FLOW THROUGH POROUS MEDIA SYMPOSIUM
J. P. AGRAWAL S. SOURIRAJAN
Reverse Osmosis he reverse osmosis process is discussed with particular
T reference to systems involving aqueous solutions and Loeb-Sourirajan-type porous cellulose acetate membranes. Mechanisms of the process and porous cellulose acetate membrane technology are briefly reviewed. Based on a general capillary diffusion model for the transport of solvent and solute through the membrane, transport equations applicable for the entire range of solute separation are presented. The results of the analysis and correlations of experimental reverse osmosis data are illustrated. O n the basis of the above equations and correlations, methods of membrane specification, expressing membrane selectivity, and predicting membrane performance are outlined. Reverse osmosis is then treated as a unit operation in chemical engineering. A set of general equations for reverse osmosis process design is then derived for reverse osmosis systems specified in terms of membrane specifications and operating conditions. T h e utility of these equations for studying system performance and process parameters is indicated. Reverse osmosis as a general concentration process and the separation of mixed solutes in aqueous solution are then briefly discussed from the points of view of process design and the predictability of membrane performance, respectively. The reverse osmosis process is a general and widely applicable technique for the separation, concentration, or fractionation of inorganic or organic substances in aqueous or nonaqueous solutions in the liquid or the gaseous phase (747-756, 777). T h e technique consists in letting the fluid mixture flow, under pressure, through a n appropriate porous membrane, and withdrawing the membrane permeated product generally at atmospheric pressure and surrounding temperature ; the product is enriched in one or more constituents of the mixture, leaving a concentrated solution on the upstream side of the membrane (77-94). No heating of the membrane and no phase change in product recovery are involved. 62
INDUSTRIAL A N D ENGINEERING CHEMISTRY
This process is a new development in the field of solute-solvent separation. Its most significant current application is in the field of water treatment, in general, and saline water conversion, in particular, for which porous cellulose acetate membranes have been found appropriate. In view of the recent advances in the above field, this paper is limited to a discussion of the reverse osmosis process involving aqueous solution systems and cellulose acetate membranes. ffOsmosis” and “Reverse Osmosis”
Under isothermal conditions, in both “osmosis” and reverse osmosis” the preferential transport of material through the membrane is always in the direction of lower chemical potential. This is a thermodynamic requirement, and it does not, and cannot, specify which component, if any, of a solution is preferentially transported through a given membrane and the mechanism by which such transport takes place. I n the literature, “osmosis” and “reverse osmosis’’ are associated with the existence of a ‘%,emipermeable” membrane; the origin of such semipermeability is still an open question. From a practical standpoint it is important to note that the reverse osmosis process is not restricted to the passage of water from aqueous solutions, that it is not restricted to 100% solute separation, that neither “osmosis” nor “reverse osmosis’’ is an explanation of the mechanism of the process involved, and that the distinction between the two terms is entirely one of arbitrary convention and popular usage.
Al
Experimental product rate and solute separation data for the system NaN03-NaCl-HzO at total molality 1M and 2 M and the systems NaCl-MgC12-H20 and NaClBaClZ-HzO a t total molalities of l M , have been reand they are in good agreement with those ported (4), calculated using Equations 141, 146, 148, 152, and 153. Similar data for the system KCl-NaCl-H20 (total molality -2M) are given in Table VI. Prediction technique. The foregoing analysis and the agreement between the experimental and calculated separation and product rate data offer a simple means of predicting membrane performance for moderate concentrations of aqueous feed solution systems involving two inorganic solutes with a common ion. For such systems, the prediction technique is as follows : From the specifications of the membrane given in terms of A and (DAM/K6),and the applicable mass transfer coefficient correlation, calculate solute separation and product rate for the single solute systems at the given total molality following the Kimura-Sourirajan analysis. Calculate NA], Nsl, NA2, and NB2 from the above solute separation and product rate data for the single solute systems. Calculate the product rate for the mixed solute system using Equation 141. Finally, calculate solute separations with respect to each solute using Equations 146, 148, 152, and 153. Some experimental results at high total concentrations. To test the validity of the above analysis for high feed concentrations, the system NaNO3-NaCl-HzO was studied recently at a total feed molality of -3M. I t was found that, under such conditions, Equation 141 was valid only when x 1 and x 2 (Equations 139 and 140) were defined in terms of molarity, instead of molality, as illustrated in Figure 28. Since molarity and molality are not too different up to about 2 M for the systems NaN03HzO and NaCl-HZO, it is probably more general to express the product rate correlation in terms of molarities, as illustrated in Figure 28. Under such conditions, the prediction procedure is slightly different and it is illustrated below with some numerical data. First, calculate the effective total molality for the single solute systems corresponding to the total molarity of the mixed solute system. For example, referring to Table VI, Run no. 556, Film no. 25, for the system NaN03NaCl-H20 [A l-A2-H20]. 0.794 molal = 0.78 molar ( m l )= ~ ~2.236 molal 2.14 molar
( m 1 ) ~ l=
VOL. 6 1
NO. 1 1
NOVEMBER 1 9 6 9
85
total molality = 3.03; total molarity = 2.92 2.92 molar NaN03 = 3.28 molal NaN08 3.10 molal NaCl 2.92 molar NaCl Therefore, the effective total molalities for the single solute systems (NaN03-HZO) and (NaCl-H20) are 3.28 and 3.10, respectively. Next, calculate solute separations, and product rates, PRAl and PRa2, for the single solute systems a t their corresponding total effective molalities calculated above from data on membrane specifications and the applicable mass transfer coefficient correlation; or such data can be obtained experimentally. Then calculate NA1, Nsl, NA2, and NBz from the above solute separation and product rate data obtained for the single solute systems. Find x 1 and x 2 from Equations 139 and 140, using molarity instead of molality; for the above examples, x1
=
0.78 = 0.267 0.78 2.14
x2
=
2.14 = 0.733 0.78 2.14
+
+
Finally, calculate as before the product rate for the mixed solute system, PRmix, from Equation 141, and solute separations with respect to each solute using Equations 146, 148, 152 and 153. A set of such results for the system NaNOS-NaCl-HzO a t the total molality of -3M is illustrated in Table VI, covering a wide range of solute separations which show good agreement between experimental and calculated data. General problem of predictability of membrane performance for mixed solute systems. The foregoing technique, though a very useful one, is only a partial answer to this general problem. Even for the type of solution systems tested, the possible applicability of the above technique for a wide range of solute systems and feed concentrations, and the extension of the technique for aqueous feed solutions containing more than two solutes with a common ion, need experimental verifications. Some preliminary experimental results with aqueous feed solutions containing mixed inorganic solutes with no common ion show that the above prediction technique is not applicable to such systems probably due to ionic interactions. Such and other systems involving inorganic and/or organic mixed solutes need further experimental and analytical studies. Systems Such as Sucrose-Water
For the system sucrose-water, (DAM/K6)is a unique function of XA2,irrespective of the particular combination of feed concentration and feed flow rate used in conjunction with the Loeb-Sourirajan-type porous 86
INDUSTRIAL AND ENGINEERING CHEMISTRY
cellulose acetate membranes (57). It is possible that several similar systems exist. For such systems, it is necessary to establish the (DAM/K6) us. X A , correlation experimentally, and include the result in the procedure for predicting membrane performance as illustrated for the system sucrose-water (57). Conclusion
Reverse osmosis is a fast growing field of applied science. It is now being extensively studied for various water treatment applications, such as sea water and brackish water conversion, water softening, water pollution control, water renovation, and waste recovery (6, 75, 38, 42, 69, 77-80, 84, 707, 705, 732-734, 140, 756, 769). Several parametric studies of the reverse osmosis
process for sea water and brackish water conversion have been made (73, 74, 46, 48, 49, 58, 727, 760) and several pilot plants have been designed, built, and operated successfully using the Loeb-Sourirajan-type porous cellulose acetate membranes ( 7 , 2, 22, 23, 70, 76, 82, 84, 700, 777, 725, 126, 757, 767). The Coalinga pilot plant, built by the University of California, Los Angeles, for brackish water conversion, has maintained a record of outstanding performance since its commission in June 1965 (76, 84, 707). There is also now growing activity on reverse osmosis studies for food processing applications (7, 57, 99, 106, 778, 748, 770). From the authors’ point of view, there are several areas of reverse osmosis work which have potentially far-reaching beneficial consequences to chemical industry. Studies on the physicochemical criteria of preferential sorption and/or preferential repulsion at solidsolution interfaces and microcapillary hydrodynamics at such interfaces, the mechanism of pore formation in the process of making asymmetric porous membranes, the methods of creating and maintaining pores of appropriate size on the surface layer of the membrane, quality control of the Loeb-Sourirajan-type porous cellulose acetate membranes in their large-scale manufacture and the utilization of their fullest potentialities (60, 63, 727), integration of the science and engineering of reverse osmosis, development of different membranes for different applications, and the application of reverse osmosis for the separation of gaseous mixtures (5, 742), organic liquid mixtures (67, 62, 746), and highly acid or alkaline aqueous solutions are all some of the areas of enormous practical interest. Further work in this field can lead to the growth of reverse osmosis in all its applications and contribute significantly to the economic prosperity and physical well-being of all mankind. Such is the scope of reverse osmosis (752). Acknowledgments
The authors are grateful to Logos Press Ltd., London, England, for permission to use in this paper several illus-
trations from the book on "Reverse Osmosis" by S. Sourirajan. One of the authors (J. P. A.) thanks the National Research Council of Canada for the award of a postdoctoral fellowship. NOMENCLATURE g-mol H2O cmzsec atm
A
pure water permeability constant,
Ao
extrapolated value of A at P = 0 weight fraction of solute in product activity of water in aqueous solution proportionality constant defined by Equation 42 (cA/cA~O) or ( X A / X A ~ O ) ( C A ~ C A ~ (~c A ) z, / c A ~ " ) , (CAa/CAIo), respectively, or ( X ~ i l x ~ i O ) (,X A Z / X A ~ O()x, A a / X A l 0 ) , respectively values of C1, CZ,and Ca, respectively, a t time t = 0 in batch process or at membrane entrance in flow process
a aw
B C Ci, C z , Ca
Cio, C2O, Cao
Ca
Ci, Cz, Ca
CA CAI, CA2, CAS
EA8
CM C M ~ ,CMa
DAB DAM (DAM /K6) d E
1/ h
= = =
K
=
k
=
H
molar density of solution, g-mol per cc molar density of feed solution, concentrated boundary solution, and the product solution, respectively, g-mol per cc solute concentration, g-mol per cc or mole fraction solute concentration in the bulk solution and the concentrated boundary solution on the high pressure side of the membrane, and in the product solution on the atmospheric pressure side of the membrane, respectively, at any point on the membrane surface at any time, g-mol per cc or mole fraction average solute concentration in product solution corresponding to a given A, g-mol per cc or mole fraction molar density ofsolution in the membrane phase, g-mol per cc molar density of solution in the membrane phase in equilibrium with cz and ca, respectively, gmol per cc diffusivity of solute in water, cma per sec diffusivity of solute in membrane phase, cm2 per sec solute transport parameter, cm per sec diameter of cell, cm longitudinal diffusion coefficient, cm2 per sec fraction solute separation average fraction solute separation maximum solute separation depth of cell, cm membrane area per unit volume of fluid space, cm-' proportionality constant defined by Equation 10 mass transfer coefficient on the high pressure side of membrane. cm Der sec
kA i k Aa
(cmij(sec)(g)
ke
= S X M B X 3600,
L
= longitudinal length over which mixing is considered, cm = thickness of the concentrated boundary solution = parameter defined by Equation 106 or concentration of solution expressed in molality unit as indicated
I M
-
-
( E A a / C A i o ) Of' ( ? A a / x A l o )
c
ffm.r
molecular weight of solute A1 molecular weight of solute A2 molecular weight of water molecular weight of solute solute molality solute molality in feed solution or bulk solution on the high pressure side of membrane molality of feed solution with respect to solute A1 molality of feed solution with respect to solute A2 solute molality in product solution molality of product solution with respect to solute A1 molality of product solution with respect to solute A2 g-mol solute flux through membrane, cmz sec flux of solute A1 through membrane for feed sysg-mol tem (AI-HzO), cm2 sec flux of solute A2 through membrane for feed sys-
solvent water flux through membrane,
g-mol cmz sec
flux of solvent water through membrane for the g-mol feed system (Al-HzO), c~ flux of solvent water through membrane for the g-mol feed system (A2-Hz0), c~ Reynolds number = Schmidt number =
feed flow rate H U
DAB kd DAB
Sherwood number =
-
operating pressure, atm quantity defined by Equation 110 product rate, g per hr per S cma of film area product rate for feed system (Al-HaO), g per hr per S cm2 of film area product rate for feed system (A2-H20), g per hr per S cma of film area product rate for feed system (Al-A2-HzO), g per hr per S cmz of film area pure water permeability, g per hr per S cma of film area product rate in batch concentration process, grams per unit area of film surface per unit time expressed by Equation 128 quantity defined by Equation 52 gas constant effective area of film surface, cm2 absolute temperature, OK time, sec or day 21/21Q average fluid velocity at any given position at any time, cm per sec value of zi: a t time = 0 volume of feed solution on the high pressure side of membrane and volume of product solution a t the atmospheric pressure side of membrane, respectively, at any time in a batch process, cc value of V I at time = 0 initial and final volume of solution on the high pressure side of membrane during the batchwise concentration process, cc = partial molal volume of water VOL. 6 1
NO.
1 1
NOVEMBER 1 9 6 9
87
= = = =
VW
(V;Y V,
W W, W W
X XA
X A I ,XAS,X
= = = = A= ~
=
X A 1‘
XAM = X A M ~X ,A M ~= X
=
x1, x2
=
z
= =
z
permeating velocity of solvent water, cm per sec value of uw at time = 0 quantity defined by Equation 40 weight of solution on the high pressure side of membrane during the batchwise concentration process, g weight of solute in the above solution, g weight of water in the above solution, g parameter defined by Equation 82 mole fraction of solute mole fraction of solute in the bulk solution and the concentrated boundary solution on the high pressure side of the membrane, and in the product solution on the atmospheric pressure side of the membrane, respectively, a t any point on the membrane surface a t any time value of X A I at t = 0 in batch process or at membrane entrance in flow process mole fraction of solute in membrane phase values of XAM in equilibrium with X A Zand X A ~ , respectively longitudinal distance along the length of membrane from channel entrance, cm quantities defined by Equations 139 and 140, respectively quantity defined by Equation 65 weight fraction of solute in the solution on the high pressure side of the membrane during the batchwise concentration process
Greek Letters = = = = = =
= =
= =
= =
= P1
=
Zi
=
T
=
+
=
constant constant parameter defined by Equation 37 fraction product recovery defined by Equation 83 effective thickness of membrane, cm normal distance towards membrane measured from edge of the concentrated boundary solution, cm fraction power recovery parameter defined by Equation 38 parameter defined by Equation 37 viscosity of water, CP kinematic viscosity of solution, cm2 per sec osmotic pressure of solution, atm osmotic pressure of solution corresponding to mole fraction XAof solute, atm density of solution, g per cc total number of moles of ions given by one mole of electrolyte parameter defined by Equation 7 3 osmotic coefficient
Suffixes
;
= initial state of feed solution = final state of feed solution
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88
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
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S., Jr., Dresner, L., and Kraus, K. A,, in “Principles of DesalinaUon,” K . S. Spiegler, Ed., Chap. 8, Academic Press, New York, 1966. (45) Johnson, J. S. and Kraus K. A. “Hyperfiltration by Dynamically Formed Membranes,” P a i e r presente6 beford Division of Water, Air, and Waste Chemistry, ACS, San Francisco Meeting, March 31-April 5, 1968. (46) Johnson, K. D. B., Grover, J. R., and Pepper, D., Desalination, 2, 40 (1967). (47) Keilin, B. “ T h e Mechanism of Desalination by Reverse Osmosis,” U S . Dept. Interior, Office of Saline Water, Research and Development Progress Report No. 84 (1963). (48) Keilin, B., in “Membrane Processes for Industry,” p 80-100, Southern Research Institute, Birmingham, Ala., 1966. (49) Keilin, B., and DeHaven, C. G., Proc. First International Symp. on Water Desalination, Washington, D.C., 1965. (Pub, U S . Dept. Interior, Office of Saline Water, Washington, D.C., Vol. 2, p 367-380). (52) Keilin, B., Saltonsta!l, C. W., Higley, W. S., Kesting, R . l3;, and Vincent, A. L., Structure and Properties of Reverse Osmosis Membranes U S . Dept. Interior, Officeof Saline Water,Research and Development Progresskeport No. 154 (1965). (51) Kesting, R . E., J . ApPl. Polym. Sci., 9, 663 (1965). (52) Kesting, R . E., Barsh, M. K., and Vincent, A. L., ibid., 9, 1873 (1965). (53) Kimura, S., and Sourirajan, S., AIChE J . , 13, 497 (1967). DESIGN DEVELOP., 7, (54) Kimura, S., and Sourirajan, S . , IND.ENO.CHEM.PROCESS 41 (1968). (55) Kimura, S., and Sourirajan, S., ibid., 7, 197 (1968). (56) Kimura, S., and Sourirajan, S., ibid., 7, 539 (1968). (57) Kimura, S., and Sourirajan, S., ibid., 7, 548 (1968). DESIGN (58) Kimura, S., Sourirajan, S., and Ohya, H., IND.ENC. CHEM.PROCESS DEVELOP., 8, 79 (1969). (59) Klem, K., and Friedman, L., J . Amcr. Chem. Soc., 54, 2637 (1932). (60) Kopefek, J., and Sourirajan, S., J . A@l. Polym. Sci.,13, 637 (1969). 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