Therefore, only a summary is presented here. The pure water permeability coefficient (A,) can be calculated from the slope (S ) of the line described by: @=I+s
($ >
(7)
where 0 is the productivity (the ratio of product flow rate to the feed flow rate), AP is the pressure difference across the membrane, and F is the feed flow rate. I and S are the intercept and the slope of the straight line obtained. For reverse osmosis membranes the intercept usually is small and can be set equal to zero [ 28,301. The pure water permeability coefficient (A,) is related to the slope (S) in a rather complicated nonlinear manner and is given by Soltanieh and Gill [32] who also showed that the linearity between Q, and AP/F is independent of the membrane transport model used. With the assumption of complete mixing in the shell side, an equation similar to eqn. (4), with R and J, replaced by average values E and J, respectively, can be applied to the whole module, regardless of the membrane model used.
179
The volume flux ((r,) is calculated from the product flow rate (Fr ) divided by the total membrane surface area (S,) . The theory describing multicomponent membrane separations is rather complicated. Since this work is intended to be experimental in nature, the theory will be discussed in more detail in a future publication. Experimental set-up and results Experiments were performed by using a DuPont B-9 hollow fiber permeator with binary NaCl solutions, binary acetic acid solutions, and ternary mixtures of sodium chloride and acetic acid. The concentration range for Na+ was 5005000 ppm and for acetic acid was 300-4500 ppm. Feed pressures ranged from 150 psig (1.03 MPa) to 400 psig (2.76 MPa), and the temperature was fixed at 20°C. The Na+ ion and the acetic acid concentration were measured using the same Orion 901 ionalyzer. The concentration measurements were made with an average error of + 0.5%. The concentration measurements were checked by the material balance on the module. The material balance requirement was met within 3%. Pure water permeability According to eqn. (7)) the pure water permeability of the membrane for the experimental conditions in this work is obtained from the slope of the line given by: @= 6.515 x 1O-6 (dP/F)
+ 0.00425
(3)
This equation is plotted in Fig. 1 and the pure water permeability (A,) of the membrane is A, =6.891x
10-‘3m2-sec/kg
(9)
Solute permeability Figures 2 and 3 show plots of l/Z? vs. l/& for various concentrations of NaCl and acetic acid binary solutions respectively, and almost perfect straight lines are obtained in all cases (correlation coefficient, CORz 1). The slopes of the lines which were shown earlier to be equal to the solute permeability coefficient (I&.), increase as the solute concentration in the feed increases. Furthermore, for the same feed concentration, the slope for acetic acid is much larger than the sodium chloride. Figures 4 and 5 compare plots of l/I? vs. l/J” for feed concentrations of 1000 and 4000 ppm for both solutes, respectively. The value of the slope for acetic acid is roughly 10 times greater than that for Na+ which means that the membrane (aromatic polyamide) is more permeable to acetic acid than to the salt by almost an order of magnitude. Some other data on the
180
I
a’
(Correlat~an
AP 7 x 10-4,
Coefflcienf,
COR
- 0 999)
DYNE.SEC. -___ CM5
Fig. 1. Pure water permeability data. Fraction of feed removed, @=FJF, pure water permeability coefficient, A,, according to eqn. (7)
vs. AP/F. Slope gives
Fig. 2. l/l?vs. l/J, for various NaCl concentrations and feed pressures of 150-400 psi (1.03-2.76 MPa). Slope is the solute permeability coefficient K,, according to eqn. (5).
separation of binary aqueous acetic acid solutions with polyetheramide (PA300) and polyether (PEC-1000) composite membranes also have been reported by Sourirajain [ 4, pp. 657-6601, but quantitative comparison with our data is not possible because those experiments were carried out with different feed concentrations and pressures (190 ppm and 1000 psia with PA-300; 50,000 ppm and 800 psia with PEC-1000). However, the level of separation is 65-70% with the PA-300 and 91% with the PEC-1000 membrane. The intercepts of all lines are close to unity which means that the reflection coefficient (a) is close to unity, or R, 41 [see eqn. (3) 1. In terms of the so-
181
Fig. 3. l/Rvs. l/J, for various acetic acid concentrations and feed pressures of 150-400 psi (1.032.76 MPa ) . Slope is the solute permeability coefficient, K,,according to eqn. (5 ) .
Fig. 4. Comparison of slopes (solute permeability coefficients) of l/Rvs. l/J” for sodium chloride and acetic acid solutions at constant concentration of 1000 ppm for both solutes and pressures from 150-400 psi (1.03-2.76 MPa).
lution-diffusion model, this means that as expected there is no convective contribution to solute transport in very tight reverse osmosis membranes. The solute permeability coefficient, K2, can be found from the slopes of the lines plotted in Figs. 2-5. Table 1 gives for binary solutions the permeability of Na+ and acetic acid in the membrane. Figures 6 and 7 show the plots of K2 vs. feed concentration for Na+ and acetic acid, respectively. As expected, & increases with increasing feed concentration for both Na+ and acetic acid up to
Fig. 5. Comparison of slopes (solute permeability coefficients) of l/I?vs. l/& for sodium chloride and acetic acid solutions at constant concentration of 4000 ppm for both solutes and pressures from 150-400 psi (1.03-2.76 MPA). TABLE 1 Permeability of Na+ and acetic acid for binary solutions Solute Sodium Chloride
Feed concentration (ppm ) 500 1000
2000 3000 4000 5000 Acetic Acid
300 700 1000
2000 3000 4000
Ks x lo7 (m/set ) 0.332 0.422 0.516 0.553 0.594 0.639 2.91 3.35 3.96 5.59 5.96 6.64
certain level of concentration, after which it remains relatively constant. These results are similar to those obtained previously by Soltanieh and Gill [ 301 for NaCl solutions. The shapes of Figs. 6 and 7 suggest that the variation of solute permeability of the membrane with feed’concentration may be described by the type of Langmuir sorption model proposed by Vieth [ 33 1. This model involves a dual sorption mechanism which includes sorbate dissolved according to Henry’s law, and that which occupies unrelaxed free volume within the membrane and
183
I
I
I
I
I
1000
2000
3000
4000
5000
FEED CONC.
(ppm of NaCI)
Fig. 6. Variation of permeability of NaCl with feed (NaCl) concentration.
0.75 zo 0: -
0.50 -
b x y"
0
, 0
1000
1
FEED CONC.
I
I
2000
3000
4000
(ppm of acetic acid)
Fig. 7. Variation of permeability of acetic acid with feed (acetic acid) concentration.
described by a Langmuir type isotherm. Since the permeability coefficient of membrane (&) is proportional to the solute solubility, the model suggested by Vieth [ 33 ] becomes:
K2 =KzH +K2==HkC+s
(10) k
where KzHand KzL are the Henry’s law and Langmuir sorption contributions to the permeability. Hk is the Henry’s law constant, & and & are the Langmuir constants, and C is the concentration of solute in the bulk. & is called the hole saturation constants, and L; the hole affinity constant which is related to the ratio of rate constants for sorption and desorption of penetrant in the holes. According to eqn. (lo), if L; C << 1 the model reduces to:
K2 = (Hk +L,L;)C
(11)
184
At sufficiently high concentrations the microvoids become saturated and will no longer sorb additional penetrant. Thus when LkC >> 1, sorption in the microvoids reaches a saturation limit, I+, and eqn. (10) reduces to: K2 =H,C+L,
(12)
the slope of which yields the Henry’s law constant. The dual sorption model predicts that an isothermal plot of K2 versus C will consist of a low-concentration linear region and a high-concentration linear region connected by a nonlinear region. Once Hk is obtained, we may calculate KzL from eqn. (10): K2L=K2-K2H=K2-HkC
(13)
Then KzL is used in the Langmuir model in the form: 1111 -
K2L -&Lh
0c
(14)
+Lk
By plotting l/K,, versus l/C, one can obtain Lk and Lk . The data of Table 1 and Figs. 6 and 7 were used to evaluate the constants of eqn. (10) by the method described above. Reasonably straight lines were obtained in all cases and the numerical values of the constants were found to be: For salt K, =3.2~1O-‘~C+
(5.05x10W6)
(0.0356)C
1+ 0.0356C
(15)
For acetic acid K2 =5.0x
10-gC+
(5.15x10-5)
(0.00194)C
1+ 0.00194c
(16)
Therefore the dual-sorption Langmuir model describes the variation of the solute permeability with feed concentration in a useful way. Effect of NaCl on acetic acid rejection (ternary results)
Figures 8 and 9 show the effect of NaCl on the acetic acid rejection at two different concentrations of 1000 and 4000 ppm acetic acid. At each concentration, the Na+ concentration varied from zero (pure acid) to 4000 ppm. For a feed of 1000 ppm acetic acid the slope was found to be 0.396X lo-” m/set. When 1000 ppm Na+ is added to the feed, the slope decreases to a value of 0.363 x 10A6. Since the slope was determined to be a measure of the solute permeability coefficient, the value of K2 decreases by 8.3% with a feed of 1000 ppm acetic acid/1000 ppm Na+, and by 18.9% with a feed of 1000 ppm acid/ 4000 ppm Na+ as compared to a feed concentration of 1000 ppm acetic acid alone. Similar results were obtained for a feed of 4000 ppm acetic acid. Therefore, acetic acid rejection increases as NaCl is added to the solution.
185
Fig. 8. Effect of NaCl concentration on the separation (or rejection) of acetic acid at a concentration of 1000 ppm.
Fig. 9. Effect of NaCl concentration on the separation (or rejection) of acetic acid at a concentration of 4000 ppm.
Effect of acetic acid on NaCl (ternary results) Figures 10 and 11 show the effect of acetic acid on Na+ rejection. For a feed of 1000 ppm Na+, the slope was determined earlier to be 0.042 X lO-‘j m/set. With a feed of 1000 ppm Na+/lOOO ppm acetic acid the slope increases by 7.1% to 0.045 x 10m6.For a feed concentration of 1000 ppm Na+/4000 ppm acetic acid the slope increases by 16.7% to 0.049 x 10w6. For a feed concentration of 4000 ppm Na+ similar results are obtained. Therefore, as acetic acid is added to salt solution, the rejection of Na+ decreases.
186
Fig. 10. Effect of acetic acid concentration on the separation (or rejection) of NaCl at a concentration of 1000 ppm.
0
I
I
2
4
I 6
p(g$
Fig. 11. The effect of acetic acid concentration on the separation (or rejection) of NaCl at concentration of 4000 ppm.
a
Conclusions
The main purposes of this work are to get a better understanding of the separation of multi-component salt/organic solutions using hollow fiber reverse osmosis systems, and to demonstrate further the usefulness of the complete mixing model. It was found that the previously observed linear relationship between the inverse of the rejection (1/R) and the inverse of the volume flux (l/J”) for salt solutions, also is valid for an organic solute such as acetic acid. Excellent
187
linear relationships were observed at all levels of concentrations considered in this study for both binary and ternary mixtures. This support the complete mixing assumption in the shell side of hollow fiber modules. Employing the simple diffusion model for transport across the membrane facilitates easy determination of the solute permeability coefficient, &. The values of K2 increase as the feed concentration increase up to a certain level, after which it remains relatively constant. This behavior is observed for both NaCl and acetic acid. The permeability of NaCl was found to be an order of magnitude smaller than that of acetic acid. The dual sorption Langmuir model describes the variation of K2 with C reasonably well. The rejection of acetic acid solution by aromatic polyamide membrane at pressure of 400 psia is roughly 70% for a feed concentration of 1000 ppm and roughly 50% for a feed concentration of 4000 ppm. This suggests that concentrated solutions of weak acids may in some cases be purified by passing most of the water and acid and rejecting ionized or particulate constituents. Such a procedure would eliminate all particulates down to those on the order of lo100 A. It was shown quantitatively that the transport of acetic acid and NaCl are coupled. The presence of the salt inhibits the transport of acid. However, the acid enhances the transport of NaCl. List of symbols A
4 B
c CP
CR (CJln F
FP FR
Hk I JS JV
J” K2 K
2H
K2L
coefficient in eqn. (4) ( - ) solvent permeability coefficient defined by eqn. (6b) ( m2-set/kg) coefficient in eqn. (4) (m3/m2-set) solute concentration in the bulk of feed (ppm) concentration of permeate (ppm ) concentration of retentate (ppm) logarithmic average concentration across the membrane (ppm) feed flow rate (m”/sec ) product flow rate (m”/sec ) reject flow rate (m3/sec) Henry’s law constant (m/set-ppm ) intercept of the line defined by eqn. (7) ( - ) solute flux (kg/m2-set) total volume flux ( m3/m2-set) F,/S, = overall average volume flux of a hollow fiber module (m”/m”set ) solute permeability coefficient, defined by eqn. (6a) (m/set) Henry’s law sorption contribution to solute permeability coefficient (m/set) Langmuir sorption contribution to solute permeability coefficient (m/ set )
188
L,, Ld phenomenological coefficients (m”-set/g) pressure difference across the membrane (Pa) 1- C&/CR= rejection coefficient ( - ) rejection coefficient at infinite flux (- ) RCC overall average rejection of a hollow tiber module (- ) R slope of the line defined by eqn. (7) (m4-set/kg) S total membrane surface area of a hollow fiber module ( m2) SIXI
AP R
Greek symbols osmotic pressure difference across the membrane (Pa) A7l XR
o CD CL)
osmotic pressure of the reject solution or retentate (Pa) reflection coefficient (- ) F,/F=productivity of the module ( - ) solute permeability at zero flux (s/m)
Acknowledgement This work was supported in part by the New York State Energy Research and Development Agency and the Eastman Kodak Company.
References R. Rautenbach 1989. 2 3
5
and R. Albrecht,
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Y.T. Lee, Separation of multi inorganic materials by reverse osmosis, Ph.D. Dissertation, Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY, 1987. 8 9 10 11
W. Kern and CA. Decker%, Chemical etching, in: J.L. Vossen and W. Kern (Eds.), Thin Film Processes, Academic Press, New York, NY, 1978. J.C. McNeil, Membrane separation technologies for treatment of hazardous wastes. Crit. Rev. Environ. Control, 18 (1988) 91-131. J.L. Siler and D. Bhattacharyya, Low-pressure reverse osmosis membrane: Concentration and treatment of hazardous wastes, Haz. Waste Haz. Materials, 2 (1985) 45-65. F.J. Sapienza, Experimental investigation of multi-component salt/organic solutions using hollow fiber reverse osmosis. M.S. Thesis, Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY, 1986.
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175
Separation of ternary salt/acid aqueous solutions using hollow fiber reverse osmosis Frank J. Sapienza Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, NY 14260 (U.S.A.)
William N. Gill and Mohammad Soltanieh* Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 (U.S.A.) (Received February
12,199O; accepted in revised form June 4,199O)
Abstract A hollow fiber reverse osmosis system was used to separate ternary mixtures of sodium chloride and acetic acid aqueous solutions to investigate interactions between an inorganic salt and a weak organic acid which does not ionize extensively. Acetic acid rejection is enhanced and permeability is decreased by adding NaCl to the solution. Conversely, the separation of NaCl is decreased and permeability increased as the concentration of acetic acid in the mixture is increased. Furthermore, the permeability of acetic acid in the polyamide hollow fiber membrane is approximately one order of magnitude larger than that of the salt. The results suggest that it may be possible to purify etching solutions of weak acids by passing water and unionized acid through the membrane and rejecting ionized and particulate constituents. The linear relationship between the inverse of salt rejection and the inverse of solvent flux, as developed by Pusch (1977) for flat membranes and later applied by Soltanieh and Gill (1981,1982,1984) to hollow fiber systems on the basis of the completely-mixed model, also is valid in this case which involves ternary solutions. The coupling between the components of mixtures shown in this study may be useful in understanding better applications as diverse as treatment by the reverse osmosis of etching solutions of microelectronic industries to wastewaters from oil shale retorting, metal finishing industries and other wastes streams involving organic/inorganic mixtures.
Introduction Membrane processes now are used in many applications including metal and metal finishing, pulp and paper, textile, electronic, pharmaceutical, petroleum production, power plants, food, medicine, and biotechnology industries [l-6]. Although most practical applications involve the separation of complex mixtures of inorganic and organic solutions, there have been only a few fundamen*On leave from Department 11365-8639, Tehran, Iran.
of Chemical Engineering,
0376-1388/90/$03.50
0 1990 -
Sharif University
Elsevier Science Publishers
B.V.
of Technology,
P.O. Box
176
ta1 studies dealing with mixtures of more than two components. Sourirajan and Matsuura [ 41 have presented a general method to predict the membrane performance (i.e. the solute separation with respect to each component and the product flow rate) in aqueous solutions of various organics or inorganic solutes. Lee [ 71 studied the separation of multicomponent inorganic mixtures by reverse osmosis. However, many industrial waste streams contain both organic and inorganic components and some, such as etching solutions, involve weak acid solutions which are not highly ionized. Examples of these types of wastes include wastes from electroless plating baths, photographic wastes, wood preservative wastes, landfill leachates, microelectronic etches which may include either strong (H&30,) or weak (HF, H3P04, CH,COOH) etching solutions as described by Kern and Deckert [ 81, and oil shale (synfuel) retorting wastewater. Recently, McNeil [9] has reviewed various applications of the membrane separation techniques for treatment of hazardous wastes. Siler and Bhattacharyya [lo] have performed extensive experiments in treating hazardous wastes by using low pressure composite reverse osmosis membranes. They have used oil shale (synfuel) wastes which contained organic and inorganic components. They also conducted experiments to treat phenolic wastes, organic acid wastes, and pesticides wastes. Despite its industrial importance, there are few reports regarding the interaction of inorganic solutes with organic components, a very good example of which is the treatment by reverse osmosis of wastewater from the oil shale retorting process. Sapienza [ 111studied separation of a ternary solution containing sodium chloride, acetic acid, and water by using a hollow fiber reverse osmosis system. Although the actual wastewater from the oil shale retorting process is far more complex than the ternary system considered here [ 10,121 it is the objective of this study to investigate the possible interactions that an inorganic solute might have with the separation of an organic solute or vise versa; this can be done best with solutions which are well defined. It is hoped that our work on well defined relatively simple mixtures will give some insight into the more complicated cases. Theoretical background Membrane transport models Basically there are two approaches for modeling mass transfer across membranes. The first is based on irreversible thermodynamics in which the membrane is treated as a black box where slow processes take place near equilibrium. The second approach assumes some mechanism of solute and solvent transport across the membrane. In the latter, one needs physicochemical data for the solute, solvent, and membrane, as well as knowledge about interactions among them.
177
The first model from irreversible thermodynamics [ 131 was derived by Kedem and Katchalsky [ 141 based on the linear relationships between fluxes (of solutes and solvent) and forces (gradients of pressure, concentrations, etc. ) . Spiegler and Kedem [ 151 have extended the model of Kedem-Katchalsky to account for the nonlinear relationship between fluxes and forces across the membrane. Starting with the Kedem-Katchalsky model for the volume flux (J,) and solute flux (J, ) : J” =Lp(dP-od7r)
(1)
and:
J,= (C,),,(l-a)J,+cLldn
(2)
Pusch [ 161 has derived the following relationship between the inverse of solute rejection, l/R = (1 - C,/C,) -l, and the inverse of the volume flux (l/J,):
or simply:
$A+B
$ 0 ”
(4)
This equation was found to be valid for a wide range of experimental data [17,18]. The second group of membrane transport models includes the solution-diffusion model [ 191, solution-diffusion-imperfection-model [ 201, preferential sorption-capillary flow model [ 51, frictional model [ 151. These models have been reviewed and critically compared with each other by Soltanieh and Gill [ 181. They showed that the linear relationship shown above also is valid when one uses the solution-diffusion model, solution-diffusion-imperfection model, or any other similar linear models. The difference would be in the interpretation of coefficients A and B. For example, if one uses the solution-diffusion model, A will be equal to unity and B will be equal to the solute permeability coefficient, K,, i.e.:
According to the solution-diffusion model, the solute permeability coefficient, K,, is defined by:
J,=K,AC
(6a)
where AC is the concentration difference across the membrane, and the volume
178
flux (J,) is related to the effective pressure difference across the membrane by the relationship: J, =A,(dP-h)
(6b)
where A,, is the hydraulic or solvent permeability of the membrane. Hollow fiber (HF) module design Several investigators have attempted to derive mathematical models that describe the hydrodynamic and mass transport in HF modules. To predict the productivity (the ratio of product or permeate flow rate to the feed flow rate) and the product concentration of the module under specified operating conditions for a given module, two approaches have been used. The first approach assumes plug flow in the shell side of the module [21-241 and proposes the idea that the fibers be considered continuously distributed sinks and develops this concept together with Happel’s mobile cell idea [ 25-28,341. More recently Bruining [ 351 and Rautenbach and Dahm [291, have discussed these mathematical models and based their approach on that of Dandavati et al. [26], Doshi et al. [ 271 and Kabadi et al. [ 281. In the second approach, it is assumed that the fluid in the shell side of the module is completely mixed, as in a CSTR, and the concentrations is uniform in the shell [ 301. The validity of this assumption has been tested independently by measuring the flow patterns in hollow fiber modules by using tracerresponse curves [ 311. Since the complete mixing model is very simple, it is used in the present study of ternary solutions. The complete mathematical model has been described by Soltanieh and Gill [ 321. Therefore, only a summary is presented here. The pure water permeability coefficient (A,) can be calculated from the slope (S ) of the line described by: @=I+s
($ >
(7)
where 0 is the productivity (the ratio of product flow rate to the feed flow rate), AP is the pressure difference across the membrane, and F is the feed flow rate. I and S are the intercept and the slope of the straight line obtained. For reverse osmosis membranes the intercept usually is small and can be set equal to zero [ 28,301. The pure water permeability coefficient (A,) is related to the slope (S) in a rather complicated nonlinear manner and is given by Soltanieh and Gill [32] who also showed that the linearity between Q, and AP/F is independent of the membrane transport model used. With the assumption of complete mixing in the shell side, an equation similar to eqn. (4), with R and J, replaced by average values E and J, respectively, can be applied to the whole module, regardless of the membrane model used.
179
The volume flux ((r,) is calculated from the product flow rate (Fr ) divided by the total membrane surface area (S,) . The theory describing multicomponent membrane separations is rather complicated. Since this work is intended to be experimental in nature, the theory will be discussed in more detail in a future publication. Experimental set-up and results Experiments were performed by using a DuPont B-9 hollow fiber permeator with binary NaCl solutions, binary acetic acid solutions, and ternary mixtures of sodium chloride and acetic acid. The concentration range for Na+ was 5005000 ppm and for acetic acid was 300-4500 ppm. Feed pressures ranged from 150 psig (1.03 MPa) to 400 psig (2.76 MPa), and the temperature was fixed at 20°C. The Na+ ion and the acetic acid concentration were measured using the same Orion 901 ionalyzer. The concentration measurements were made with an average error of + 0.5%. The concentration measurements were checked by the material balance on the module. The material balance requirement was met within 3%. Pure water permeability According to eqn. (7)) the pure water permeability of the membrane for the experimental conditions in this work is obtained from the slope of the line given by: @= 6.515 x 1O-6 (dP/F)
+ 0.00425
(3)
This equation is plotted in Fig. 1 and the pure water permeability (A,) of the membrane is A, =6.891x
10-‘3m2-sec/kg
(9)
Solute permeability Figures 2 and 3 show plots of l/Z? vs. l/& for various concentrations of NaCl and acetic acid binary solutions respectively, and almost perfect straight lines are obtained in all cases (correlation coefficient, CORz 1). The slopes of the lines which were shown earlier to be equal to the solute permeability coefficient (I&.), increase as the solute concentration in the feed increases. Furthermore, for the same feed concentration, the slope for acetic acid is much larger than the sodium chloride. Figures 4 and 5 compare plots of l/I? vs. l/J” for feed concentrations of 1000 and 4000 ppm for both solutes, respectively. The value of the slope for acetic acid is roughly 10 times greater than that for Na+ which means that the membrane (aromatic polyamide) is more permeable to acetic acid than to the salt by almost an order of magnitude. Some other data on the
180
I
a’
(Correlat~an
AP 7 x 10-4,
Coefflcienf,
COR
- 0 999)
DYNE.SEC. -___ CM5
Fig. 1. Pure water permeability data. Fraction of feed removed, @=FJF, pure water permeability coefficient, A,, according to eqn. (7)
vs. AP/F. Slope gives
Fig. 2. l/l?vs. l/J, for various NaCl concentrations and feed pressures of 150-400 psi (1.03-2.76 MPa). Slope is the solute permeability coefficient K,, according to eqn. (5).
separation of binary aqueous acetic acid solutions with polyetheramide (PA300) and polyether (PEC-1000) composite membranes also have been reported by Sourirajain [ 4, pp. 657-6601, but quantitative comparison with our data is not possible because those experiments were carried out with different feed concentrations and pressures (190 ppm and 1000 psia with PA-300; 50,000 ppm and 800 psia with PEC-1000). However, the level of separation is 65-70% with the PA-300 and 91% with the PEC-1000 membrane. The intercepts of all lines are close to unity which means that the reflection coefficient (a) is close to unity, or R, 41 [see eqn. (3) 1. In terms of the so-
181
Fig. 3. l/Rvs. l/J, for various acetic acid concentrations and feed pressures of 150-400 psi (1.032.76 MPa ) . Slope is the solute permeability coefficient, K,,according to eqn. (5 ) .
Fig. 4. Comparison of slopes (solute permeability coefficients) of l/Rvs. l/J” for sodium chloride and acetic acid solutions at constant concentration of 1000 ppm for both solutes and pressures from 150-400 psi (1.03-2.76 MPa).
lution-diffusion model, this means that as expected there is no convective contribution to solute transport in very tight reverse osmosis membranes. The solute permeability coefficient, K2, can be found from the slopes of the lines plotted in Figs. 2-5. Table 1 gives for binary solutions the permeability of Na+ and acetic acid in the membrane. Figures 6 and 7 show the plots of K2 vs. feed concentration for Na+ and acetic acid, respectively. As expected, & increases with increasing feed concentration for both Na+ and acetic acid up to
Fig. 5. Comparison of slopes (solute permeability coefficients) of l/I?vs. l/& for sodium chloride and acetic acid solutions at constant concentration of 4000 ppm for both solutes and pressures from 150-400 psi (1.03-2.76 MPA). TABLE 1 Permeability of Na+ and acetic acid for binary solutions Solute Sodium Chloride
Feed concentration (ppm ) 500 1000
2000 3000 4000 5000 Acetic Acid
300 700 1000
2000 3000 4000
Ks x lo7 (m/set ) 0.332 0.422 0.516 0.553 0.594 0.639 2.91 3.35 3.96 5.59 5.96 6.64
certain level of concentration, after which it remains relatively constant. These results are similar to those obtained previously by Soltanieh and Gill [ 301 for NaCl solutions. The shapes of Figs. 6 and 7 suggest that the variation of solute permeability of the membrane with feed’concentration may be described by the type of Langmuir sorption model proposed by Vieth [ 33 1. This model involves a dual sorption mechanism which includes sorbate dissolved according to Henry’s law, and that which occupies unrelaxed free volume within the membrane and
183
I
I
I
I
I
1000
2000
3000
4000
5000
FEED CONC.
(ppm of NaCI)
Fig. 6. Variation of permeability of NaCl with feed (NaCl) concentration.
0.75 zo 0: -
0.50 -
b x y"
0
, 0
1000
1
FEED CONC.
I
I
2000
3000
4000
(ppm of acetic acid)
Fig. 7. Variation of permeability of acetic acid with feed (acetic acid) concentration.
described by a Langmuir type isotherm. Since the permeability coefficient of membrane (&) is proportional to the solute solubility, the model suggested by Vieth [ 33 ] becomes:
K2 =KzH +K2==HkC+s
(10) k
where KzHand KzL are the Henry’s law and Langmuir sorption contributions to the permeability. Hk is the Henry’s law constant, & and & are the Langmuir constants, and C is the concentration of solute in the bulk. & is called the hole saturation constants, and L; the hole affinity constant which is related to the ratio of rate constants for sorption and desorption of penetrant in the holes. According to eqn. (lo), if L; C << 1 the model reduces to:
K2 = (Hk +L,L;)C
(11)
184
At sufficiently high concentrations the microvoids become saturated and will no longer sorb additional penetrant. Thus when LkC >> 1, sorption in the microvoids reaches a saturation limit, I+, and eqn. (10) reduces to: K2 =H,C+L,
(12)
the slope of which yields the Henry’s law constant. The dual sorption model predicts that an isothermal plot of K2 versus C will consist of a low-concentration linear region and a high-concentration linear region connected by a nonlinear region. Once Hk is obtained, we may calculate KzL from eqn. (10): K2L=K2-K2H=K2-HkC
(13)
Then KzL is used in the Langmuir model in the form: 1111 -
K2L -&Lh
0c
(14)
+Lk
By plotting l/K,, versus l/C, one can obtain Lk and Lk . The data of Table 1 and Figs. 6 and 7 were used to evaluate the constants of eqn. (10) by the method described above. Reasonably straight lines were obtained in all cases and the numerical values of the constants were found to be: For salt K, =3.2~1O-‘~C+
(5.05x10W6)
(0.0356)C
1+ 0.0356C
(15)
For acetic acid K2 =5.0x
10-gC+
(5.15x10-5)
(0.00194)C
1+ 0.00194c
(16)
Therefore the dual-sorption Langmuir model describes the variation of the solute permeability with feed concentration in a useful way. Effect of NaCl on acetic acid rejection (ternary results)
Figures 8 and 9 show the effect of NaCl on the acetic acid rejection at two different concentrations of 1000 and 4000 ppm acetic acid. At each concentration, the Na+ concentration varied from zero (pure acid) to 4000 ppm. For a feed of 1000 ppm acetic acid the slope was found to be 0.396X lo-” m/set. When 1000 ppm Na+ is added to the feed, the slope decreases to a value of 0.363 x 10A6. Since the slope was determined to be a measure of the solute permeability coefficient, the value of K2 decreases by 8.3% with a feed of 1000 ppm acetic acid/1000 ppm Na+, and by 18.9% with a feed of 1000 ppm acid/ 4000 ppm Na+ as compared to a feed concentration of 1000 ppm acetic acid alone. Similar results were obtained for a feed of 4000 ppm acetic acid. Therefore, acetic acid rejection increases as NaCl is added to the solution.
185
Fig. 8. Effect of NaCl concentration on the separation (or rejection) of acetic acid at a concentration of 1000 ppm.
Fig. 9. Effect of NaCl concentration on the separation (or rejection) of acetic acid at a concentration of 4000 ppm.
Effect of acetic acid on NaCl (ternary results) Figures 10 and 11 show the effect of acetic acid on Na+ rejection. For a feed of 1000 ppm Na+, the slope was determined earlier to be 0.042 X lO-‘j m/set. With a feed of 1000 ppm Na+/lOOO ppm acetic acid the slope increases by 7.1% to 0.045 x 10m6.For a feed concentration of 1000 ppm Na+/4000 ppm acetic acid the slope increases by 16.7% to 0.049 x 10w6. For a feed concentration of 4000 ppm Na+ similar results are obtained. Therefore, as acetic acid is added to salt solution, the rejection of Na+ decreases.
186
Fig. 10. Effect of acetic acid concentration on the separation (or rejection) of NaCl at a concentration of 1000 ppm.
0
I
I
2
4
I 6
p(g$
Fig. 11. The effect of acetic acid concentration on the separation (or rejection) of NaCl at concentration of 4000 ppm.
a
Conclusions
The main purposes of this work are to get a better understanding of the separation of multi-component salt/organic solutions using hollow fiber reverse osmosis systems, and to demonstrate further the usefulness of the complete mixing model. It was found that the previously observed linear relationship between the inverse of the rejection (1/R) and the inverse of the volume flux (l/J”) for salt solutions, also is valid for an organic solute such as acetic acid. Excellent
187
linear relationships were observed at all levels of concentrations considered in this study for both binary and ternary mixtures. This support the complete mixing assumption in the shell side of hollow fiber modules. Employing the simple diffusion model for transport across the membrane facilitates easy determination of the solute permeability coefficient, &. The values of K2 increase as the feed concentration increase up to a certain level, after which it remains relatively constant. This behavior is observed for both NaCl and acetic acid. The permeability of NaCl was found to be an order of magnitude smaller than that of acetic acid. The dual sorption Langmuir model describes the variation of K2 with C reasonably well. The rejection of acetic acid solution by aromatic polyamide membrane at pressure of 400 psia is roughly 70% for a feed concentration of 1000 ppm and roughly 50% for a feed concentration of 4000 ppm. This suggests that concentrated solutions of weak acids may in some cases be purified by passing most of the water and acid and rejecting ionized or particulate constituents. Such a procedure would eliminate all particulates down to those on the order of lo100 A. It was shown quantitatively that the transport of acetic acid and NaCl are coupled. The presence of the salt inhibits the transport of acid. However, the acid enhances the transport of NaCl. List of symbols A
4 B
c CP
CR (CJln F
FP FR
Hk I JS JV
J” K2 K
2H
K2L
coefficient in eqn. (4) ( - ) solvent permeability coefficient defined by eqn. (6b) ( m2-set/kg) coefficient in eqn. (4) (m3/m2-set) solute concentration in the bulk of feed (ppm) concentration of permeate (ppm ) concentration of retentate (ppm) logarithmic average concentration across the membrane (ppm) feed flow rate (m”/sec ) product flow rate (m”/sec ) reject flow rate (m3/sec) Henry’s law constant (m/set-ppm ) intercept of the line defined by eqn. (7) ( - ) solute flux (kg/m2-set) total volume flux ( m3/m2-set) F,/S, = overall average volume flux of a hollow fiber module (m”/m”set ) solute permeability coefficient, defined by eqn. (6a) (m/set) Henry’s law sorption contribution to solute permeability coefficient (m/set) Langmuir sorption contribution to solute permeability coefficient (m/ set )
188
L,, Ld phenomenological coefficients (m”-set/g) pressure difference across the membrane (Pa) 1- C&/CR= rejection coefficient ( - ) rejection coefficient at infinite flux (- ) RCC overall average rejection of a hollow tiber module (- ) R slope of the line defined by eqn. (7) (m4-set/kg) S total membrane surface area of a hollow fiber module ( m2) SIXI
AP R
Greek symbols osmotic pressure difference across the membrane (Pa) A7l XR
o CD CL)
osmotic pressure of the reject solution or retentate (Pa) reflection coefficient (- ) F,/F=productivity of the module ( - ) solute permeability at zero flux (s/m)
Acknowledgement This work was supported in part by the New York State Energy Research and Development Agency and the Eastman Kodak Company.
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