Study of solute rejection models for thin film composite polyamide ro membranes

Journal of Membrane Science, 52 (1990) 19-41 Elsevier Science Publishers B.V., Amsterdam

19

STUDY OF SOLUTE REJECTION MODELS FOR THIN FILM COMPOSITE POLYAMIDE RO MEMBRANES VITO L. PUNZI*, GREGORY P. MULDOWNEY** and KAREN B. HUNT*** Department of Chemical Engineering, Villanova University, Villanova, PA 19085 (U.S.A.) (Received February 10,1989; accepted in revised form March 8,199O)

Summary Experimental separation data collected for the system water-sodium chloride-thin film composite polyamide membranes are used to compare four theoretical rejection equations. In addition, mechanistic (physical) parameters which characterize thin film composite membranes are estimated, and then compared to the values obtained earlier for the system water-sodium chloridecellulose acetate. The general results of this study are similar to the results obtained for cellulose acetate membranes: although ideal membrane models provide a reasonable description of membrane behavior, models corrected for solute passage produce significantly better results; and, solute separation is accurately predicted over a wide range of pressure, feed rate, and feed concentration by either the corrected diffusive flow model or the corrected viscous flow model. The mechanistic parameters determined for thin film composite polyamide membranes show trends similar to those obtained using cellulose acetate membranes but are generally one order of magnitude larger.

Introduction Reverse osmosis (RO) is now used in many applications besides its traditional use for desalination. However, there is still disagreement both in the literature and among practitioners over which solute rejection mechanism best describes semipermeability over a wide range of operating conditions and membrane materials. This paper addresses three issues critical to the understanding of the solute rejection mechanism: 1. whether mass transport is diffusive or convective, since the microscopic structure of RO membranes suggests either mode could prevail [ 11; 2. what mechanistic (physical) parameters best characterize a real membrane with respect to an ideal (perfect) separator; and, 3. whether ideal and real models can be applied in parallel to quantify nonidealities present in real membranes. *To whom correspondence should be addressed. **Present address: Mobil R&D Corp., Paulsboro, NJ (U.S.A.). ***Present address: Sun Company, Marcus Hook, PA (U.S.A.).

0376-7388/90/$03.50

0 1990 -

Elsevier Science Publishers B.V.

20

In addition, this paper compares the results obtained in the present study with the results obtained earlier [2] for the system water-sodium chloridecellulose acetate. All of the analyses described in this paper are performed using a single RO data base collected using the system water-sodium chloride-thin film composite polyamide membranes, and parallels the study [2] which used cellulose acetate membranes. Thin film composite polyamide RO membranes are of interest because their use is likely to increase significantly in the future: they can operate at higher temperatures, are more selective than cellulose acetate membranes and are not subject to hydrolysis and biological attack [ 1,3,4]. Theory

General Diffusion and convection define the possible extremes of mass transport. This study tests the basic diffusive and convective transport models as predictors of membrane performance. Further, a comparison of the ideal membrane version of each model to that corrected for solute passage allows nonidealities present in real membranes to be quantified. (The concept of an ideal membrane [ 6-81 and the development of models corrected for solute passage [ 2,5] are discussed elsewhere. ) For highly selective membranes, the most sensitive measure of performance is the solute separation factor ~1,defined as [ 1 ] :

Solute rejection models relate separation to a solvent-solute flux ratio. A practical model expresses cy in terms of pressure, flow rate, temperature, and parameters specific to the solvent-solute-membrane system. For greatest utility these parameters should be insensitive to driving forces. Each derivation is presented in greater detail elsewhere [ 21 and is highlighted below. Solution-diffusion mechanism The solution-diffusion mechanism assumes that solvent and solute molecules dissolve into the membrane on the high-pressure side, diffuse through independently, and emerge on the low-pressure side. A separation results because the solvent and solute diffusion rates are different. This mechanism is described elsewhere [g-11], along with the hydrogen bonding model [ 12,131, which also describes mass transport in terms of a diffusive mechanism. The distinction between these models is finer than the scope of this study, and may be impertinent because the hydrogen bonding model is keyed to cellulose acetate. In the solution-diffusion model, solvent and solute fluxes are uncoupled.

21

Each diffusive flux Ji is first expressed in terms of the chemical potential gradient across the membrane and then in terms of pressure and temperature [2,4,14]. Since this mechanism involves no other significant transport processes, the total flux N; of either species is equal to Ji. Additional refinements yield:

(2) Equation (2) summarizes a key consequence of the solution-diffusion mechanism: separation is independent of membrane thickness. The diffusion coefficients Di, and Dzm are averages for the membrane, and would be expressed rigorously as the integral of a positionally dependent diffusivity over the active layer thickness. Because the spatial dependence of Di, and Dzm is usually not available and is generally weak, constant diffusivity per Fick’s law is assumed in most treatments [ 111, including that leading to eqn. (2). For the equation to be of value the Camterms must be eliminated and all concentrations collected on the left-hand side. An ideal membrane may permit solute dissolution at the high-pressure side, but no solute diffusion to the low-pressure side. The permeate is thus pure solvent for which C&, is zero and ,,, is negligible. Using the feed-side solute distribution coefficient K~=C&/C~, and the permeability P,-DrmK:’ for each species yields:

Equation (3 ) is termed the ideal diffusive flow model. The permeability ratio (Pi/P,) refers to the low-pressure side of the membrane owing to KY in the definition of Pi - the positional dependence of the diffusivity ratio has been neglected so that (D’;,/D&,) equals (D,,/D2,), absorbing the latter from eqn. (2). Inaccuracy imparted by neglecting the spatial variation of Dim is minimized because diffusivities and permeabilities appear exclusively as ratios. Perfect separation in the solution-diffusion model occurs because solute cannot diffuse through the membrane. This implies zero solute permeability P2 and, by eqn. (3), an infinite (Y*. A real membrane permits some solute passage; permeate thus exists with nonzero solute concentration C& and osmotic pressure ,,, . To describe this case, eqn. (2) is recast using distribution coefficients, which upon rearrangement yields: (4)

22

Equation (4) represents the corrected diffusive flow model. In this study, the grouping [film (dp -l7’ ) /RT] is termed the diffusive transport parameter, Xn. In the classical solution-diffusion equations, solute concentrations in the membrane and the bulk solution are interrelated through the same distribution coefficient K2 on both sides of the membrane [ 1,4,11,14]. This procedure assumes Kg/K; is unity. As shown previously [2] and confirmed here, the restriction of equal distribution coefficients severely inhibits the applicability of the diffusive flow equations. The two forms given by eqns. (3) and (4) accommodate possibly unequal coefficients Kl and KL. This difference in methodology is significant and distinguishes the present appraoch from previous investigations. Convective transport mechanism The convective transport mechanism assumes the existence of discrete membrane pores through which solvent passes in viscous flow, conveying solute with it. A separation is achieved if the solute concentration in the pore liquid differs from that in the solution on the high-pressure side. Numerous explanations of the concentration change on entering a membrane pore are summarized elsewhere [ 4,151. One such theory proposes that solvent is preferentially adsorbed on the membrane to the exclusion of solute [ 16-181. The “finely porous” [ 141 and “capillary flow” [ 181 models are special cases of the convective transport mechanism, and are collectively represented here by a general treatment. In the convective transport mechanism, viscous flow of solvent couples the solvent and solute fluxes. Pore liquid of solute concentration C,, flowing at mean velocity u, constitutes a flux upC,,. Solute also diffuses in the (moving) solvent due to a concentration gradient along the pore. Total solute flux NZpis the sum of these processes. Tortuosity r (the mean ratio of pore length to membrane thickness) and porosity E (the mean ratio of pore area to total area) are used to relate pore quantities to the macroscopic variables u, x, N2 and CZ,. Expressing permeate velocity u in terms of the volumetric flow V” and the membrane area A, and solving for C,, yields: C,,=Cie+(K$C;-cC;I)

exp[-T(s)&]

Thus the convective transport mechanism yields an exponential profile where the solution-diffusion mechanism leads to a linear one. A form of eqn. (5) is sought which gives a! in terms of quantities other than concentration. The ideal membrane delivers a permeate of zero solute content at the lowpressure side. This case is described by eqn. (5) with C,, = 0 at x =3,, which is rearranged to obtain:

23

a*+&-,,( -:g)]

(6)

Equation (6) summarizes the ideal viscous flow model. A membrane governed by convective transport can achieve perfect separation only if no solute enters the pores, since all pore liquid reaches the permeate. The solute rejection mechanism must occur at the high-pressure surface, requiring that CL, be zero. This leads to zero K; and an infinite a*. In a real membrane the concentration profile is nonzero through the pore and reaches a value C&, at the low-pressure side. The general condition CPm= Kg (2’;at x = 3,is imposed on eqn. (5 ) to obtain CI!for this case: a=&

[I-exp(-$i$)]+gexp(-Tz&-)

(7)

which is the corrected viscous flow model. In this study, the grouping [ -exp ( - V” 7;l)/ (A EI&) ] is termed the convective transport parameter, Xv. In contrast to the diffusive flow equations, both viscous flow models feature a dependence on membrane thickness. Analysis

Development of the models as four equations of similar form is central to this study. Within each pair, the first equation assumes a perfect membrane while the second includes a correction for solute passage. In all analyses involving eqns. (3 ) , (4 ) , (6 ) and (7 ) , three groups of information must be measured or known: 1. RO process variables (a, dp, V”, 2’) which are usually measured experimentally or computed from experimental measurements. A representative data set and (intermediate) computed values are presented for one membrane at one nominal feed concentration in Tables l-4. 2. Solvent-solute data (V;,, I7, DZl) which are usually obtained from the literature [ 181, and 3. Membrane structure data (A, a, 7, E) which are usually obtained or derived from discussions of membrane morphology. Membrane performance is measured in terms of the solute separation factor, cr (or cy*) , the dependent variable in all four equations. Known properties of the solvent-solute pair, membrane, and RO process are then collected in an independent variable (X,) defined uniquely for each model K. In each case, a linear relationship results. Values of a! and the various X, for the sample data set are shown in Table 5. The dominant mode of transport is suggested by the relative capacity of the corrected diffusive flow model (eqn. 4) and the corrected viscous flow model

24 TABLE

1

Feed concentration data using thin film composite polyamide membranes and sodium chloride solutions Run set

24 25 26 27 28 29 30 31 32

Actual feed chloride concentrations (mg/L) 1

2

3

2392.5 2321.4 2413.4

2402.7 2321.4

2434.3 2423.8 2444.6

2597.2 2349.4 2308.2 2298.2 2456.5 2456.5

2498.0 2574.7 2370.5 2412.8

2563.1 2412.8 2402.0

2339.3 2589.2 2456.5

2360.1 2489.2 2456.5

(eqn. 7) to correlate RO separation data. Specifically, the capacity of any model to predict cz from X, is determined via linear regression in terms of three statistical quantities: the total sum of squares; the sum of squares removed; and, the residual sum of squares [ 19,20 1. The models are compared in terms of the residual sum of squares, the smaller residual indicating the better correlation. Models with the same number of fitted parameters have identical total sums of squares and therefore may be evaluated using the fraction of squares removed- the squares removed divided by the total sum of squares. Equations (3)) (4), (6) and (7) can also be used to determine system-specific mechanistic parameters which summarize the solvent-solute-membrane interaction. These parameters follow from the data fit and are used to describe membrane behavior in physical terms: (P,/PZ) for diffusion, (E/K&) for convection, and (Kg/K;) for both modes. All three are ratios of like variables (E FZK; ) for dilute pore liquids [ 141) expected to be insensitive to pressure and flow rate over the ranges tested. (The pressure-independence of the partition coefficients is discussed in the literature [4] ). Any concentration effects are established by separately analyzing data sets of variant V” and Ap at several feed concentrations. Finally, eqns. (3 ), (4)) (6) and (7) can be used to describe membrane nonideality. Though only special cases of the corrected models (valid as o+co), the ideal equations might provide acceptable predictions of selectivity even for somewhat imperfect membranes. Thus, the ideal forms determined from eqns. (3) and (6) are used to establish whether the values of (PI/P,)*, (r/K;)*, and (&‘/IQ)* bear any relation to those obtained via the two corrected models (eqns. 4 and 7). The ideal parameters lose their physical significance when

25 TABLE 2 Individual concentration data using thin film composite polyamide membranes and sodium chloride solutions Run

Chloride concentration (mg/L) Concentrate 2905.8

Run

Permeate

24.1 24.2 24.3 24.4 24.5 24.6 24.1

2402.7 2642.4 2711.6 2608.3 2608.3 2631.0 2563.1

25.1 25.2 25.3

2676.8 2631.0 16.821 12.939 2530.9 2608.3 12.119 12.523 2563.7 2574.7 13.705 14.162 30.1 30.2 2563.7 2711.6 19.573 19.573 30.3 2758.9 2770.8 16.612 16.013 2170.8 2758.9 16.144 15.754 31.1 2170.8 2758.9 15.433 15.497 31.2 2654.0 2735.3 15.497 15.560 31.3 2631.0 2619.8 16.413 17.525 31.4 2619.8 2597.2 17.596 17.453 31.5 2631.0 2665.6 17.813 17.739 31.6 2711.6 2735.3 18.331 18.633 31.7 31.8 2807.3 2783.1 20.814 20.814 31.9 2831.5 2831.5 19.412 19.254 2819.1 2795.1 19.333 19.254 32.1 2723.8 2699.9 21.419 22.224 32.2 32.3 2456.0 2412.8 31.353 31.353 32.4 2412.8 2456.0 22.141 21.242 32.5 2521.8 2466.9 20.463 21.419 32.6 2510.8 2544.5 21.333 21.580 32.7 2544.5 2544.5 21.242 21.687 32.8 2533.2 2477.6 21.955 21.242 2533.2 2578.6 21.508 21.777 2402.0 2423.4 23.654 25.702

26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27.1 27.2 27.3 21.4 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8

2711.6 2770.8 2654.0 2642.4 2665.6 2563.7

20.477 9.958 10.94 10.329 10.329 11.68 11.49

11.490 10.288 11.258 10.673 10.718 11.920 11.777

29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9

Chloride concentration (mg/L) Concentrate

Permeate

2412.8 2288.1 2466.9 2370.5 2477.6 2423.4 2499.6 2412.8 2308.2

26.236 29.099 25.702 24.150 24.150 23.751 25.216 24.052 23.558

2391.6 2391.6 2544.5 2456.0 2533.2 2499.6 2510.8 2412.8 2328.1

26.236 26.236 25.276 24.452 24.965 24.553 25.276 24.052 26.567

35.946 2328.7 2328.7 35.946 2328.7 2360.1 29.711 29.219 2370.5 2360.1 29.099 30.206

2533.4 2489.2 2566.8 2612.3 2456.5 2489.2 2424.5 2500.0 2533.4

2544.3 2589.2 2635.2 2500.0 2511.1 2435.4 2522.2 2578.2

2467.5 2467.5 2500.0 2533.4 2467.5 2578.2 2467.5 2544.3

2424.5 2456.5 2500.0 2522.2 2522.2 2578.2 2489.2 2624.0

2646.9

18.071 30.972 32.668 33.474 31.872 30.100 26.525 38.302 41.556 29.979

38.457 42.075 41.725 42.766 44.185 43.291 43.643

27.292 32.397

33.335 34.300 32.792 32.003 31.355 40.554 42.593 30.348 40.217 43.111 45.953 44.185 43.643 43.470 43.832

applied to data from imperfect membranes. However, they may retain value as measures of membrane nonideality on comparison to parameters obtained from the corrected models. In eqns. (3), (4), (6) and (7), (II (or cu*) refers to concentrations at mem-

26 TABLE

3

Converted temperature, pressure and flow rate data using thin film composite branes and sodium chloride solutions Run

24.1 24.2 24.3

Temperature,

Pressure,

T(K)

P (psia)

296.6 296.6 296.6 296.6

24.4 24.5 24.6 24.7

296.6 296.6 296.6

25.1 25.2

293.1 293.1

25.3

293.1

26.1 26.2 26.3 26.4

293.1

26.5 26.6 26.7 26.8 26.9 27.1 27.2 27.3

293.1 293.1 293.1 293.1 293.1 293.1 293.1 293.1

264.7 264.7 244.7 244.7 244.7 219.7 219.7

polyamide

Temperature,

Pressure,

T(K)

P

Permeate

Permeate flow v” (cm3/min)

Run

179.2 179.2 150.0 147.3

29.1 29.2 29.3

293.1 293.1

119.7 119.7

32.2 32.2

293.1

29.4 29.5 29.6 29.7 29.8 29.9

293.1 293.1 293.1 293.1 293.1 293.1

119.7 119.7 119.7 119.7

32.2 32.2 32.2

147.3 120.2 120.2

Ma)

flowV”

(cm3/min)

119.7 119.7 104.7

29.8 29.8 32.2 23.1

104.7 104.7 104.7

23.1 23.1 23.1

219.7 219.7 194.7

125.6 120.2 98.5

30.1 30.2

194.7 194.7 194.7 194.7 194.7 169.7

101.3

30.3

293.1 293.1 293.1

95.8 95.8 95.8 93.1

31.1 31.2

296.1 296.4

104.7 104.7

29.0 25.0

31.3 31.4

296.4 296.4 296.4

104.7 104.7

25.0 25.0 25.0

169.7 169.7 169.7

73.0 73.0 73.0 73.0

169.7 169.7

75.4 73.0

27.4

293.1 293.1 293.1 293.1

169.7 144.7

73.0 49.0

28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8

293.1 293.1 293.1 293.1 293.1 293.1 293.1 293.1

144.7 144.7 144.7 144.7 144.7

49.0 49.0 44.2 49.0 49.0 49.0 46.6 29.8

144.7 144.7 119.7

mem-

31.5 31.6 31.7 31.8 31.9 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8

296.4 296.4 296.4 296.4 293.1 293.1 296.1 293.1 293.1 293.1 293.1 293.1

104.7 104.7 89.7 89.7 89.7 89.7 89.7 89.7 89.7 89.7 89.7 89.7 89.7

23.1 15.9 15.9 15.9 15.9 9.2 10.8 10.8 10.8 12.5 12.5 12.5

brane surfaces, which may differ from bulk stream solute levels due to concentration polarization. However, because the concentrations are related through a mass transfer coefficient k, concentration polarization effects can be absorbed into the mechanistic parameters which follow from the data fit if both

27

TABLE 4 Values of solute separation factor (CX)and rejection using thin film composite polyamide membranes and sodium chloride solutions Run

CY

Rejection (% )

Run

24.1

178 250

99.4 99.6 99.5

29.1 29.2 29.3

99.6 99.6 99.5 99.5

24.2 24.3 24.4 24.5 24.6 24.1 25.1 25.2

231 239 238 214 213

25.3

176 199 176

99.4 99.5 99.4

26.1 26.2 26.3 26.4

131 161 164 168

99.2 99.3 99.4

26.5 26.6

166 148 144

26.7 26.8 26.9 27.1 27.2 27.3 21.4 28.1 28.2 28.3 28.4 28.5 28.6 28.1 28.8

99.4 99.4 99.3 99.3

cx 91 87

98.9 98.9

29.4 29.5

96 99 99

98.9 99.0

29.6 29.7 29.8 29.9

100 97 100 92

99.0 98.9 99.0 98.9

30.1 30.2 30.3

65 80 79

98.4 98.7 98.7

31.1 31.2

106 79 77

99.0 98.7 98.7

76 71

98.6 98.7

80 83 63 60

98.8 98.8 98.4

98.8 98.4

31.3 31.4 31.5 31.6 31.7 31.8

144 140

99.3 99.2

129 140

99.2 99.3 99.3

31.9 32.1

81

99.1

32.2 32.3 32.4 32.5 32.6 32.7

62 58 56 57 57 51 58

140 120 77 112 115 114 114 113 114 96

98.7

99.1 99.1 99.1 99.1 99.1 99.1 98.9

Rejection (% )

32.8

99.0

98.3

98.3 98.2 98.2 98.2 98.2 98.2

are linear processes. Further, it has been shown [2] that the values of the mechanistic parameters are affected solely by a multiplicative factor of the form [ exp ( - V” /AK) 1. For cellulose acetate membranes, this factor is of magnitude 0.96-0.99. Thus it was concluded that not only could concentration polarization effects be absorbed into the fitted mechanistic parameters, but also that the effect on the values of these parameters was negligible.

28 TABLE

5

Fitting parameters chloride solutions Run

24.5 24.6 24.7 25.1 25.2 25.3 26.1

1 using thin film composite

polyamide

membranes

x 103

x;

x 102

and sodium

Ordinate

Calculated abscissa values x;,

24.1 24.2 24.3 24.4

for membrane

xn x 103

-x,x10 8.91 8.90 9.07 9.09

cr (or a*) 178

10.17 10.20 9.16 9.21 9.21 7.94 7.98

10.95 10.96 9.26

10.19 10.21 9.17

9.10 9.10 7.49 7.49

9.22 9.22 7.95 7.99

8.08 8.11 6.84

8.41 8.07 6.66

8.10 8.13 6.86

9.16 9.19 9.33

176 199 176

6.75 6.70

6.83 6.48 6.48

6.77 6.72

9.32 9.35

131 161

6.72 6.72 6.75 5.51 5.52 5.50 5.46

9.35 9.35 9.37 9.50

164 168 166 148 144 144 140

5.38 5.36 5.37 4.14

9.49

9.66

9.66 9.66 9.66 9.68 9.79

26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9

6.71 6.71 6.73 5.50 5.50 5.48 5.45

27.1 27.2 27.3 27.4

5.36 5.34 5.35 4.12

5.13 4.97 4.97

28.1 28.2

4.35 4.34

3.36 3.36

28.3 28.4 28.5 28.6 28.7 28.8

4.32 4.30 4.29 4.31 4.28 3.07

3.04

4.38 4.36 4.34

3.36 3.36 3.36 3.20 2.06

4.32 4.31 4.33 4.30 3.10

6.48 6.30 4.97 4.97 4.97 4.97

3.36

9.09 9.25 9.25

9.50 9.50 9.50

9.50 9.50 9.66

9.66 9.70

250 231 239 238 214 213

129 140 140 120 77 112 115 114 114 113 114 96

29

TABLE 5 Cont.

Run

Calculated abscissa values x;, x lo3

29.1

3.08

29.2 29.3 29.4 29.5 29.6 29.7

3.10 3.03 3.07 3.03 3.05 3.03

29.8 29.9

3.08 2.35

30.1 30.2

x; x lo2

x,x

103

-x,x10

a (or a*)

3.11

9.78

2.22 2.22 2.22 2.06 2.06 2.22

3.13 3.05 3.09 3.05 3.07 3.06 3.10

9.18 9.78 9.78 9.78 9.79 9.79

9.78

96 99 99 100 97 100

1.60

2.38

9.84

92

30.3

2.37 2.36 2.35

1.60 1.60 1.60

2.41 2.39 2.38

9.84 9.84 9.84

65 80 79

31.1

2.11

1.93

2.15 2.12 2.10 2.17

1.61 1.61 1.61 1.61

2.13 2.18

9.81 9.84

106

31.2 31.3

2.16 1.43 1.39 1.37

1.49 1.03 1.03 1.03

2.15 2.13 2.20 2.19 1.46 1.43 1.41

9.84 9.84 9.84 9.85 9.90 9.90 9.90

1.49 1.48 1.43

1.10 0.64 0.70

1.52 1.52

9.89 9.94 9.93

81 62 58

1.45 1.46 1.46

0.75 0.75 0.87

1.47

0.87

9.92 9.92 9.91 9.91

56 57 57 57

1.42

0.87

9.91

58

31.4 31.5 31.6 31.7 31.8 31.9 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8

2.22 2.22

Ordinate

1.47 1.50 1.50 1.47 1.51 1.46

91 87

79 77 76 77 80 83 63 60

30

The thin film composite polyamide membranes used in this study have an identical feedside channel configuration as the cellulose acetate membranes used earlier. Further, similar feedside concentrations of the same solute were used in both studies. Thus, it is expected that mass transfer coefficients for the polyamide membranes would be similar to those used for cellulose acetate. Further, since the product flux ( V” /A ) is lower for the polyamide membranes than for the cellulose acetate membrane, the values of the factor [ exp ( - V” / Ah) ] is even closer to unity for the polyamide membranes. Membrane

morphology

The skin layer thickness (3L)in thin film composite polyamide generally range from 0.0%O.lOpm [ 3,4,21]. Electron microscopy studies of pore size and density in this layer suggest a porosity (E) between 0.005 and 0.052 [1,21]. Polymer segments in the skin form a random network for which the mean tortuosity (7) is 2.5; a typical range is 2-3 [ 1,4]. Assimilating the three ranges gives (AZ/E) values of 0.77-60 pm. Both viscous flow models are tested here using in turn (AT/E) of 0.77,60, and 6.8 pm (the geometric mean). The topcoat is a cross-linked thin film composite polyamide material; the surface charge on these membranes is slightly anionic. The substructure is polysulfone cast on a polyester nonwoven substrate. While the formation process for the membranes is proprietary, the general formation scheme involves an interfacial polycondensation (or polymerization) reaction [ 1 ] between multifunctional groups belonging to the aromatic acid halide and amine moieties. Membranes 1 and 2 used in this study were produced in one lot; membrane 3 was manufactured several months later. Experimental

Separation data are obtained using an Osmonics OSMO 3319-SB representative of commercial RO systems. The unit features three spiral-wound membranes; each has an area of 1.05 m2 (11.3 ft2) and provides 0.0047 kg/m2set ( 10 gpd/ft2) maximum product water flux. The system allows independent feed rate control to each membrane. The experimental data collected directly from membrane 1 at a nominal feed concentration of 2500 mg/L is featured in the discussion presented below, and is presented in Tables 1, 2 and 3. Calculated values of the rejection provided by these membranes is presented in Table 4. A total of 60-65 conditions (combinations of feed flow rate and feed-side gauge pressure at a nominal temperature of 20’ C ) are studied at each of six nominal feed chloride concentrations (250, 1000, 2500,3750, 5000, and 7500 mg/L). In the sample data set (2500 mg/L), 60 conditions were studied, and are

31

identified as Runs 24.1-32.8 in Tables 1-5. Table 1 shows that the actual feed concentrations in the sample data set ranged between 2300 and 2600 mg/L, and Table 3 shows that the actual operating temperatures ranged between 20 and 235°C. Flow rates are 12.1-27.3 cm3/sec (11.5-26 gph) and pressures 517-1723 kPa (75-250 psig) . The same settings of these two process variables were used at each feed concentration in this study. At each condition the concentrate and permeate from each membrane are sampled twice over a 20-minute period. Chloride content in the samples is recorded, along with the pressures on feed and permeate sides, and the flow rates of feed, concentrate and permeate. Chloride content data for the sample data set are presented in Tables 1 (feed) and 2 (concentrate, permeate). Permeate flow rate data for the sample data set are presented in Table 3. Solute concentrations (CL and C$’ ) are determined to at least four significant figures using Orion chloride selective and reference electrodes and a Fisher Accumet pH/mV/Ion meter. Pressures are measured by Bourdon gauges and flow rates by rotameters, each to two significant figures. The experimental data base is analyzed using in turn one of the four solute rejection models. (The values for the sample data set which produce the results for membrane 1 at 2500 mg/L are presented in Table 5 ) . All measured data values are included. Computations are performed in BASIC on a VAX 11/780, using double precision to minimize subtraction errors in calculating the mechanistic parameters. Final results are reported to two significant figures, consistent with the least precise experimental measurements. General results The discussion presented below emphasizes the results obtained using thin film composite polyamide membranes. However, a broader context is established by comparing the results of this study with the results which used the same methodology to study cellulose acetate membranes [ 21. The solute separation factor a! and permeate flow rate V” are found to differ among the three test membranes at each set of operating conditions. Values of cy for membranes 1 and 2 range from 11 to 270 (90.5-99.6% rejection); clustering occurs at an cy value of approx. 120 (99% rejection). Although solute rejection is similar for these two membranes (as they are from the same lot), membrane 1 provides higher selectivity than membrane 2 at all conditions. For membrane 3, values of (x range from 10 to 140 (89.7-99.3% rejection); clustering occurs at an CYvalue of approx. 80 (98.7% rejection). Flow rates V” range from 1.2 to 276 cm3/min. Permeation is without exception greater for membrane 2 than for membrane 1, illustrating the familiar trade-off between solute rejection and permeate flow [2,11]. Both cz and V” increase with increasing applied pressure and decrease with increasing feed concentration.

32

For membrane 1, at a nominal feed concentration of 2500 mg/L, Table 4 shows that c~values range from 56 to 250 (g&2-99.6% rejection). As shown in Table 3, permeate flow rates range from 9.2 to 179.2 cm3/min in the sample data set detailed herein. Comparison of solute rejection models The results of the regression analysis performed using each of the four solute rejection models are useful in evaluating both membrane nonideality and the mechanism of semipermeability. It should be noted that data point counts for each nominal feed are different and are taken into account when comparing total or residual squares. This is particularly significant at 7500 mg/L where smaller data sets occur because those pressures in the standard matrix of experimental operating conditions which fall below the solution osmotic pressure at 7500 mg/L are omitted. In addition, some inconsistencies are noted at 250 mg/L, most likely caused by permeate concentrations near the low end of the chloride electrode measurement range. As in the earlier study, the fit of the convective transport equations is not affected by the quantity (AZ/E). The results discussed below for the two viscous flow models are those at (AT/E) of 60 pm. Ideal vs. corrected models The results of the regression analysis indicate that the ideal models reduce the unaccounted variation in cry*from an order of lo5 or lo6 (total squares) to 8 x lo4 or less (residual squares). Thus the ideal models provide a reasonable first approximation to solute rejection behavior in the test membranes. The corrected equations result in a significant improvement over the ideal models, achieving residual squares in all cases of less than 3.5 x lo4 and most of order 103. Further, the improvement in fit upon correcting for nonideality is generally larger at higher feed concentration, and greater for membranes 1 and 2 than for membrane 3. These trends are consistent with the theoretical basis of the ideal models, expected to hold most strongly for a highly selective membrane in a highly dilute solution. Corrected diffusive flow model vs. corrected viscous flow model Identification of the solute rejection mechanism is sought in the results of the corrected diffusive flow and corrected viscous flow models, compared by using the fraction of squares removed. The corrected diffusive flow model removes 83-97% of the total squares. The fit is very good throughout, with no strong dependence on concentration or membrane. Feed concentration dependence is also well correlated, evident from the 77-81% squares removed in the pooled data sets, values which are com-

33

parable to the individual-case results. Figure 1 illustrates the typical performance of the corrected diffusive flow model using the values of the model variables (shown in Table 5) obtained in the sample data set. Since the results of this regression analysis are similar to those obtained with cellulose acetate, it appears that a two-parameter linear functionality of cy to the pressure difference @p-&7) adequately describes solute rejection over the range of operating conditions studied. The relatively small individual-case residuals provide additional confirmation that variability due to boundary layer effects on feedside concentration is adequately absorbed into the fitted mechanistic parameters. The corrected viscous flow model accounts for 77-99% of the total squares, and performance depends insignificantly on the value of (AT/C). Excellent performance for all membranes in the pooled data sets (78-87% squares removed) verifies that the model accommodates concentration effects extremely well. Figure 2 illustrates the typical performance of the corrected viscous flow model using the values of the model variables (shown in Table 5) obtained in the sample data set. Since these results are similar to those obtained in the earlier study, it appears that a two-parameter exponential dependence of CIon permeate flow V” can also be used to describe mass transport in RO under the given test conditions. As discussed above, the small individual-case residuals indicate that boundary layer effects are adequately absorbed into the mechanistic parameters. The foregoing results demonstrate that either the corrected diffusive flow or the corrected viscous flow model will accurately predict solute separation in highly selective membranes of thin film composite polyamide or cellulose acetate. This observation appears to further the persistent disagreement over the

Corrected

Diffusive Modeli Membrane 1 1 2500 Tg,/L

25

t

0 0

1

2 Diffusive

3

4

Transport

5

6 Parameter,

7

8 XD

9

10

11

(x 1 03)

Fig. 1. Performance of the corrected diffusive flow model in correlating solute separation data for a 2500 mg/L feed.

34 250 225 200 175 150 125 100 75

&ec:ed

50 25 0 - 1 .ooo

-0

980 Convective

Fig. 2. Performance 2500 mg/L feed.

Viscous Membrane 2500 mg/L

-0.960 Trorsport

Model

1

-0.940

t

-0.920

Parameter,

-0

900

Xv

of the corrected viscous flow model in correlating

solute separation

data for a

solute rejection mechanism in reverse osmosis. Though theoretically different, the solution-diffusion and convective transport mechanisms lead to two equally successful rejection model equations, suggesting that some overlap exists in the respective mathematical forms. This implies a relationship coupling the independent variables of the two equations through physical quantities - separate from the solute rejection mechanism. Regression analysis of experimental data obtained using cellulose acetate membranes [22] found partial coupling between V” and p. The same relationship is noted here: permeate flow rate increases with increasing applied pressure and decreases with increasing feed concentration. This explains the comparable correlation of membrane separation data by two rejection models representing theoretical extremes of solute transport. Interpretation of mechanistic parameters

Tables 6 and 7 present the fitted mechanistic parameters of the four solute rejection models - parameters which are used to quantify membrane nonideality. Distribution coefficient ratios (Kl/Kb) are calculated from each corrected model equation and compared. Values of the physical quantities (P,/P,), K; and Kg obtained from the corrected parameters are also presented. In general, since the polyamide membranes used in this study are more selective than the cellulose acetate membranes used earlier, trends which reflect that the polyamide membranes more closely approach “ideal” membranes are expected and confirmed. This is illustrated by the higher numerical values (i.e. closer to “infinity”) of the mechanistic parameters than those obtained using cellulose acetate membranes.

35 TABLE

6

Best-fit mechanistic parameters for the ideal and corrected solute rejection models Nominal Membrane Diffusive flow models feed cont. Ideal (mg/L) 250

Corrected

Ideal

Corrected

[WI/P,)* uGIKh)*l

[ (P,lP,) UWW 1

(e/G)*

(E/K;)

20 000 15 000 9 500

19 000 12 000 10 000

2 300 1600 2 100

1700 950 1700

19 000 16 000 8 100

17 000 14 000 8 000

2 700 2 000 2 300

2 100 1500 2 000

25 000 21000 11000

20 000

2 700 2 000

30 000 25 000 13 000

25 000 20 000 10 000

2 700 1300 2 400

2 200

30 000 25 000

28 000 23 000

2 600

2

2 300 1700

3

15 000

14 000

1900 2 300

1 2 3

22 000 19 000 13 000

19 000 16 000 10 000

1800 1300 1600

1 2 3

1000

1 2 3

2500

1 2 3

3750

1 2 3

5000

7500

Viscous flow models

1

16 000 8 700

2 200

1800 1300 1400

900 1900

1900 1300 960 1 100

Ideal vs. corrected parameters The ideal diffusive parameters [ (P1/P2)* (K;/K;)*] averages 23,000, 18,000, and 10,000 for the three membranes tested, values which are approximately 20 times larger than those obtained for cellulose acetate. The parameter steadily increases with increasing concentration for all membranes, except at 7500 mg/L. The most likely reason for the inconsistency is that at high concentration the osmotic pressure of the feed-side solution approaches the applied pressure, whence a typical measurement error in Ap causes a large relative error in the independent variable. The slope of the line which results from the values of cz* and Xg presented in Table 5 is the single value of the ideal diffusive parameter (25,000) shown in Table 6 for membrane 1 at a nominal feed concentration of 2500 mg/L. The corrected diffusive parameter [(PI/P,) (KG/K;) ] averages 19,000, 14,000, and 8500 for the three membranes tested, values which are approxi-

36 TAB LE 7

Solute distribution coefficient ratio predicted by the corrected rejection models Nominal feed cont. (mg/L) 250

1000

Membrane

Diffusive flow K;IK;

Viscous flow K;/K;

1 2

8.3 24

3

(
48 52 18

1

13 12 0.63

33

33

52 44

2 3 2500

1 2 3

3750

1 2 3

5000

1 2 3

7500

Corrected rejection models

1 2 3

30 13 27 27 16

28 9.0

23 31 49 16

7.8 8.0 4.6

20 15 11

7.7

20 16

6.0 6.5

13

mately 35 times larger than those obtained using cellulose acetate. In general, mean corrected parameters are 80% of the corresponding ideal values. The slope of the line which results from the values of cxand Xn presented in Table 5 and on Fig. 1 produces the single value of the corrected diffusive parameter (20,000) shown in Table 6. In nearly every membrane-feed case both the ideal and the corrected diffusive parameters increase in the order 3,2,1, paralleling membrane selectivity. Although membranes 1 and 2 were manufactured in one lot, the mean value of the ideal diffusive parameter is 25% larger for membrane 1 than for membrane 2, and the mean value of the corrected diffusive parameter is 30% larger for membrane 1. The ideal convective parameter (e/K;)* at (,l7/~) of 60 ,um averages 2500, 1600, and 2200 for the three membranes tested, and generally increases with

31

concentration. These values are about 35 times larger than the comparable values obtained for cellulose acetate. The slope of the line which results from the values of (x* and Xc is the single value of the ideal convective parameter (2700) reported for this membrane at a feed concentration of 2500 mg/L. The corrected convective parameter (e/K;) at (AZ/E) of 60 pm averages 2000,1100, and 1700 - larger by a factor of about 50 than those obtained using cellulose acetate. In general, mean corrected parameters are 75% of the corresponding ideal values. The difference between the slope and the intercept of the line produced from the values of (x and Xv presented in Table 5 and on Fig. 2 is the single value of the corrected convective parameter (1800) shown in Table 6 for membrane 1 at a nominal feed concentration of 2500 mg/L. In every membrane-feed case both the ideal and the corrected viscous parameters uniformly increase in the order 2,3,1, a pattern which does not parallel the membrane selectivity trend. Although membranes 1 and 2 were manufactured in one lot, the mean value of the ideal convective parameter is 55% larger for membrane 1 than for membrane 2, and the mean value of the corrected convective parameter is 70% larger for membrane 1. Since the corrected mechanistic parameters show no clear dependence on concentration, each membrane is best characterized by the mean values cited. Thus for each corrected rejection model one mechanistic parameter t WIlP2) (G/G) 1or (MG) - may be reliably estimated as 75-80% of the corresponding ideal value for this type of highly selected membrane material. It is expected that as selectivity increases the mechanistic parameters obtained from the corrected models would more closely approximate the ideal parameters. This trend is confirmed in the two studies performed thus far using two different types of membrane material. Corrected diffusive flow vs. corrected viscous flow parameter Table 7 presents the solute distribution coefficient ratio (Kz/Kh) calculated from each corrected model. Results using the three (AZ/E) values differ by less than 6%; those based on 60 pm are listed. Except at 250 mg/L, &i/K;) is generally larger at low chloride levels and greater for membranes 1 and 2. Ratios calculated from the corrected viscous flow model, which range from 9.0 to 52, are generally higher than those based on the corrected diffusive flow model, which typically range between 4.6 and 33. The similarity among the predicted values is of particular interest because of the very different theoretical bases used to arrive at these estimates. Ratios calculated by either approach show no strong concentration dependence, as predicted [ 41 for small concentration and pressure ranges as used in this study. It should be noted that the values of (PC;‘/&) obtained using the polyamide membranes are approximately 5-10 times larger than those obtained for cellulose acetate. It is clear from Table 7 that (J-C;‘/&) differs unity by at least an order of

38

magnitude. A smaller but significant departure from 1.0 was also found for cellulose acetate membranes. Thus, assuming Kz constant across the membrane severely compromises any comparisons of diffusive and convective models. Though physically inexact, the assumption that (Kz/Kz) is 1.0 is made in many investigations [4,14] in order to simplify the mathematics. Development of (Kg/K; ) as a mechanistic parameter yields from the same experimental data base significant improvement in predictions of cy,consistency of fitted parameters, and agreement of physical constants with literature data. Predicted physical quantities

Mean permeability ratios ( PI/P2 ) and mean distribution coefficients K; and Kg are also calculated in this study. At all concentrations, permeability ratios parallel selectivity. At feed concentrations up to 3750 mg/L the test membranes are, respectively, 940,800 and 660 times more permeable to solvent than to solute. At the higher feed concentrations the test membranes are, respectively, 3000,280O and 2300 times more permeable to solvent than to solute. At present, the increase in the relative size of these ratios cannot be explained, but a similar trend was observed for cellulose acetate. Although no literature data are available at exactly the rejection levels observed here, values of (PI/P,) reported for high-rejection aromatic polyamide membranes separating aqueous sodium chloride solutions are on the order of lo3 [ 41. In addition, Merten [ 141 indicates that a concentration reduction factor of 100 (from a 5 wt.% to 500 mg/L total solids content) is attainable at room temperature for a permeability ratio (defined somewhat differently than in this study) equal to 2100. Usinge = 0.005,calculatedfeed-sidesolutedistributioncoefficients,K~ ,range between 2.6 X 10 e-6 and 4.1 X 10P6, indicating that the solute is 300,000 times less concentrated in the high-pressure side of the membrane than in the feed solution. Values of the permeate-side distribution coefficient, Ki, range between 4.5 x 10 -’ and 1.4 x 10e4, designating a 13000-fold partitioning of solute. Corresponding K; and Ki values for cellulose acetate are 300 to 400 times larger, illustrating the substantially greater selectivity of thin film polyamide. Conclusions

The solute rejection mechanism in thin film composite polyamide RO membranes of high selectivity is accurately described over a wide range of pressure, feed rate, and feed concentration by either the corrected diffusive flow model or the corrected viscous flow model. This is the second membrane material for which this general conclusion has been reached. A dependence of permeate flow rate on applied pressure couples the independent variables in the two models, a relationship which must be studied further. Two membrane-specific

39

parameters are required for either model and may be obtained from minimal separation data. In addition, the models offer great utility in predicting both solute separation and the physical parameters which characterize a solvent-solute-membrane system. Distribution coefficient ratios (Ki/K;) predicted by either corrected rejection model range from 4.6 to 52. Thus it is possible to produce similar, yet independent estimates of this ratio starting with theoretical equations which represent physical extremes of solute transport. Because (Kg/K;) is very different from unity, the assumption of equal solute partitioning on both sides of the membrane is refuted. Finally, ideal membrane models provide a reasonable description of the physics of semipermeability at the high rejection levels studied. The corrected mechanistic parameters are 7580% of the corresponding ideal parameters, approaching the characterization of an ideal membrane. Acknowledgement This paper is based on research supported by the National Science Foundation, under Grant CBT-8519698. List of symbols A

c; En Dij Ji K; k Ni pi

P R T U V"

2

&

xv x

membrane cross-sectional area concentration of species i at membrane surface s concentration of species i within membrane at surface s diffusivity of species i in medium j diffusive flux of species i distribution coefficient of species i at membrane surface s feed-side mass transfer coefficient net flux of species i due to diffusion and convection permeability of species i pressure universal gas constant absolute temperature center-of-mass velocity volumetric flow rate at surface s partial molar volume of species i in membrane abscissa value defined for the diffusive flow model independent variable defined uniquely for model k abscissa value defined for the viscous flow model nosition coordinate

40

Greek a E,A, z n

symbols solute separation factor membrane active layer porosity, thickness and tortuosity solution osmotic pressure

Superscripts I feed-side surface of membrane ,, permeate-side surface of membrane * ideal-case model Subscripts solvent 1 solute 2 membrane m pore P

References 1

2

3 4 5 6 7 8 9 10 11 12 13 14

R. Kesting, Synthetic Polymeric Materials, Wiley, New York, NY, 1985. G.P. Muldowney and V.L. Punzi, A comparison of solute rejection models in reverse osmosis membranes. System: Water-sodium chloride-cellulose acetate, Ind. Eng. Chem., Res., 27 (1988) 2341. R.L. Riley, R.L. Fox, C.R. Lyons, C.E. Milstead, W.E. Seroy and M. Tagami, Spiral-wound poly(ether/amide) thin-film composite membrane systems, Desalination, 19 (1976) 113. M. Soltanieh and W.N. Gill, Review of reverse osmosis membranes and transport models, Chem. Eng. Commun., 12 (1981) 279. G.P. Muldowney, Unpublished manuscript, Villanova Univ., 1985. A.J. Staverman, The theory of measurement of osmotic pressure, Rec. Trav. Chim., 70 (1951) 344. A.J. Staverman, Apparent osmotic pressure of solutions of heterodisperse polymers, Rec. Trav. Chim., 71 (1952) 623. A.J. Staverman, Non-equilibrium thermodynamics of membrane processes, Trans. Faraday Sot., 48 (1952) 176. K.J. Laidler and K.E. Shuler, The kinetics of membrane processes. I. The mechanism and the kinetic laws for diffusion through membranes, J. Chem. Phys., 17 (1949) 851. H.K. Lonsdale, U. Merten and R.L. Riley, Transport properties of cellulose acetate osmotic membranes, J. Appl. Polym. Sci., 9 (1965) 1341. H.K. Lonsdale, Properties of cellulose acetate membranes, in: U. Merten (Ed.), Desalination by Reverse Osmosis, M.I.T. Press, Cambridge, MA, 1966, pp. 93-160. E.J. Breton, Water and ionic flow through osmotic membranes, U.S. Dept. Interior, Office of Saline Water Research and Development Progress, Report No. 16, Washington, DC, 1957. C.E. Reid and E.J. Breton, Water and ionic flow across cellulosic membranes, J. Appl. Polym. Sci., 1 (1959) 133. U. Merten, Transport properties of osmotic membranes, in: U. Merten (Ed.), Desalination by Reverse Osmosis, M.I.T. Press, Cambridge, MA, 1966, pp. 15-54.

41 15

16 17 18 19

20 21 22

V.L. Punzi and G.P. Muldowney, An overview of proposed solute rejection mechanisms in reverse osmosis, Rev. Chem. Eng., 4 (1987) 1. S. Sourirajan, Mechanism of demineralization of aqueous sodium chloride solutions by flow, under pressure, through porous membranes, Ind. Eng. Chem., Fundam., 2 (1963) 51. S. Sourirajan, Characteristics of porous cellulose acetate membranes for separation of some organic substances in aqueous solution, Ind. Eng. Chem., Fundam., 3 (1964) 206. S. Sourirajan, Reverse Osmosis, Academic Press, New York, NY, 1970. G.E.P. Box, W.G. Hunter and J.S. Hunter, Statistics for Experimenters, Wiley, New York, NY, 1978. W. Volk, Applied Statistics for Engineers, 2nd edn., McGraw-Hill, New York, NY, 1969. Osmonics, Inc., Verbal communication and product literature, 1988. G.P. Muldowney, A theoretical and experimental investigation to characterize and optimize the reverse osmosis separation process, M. Ch. E. thesis, Villanova University, Villanova, PA. 1983.