r e = fractional entrainment tL = average liquid residence time, h U,, ,Ug = vapor velocity based on active bubbling tray area, ft/s W = weir height, in. x = liquid composition, mole fraction y = vapor composition, mole fraction 2 = column height or height in column, in. z = measured bed height, in. 2, = clear liquid height, in. 21 = froth height, in. 2 , = length of liquid travel across tray Greek Letters h = molar latent heats of vaporization, Btu/lb-mol, or relative volatility of two components t = dimensionless entrainment factor p = density, lb/ft3 0 = surface tension, dyn/cm, or standard statistical deviation Superscripts and Subscripts j = componentj L = liquid phase
n = trayn T = total V = vapor phase 1 = component 1 2 = component2
Literature Cited "A.1.Ch.E. Bubble-Tray Design Manual", American Institute of Chemical Engineers, New York. N.Y., 1958. Anderson, R. H., M.S. Thesis, University of Texas at Austin, 1974. Box, G. E. P., Behnken, D. W., Technometrics, 2, 455-475 (1960). Lewis, W. K.. Ind. Eng. Chem., 14, 492 (1922). Lu, B. C. Y., Can. J. Techno/., 34, 468-472 (1957). Murphree, E. V., Ind. Eng. Chem., 17, 747 (1925). Prabhu, P. S.,Van Winkle, M., J. Chem. Eng. Data, 8, 210-214 (1963). Sawistowski, H., Smith, W., Ind. Eng. Chem., 51, 915-918 (1959). Sawistowski, H., Smith, W., Chem. Ing. Tech., 45 (le), 1093-1098 (1973a). Sawistowski. H., Smith, W., Chem. Ing. Tech., 45 (le), 1114-1117 (1973b). Todd, W. G., Ph.D/ Dissertation, University of Texas at Austin, 1971.
Received for reuiew January 20, 1976 Accepted June 9,1976
Supplementary Material Available. Tables I, 11, IV, and V of design and experimental column data (9 pages). Ordering information is given on any current masthead page.
Predictability of Reverse Osmosis Separations of Higher Alcohols in Dilute Aqueous Solutions Using Porous Cellulose Acetate Membranes Takeshi Matsuura, A. G. Baxter, and S. Sourirajan' Division of Chemistry, National Research Council of Canada, Ottawa, Canada, K 1A OR9
The polar free energy parameter -AAG/RT, and the nonpolar (hydrophobic) parameter w * Xs* together govern reverse osmosis separations of C1 to C9 alcohols in dilute aqueous solutions using porous cellulose acetate for alcohols in terms of the above paramemembranes. An expression for solute transport parameter (DAMlK6) ters is given for the case where water is preferentially sorbed at the membrane-solution interface, which case extends up to w'ZS" = 2.5. Using this expression, reverse osmosis separations of above alcohols for membranes of different surface porosities can be predicted from data on membrane specifications only, given in terms of pure water permeability constant and D A M I Kfor ~ NaCI.
Introduction Reverse osmosis separations of higher alcohols in aqueous solutions using porous cellulose acetate membranes have been briefly studied and discussed in the literature (Duvel and Helfgott, 1975; Kesting and Eberlin, 1966). Since the chemical nature of cellulose acetate material has both polar and nonpolar characteristics, reverse osmosis separations involving cellulose acetate membranes may be expected to be affected by both polar and nonpolar (hydrophobic) characters of the solute and solvent molecules. Experimental studies on reverse osmosis separations of alcohols and monocarboxylic acids in dilute aqueous solutions have shown (Matsuura and Sourirajan, 1973a,b) that the nonpolar effect may be considered to be negligible if the molecular structure of the solute contains a straight chain involving no more than three carbon atoms not associated with a polar functional group; for solute molecules involving more than three such carbon atoms, the nonpolar effect on reverse osmosis separations is significant. With reference to alcohol solutes (and other undissociated polar organic solutes) for which the above nonpolar effect can 82
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
be neglected, the technique for predicting reverse osmosis separations from data on membrane specifications based on NaCl solute only, has been established and reported (Matsuura et al., 1976). This work extends the above technique for predicting reverse osmosis separations of higher alcohols in dilute aqueous solutions, where nonpolar effect is significant. Since Taft's polar parameter U* (Taft, 1956) for the substituent group in the alcohol molecule is less than that for water, the polar effect of alcohol-solute relative to that of water is a repulsive force contributing to preferential sorption of water a t the membrane-solution interface (Matsuura and Sourirajan, 1971). On the other hand, the nonpolar effect arising from the hydrophobic nature of the alcohol solute is an attractive force for the solute toward the membrane surface, contributing to a decrease in preferential sorption of water a t the membrane-solution interface. Consequently, when both polar and nonpolar effects govern reverse osmosis separation, the magnitude of preferential sorption of water at the membrane-solution interface is subject to two opposing
Table I. Physiochemical Data on Alcohol Solutes Studied Solute NO. 10
9 8 4 6 3 7 1
14 19 20 21
15 22
23 24 25 26 27 28 29 16 30 31 32
Name
Formula
Methanol CH:rOH Ethanol CH:ICHPOH 1-Propanol CH,ICH&HrOH 2-Propanol CH:jCHOHCH:r 1-Butanol CH:r(CH2)2CHzOH 2-Butanol CH:,CHyCHOHCH:j 2-Methyl-1-propa- (CH:r)&HCH?OH no1 2-Methyl-2-propa- (CH:&jCOH no1 1-Pentanol CH:j(CH2)3CH20H 3-Pentanol CH:iCH2CHOHCH&H:j 3-Methvl-1-butanol (CH&CHCH&H20H 2,2-Dimethyl-l(CH:r):jCCH20H propanol 1-Hexanol 2-Hexanol 3-Hexanol 2-Methyl-1-pentano1 3-Methyl-1-pentano1 4-Methyl-1-pentano1 3-Methyl-2-pentano1 2-Methyl-3-pentano1 3,3-Dimethyl-2butanol 1-Heptanol 2-Heptanol 3-Heptanol 4-Heptanol
h x 104 cmh"
(-AAG/
32.0 46.1 60.1 60.1 74.1 74.1 74.1
24.9 20.6
BE,
ZS*~
7.10
0
18.2 16.5 16.5 16.5
6.26 5.56 4.78 4.64 4.66 4.66
-0.07 -0.36 -0.70 -0.39 -1.13 -0.93
214 347 480 456 613 589 589
0 0 0 -24 0 -24 -24
0 0
74.1
16.5
3.32
-1.54
549
-64
-0.55
88.2
4.52 4.54 4.54 4.15
-0.40 -1.98
88.2 88.2
15.3 15.3 15.3 15.3
746 722 722 682
-24 -24 -64
102.2 102.2 102.2 102.2
14.3 14.3 14.3 14.3
4.41 4.42 4.42 4.42
879 855 855 855
-24 -24 -24
1.85 1.03 1.03 1.03
102.2
14.3
4.42
855
-24
1.03
102.2
14.3
4.42
855
-24
1.03
102.2
14.3
4.44
831
-48
0
102.2
14.3
4.44
831
-48
0
102.2
14.3
4.05
-3.33
791
-88
-1.74
116.2 116.2 116.2 116.2
13.5 13.5 13.5 13.5
4.29 4.30 4.30 4.30
-2.11
1012 988 988 988
0 -24 -24 -24
2.13 1.19 1.19 1.19
964 964
-48 -48
0
948
-64
-0.95
948
-64
-0.95
940
-72
-0.49
924
-88
-2.03
1145 1121 1121
-24 -24
1278 1254 693
24 186
Mol wt
88.2
33 34
18.2
RT)
-1.74
2-Methyl-3-hexanol (CH:~)~CHCHOH(CH~)&H:I 116.2 4.32 13.5 4-Methyl-3-hexanol CH:jCH2CH(CH:j)CHOH116.2 13.5 4.32 CH2CH:j 35 3-Methyl-3-hexanol CH:I(CH~)~COH(CH:~)- 116.2 13.5 3.92 CH2CH:j 36 2,2-Dimethyl-1CH:I(CH~)*C(CH:~)~CH*OH 116.2 13.5 3.92 pentanol (CH:I)~CHCHOHCH(CH:~)~ 116.2 37 2,4-Dimethyl-313.5 3.93 pentanol CH:jCH&HOHC(CH& 38 2,2-Dimethyl-3116.2 13.5 4.34 pentanol 17 1-Octanol 130.2 CH:](CH?)sCH?OH 12.9 4.17 39 2-Octanol CH:{CHOH(CH~)SCH:I 130.2 12.9 4.19 40 4-Octanol CH:,(CHa)2CHOH(CH2):]130.2 12.9 4.19 CH:r 18 1-Nonanol 144.3 12.3 CH:r(CH2);CHzOH 4.05 41 5-Nonanol 144.3 12.3 4.07 (C4Hg)zCHOH 5 Cvclohexanol JCH'J)KCH(OH), 100.2 15.3 3.71 -0.79 , _,., , ' I ( I The values of k correspond to the experimental conditions used in this work. (cal'/"cc'/')/g-mol. tendencies. When the nonpolar effect is negligible, water is always preferentially sorbed; as the nonpolar effect becomes progressively more significant, the magnitude of preferential sorption of water decreases. When the nonpolar effect becomes sufficiently high, it is reasonable t o expect the magnitude of preferential sorption of water t o change from positive t o negative, resulting in preferential sorption of solute a t the membrane-solution interface. It is also the object of this work t o locate the point or region of the above change with respect to alcohol solutes.
Experimental Section Thirty-three higher (C4 to C,) alcohols listed in Table I (along with some relevant physiochemical data) were used in
w*Bs*
0
0
0
0
0 0 0 0
1.29
1.57 0 0
-0.68
0
2.40 1.35 1.35 2.68 1.50 0
this work in single-solute aqueous solution systems. Four lower (C, to C:]) alcohols (Table I) were also included in this study for purposes of comparison of results. The apparatus and experimental procedure used in reverse osmosis experiments were the same as those reported earlier (Matsuura and Sourirajan, 1971; Sourirajan, 1970a). Batch 316 (10/30)-type cellulose acetate membranes (Pageau and Sourirajan, 1972) of different surface porosities were used a t the operating pressure of 250 psig. The specifications (Sourirajan, 1970b) of the membranes used are given in Table I1 in terms of pure water permeability constant A (in g-mol of H,O/cm* s atm) and solute transport parameter D A M / K(treated ~ as a single quantity, in cm/s) for sodium chloride. Table I1 also includes solute separation and product rate data for the membranes Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
83
Table 11. Specifications of Cellulose Acetate Membranes Used Film no.
Operating pressure: 250 psig Pure water permeability constant A , [g-molof H~O/(cm'-s-atm)]X lo6 Solute transport parameter, ( D A M / K ~ ) N(cm/s) ~ ( ' ~ , x lo5 In ( D A M I K ~ ) N , ~ ( . I In C*Nd('l Solute separation, % Product rate, g/hn ( I Area of film surface = 13.2 cm2. Feed solution: 3500 ppm of NaC1-H20. used a t feed flow rates corresponding to a mass transfer cm/s, using 3500 ppm of NaCl-HZO coefficient k of 22 X as the feed solution. The values of k applicable for the organic solutes under the experimental conditions studied were calculated by the method given in Matsuura et al. (1974b). These values of h , given in Table I, quantitatively express concentration polarization in each case on the high pressure side of the membrane in terms of the Kimura-Sourirajan transport equations (Sourirajan, 1970b). In all experiments involving organic solutes, the solute concentration in the feed solution was about 200 ppm so that the osmotic pressure of the feed solution was negligible compared to the operating pressure. All experiments were of the short-run type which means that no significant change in PR with time was involved in this work. In each experiment, steady-state conditions were reached within 20 min; the entire run was over within the next 60 min during which time the change in flux with time was negligible. After the run, the system was depressurized and the membrane was allowed to relax for a t least 2 h before the next experiment. Further, all experiments were carried out a t the laboratory temperature (23-25 "C). The product rate (PR) and pure water permeation rate (PWP) data used in the calculations are those corrected to 25 "C using the relative viscosity and density data for pure water. The terms "product" and "product rate" refer to membrane permeated solution. The fraction solute separation f obtained in each experiment was calculated from the relation:
f=
(solute ppm in feed) - (solute ppm in product) (1) (solute ppm in feed)
In each experiment, PWP and PR in grams per hour per given area of film surface (13.2 cm2 in the apparatus used in this work) and f were determined a t the operating conditions used. A Beckman total carbon analyzer Model 915 was used to measure the concentrations of the organic solute in feed and product solutions. The analytical procedure was the same as that reported earlier (Matsuura and Sourirajan, 1971). The concentrations of sodium chloride were determined using a conductivity bridge. From the experimental f and (PR) data, ~ the alcohols used were obtained from values of D A M / Kfor the expression (Matsuura and Sourirajan, 1973a):
where S = effective film area ( = 13.2 cm2) and d = density of solution (= density of pure water). All data presented are for 25 "C. Results a n d Discussion Basic Relation for Estimation of D A M I Kfor ~ Alcohols from D a t a on DAM/KBf o r NaCI. Data on membrane specification (Table 11) provide the value of D A M I Kfor ~ NaCl for any particular film under consideration. The latter quantity 84
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
1
2
3
4
5
1.72 1.69 -10.99 -12.36 93.5 20.4
1.57 2.06 -10.79 -12.16 92.2 18.9
2.90 4.68 -9.97 -11.34 85.8 34.4
3.50 16.17 -8.73 -10.10 74.0 42.2
5.28 17.87 -8.63 -10.00 62.7 62.9
is related to the free energy parameter ( - A S G I R T ) for Na+ and C1- ions by the expression (Matsuura et al., 1975, 1976): In (DAMIK6)NaCi= In C*NaCI
)"-(I+
RT
Na+
+(-")R T
CI-
1
(3)
where In C * N ~ C is Ia constant. The values of -AAGIRT for Na+ and C1- ions for the cellulose acetate membrane material used are 5.79 and -4.42, respectively (Matsuura et al., 1975). From the known values of ( D A M / K ~ ) N(-AAG/RT)N,+ ~cI, and (-AAG/RT)cl-, the value of In C * N ~ can C I be calculated from eq 3 for the particular film under consideration. I t may be recalled that for a given membrane material (cellulose acetate in this work), the quantity In C*N,CI is simply an expression for the porous structure of the membrane surface given in terms of reverse osmosis data for the reference solute NaC1. The concept of free energy parameter with reference to reverse osmosis has been discussed extensively (Matsuura et al., 1975, 1976). The quantity -AAG/RT is a dimensionless polar parameter for the solute in aqueous solutions. The term LAG is defined as (AGI - AG,) where AG represents the free energy of hydration and the subscripts I and B represent the membrane-solution interface and the bulk solution phase respectively, and the symbols R and T in the free energy parameter represent gas constant and absolute temperature, respectively. The numerical value of -AAG/RT depends only on the chemical nature of solute, solvent, and membrane material, and it is independent of the porous structure of the membrane surface. It has been established (Matsuura et al., 1976) that for nonionized polar aliphatic and alicyclic organic solutes in aqueous solutions, where (i) reverse osmosis separations are governed by polar and/or steric effects and preferential sorption of water a t the membrane-solution interface, and (ii) the contribution of nonpolar effect to solute transport parameter is assumed equal to zero for solute molecules containing no more than three straight-chain carbon atoms not associated with a polar functional group, the quantity D d K 6 can be estimated from the general relation: In ( D A M I K ~ = )In C * N ~ C+I In A*
-+ (--',",") + 6*ZE,
(4)
The meaning of the quantities on the right side of eq 4 must C I from eq 3. The quantity be clear. The quantity In C * N ~ arises l In A* is a scale-factor, and it is a function of In C * x a ~only. The correlation of In A* with In C*N,CIhas been experimentally established for the cellulose acetate membrane material as given in Figure 3 in Matsuura et al. (1976); this correlation is used in this work. This correlation simply establishes a scale which permits one to use the particular numerical values
chosen to express the polar and steric parameters involved in eq 4.For the establishment of this scale, solute separation data for various polar organic solutes (including alcohols, aldehydes, ketones, and ethers) have been used as stated in the paper cited above, but once the correlation is established, it is independent of any solute under consideration (including alcohols) as shown in the paper cited above. The polar pa~ computed ~ on the rameter ( - S A G I R T ) for the solute c a be basis of its molecular structure using the data on structural group contributions for AGR and given in Table IV in Matsuura et al. (1976) for the cellulose acetate material. The dimensionless quantity 6* Z E , represents the contribution of steric effect to solute transport parameter. BE, represents Taft’s steric parameter for the substituent group in the solute molecule (Taft, 1956); the associated coefficient 6* is a function of the porous structure of the membrane surface and the chemical nature of both the membrane material and solute molecule as illustrated by the experimental correlation of 6* vs. In C * N ~ C for I cellulose acetate material given in Figure 1 in Matsuura e t al. (1976) for ether- and ketone-solutes. Equation 4 does not contain an explicit independent term to represent the contribution of nonpolar effect to D A M I K ~ . This means that eq 4 applies strictly only when the contribution of nonpolar effect to D A M / Kis~not significantly different from that due to solute molecules containing no more than three straight-chain carbon atoms not associated with a polar functional group. When such is not the case, an additional term is required on the right side of eq 4 to account for the contribution of nonpolar effect to DAMIK6. The form of this term has already been suggested (Matsuura et al., 1974a) as the dimensionless nonpolar parameter w * Z s * where Zs* (in cc1P2/g-mol)is the modified Small’s number (Matsuura and Sourirajan, 1 9 7 3 ~for ) the substituent group in the ) the associated solute molecule, and w* (in g-mol/ca11/2C C ~ ’ ~ is coefficient for Bs* applicable for the class of solutes studied. Incorporating the above nonpolar parameter, eq 4 assumes the more general form:
+
In (DAbfIK6) = In C*hac1 In A*
Equation 5 may now be considered as the most general expression for DAMIK6 for nonionized polar aliphatic and alicyclic organic solutes in aqueous solutions where reverse osmosis separations are governed by polar, steric, and/or nonpolar effects and preferential sorption of water a t the membrane solution interface. With respect to alcohol-solutes, it has been shown (Matsuura et al., 1974a) that 6* = 0 in the Z E , range 0 to -1.54. The available data on ZE, for the alcohols used in this work are in the range 0 to -3.33 (Table I). In order to find out whether or not 6* may be taken to be zero for this extended range of Z E , values, the reverse osmosis data for 12 alcohol-solutes (numbers 1, 3, 4, 6, 7 , 9, 10, 14, 19, 21, 29, and 32 (Table I) whose Z E , values lie in the range 0 to -3.33) were analyzed in terms of eq 5 . Just as the polar parameter -AAG/RT, the nonpolar parameter w * Z s * should be independent of the porous structure of the membrane surface. Consequently, the plot of In ( D A M I K vs. ~ ) the quantity (In C*N~CJ In A*) must be a straight line with a slope of unity when 6* = 0. This cor~ obrelation was tested with the experimental D A M I K data tained with five membranes of different surface porosities. ~ ) obtained with these membranes were The In ( D A M I K data subjected to least-squares analysis for the above straight-line correlation, and the slopes of these lines were determined for each of the above 12 solutes. The values of these slopes (denoted simply as “slope”) are plotted in Figure l as a function of SE,.Figure 1shows no definite trend in the change of slope
+
- 2.0
-3.0
-1.0
0
=Es
Figure 1. Correlation of “slope” and ZE,.
I
I
I
I
I
J z
0 d
N’JMBERS
1
a: a W
-IO
-9
-7
-8
-6
-E
+
Figure 2. Effect of (In C * N ~ C+I In A* (-AAG/RT) + 6*ZEs)on solute separation and product rate for film 1. Film type, cellulose acetate (Batch 316 (10/30));operating pressure, 250 psig; feed concentration, 0.001 0.005 g-molfl.; k values and solute numbers, same as in Table I.
-
with change in ZE,; the available data scatter about equally on both sides of slope = 1which corresponds to 6 = 0. Further, as will be shown later, solute separation data calculated on the basis 6 = 0 are in good agreement with the experimental results. For these reasons, for practical purposes, the quantity 6 was assigned a value of zero for alcohols in the extended range of Z E , values involved in this work. When 6* = 0, eq 5 reduces to the form:
+
In ( D A M I K = ~ )In C * N ~ CIn~ A*
+ (--’,”,”)
+w*Zs*
(6)
On the basis of the foregoing discussion, eq 6 emerges as the basic relation for estimation of DAMIKb for alcohol-solutes applicable for cellulose acetate membranes of different surface porosities specified in terms of D&K6 for NaC1. Applicable Values of a* for Alcohols. In order to use eq 6 to calculate D A M / K for ~ an alcohol-solute for any given membrane, all quantities on the right side of eq 6 should be known. The method of obtaining the applicable values of In C*N~C In~A* , and -AAG/RT has already been stated above. Regarding the quantity w * Z s * , the value of Zs* for the substituent group in the alcohol molecule can be computed on the basis of the molecular structure of the solute, using the data on structural group contributions to modified Small’s number given in Table 111in Matsuura and Sourirajan (1973~). These computed values of Zs* for the alcohols used in this work are given in Table I. The only other unknown quantity is the numerical value of a*.I t is the object of this part of the discussion to establish the applicable values of w* on the basis of the molecular structure of the alcohol solutes. For the above purpose, the experimental reverse osmosis data obtained with 29 alcohol-solutes (noted in Figure 2) were analyzed. These solutes included all the varieties of alcohols Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
85
F I L M NO
21
0
F I L M NO
As*=O
+ z W
s W
a
-6
-7
X
W
e
I
-8
\
1
27 0--S
SOLUTE NUMBERS
-2
33
-9
v
34 -I
%*x
I
I
I
1
1
I
A 1,
-37
0 0.
-1
I
.-
O
3
I
I
@
Table 111. Applicable Values of w * for the Substituent Groups in Alcohols
I
I
I
I
I
I
4
5
6
7
8
9
CARBON NUMBER, nc
Figure 3. w * values as the function of As* and carbon number nc. studied in this work; for example, their carbon numbers ranged from 1 t o 9, and the Zs* values ranged from 214 to 1254. The experimental data obtained with film 1 (given in Figure 2) were used for analysis. These data were particularly appropriate for this analysis because the reverse osmosis separations obtained with film 1 for the solutes tested covered a very wide range (6 t o 93%). Using the experimental reverse osmosis data, the values of D A M I Kfor ~ all the solutes were calculated using eq 2. The experimental D A M / Kvalue, ~ the known values of In C * N ~ ( ' ~ and In A* for the film, and the computed values of -AAG/RT and Zs* were then used in eq 6 to calculate the w * value for each solute. An examination of the w* values showed that they were functions of both the number of carbon atoms and degree of branching in the molecular structure of the alcohol--solutes. T o serve as a quantitative measure of the latter variable, a quantity As* was generated, defined by the relation: As* (alcohol) = Zs* (alcohol) - Zs*
(straight chain primary alcohol with the same number of carbon atoms) For example
(7)
AS* (CH:jCHOHCHj) = Z's* (CH:jCHOHCH*j) - ZS* (CH
