Selectivity and characteristics of direct contact membrane distillation type experiment. I. Permeability and selectivity through dried hydrophobic fine porous membranes

Journal of Membrane Science, 12 (1992) 53-72

53

Elsevier Science Publishers B.V., Amsterdam

Selectivity and characteristics of direct contact membrane distillation type experiment. I. Permeability and selectivity through dried hydrophobic fine porous membranes* Yoshishige Fujii, Shoji Kigoshi, Hidetsugu

Iwatani and Masatoshi

Aoyama

Research Association for Basic Polymer Technology, 2-5-21 Toranomon, Minato-ku, Tokyo (Japan)

(Received January 29,199l; accepted in revised form April 29,1992)

Abstract Permeability and selectivity through fine porous membranes of hydrophobic polymers and direct contact membrane distillation (DCMD) type separation with such membranes have been studied. The permeability of an organic solute in dilute aqueous solution through the dried hollow fiber membranes depends on the partial vapor pressure of the solute. The selectivity for alcohol observed in a pervaporation type experiment depends on the ratio of the mean pore radius of the membrane to the radius of the alcohol molecule. The fluxes of ethanol and water in DCMD type separation are directly proportional to the partial vapor pressure differences, and the selectivity for ethanol varies with the properties of the polymers and the membranes. Polarization of temperature and concentration and heat transport characteristics are also studied. Keywords: direct contact membrane;

poly(vinylidene

distillation; fluoride); polysulfone

1. Introduction Membrane separation processes are expected to be the most energy-saving method for the production of alcohol, which is currently achieved by distillation. For the dehydration of concentrated alcohol solutions, numerous experimental results on water-selective pervaCorrespondence to: Y. Fujii, Membrane Research Laboratory, Toray Industries, Inc., 2-1, Sonoyama 3-chome, Otsu-shi, Shiga, 520 Japan. *Part of this study was presented at the 6th Int. Symp. on Synthetic Membranes in Science and Industry, Tiibingen, September 4-E&1989.

0376-7388/92/$05.00

fine porous membrane; hollow fiber; alcohol selectivity;

poration (PV) membranes have been published, and PV membranes with high permeability and high selectivity have been developed for practical use [l-3]. For concentration from weak alcohol solutions, however, only a few alcohol-selective membranes have been found, and their permeability and selectivity are still too low for practical use [ 4-81. The mechanism of the PV separation is usually described in terms of the solution-diffusion model on the assumption of non-porous membranes [ 91, and higher selectivity is expected for PV membranes. Membrane distillation (MD) is also appli-

0 1992 Elsevier Science Publishers B.V. All rights reserved.

Y. Fujii et al./J.Membrane Sci. 72 (1992) 53-72

54

cable for the concentration of weak alcohol solutions [ 10-131, but it is believed that only selectivity lower than the vapor-liquid equilibrium can be expected because the membrane itself has no selectivity to any components in the solution [ 141. MD is defined as an evaporative process using hydrophobic microporous membranes, as for microfiltration purposes, and is classified into three types of process: direct contact membrane distillation (DCMD ) , low pressure membrane distillation (LPMD ) and sweep gas membrane distillation (SGMD) [ 151. In DCMD the permeate is collected in a low temperature solution, and cold traps and vacuum pumps are unnecessary. Until recently, many investigations on MD have been published, but few results exist that were obtained with fine porous membranes having pore sizes smaller than those of microfiltration membranes prepared by the solution casting method. Using such membranes, we may expect more intensive interaction between the membrane polymer and the permeate molecules, resulting in selectivity improvement. We report here studies on permeability and selectivity through dried fine porous membranes: the permeability of organics from dilute aqueous solutions in a dialysis type experiment; the selectivity for alcohol relative to water in a PV type experiment; the permeability of ethanol and water and the selectivity for ethanol in a DCMD type experiment. The polarization of temperature and concentration is also discussed. 2. Experimental 2.1. Membranes Spinning solutions and methods The membranes studied here were of the hol-

low fiber type prepared by dry-jet wet spinning from polymer solutions with tube-in-orifice type nozzles. An aqueous solution of the same solvent as was used for the spinning solution was used for the coagulation solution, which was injected into the hollow fiber bores. In some cases air was used as the bore fluid. The polymers and the solvents of the spinning solutions are summarized in Table 1. Variation of pore sizes was achieved mainly by altering the concentration of the polymer solutions. The spun hollow fibers were washed well by water. The dried membranes were prepared by soaking the water-wet fibers in methanol, replacing the methanol by n-hexane, and airdrying at room temperature. Characterization of hollow fiber membranes The outer and inner diameters were measured by a microscope with a micrometer scale. The water content of the wet membrane (&,) was determined from the weights of the wet and the dried membrane. The mean pore radius (R,) and the tortuosity (7) of the membrane were estimated from the solute permeability (Pm) and the hydraulic permeability (L,) . The P, value was measured by a dialysis experiment, which was carried out with the apparatus shown in Fig. 1 at 298 K with dilute ethanol solution (ca. 10m5mol-cm-3 ). LPwas the water permeability calculated from the ultrafiltration rates measured at 298 K with ultrafiltered distilled water under 16.7 kPa of transmembrane pressure by using a miniature hollow fiber module fabricated in a glass tube (see Appendix 1) . The R, and 7 values are not ideal for representing the features of a heterogeneous membrane, especially for an asymmetric membrane, but the values are considered to represent the averaged features of permeation across the membrane.

55

I’. Fujii et al./J.Membrane Sci. 72 (1992) 53-72 TABLE 1 Preparation of hollow fiber membranes Membrane material

PVdF (Kynar460/740) PS (Udel P-3500) PPO (Aldrich Chem) PAN (Prepared) CTA (Eastman Chem)

Spinning solution

Injected fluid

solv.

cont. (wt.%)

temp. (K)

aq. soln. (wt.%)

temp.(K)

DMSO NMP NMP DMSO DMSO

27-35 25-38 28 28 24

347-363 333-353 372 335 349

DMSO (80) NMP (85) NMP (90) (air) (air)

293-318 283-313 313 313 319

Key: PVDF = poly (vinylidene fluoride) ; PS = polysulfone; PPO = poly (phenylene oxide); CTA = cellulose triacetate; DMSO = dimethyl sulfoxide; NMP = N-methyl-2-pyrrolidone.

Fig. 1. Schematic view of the apparatus for permeability measurement of a hollow fiber membrane: ( 1) reservoir of solution; (2) magnetic stirrer; (3) pump; (4) hollow fiber bundle; (5) reservoir of dialysate; (6) pump; (7) perforated plate for flow adjustment.

PAN = polyacrylonitrile;

Pervaporation type experiment Pervaporation type experiments were carried out with the apparatus shown in Fig. 2 by using small hollow fiber modules of crossflow type. The hollow fibers were thoroughly dried before fabrication of the modules and were dried in a vacuum drier when the measurement was repeated. The feed solution was circulated into the bores of the hollow fibers. The temperature of the feed solution was kept at 298 K. The permeate side pressure was kept at 1.33 kPa by using a vacuum pump and an electromagnetic controller. The permeated vapor was collected in a trap cooled with liquid nitrogen, and was weighed and analyzed after the experiment.

Dialysis and pervaporation type experiment

2.2.

Dialysis type experiment Dialysis type experiments were carried out analogously to the measurement of P, with the same apparatus for various solutes. The membrane used was a dried membrane, which was compared with a wet membrane of the same hollow fiber sample. The apparent solute permeability through the dried membrane was calculated similarly to that for the wet membrane.

Fig. 2. Schematic view of the apparatus for PV experiment: ( 1) feed solution; (2 ) magnetic stirrer; (3 ) pump; (4) water bath; (5) hollow fiber module; (6) two way cock; (7) cold trap; (8) vacuum controller; (9) vacuum pump.

56

2.3. DCMD type experiment Experimental procedure The DCMD type experiments were carried out with the set-up shown schematically in Fig. 3. Normal experiments were carried out to circulate the warm solution (feed solution) in the bores of the hollow fibers and the cooled solution (permeate side solution) along the outside of the fibers (shell side). Alcohol concentration was measured at set intervals. The weights of both solutions in the reservoirs of the feed and the permeate were measured after the experiment, and the permeation rate was calculated from the initial and final weighs. The temperatures of the solutions were adjusted by means of water baths and the module was put into a heat-insulating box. The permeate side pressures were kept at set values and the pressures at the inlets of the feed and the permeate were adjusted to control the transmembrane pressure (TMP ) .

Fig. 3. Schematic view of the apparatus for DCMD type experiment: ( 1) solution for bore interior; (2 ) stirrer; (3) pump; (4) water bath; (5) hollow fiber module; (6) solution for shell side; (7) stirrer; (8) water bath; (9) pump; (10) transducer for pressure measurement; (11) platinum resistance thermometer; (12) insulating box.

Y. Fujii et al./J. Membrane Sci. 72 (1992) 53-72

Miniature module for DCMD type experiment The arrangement of the hollow fibers was studied, and we chose the best type for the membrane module by comparing pressure drops and heat and mass transport characteristics. The module was fabricated as follows. A nylon monofilament (diameter 0.165 mm) was wound spirally around a hollow fiber as a spacer, and another monofilament was wound in reverse on the hollow fiber. The hollow fibers with double spacer yarns were tied up in a bundle, the bundle was inserted into a shell made of poly (methyl methacrylate ) (PMMA) tube which was sealed with an epoxy resin at each end, the tube was cut to expose the fiber ends, and headers and inlet and outlet nozzles were attached to it. The features of the module used for the fundamental studies on DCMD type separation are shown in Table 2. Study on heat transfer coefficient The relationship between heat transfer coefficients and flow rates was determined to estimate the temperature on the membrane surface. The temperature differences were measured with platinum resistance thermometers at the module inlet and outlet of both high and low temperature solutions by using the same apparatus as for the DCMD type experiments. Measurements were carried out by varying the flow rates outside the hollow fiber. Distilled water was used as the circulating liquid. Just before an experiment, the flowmeters were corrected by weighing the actual water that had flowed. Study on mass transfer coefficient The relationship between overall mass transfer coefficient (I&,) and the dialysate flow rates was determined to estimate the concentration on the membrane surface. The R& value was calculated from the decreasing rates of the

Y. Fujii et al./J.Membrane Sci. 72 (1992) 53-72

57

TABLE 2 Features of the hollow fiber module for DCMD type experiments Hollow fiber Polymer Dimension Properties

PVDF 93-2 OD = 1.024 mm; ID =0.844 mm c = 0.58; R, = 4.07 nm; T= 3.06

Module Spacer Number of hollow fibres Length Effective membrane area Flow area of hollow fiber

two nylon monofilaments (wound in opposite senses) 14 1,,=0.17; &,,=0.188 m 6.31 x 10e3 m2 outside: 1.73 X 10e5 mz inside: 0.783 X 10e5 m2

ethanol concentration measured in dialysis experiments at various flow rates on the shell side. The dialysis experiments were performed with the same setup as for the DCMD type experiment by reducing the line volumes and increasing the reservoir volume of water (dialysate) to make it possible to analyze the results on the assumption of a perfectly mixing reservoir (see Appendix 2 ) .

3. Results and discussion 3.1. Permeability and selectivity in dialysis type experiment Figure 4 shows that the ratio (odry)/ (c~~,~), where o values were measured with a poly (vinylidene fluoride ) (PVDF ) membrane, depends on the partial vapor pressure (p,) on a log-log scale. Permeation of some solutes, 5.100

2.4. Solutes and analysis

Y. O.46.Xo.‘37 R -0.62 P < 0.005

3 \ E 019 010 f 3

The aqueous solutions used here were made from solutes of analytical grade and distilled water. The concentration of the volatile solute was measured with a gas chromatograph (Shimazu GC-7A) and that of the low volatility solute was measured with a refractive index detector (Shimazu RID-2A) . The partial vapor pressure (p,) was estimated from the mole fractions and the activity coefficients of the solute and water estimated by the Van Laar equation. The vapor pressure of the pure liquid was calculated by using the Antoine equation,

100.

10-I

lo-’

10-l

Id)

IO’

Id

P./Pa Fig. 4. (wh) / (co,.*) vs. p. obtained in dialysis type experiments with the PVDF membrane: (1) methanol; (2) ethanol; (3) n-propanol; (4) i-propanol; (5) n-butanol; (6) i-butanol; (7) t-butanol; (8) ally1 alcohol; (9) cyclohexanol; (10) phenol; (11) acetone; (12) ethyl methyl ketone; (13) ethyl acetate; (14) tetrahydrofuran; (15) 1,4-dioxan; (16) ethylene carbonate; (17) y-butyrolactone; (18) acetonitrile; (19) acetic acid.

58

Y. Fujii et al./J. Membrane

such as DMSO, was not observed, even though they had a strong affinity for the membrane. The dried PVDF membrane was not wetted by the dilute aqueous solutions tested here, and did not permit water permeation up to about 0.69 MPa of TMP from inside to outside or vice versa. Quite a similar result was observed with the polysulfone (PSF) membrane. These results suggest that the solutes evaporate at the membrane surface and penetrate into the membrane pores: the vapor of the solutes permeates through the pores driven by the partial vapor pressure differences. 3.2. Selectivity in pervaporation type experiment Table 3 shows the selectivity through four types of PSF membrane for four alcohols, and Table 4 shows the ethanol selectivity through dried PVDF membranes having different pore sizes. The permeation rate and the separation factor were calculated by the following equations: J=P/(At) -e

Sci. 72 (1992) 53-72

ratio Rp/rV,,where r,, is the radius of the alcohol molecule calculated from the molar volume. The value of c&$‘hp’ increases with increasing RJr,, and the membranes permit selective permeation of the alcohols when R,/r,, in each case is larger than ca. 7, even though the membrane polymers and the alcohols differ. This result shows that the permeability and selectivity depend on the pore radius of the membrane and the molecular size of the permeants. Taking the results mentioned in Section 3.1 into account, one can understand that alcohol and water permeate in the vapor state through a dried porous membrane which was prepared from a hydrophobic glassy polymer. If this is so, the preferential permeation of alcohol might be difficult because the membrane has the function of a porous sieve owing to steric hindrance in the pores. However, we think that, if the mean pore radius is larger than the critical radius, the membrane will permit the preferential permeation of alcohol because the relative volatility of alcohol is rather high. 3.3. DCMD type experiment

(1)

~pe/C,w w= GJGV

(2)

CY

Figure 5 shows a plot of cr$!$~’ against the

Experimental results for fundamental studies Table 5 shows the experimental conditions and the results from studies on the fundamen-

TABLE 3 Results of pervaporation type experiments (1) Hollow fiber No. PS23-8 PS23-2 PS22-1 PS22-6

Dimensions ID

OD

260 274 275 264

350 350 368 363

R, (nm) 0.55 1.28 2.45 2.90

/ylcohol water

Q (kg-m-‘h-i)

MeOH

EtOH

n-PrOH

n-BuOH

MeOH

EtOH

n-PrOH

n-BuOH

0.73 0.94 1.85 2.49

0.34 0.62 1.73 2.48

0.25 0.40 1.47 2.84

0.14 0.36 1.40 2.75

0.32 0.42 0.59 0.63

0.33 0.42 0.58 0.66

0.30 0.39 0.52 0.65

0.30 0.37 0.54 0.98

Unit of ID and OD = pm. r,,: MeOH 0.251; EtOH 0.285; n-PrOH 0.310; n-BuOH 0.331 nm. Feed: alcohol concentration 1 wt.%; temperature 293 K.

Y. Fujii et al/J. Membrane TABLE

59

Sci. 72 (1992) 53-72

4

Results of pervaporation type experiments (2) Hollow fiber No.

ID (mm)

PS105-2 PVDF36-1 PVDF35-2 PVDF55-3 PVDF41-1 PVDF93-2 PVDF90-3

0.854 0.709

UFRS”

0.887

1.112

0.259 0.259 0.297 0.259

0.369 0.377 0.382

87.0 0.34 3.08 9.23

0.70 0.60 0.60 0.65

16.7 0.92 2.38 3.47

2.97 0.32 1.00 2.18

15.45 16.05 37.7

0.60 0.56 0.60

64.8 99.3

0.63 0.65

4.68 6.95 9.73 14.05

1.96 5.28 3.90 4.13

PVDFSI-1 PVDF95-2

0.876 0.852

17.5

5.40

0.396 1.035 0.861 1.069 1.059

&

J (k-m

OD (mm)

4 (nm)

-2_hr-1)

G EtOH%

1.30 0.27

4.4 5.0

0.66 0.52 0.68 0.54 0.86

5.0 1.0 5.0 5.0 5.0 5.0

0.53 1.03

5.0

YJFRS, x lo-’ ml-m-2-hr-‘-Pa-‘.

Relationships between permeation rate and concentration The permeates of ethanol and water are expressed as:

IO' Rp/r,,

Fig. 5. a$r$ vs. R,/r,. observed in PV type experiments. For polysulfone hollow fiber membranes: (0 ) methanol; (0 ) ethanol; ( A ) n-propanol; (0 ) n-butanol. For PVDF hollow fiber membranes: ( n ) ethanol.

P,(t) =AJ‘dJ.dt

(3)

P,(t)

(4)

p(t)

=AJ;JWdt =P,(t)

+pW(t)

The total permeates are determined from the high and low temperature side results as: mn(t) =mn(O) -&(t)

tal characteristics of DCMD type separation using the module shown in Table 2. The CHe and CLein the experiments both started as the same concentration. Figure 6 shows the change of ethanol concentration during typical DCMD type experiments. These results indicate that J, (t ) is an decreasing function, and J,(t) is considered to be constant because the alcohol concentration is so low that the water mole fraction changes little. The J, functions and J, describe the time dependence of the ethanol and water fluxes during the experiment.

(5)

mL(t) =mL(6) +&(t)

- CSn(n) - &S(n)

(6) (7)

The values mH (t) and mL (t) should be identical within the range of the experimental error. The ethanol concentrations for the high and low temperature side respectively are written in the following form: G,(t)

={mn(O)Cn,(O) -C

-Pn(t)Lk(t)

[G,(L)&(n)

l}lmH(t) G,(t) ={mL(0)CLe(O) +h,(tGb(t)

(8)

- 1 [G,(Wk(n)

(9)

1)/e(t)

60

Y. Fujii et al./J.Membrane Sci. 72 (1992) 53-72

TABLE 5 Operating conditions and results of DCMD type experiments Exp. Init. EtOH No. cont. (wt.%)

1 2 3 4 5 6 7 8 9 10 11 12 13

Solution temperature (K)

Solution pressure (kPa)

G(0)

G(O)

‘I’m

Tuo

7”r.i

TLO

PLY

PLO

Time Final EtOH of cont. (wt.%) exp. (hr) G(E) G(E)

5.02 4.97 5.05 5.14 4.85 5.01 1.12 9.68 4.77 4.97 5.15 5.02 4.80

5.07 5.19 5.08 5.42 5.07 5.10 1.39 9.68 4.72 5.25 5.39 5.20 5.11

328 319 308 329 318 308 318 318 319 318 318 318 319

322 314 306 324 315 306 313 314 314 314 314 315 315

290 289 289 294 294 294 289 290 289 289 289 289 290

294 292 290 298 296 295 292 294 292 292 294 291 292

92.5 90.5 90.5 90.5 89.5 90.5 91.5 89.5 91.0 68.0 90.5 89.5 92.5

88.6 85.6 85.6 85.6 84.6 85.6 87.5 84.6 87.1 67.0 85.6 84.6 88.6

4.0 7.0 7.0 4.3 6.0 7.0 7.0 6.0 7.0 6.0 6.0 7.0 7.0

1.54 1.91 2.85 1.42 2.30 3.36 0.50 6.36 1.60 1.90 2.48 2.04 1.74

6.25 6.23 6.03 6.64 6.08 5.80 1.64 11.99 5.77 6.36 6.55 6.35 6.32

Features of the module are shown in Table 2. Flow rate (10W6m3-set-‘): qn~6.67; qL= 13.3 in Nos. l-10,5.5 in No. 11,lO.O in No. 12,15.0 in Inletpressure (kPa):p,i=110.1andp~o=100.3;inNo.9,p,i=92.5andp~o=84.6.

where assumed:

the

~&W&ek)

~&hG?@n) 0

2

4

6

6

Time/h

Fig. 6. Change of ethanol concentration during DCMD type experiments: Nos. 2,7 and 8 are the experiment numbers in Table 5; lines are those calculated.

The average concentrations total permeate are expressed

of ethanol in the as:

Permeate ( 1O-3 kg) Pn

PL

72.1 65.1 62.5 76.5 57.2 46.5 59.1 63.6 72.5 62.2 63.1 67.6 70.3

72.9 66.8 58.1 77.2 54.8 49.0 57.1 60.4 74.3 60.4 57.3 64.8 69.0

No. 13.

following

relationships

1G-k = [~fw~) lcze = [~&-I(n)

The average concentrations

G-k!(t)=

&I(t) -G(O) ln[G(t)/G(O)

GE(t)=

CL,(t)-G(O) ln[G(t)/G,(O) 1

1

are

(12) (13)

are given by: (14)

(15)

The separation factor for ethanol relative to water at time t and the average value are given by: a;(t)=

J,(t)/&(t) G,(t)lG,(t)

(16) (17)

61

Y. Fujii et al/J. Membrane Sci. 72 (1992) 53-72

From the observed concentration, another die can be calculated by the following equation:

(18) The best functions to describe the time dependence of the concentration and the total permeate, determined by curve-fitting with eqns. (3)-(11) are: J,(t) =ueeebt

(19)

J,(t) =a,

(20)

The values of a,, b and a, determined for the experiments in Table 5 are shown in Table 6. The concentration calculated from the functions by using the determined constants agrees well with the measured value. Ethanol selectivity The average separation factors calculated by eqn. (17) and those calculated by eqn. (18)) as shown in Table 6, are in good agreement.

The initial value cuk(0) values calculated for these experiments with the same module range from 2.18 to 4.19, corresponding to the different operating conditions.

Relationships between permeation rates and operating conditions The experiments in Table 6 were conducted to compare the effects of the operating conditions. From Table 6 one can see that the permeation rates of ethanol and water remain stable over the range of experiments. The temperature and the concentration have effects on the permeation rates of ethanol and water. However, the transmembrane pressure between the bore side and the shell side has little effect on them: the TMP of experiment No. 9 was 0.487 kPa and the bore side pressure was lower than the shell side; the value in experiment No. 10 was 37.8 kPa. The flow rate on the shell side has little effect on the permeation rates.

TABLE 6 Calculated results for the DCMD type experiments shown in Table 5 Exp. No.

Permeation rate ethanol

Ethanol cont. of permeate (wt.%)

Separation factor cze

a, (kg-m-‘4-l)

b (hr-‘)

water a, (kg-m -2_hr-’ )

1 2

0.532 0.308

0.417 0.270

2.62 1.37

8.80 8.81

3.84 4.19

3 4

0.161 0.554

0.110 0.424

1.25 2.59

8.25 8.92

2.43 3.95

3.15 2.99 2.20 3.29

5 6 7 8 9 10 11 12 13

0.242 0.114 0.060 0.451 0.311 0.288 0.267 0.265 0.276

0.234 0.067 0.254 0.174 0.283 0.233 0.223 0.220 0.236

1.34 0.99 1.29 1.35 1.55 1.48 1.43 1.36 1.45

8.81 8.25 2.18 15.94 7.96 9.18 9.17 8.89 8.34

3.54 2.18 4.11 3.12 4.01 3.73 3.43 3.68 3.77

2.46 2.10 2.83 2.79 2.90 3.09 2.69 2.86 2.95

initial

average

eqn. (16)

eqn. (17)

eqn. (18) 3.16 2.92 2.24 3.29 2.72 2.08 2.87 2.11 2.88 3.06 3.06 2.84 2.92

Y. Fujii et al./J. Membrane Sci. 72 (1992) 53-72

62

(a) 0.8 y=o.19o.x

0.6

;i;r k ,”

\ 8

0.4 0.2 0

0

I

2

3

4

5

(Ape)lm/kPa lb)4 Y * 0.228.X 5

N

3

‘E

02 Y \ B

1 m I

I 0

2

4

6

IO

8

12

Fig. 9. Concentration profiles across the membrane DCMD type separation.

14

(Ap,)lm/kPa

Fig. 7. (a) Initial ethanol permeation rate vs. partial vapor pressure difference of ethanol. (b). Initial water permeation rate vs. partial vapor pressure difference of water.

Fig. 8. Temperature profiles across the membrane DCMD type experiment.

9. The (Ape h, values are calculated by using the temperatures and concentrations on the membrane surfaces (see Appendix 3 ) . The temperatures of the interface between the membrane surface and the solution are expressed as: THm= TH -AT,,

(21)

TLm=TL+ATL,

(22)

The temperature membrane surface given by:

-TL

during

AT,,

=

Relationships between permeation rates and CAP& The temperature profiles and concentration profiles across the membrane during the DCMD type separation are represented in Figs. 8 and

differences between and the bulk solution

Qiil(hnA~)

AT,,,, =QU(knd~)

Figure 7 shows that the initial permeation rates in Table 6 are directly proportional to the partial vapor pressure differences ( (&I),~), where the (&I),, are estimated from the initial conditions by the procedure mentioned later.

during

the are

(23) (24)

where

(25) Q;;=Qk'ob,~+Jmta,AHv (26) Q';. =Qk'oon~ -Jtota,A& Here, Qk is due to thermal conduction, AH”

is the heat of vaporization and AH, is the heat of condensation of the permeate. These values are calculated from the measured permeation rates and the latent heats of ethanol and water. Because the hydrodynamic conditions of the bore side and the shell side are quite similar, as

Y. Fujii et al/J. Membrane Sci. 72 (1992) 53-72

63

shown in Table 7, hi, and II,,, were calculated from the equation: 1/U,,1=1.373x10-3+1.656x10-5~,o~s

(27)

which was obtained from the experimental results listed in Table 8. The concentrations at the interface between the membrane surface and the solution are expressed as: c Hme

= CHe

GIle

= CL,

-

AcHe

(28) (29)

+ Ge

The concentration differences are given by the following equations with an approximate estimate of coupling induced flow:

1

(31)

The mass transfer resistance (Ri, ) is calculated from the relationships in the literature is estimated by the following equa[161; Rout tion obtained from the dialysis experiment:

Rail= ( 1.141+0.05392u{“.75)

a similar range. The AC’,, and AC,, values are similar, and range from 0.03 to 0.51 wt.%. Figure 10 shows that the J, values are directly proportional to the (AP~),~values, which were estimated from the values of AT, and AC, obtained by the above mentioned procedure. For all DCMD type experiments conducted here, the J, values were plotted against ( AP,)~ to give a straight line passing through the origin.

x lo6

(32)

The results are shown in Table 9 referred to as Case D. The AT, values range from 0.18 to 0.79 K and the values of ATH, and AT,, are in

Membrane coefficients The slope of the J- (Ap),, line represents the permeability coefficient of the membrane: MC,, MC,. The mean value of the slopes of the J,(Ap,) Imlines calculated for the experiments in Table 5 is 0.189 20.02 (std. error) kg-mV2hr-l-Pa-’ and agrees well with the value determined from the initial J, values shown in Fig. 7(a). The change of (AP~)~, during one experiment is small. However, (AP~)~, is also calculated in the same procedure and the MC, can be obtained. The mean value of the MC, determined from the slopes of Jw-(Apw)l, lines is 0.247 +-0.057 (std. error), and also agrees with the results in Fig. 7 (b ) . The operating conditions examined here have little effect on the values of MC, and MC,.

TABLE 7 Hydrodynamic conditions of the hollow fiber module for DCMD type experiment Flow condition

Bore side

Shell side

Diameter (equivalent dia. ) (mm) Length (m) Flow area ( IOe6 m”) Flow rate ( 10m6 m3-set-I) Flow velocity (m-set-‘) Average temp. (“C) Re

0.844 0.188 7.83 6.67 0.852 325.7 1200

0.901 0.170 17.3 8.33 0.482 290.7 724

Permeability and selectiuity through other polymeric membranes Table 10 shows the characteristics of the hollow fiber modules and the initial permeation rates. The hollow fiber membranes were prepared from PSf, polyacrylonitrile (PAN), polyphenylene oxide (PPO ) and cellulose triacetate (CTA), and were fabricated into miniature modules after the fibers had been soaked in methanol and dried. The mean pore radius and the tortuosity were measured with water-wet hollow fibers, which

64

Y. Fujii et al/J. Membrane

Sci. 72 (1992) 53-72

Heat flux (kW-m-‘)

Heat transfer coeff. (W-m-’ K-l)

TABLE8 Heat fluxes and heat transfer coefficients of hollow fiber modules Module No.

Ex. No.

Flow rate (ml-min-‘) Qm

1

2

Temperature inlet

outlet

TL

T HO

TLi

TLO

(K-l)

on

Q

Q:’

1 2 3 4 5 6 7

400

330 380 450 650 700 800 1500

318.0 317.8 317.2 317.8 317.5 317.5 318.7

313.7 313.6 312.9 313.3 312.8 313.0 314.2

287.9 288.9 287.8 287.8 287.1 287.8 289.0

292.8 293.5 291.6 291.2 292.5 292.8 292.2

19.02 18.57 19.02 19.90 20.79 19.90 19.90

1.03 1.00 0.99 1.03 1.01 1.01 1.10

705.5 714.2 712.6 726.0 752.0 779.4 699.3

1 2 3 4 5 6 7

400

330 460 700 IO0 850 720 1500

317.8 317.5 317.5 317.1 317.4 317.5 318.7

313.7 313.2 313.1 312.7 313.0 312.8 314.2

287.8 287.8 287.6 287.6 287.4 286.9 289.0

292.6 292.9 292.8 292.2 292.0 291.8 292.3

18.07 18.96 19.40 19.40 19.40 20.73 19.84

1.02 1.02 1.02 1.00 1.01 1.02 1.10

671.2 706.0 692.4 712.8 698.7 740.8 699.3

Module No. 1 shown in Table 2. Module No. 2: ID and OD ~0.846 and 1.035 mm, 1,,=0.17 m, Ainz0.786 X lo-‘ rn’, A,,= m’; hollow fibers same as module No. 1. Q:’ estimated from QG= J,., AH,, Jw=2.48X lo-*(dp,.,)i,,, (kg-m-‘-hr-‘I.

were re-wetted by soaking the dried fibers in methanol and replacing the methanol by water. In all cases the J, values are directly proportional to (dp,)r,, and the MC, and MC, values were determined from these relationships. Table 11 shows the separation factors and the membrane coefficients. The cut of the PPO membrane is highest and those of PVDF are next; PSf and CTA yield lower a: values. The c$ of the PAN membranes were less than 1, but some selectivity was observed after the membranes had been treated with silicone prepolymer. Table 11 suggests that higher selectivity is obtained for higher MC,/MC,, and MC,/MC, seems to depend on the hydrophobicity of the membrane polymers. Figure 11 shows that the log MC, and log MC,

17.0 X 10e5 m*,A,=633

X 1W3

are inversely proportional to log ( WTz,) , which means the real length of the membrane pore for the permeate molecules. Also, log(MC,) seems to be proportional to log RP,because the correlation between log MCJMC, and R, is statistically significant: the relationship between log MC, and R, is not clear. On the permeability and selectivity The ethanol permeability in the DCMD type experiments obtained here is fairly constant, but the water permeability varies widely with the different conditions and membranes. The scattered MC, values of the PVDF membranes suggest that there may be some other factor having an effect on the permeability. The results obtained with the PAN membranes treated with silicone show that the selectivity

Y. Fujii et al./J. Membrane TABLE

Sci. 72 (1992) 53-72

65

9

Estimation of AT and AC at the inlet for the experiments listed in Table 5 No.

Temp. difference (K )

Concentration difference (wt.% )

cases A and B

case D

AT,,,,

ATI.,

AT,,,,

AT,,,,

G,,

AC,

ACEI,

AG.,

A’&,

ACL,

0.29

0.59 0.41

0.22

0.44

0.27 0.60 0.32

0.15 0.07 0.22 0.11

0.31 0.16 0.44 0.23

case A

case B

case D

1

6.90

0.79

2

6.04

0.54

0.47 0.41

0.79 0.54

0.32 0.21

0.68 0.47

3 4 5

2.77 5.84 3.79

0.29 0.67 0.44

0.18 0.40 0.25

0.29 0.67 0.44

0.12 0.32 0.16

0.29 0.68 0.35

0.19 0.12 0.30 0.15

6 7 8 9 10 11

2.41 5.10 5.34 4.97 4.74 4.74

0.25 0.54 0.64 0.57 0.50 0.77

0.16 0.34 0.36 0.33 0.32 0.32

0.25 0.54 0.64 0.57 0.50 0.77

0.08 0.04 0.36 0.21 0.19 0.22

0.20 0.09 0.80 0.47 0.43 0.50

0.08 0.04 0.33 0.19 0.18 0.21

0.19 0.08 0.71 0.42 0.39 0.45

0.04 0.03 0.24 0.15 0.13 0.16

0.10 0.06 0.51 0.32 0.28 0.34

12 13

4.15 4.74

0.40 0.35

0.28 0.32

0.40 0.35

0.18 0.18

0.39 0.41

0.16 0.17

0.36 0.37

0.12 0.13

0.26 0.27

0

I

2 (Qp.h

3

/kPo

Fig. 10. J, vs. (Ape),,,, for experiments No. 2, 7 and 8 in Table5:(0)No.2;(0)No.7;(A)No.8.

in the DCMD type experiment depends on such polymer properties as hydrophobicity. Franken et al. reported that the selectivity obtained by the usual DCMD with a polypropylene capillary membrane was in the range 1.6-3.2 [ 141, and Honda et al. reported a value of 2.7 with a PTFE filter membrane [lo]. The selectivity of the present DCMD type separation ranges from 1.1 to 7.3 and the selectivities for PVDF and PPO are higher than those reported. In conventional LPMD, selectivity higher than the vapor-liquid equilibrium was reported [ 171.

From such results we may expect much higher selectivity to result in DCMD type separation if the interaction between the membrane and the permeate molecule can be utilized by using a fine porous membrane of a polymer having suitable properties. It has been reported that fluxes from 5.2-13.7 kg-m-2-hr-1 were obtained by conventional DCMD with a polypropylene capillary membrane at temperatures of 346 K for the feed and 302 K for the permeate side solution [ 141. These fluxes are almost identical with the results we obtain here if the differences between the imposed temperature gradients are taken into account. 3.3. Heat transport characteristics Heat transfer coefficients of the boundary layers The hi, calculated by eqn. (27) for experiment No. 1 in Table 6 as a typical case is 53.1 kW-m-2-K-‘, and boutcalculated by the same equation is 33.7 kW-m-2-K-1.

66

Y. Fujii et al./J. Membrane Sci. 72 (1992) 53-72

TABLE 10 Characteristics of the hollow fiber modules of other polymeric membranes and results of DCMD type experiments Polymer No.

Hollow fiber No.

PPO CTA PVDF-1 -2 -3 -4 PSf-1 -2 -3 -4 PAN-l -2 -3 -4

R, (nm)

Module

Permeation rate

r,

OD (mm)

ID (mm)

N

AoutCe)

aeCb’

b Cc)

%(b)

110-7 75-2

2.71 1.95

3.79 2.26

0.445 0.483

0.359 0.390

45 45

2.05 1.93

0.168 0.177

0.413 0.066

0.422 2.962

93-2 92-2 95-2 43-l

4.27 7.32 13.6 24.8

3.06 2.48 2.21 2.93

1.024 1.071 0.982 0.983

0.844 0.863 0.817 0.675

14 14 14 14

1.73 1.82 1.62 1.82

0.309 0.441 0.640 0.239

0.270 0.327 0.543 0.236

1.371 2.231 2.314 0.878

107-l 105-2 103-l 103-1s

2.57 6.81 9.61 6.36

3.40 2.42 1.94 2.64

1.226 1.086 1.039 1.052

1.039 0.866 0.863 0.855

14 14 14 14

1.23 1.59 1.70 1.67

0.272 0.652 0.961 1.210

0.259 0.230 0.541 0.700

1.637 8.023 9.400 10.34

88-3a 88-3b 88-3~ 88-3d

3.93 3.11 1.76 0.71

6.05 6.08 8.74 7.97

0.555 0.554 0.555 0.561

0.464 0.459 0.460 0.457

45 45 45 45

1.66 1.66 1.66 1.64

0.199 0.132 0.079 0.045

0.129 0.156 0.198 0.086

2.737 1.407 0.426 0.307

Other conditions: temperature of feed at inlet, 316-319 K; temperature of permeate at inlet, 287-300 K; initial ethanol concentration, 4.8-5.2 wt.%. Units: (a) 10v5m2; (b) kg-m-2-hr-‘; (c) hr-‘. Samples from PSf 103-1s to PAN 88-3d were soaked in n-hexane solution of silicone RTV prepolymer and cured at 353 K for 18 hr. Soaking conditions: PSf 103-1s. 0.5 wt.%: PAN 88-3a, 0.01 wt.%; PAN 88-3b, 0.1 wt.%; PAN 88-3c, 0.5 wt.%; PAN 88-3d, 0.8 wt.%.

It has been reported that hi, is 3.10 kW-me2K-l at 0.3 m-set-l feed velocity and h,,, is 2.20 kW-mV2-KP1 at 0.35 m-see-l permeate velocity [ 141, and a value of 1.10 kW-m-2-K-1 has been reported for both sides [ 181. The value of hi, is also calculated by the following equation from the hydrodynamic conditions [ 191:

1.75{~+0.04[(;),,

PrTT

(33)

The value of hi, obtained from eqn. (33) is 3.59 kW-m-2-K-1 and is similar to the values in the literature.

This last hi, is about 10% of the ho, value despite the similar hydrodynamic conditions shown in Table 8. Table 9 shows the temperature and concentration differences between the membrane surface and the solution estimated in three cases. In cases A and B, the LIZ’,, values are calculated by using the last hi,; in case D, the dTn, are calculated by using the first hi,. In case A, the effect of coupling flow caused by the mass flux is neglected; in cases B and D, the coupling flow was corrected by means of eqns. (30) and (31). The effects of the coupling flow for dTn, and AT,, are less than 5% and are negligible, and thus the results in cases A and B are identical. The dTu, values in cases A and B are more

67

Y. Fujii et al./J.Membrane Sci. 72 (1992) 53-72 TABLE 11 Membrane coefficients of various polymers Polymer

Hollow fiber No.

(Y;

MC,

MC,,,

MC,/ MC,

WTr, (mm)

PPO

110-7

7.32

1.16

0.84

1.31

0.163

PVDF

93-2 92-2 95-2 D43-1

4.19 3.73 5.17 5.10

1.94 2.67 3.84 1.70

2.22 3.28 3.29 1.59

0.87 0.70 1.17 1.07

0.275 0.258 0.182 0.451

PSf

107-l 105-2 105-2 103-l

3.05 1.61 1.89 2.19

1.77 5.80 6.38 8.71

2.86 15.78 16.82 16.93

0.62 0.37 0.38 0.51

0.318 0.266 0.266 0.171

PAN

88-3a 88-3b 88-3~ 88-3d

1.33 1.78 3.24 2.78

2.35 1.41 0.65 0.37

6.52 3.66 1.10 0.67

0.36 0.39 0.59 0.55

0.275 0.289 0.415 0.414

CTA

75-2

1.12

2.93

13.34

0.21

0.105

Unit of MC. and MC,, kg-m-2-r-‘-Pa-‘.

for the mass flux are effective. Some values of dCL, in case B, e.g. PVDF-3, PVDF-4, PSf-1 and PSf-4, become negative when the correction is neglected, and in case D reasonable values are obtained for all experiments. The correction of AT,, has little effect on A&, and A&,. In case D, correction for the mass flux was, however, applied to the calculations of AT,, despite the slight effect. Figure 12 shows the relationships between the J, and (AAL values compared for the three cases. In cases A and B, unreasonable (AP~)~~ values are obtained and the J, values do not fall on a line. In case D, however, the J, values are reasonable and can be plotted on a line passing through the origin. The hi, values estimated from eqn. (27) thus seem to be reasonable and yield probable AT,, values. For a more detailed discussion focused on this point, hi, should be directly determined by varying the flow velocity of the bore side. However, precise measurement was difficult

5-10’

‘0 a

IO’ Tc @J 5.10° ‘E m < g

IO0 5.16’

5+ss IO-’

5-d

IO0 2.18

WT. re I2

Fig. 11. MC, and MC, vs. WTz, obtained with membranes of PVDF. PSf and PAN.

T-

Case D

YE0.8 1”

than ten times the AT,, values. These differences are too large to be true because of the similar hydrodynamic conditions. However, the LIT,, values in case D are close to the corresponding AT,,. For dCn, and EL, however, the corrections

f

1 :

04 0

0

0.5

I.0 (Ape)lm/kPa

1.5

20

Fig. 12. J, vs. (L&,)~ compared for three cases with a polysulfone hollow fiber membrane; R, values are: No. 18,25.7 nm; No. 16,68.1 nm; No. 19,96.1 nm.

68

Y. Fujii et al./J. Membrane

because the shell side temperature was affected by external conditions and the experimental error in measuring the shell side temperature was too large. Heat transfer coefficient of the PVDF membrane From the results listed in Table 7, the heat transfer coefficient across the membrane (h,) of the PVDF hollow fiber is obtained as 0.755 kW-mM2-K-l, which is calculated by subtracting the latent heat of the permeated water vapor (9.10 W ) from the measured heat flow, and the hi, and h,,, from eqn. (27) are used. The permeated water vapor was calculated from MC,, (L@~)~,, and the effective membrane area. The h, is also estimated from the thermal conductivity of the polymer and the porosity of the membrane (E) as:

Sci. 72 (1992) 53-72

[ 181 but

is close to the k,,,=O.O689W-m-l-K-’ calculated from the experimentally obtained h,. Heat fluxes The observed heat flux, for example, of experiment No. 1 in Table 6 is 26.0 kW-mm2 and agrees with the estimated value of 26.2 kW-mm2 which is obtained from the hi, and bout calculated from eqn. (27 ) and the h, predicted from eqn. (34). The heat flux due to the vaporization and condensation of the permeate is estimated as 1.86 kW-me2. By using the hi, and boutfrom eqn. (33) and is obthe predicted h,, 0.56 kW-m-2-K-’ tained as the U,,, and the heat flux become 20.4 kW-me2. These results are compared in Table 12 with other cases.

Temperature polarization coefficients The temperature polarization coefficients By using 0.126 W-m-l-K-l for the IZpolymer (TPC) [ 151 calculated by using the LIT,, and AT,, values in case D are in the range 0.96[20], 0.027 W-m-‘-K-’ for IZ,irand 0.58 for E, 0.97 at 309-329 K for THi and 289-294 K for the thermal conductivity of the membrane (&) TLi. The values are higher than that estimated becomes 0.0686 W-m-‘-K-’ and h, becomes 0.762 kW-m-2-K-‘. The former value of h, in literature [ 181, but close to the results obagrees well with the latter estimate. The lz, is tained experimentally by Franken et al. under slightly higher than the value in the literature similar conditions [ 141. They obtained 0.90 as

h,=[(l-E)1Zpolymer+EIZairl)/WT

(34)

TABLE 12 Heat transfer coefficients and heat fluxes studied in the case of experiment No. 1 Heat transfer coefficients and others

From eqn. (27) and observed heat flux

From eqn. (27) and estimated h, and heat flux

hi, (kW-m-2-K-‘) h,,, (kW-m-2-K-‘)

(kW-m-‘-K-‘)

53.1 33.7 0.755

53.1 33.7 0.762

3.59 5.12 0.762

3.59 33.7 0.762

U,,, (kW-m-‘-K-‘) Heat flux (kW-m-‘)

0.729 26.0

0.735 26.2

0.560 20.4

0.617 22.3

h,

AH,=

1.86 kW-mm2 was added to the heat flux.

From eqn. (33) and estimated h, and heat flux

From eqn. (33) for hi,, eqn. (27) for h,, and estimated h, and heat flux

Y. Fujii et al/J. Membrane Sci. 72 (1992) 53-72

the TPC at 0.3 m-set-’ feed velocity and 0.35 m-see-l permeate velocity at ca. 345 K for THi and ca. 296 K for TLi by using a microporous polypropylene capillary membrane. They also predicted that the TPC would increase from 0.9 to 0.95 as the velocity increased by a factor of 2.4. The velocity of the feed solution in our experiment is 2.8 times theirs and the permeate velocity is 1.4 times. The wound spacer yarn and the improved module structure would be expected to regulate the flow condition and to reduce the heat transfer resistance. Taking these features into account, the TPC values obtained here may be almost identical with the results for the polypropylene capillary membrane.

69

heat transfer coefficients of the boundary ers are calculated from the experimentally tained equation.

layob-

Acknowledgments This work has been performed under the management of the Research Association for Basic Polymer Technology as a part of a project on Basic Technology for Future Industries sponsored by the Agency of Industrial Science and Technology, Ministry of International Trade and Industry; it was sponsored by the New Energy and Industrial Technology Development Organization (NED0 ) . List of symbols

4. Conclusions Permeability and selectivity through dried fine porous membranes have been studied with the types of hollow fibers prepared from PVDF and PSf and some other polymers by the dryjet wet spinning method. In dialysis type experiments the volatile organics in dilute aqueous solution permeate through the dried membranes, and log(c+& awet) depends on the partial vapor pressures of the solutes. In pervaporation type experiments the selectivity for alcohols increases with the increase of RP/rv,, and membranes permit preferential permeation of alcohols when R,/r,, is higher than ca. 7. In the DCMD type experiments, the ethanol and water fluxes are directly proportional to their partial vapor pressure differences. The log MC, values decreases with increasing log ( WT7,), and increases with increasing log R,. The selectivity for alcohol over water observed with a PPO membrane is ca. 7 and the value with PVDF membranes is ca. 5. Almost all relationships in DCMD type experiments are reasonably described when the

c CP D Gr

AH h ID

J k L L* 1 MC

G P P

membrane area ( m2 ) permeation rate (kg-m-‘-hr-l) time dependence of solute permeation rate (set- ’ ) concentration (wt.% or weight fraction) heat capacity (J-kg-l-K-l) diameter (mm or pm ) Grashof number latent heat (J-kg-l) heat transfer coefficient ( W-md2K-l) inside diameter of hollow fiber (mm) permeation rate/flux (kg-m-2-hr-1) thermal conductivity (W-m-‘-K-l) length (m) hydraulic permeability (cm3-dyn-lset-l) length of hollow fiber in the test module (m) membrane coefficient ( kg-m-2-hr-1Pa-‘) weight of solution (kg) number of hollow fibers in test module permeate in t hrs (kg) pressure (Pa)

70

(APL,

Pr Re

Q" Qf

R R, rv, S T TMP t tll u

U

UFRS W

WT

Y. Fujii et al/J. Membrane

logarithmic mean partial vapor pressure difference (Pa) solute permeability through membrane (m-set-’ ) Prandtl number Reynolds number heat flux (W-m-“) flow rate (1-hr-l) mass transfer resistance (set-m-l ) mean pore radius (nm) radius of molecule calculated from molar volume ( nm) weight of sampling solution (kg) temperature (K) transmembrane pressure (kPa) time (hr) time at the n-th sampling (hr ) overall heat transfer coefficient (Wm-z-K-1) velocity of circulating solution (mset-l) ultrafiltration coefficient (ml-m-2hr-l-Pa-l) mass flow rate (kg-set-l) wall thickness of hollow fiber (pm)

Greek letters selectivity

p &V z co

for e (ethanol)

Subscripts all C con e eff

to w (water )

porosity water fraction viscosity of solution (Pa-see ) viscosity of solution at wall (Pa-set) tortuosity factor solute diffusive permeability (moldyn-I-set-l)

overall or total conduction condensation ethanol effective

f H i in L m

Sci. 72 (1992) 53-72

feed solution high temperature side inlet inside of the hollow fiber low temperature side membrane outlet outside of the hollow fiber permeate solute/solution vaporization water

0 out

P \ W

Other

,(A Am logarithmic statistically

mean difference estimated value

References H.E.A. Bruschke, G.F. Tusel and R. Rautenbach, Pervaporation membranes application in the chemical process industry, in: S. Sourirajan and T. Matsuura (Eds.), Reverse Osmosis and Ultrafiltration, ACS, Washington, DC, 1985, p. 465. A. Mochizuki, S. Amiya, Y. Sato, H. Ogawara and S. Yamasita, Pervaporation separation of water/ethanol mixtures through polysaccharide membranes. III. The permselectivity of the neutralized chitosan membrane and the relationships between its permselectivity and solid state structure, J. Appl. Polym. Sci., 37 (1989) 3385. M. Tuyumoto, H. Karakane, Y. Maeda and H. Tsugaya, Development of polyion complex hollow fiber membranes for separation of water-alcohol mixtures, Proc. 4th Int. Conf. on Pervaporation Process in the Chemical Industry, Ft. Lauderdale, FL, Dec. 3-7,1989. S. Kimura and T. Nomura, Pervaporation of alcoholwater mixtures with silicone rubber membrane, Maku, 1’7 (1982) 353. Y. Fusaoka, E. Imazu and N. Kawabe, Ethanol-water separation through poly (substituted acetylene) membranes, Proc. of the 1987 Int. Congress on Membranes and Membrane Processes, June 8-12, 1987, Tokyo, Japan, 1987, p. 245. H.J.C. te Hennepe, D. Bargeman, M.H.V. Mulder and C.A. Smolders, Zeolite-filled silicone rubber membrane, Part I. Membrane preparation and pervaporation results, J. Membrane Sci., 35 (1987) 39.

Y. Fujii et al/J. Membrane Sci. 72 (1992) 53-72

7

8

9

10

11

12

13

14

15 16

17

18

19 20

M. Nakamura, S. Samejima and T. Kawasaki, Liquid separation with fluorinated polymer membranes, J. Membranes Sci., 36 (1988) 343. K. Ishihara and K. Matsui, Pervaporation of ethanolwater mixture through composite membranes composed of styrene-fluoroalkyl acrylate graft copolymers and crosslinked polydimethylsiloxane membrane, J. Appl. Polym. Sci., 34 (1987) 437. M.H.V. Mulder, A.C.M. Franken and C.A. Smolders, On the mechanism of separation of ethanol/water mixtures by pervaporation. II. Experimental concentration profiles, J. Membrane Sci., 23 (1985) 41. Z. Honda, H. Komada and M. Kai, Nonisothermal mass transport of organic aqueous solution in hydrophobic membrane, in: E. Drioli and M. Nakagaki (Eds. ) , Membranes and Membrane Processes, Plenum, New York, NY, 1986, p. 587. H. Ohya, H. Matsumoto, Y. Negishi and K. Matsumoto, Concentration of ethanol from its aqueous SOlution by pervaporation using porous polypropylene hollow-fiber membrane, Maku, 11 (1986) 231. C. Gostoli and G.C. Sarti, Separation of liquid mixtures by membrane distillation, J. Membrane Sci., 41 (1989) 211. S. Nakao, F. Saitoh, T. Asakura, K. Toda and S. Kimura, Continuous ethanol extraction by pervaporation from a membrane bioreactor, J. Membrane Sci., 30 (1987) 273. A.C.M. Franken, J.A.M. Nolten, M.H.V. Mulder and C.A. Smolders, Ethanol-water separation by membrane distillation: effect of temperature polarization, in: B. Sedlacek and J. Kahovec (Eds.), Synthetic Polymeric Membranes, Walter de Gruyter, Berlin, 1987, p. 531. K. Smolders and A.C.M. Franken, Terminology for membrane distillation, Desalination, 72 (1989) 249. L. Wolf, Jr. and S. Zaltzman, Optimum geometry for artificial kidney dialyzers, Chem. Eng. Progr., Symp. Ser., 64 (84) (1968) 105. E. Hoffmann, D.M. Pfenning, E. Philippsen, P. Schwahn, M. Sieber, R. Wehn, D. Woermann and G. Wiedner, Evaporation of alcohol/water mixtures through hydrophobic porous membranes, J. Membrane Sci., 34 (1987) 199. R.W. Schofield, A.G. Fane and C.J.D. Fell, Heat and mass transfer in membrane distillation, J. Membrane Sci., 33 (1987) 299. M.H. McAdams, Heat Transmission, 3rd edn., McGraw-Hill, New York, NY, 1954, p. 235. C.A. Sperati, Physical constants of fluoropolymers, in: Polymer Handbook, Wiley, New York, NY, 3rd edn., 1989, p. V/35.

71

Appendix 1 Solute permeability

If a perfectly mixing reservoir is assumed for solute permeation through the membrane in the experiment shown in Fig. 1, the solute permeis calculated by the folability P, (=1/R,) lowing relationships:

1

In #(l+u)--u [ 9

=

-Qfs(l-e-nT) % =

(l/&)

(l+u)+

S

(Alqd

(1)

(2)

Rm= L - t&n +Rout)

(3)

Rail= R, + Ri, + Rout

(4)

where v = VJ V,. The Ri, value is estimated from the equation in the literature [ 161; Routis neglected because measurement was carried out at a flow velocity so high that Rout was confirmed as being negligible. Mean pore radius and tortuosity The mean pore radius and tortuosity of the membrane are calculated by the following equations: 7, = fswlf :w

(5)

f fw=RT/D

(6) (7)

(8)

72

Here, z, is the tortuosity for water and is assumed to be ca. 1 in eqn. (8). For example, for the hollow fiber PVDF 932: P,= 0.864 X 10-4m-sec-‘; I+,= 1.627 x 10WIO cm3-dyn-‘-set-l; f,,= 1.21 x 1016 dyn-seccm-’ -mol-‘. Appendix 2 In the experiment to determine the relationship between R outand the flow velocity with the module for DCMD type separation, nr is calculated from the following equation:

Y. Fujii et 01./J. Membrane Sci. 72 (1992) 53-72

-(l-e-“T)(l+v)t*

(9)

S

Appendix 3

(dp ) Im=

bHi

--PLO

) -

$Hi PHo

@Ho -$ka

-PLi

-PLi

)