Journal of Membrane Science, 24 (1985) 43-57 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

43

BROMINE RECOVERY WITH HOLLOW FIBER GAS MEMBRANES

ZHANG QI

Institute of Salt Lake, Academia Sinica, Xining, Quinghai (PeopJe’s Republic of ChinaJ

and

E.L. CUSSLER

Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis, MN 55455 (U.S.A. J

(Received May 21, 1984; accepted in revised form March 13, 1985)

Summary

Gas membranes supported by microporous hollow fibers have been used to concen- trate bromine from a variety of brines similar to seawater. The bromine transport is

governed by diffusion in the brine, and hence is almost independent of membrane proper-

ties except the surface area per volume. In some cases, this type of membrane can be an alternative to packed towers, simultaneously carrying out both absorption and stripping.

Introduction

This paper describes a new method for separating and concentrating bromine from dilute aqueous solutions. The separation is fast because it uses microporous hollow fibers to provide a large surface area per volume. The unusual aspect of the hollow fibers is that their pores are filled with air, so that the separation essentially occurs across a gas membrane.

The characteristics of these gas membranes are best appreciated by com- paring them with a packed tower. Such a tower can be visualized as a piece of pipe, set on its end and filled with an inert packing. A dilute solution containing the volatile species flows into the top of the tower and then slowly trickles down through the tower’s packing. This liquid flow, which effects a large surface area per volume between gas and liquid, must be moderate to avoid “flooding” the tower [l] . Gas is blown countercurrent- ly from the bottom of the tower, stripping out the volatile species. The gas is later washed in another similar tower with a second solvent to absorb and recover that volatile species. Packed towers frequently give rapid mass transfer because they can provide a large surface area between gas and liquid.

In contrast, the hollow fiber membranes used here are akin to a shell-tube heat exchanger [2, 31. The dilute solution containing the volatile solute is

03767388/85/$03.30 0 1985 Elsevier Science Publishers B.V.

44

pumped through the inside of the microporous hollow fibers, and the solvent used for gas absorption flows around the outside of the fibers. The volatile solute evaporates from the inner solution, diffuses across the fibers’ walls, and is absorbed in a concentrated form at the fibers’ outside wall. Thus, both gas stripping and gas absorption are accomplished in the same compact process unit. This unit can potentially give more rapid mass transfer than conventional packed towers because it has a larger surface area and because it is unhindered by flooding. These advantages must be weighed against the cost and the pressure drop characteristic of the fibers.

As an example of this type of membrane process, we decided to study the recovery of bromine from dilute solutions [4]. In the United States, bromine is largely produced from brine wells containing high concentrations of bromides. Elsewhere in the world, bromine is produced from the sea. The basic process for seawater, which is 90 years old [ 51, is as follows. Seawater containing about 65 ppm bromide is treated with chlorine to produce a dilute solution of bromine. The bromine is stripped out with air; this “blow- out” is the most expensive process step. The large volume of air is then washed with base to give a concentrate of bromide and bromate. Bromine is recovered from this concentrate by adding acid and stripping with steam.

In our experiments, we imitated the blow-out and washing steps of this industrial process. We used a dilute solution of around 65 ppm bromine as a feed, various bases as washing solutions, and diffusion through air to transport the bromine from the dilute feed into the concentrated wash. However, the air we used was just that tiny amount trapped within the pores of our hollow fiber membranes. How this process actually functioned is described in the sections below.

Experimental

All materials were of reagent-grade purity and were used as received. Bromine concentration was determined by adding an excess of potassium iodide and then titrating the iodine which was released using sodium thio- sulfate and starch as an indicator [6].

Two different types of membrane experiments were made. Every experi- ment, regardless of type, was made at least in triplicate. Experiments of the first type, which used flat sheets of membrane, were made to investigate the properties of the membranes themselves. Experiments of the second type, which utilized hollow fibers, show what bromine fluxes are possible with feeds like those available commercially.

Experiments with flat membrane sheets used modified diaphragm cells shown in Fig. 1 - left. These cells, which are similar to those developed for other types of membrane experiments [7], consist of two compartments, each about 20 cm3 in volume, and separated by a flat sheet of the membrane of interest. Each compartment is stirred magnetically at 240 rpm. The membrane itself was most commonly a sheet of microporous polypropylene

45

(Celgard, Celanese, Charlotte, NC). Some experiments were made with microporous polytetrafluoroethylene (Gortex, T.L. Gore Assoc., Elkton, MD). In most experiments, the membranes were used as received, so that the pores were filled with air only. In a few experiments, the pores were filled under vacuum with organic solvents like decane, which wet the poly- mer film. These organic liquids are held in the pores by capillary forces.

The basic procedure followed that used in earlier diaphragm cell experi- ments. The initial bromine flux J was determined from

J= V,PW 0

2A

This equation is easily found by rearranging the basic relations for the diaphragm cell [8].

Experiments with hollow fibers used the modules shown schematically in Fig. 1 - right. These modules, which are one inch in diameter and eight inches long, fit directly into an Amicon Model CH2 ultrafiltration system (Amicon Corp., Bedford, MA). The modules, made of polymethyhnetacryl- ate, contain microporous polypropylene fibers glued in place with poly-

stirring chamber

bromine solution

feed

A

hollow fibers

t depleted bromine solution

Fig. 1. The two types of membrane apparatus. The diaphragm cell shown at the left was used to study the properties of the gas membranes themselves. The modules, illustrated at the right, have the general configuration of a shell tube heat exchanger. They were used to measure the large bromine fluxes possible across hollow fibers.

46

urethane cement. Those used in most of the experiments contained 300 microporous polypropylene fibers of 381 pm internal diameter, 29 pm thick, with a 40% void fraction and a total surface area of 538 cm’ (Celgard X20, Celanese, Charlotte, NC). This gives a surface area per volume of 550 m2/m3 (150 ft2/ft3). The modules used in the remaining experiments contained 400 fibers of 397 pm internal diameter and 24 pm thick, with a void fraction of 20% and a total surface area of 760 cm2 (Celgard X10, Celanese, Char- lotte, NC). These modules have a surface area per volume of 820 m2/m3 (270 ft2/ft3). Bromine solution is recycled through the fibers using the peristaltic pump supplied with the ultrafiltration apparatus. This pump produces velocities around 0.2 m/set at pressure drops of about 0.2 atm. The basic solution for recovering the bromine was slowly pumped along the outside of the fibers using a Manostat Varistaltic pump.

The experimental procedure with these modules was straightforward. The modules were clamped into the ultrafiltration apparatus. The bromine solu- tion and the basic scrubbing solution were poured into the “feed” reservoir and the “filtrate” reservoir, respectively, and the pumps were turned on. The bromine solution was periodically sampled and its concentration was deter- mined. These concentrations were analyzed in terms of a mass transfer coef- ficient k

V k=- In [Br2(t=O)l

nNdLt DWt)l

The derivation of this equation is given in the Appendix.

(2)

Results

As explained above, we made two types of membrane experiments in this research. First, we measured bromine transport across flat membranes mounted in diaphragm cells. Second, we studied the performance of hollow fiber modules to determine the industrial potential of this type of separation process. Each type of experiment is discussed below.

The flux of bromine across flat membranes is found to be proportional to the bromine concentration in the feed, as shown in Fig. 2. These results show that bromine transport is a first order process, but they do not show whether this transport is governed by diffusion or chemical reaction. The results in Fig. 2 illustrate good reproducibility, since the fluxes reported are calculated from derivatives of the actual experimental data, as exemplified by those in the insert in this figure.

The bromine flux for different membranes is shown in Table 1. All fluxes fall within a factor of two. For example, the membrane Celgard 2400 has half the thickness of the membrane Celgard 2402, but the fluxes across these membranes are within 20%. The fluxes across Celgard 2500 are ilO% whether the pores are filled with air, decane, or dichlorobenzene. The fluxes across the Gortex films are close to those across Celgard, even though

47

the membrane thickness and porosity are significantly different. All these fluxes are much faster than those described in a recent patent application using a solid polymer membrane [ 91.

It was surprising that the membrane had so little effect on bromine trans- port. We originally set out to construct supported liquid membranes made of kerosene. Kerosene was chosen because it is inexpensive, so the mem- branes could easily be regenerated once they failed. We expected such mem- branes to fail frequently, since previous studies of liquid membrane lifetimes have often been discouraging [lo, 111. Yet we found that the membranes worked as well when deliberately omitting the membrane liquid, which we had thought was essential. Later, we found that flat gas membranes had been suggested for iodine separations by Watanabe and Miyauchi [12], and that both tubular and spiral wound gas membranes had been used for iodine and

r , ,

;

I L

I -

+ 0 200 400

Bromine Cont. (ppm)

Fig. 2. Bromine flux vs. concentration. The membrane in these studies was microporous

polypropylene (Celgard 2500) with air-filled pores. The feed contained 0.5 N NaCl at

pH 3.5, and the stripping solution is 0.1 N NaOH. The mass transfer coefficient inferred from these data is 0.03 cm/set, high for transport in liquids but lower than that expected

for gases.

48

TABLE 1

Similarity of bromine fluxes across different flat membranes

The source solution contained 63-68 ppm bromine in 0.5 N NaCl at pH 3.5; the basic solution contained 0.1 N NaOH; all experiments were made at 25°C

Membrane Manufacturers Porosity Thickness Pores

material description e (rm) contain

Initial flux

( 10m6 g/cm*-set)

Polypropylene Celgard 2500 0.45 25 air 2.3 kerosene 1.8

decane 2.2 diclorobenzene 2.3

Celgard 2400 0.38 25 air 2.1

Celgard 2402 0.38 50 air 1.7

Polytetra- fluoroethylene Gortex 0.50 76 air 1.3

Gortex 0.84 76 air 1.7

for ammonia separations by Miyauchi et al. [13] and by Imai et al. [14] . We appear to be the first to use hollow fiber gas membranes for bromine.

The bromine flux is largely independent of the salt concentration in the feed solution, as shown by the results at the top of Table 2. The bromine flux from pure water is about 25% higher than the other values, which all cluster around 2.3 X lo-‘ g/cm2-sec. We suspect that the high value in pure water reflects lack of interactions between bromine and the other solutes; that such interactions are significant may be inferred from the altered solubilities and the reduced vapor pressure of bromine in various salt solu- tions 14, 151. The small but systematic flux decrease in the various sodium chloride solutions probably reflects increases in viscosity and decreases in diffusion coefficient. The bromine flux also varies little with the concentra- tions of hydroxide, bromide, and bromate present in the stripping solution as shown by the data at the bottom of Table 2.

Finally, the results in Table 2 suggest that the gas membranes are stable. The value in parentheses corresponds to a flux measured on a membrane used for 50 days. This value is within experimental error of the fluxes ob- served initially. The bromine flux is a strong function of the temperature, as shown by the diaphragm cell results in Fig. 3. The obvious rationalization of these results is that increasing the temperature increases the bromine vapor pressure and hence the flux across the membrane. The results do show a roughly exponential form characteristic of vapor pressure data. However, as discussed below, we believe that a different explanation is more likely.

The mass transfer coefficients found with hollow fiber membranes are shown in Table 3. These experiments are best considered as five groups. In the first group, experiments 1-4, the brine contains bromine at a concen- tration like that obtained after chlorination of seawater. The other salts in

49

TABLE 2

Bromine flux variations with feed and base concentrations

All experiments were at 25°C and used a feed containing 65 ppm bromine at pH 3.5 and

a flat membrane of Celgard 2500

Feed Basic

solution solution

Initial flux (10e6 g/cm*-see)

0 0.5 N NaOH 3.0 0.5 N NaCl 2.3 (2.3a)

1 .O N NaCl 2.3 2.0 N NaCl 2.2 3.0 N NaCl 2.1

4.0 N NaCl 1.8

2.0 N Na,SO, 0.5 N NaOH 2.3

2.0 N CaCl, 2.4 2.0 N MgCl, 2.2

0.5 N NaCl 0.2 N NaOHb 2.3

0.4 N NaOHb 2.3 0.6 N NaOHb 2.1

0.8 N NaOHb 2.2

1.0 N NaOHb 2.2

a This value is for a membrane used for 50 days.

bin these experiments, the concentration of hydroxide plus bromide plus bromate always

totalled 1.0 N, and the ratio of bromide to bromate was always 5.

the brine approximate those present in the sea. However, the pH has been adjusted with HCI to that value used in the present commercial extraction of bromine from the sea.

The other groups of experiments imitate other brines in which bromine extraction has been studied. Because some of these brines contain much higher bromine concentrations, the technology with which hollow fibers must compete may be steam stripping rather than the air “blow-out” men- tioned above [4, 161. Experiments 5-7 parallel a Russian brine [17] ; experiments 8-11 are similar to a Black Sea bittern [18] ; experiments 12-14 copy a Middle Eastern brine [19] ; and experiments 15 and 16 re- semble the solutions used in a German process [20] .

The mass transfer coefficients in all these experiments are similar, averag- ing about 2 X 10e3 cm/see. This small range occurs in spite of the widely differing concentrations of the brine feeds, including bromine concentra- tions which vary by a factor of 50. We believe that the differences between the values given are probably due to changes in flow rate, temperature, viscosity and bromine activity.

The bromine flux per area is largely independent of the type of hollow fi- ber, as shown by the results in Table 4. The data reported are for two fiber

50

TABLE 3

Extraction of bromine using hollow fiber supported gas membranes

The hollow fiber module used in these experiments (Celgard X20) had 300 filaments of 381 pm

internal diameter and 29 pm thick, giving a total projected area of 538 cm’

N0.a Time T Source Stripping Bromine Bromine Mass

(min) (“C) solution solution concentration recovery transfer

flow rate (ppm) (%) coefficient, k

(cmisec) In In

(lo-” cm/set)

source residual

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

15 25.8 12.9

13 23.6 21.2

10 24.5 29.7

10 25.5 22.9

20 25.5 20.0

25 24.8 16.8

20 23.2 24.4

20 27.3 21.7

30 24.1 16.9

30 25.0 12.5

23 26.4 18.7

50 23.4 13.4

40 24.6 16.2

28 25.3 24.1

30 24.3 31.6

40 25.5 21.7

2.5% Na,CO,

5.0% Na,CO,

2% NaOH

2% NaOH

5% Na,COS

5% Na,COB

2% NaOH

5% Na,CO,

2.5% Na,CO,

2% NaOH

2% NaOH

2.5% Na,CO,

5% Na,CO,

2% NaOH

2% NaOH

5% Na,CO,

62.3 10.5 83.1 1.9

64.7 10.4 83.9 2.2

64.7 11.0 83.0 2.8

61.9 11.5 81.4 2.6

336 42.3 87.4 1.6

344 31.6 90.8 1.5

376 26.0 93.1 2.1

836 40.7 95.1 2.4

933 32.0 96.6 1.8

1009 41 .o 95.9 1.7

1162 45.9 96.0 2.2

3021 79.1 97.4 1.1

2669 32.0 98.8 1.7

2741 120 95.6 1.7

3029 216 92.9 1.4

2989 115 96.2 1.3

aThe brine in these experiments contained bromine plus the following:

Experiments Nos. 14: MgCl,, 5.00 g/l: Na,SO,, 3.98 g/l: NaCl, 23.55 g/l; KCl, 0.75 g/l; C&l,,

1.11 g/l; PH 3.3.

Experiments Nos. 5-7: Mgaf, 32.4 g/l: Cl-, 136.5 g/l; SO:-, 59.2 g/l; K+, 2.56 g/l; CO;-, 0.498

g/l; HCO,, 0.244 g/l: N&l, 53.5 g/l; pH 3.1.

Experiments Nos. 8-l 1: NaCl, 120 g/l: pH, 3.3.

Experiments Nos. 12-14: MgSO,, 63.5 g/l; MgCI,. 115.3 g/l: KCl, 134.2 g/l; N&l, 57.3 g/l;

PH 3.2.

Experiments Nos. 15, 16: MgCl,, 260 g/l: MgSO,. 30 g/l: KCl, 35 g/l; NaCl, 57.3 g/l; pH 3.2.

modules, described in detail in the experimental section above. The chief difference between these fibers is that the first (X10) has half the porosity of the second (X20). However, at equal flow, the mass transfer coefficient of the first, based on the projected membrane area and not the free area, is only about 15% less than that across the second. This is consistent with the results for the flat sheet membranes given in Table 1, although the mass transfer coefficients in the two types of experiments are not comparable because the fluid mechanics are different. These observations and others drawn from these data are discussed in the next section.

Discussion

In this paper, we investigate the properties of gas membranes for bromine recovery. We do so in two steps. First, we determine the mechanism by

51

01 0 10 20 30

Temperature (“Cl

Fig. 3. Bromine flux vs. temperature. The feed solution in these experiments contained 66 ppm bromine at the various temperatures shown. Other experimental conditions are like those in Fig. 2. AS explained in the text, the increases in flux probably result less from increases in bromine vapor pressure than from augmented mass transfer in the feed solution.

TABLE 4

Similarity of bromine fluxes across different hollow fibers

The feed stream contains bromine and 0.5 N NaCl at pH 3.3 and 26°C; the stripping solution is 0.34 N NaOH

Fiber module Concentration Feed flow Mass transfer coefficient

Br, (ppm) (cmisec) (10-j cm/see)

Celgard X10 64.3 24.1 2.1 (20% porosity) 65.9 26.4 2.2

Celgard X20 59.9 9.1 1.6 (40% porosity) 65.4 9.3 1.4

65.5 11.4 1.8 64.7 14.3 2.0 64.7 18.7 2.2 65.1 22.9 2.4 64.7 29.7 2.8 64.3 36.3 3.0

52

which the bromine separation proceeds, because an understanding of this mechanism is the key to improving the separation. Second, we expand the comparison between hollow fiber gas membranes and packed towers sug- gested in this paper’s introduction. This comparison aids evaluation of prac- tical applications.

The mechanism by which bromine transport occurs is conveniently ideal- ized as three sequential steps. (1) Bromine diffuses out of the brine to reach the surface of the membrane. (2) Bromine evaporates into the gas-filled pores of the membrane and dif-

fuses across them. (3) Bromine diffuses into the basic solution and reacts producing bromide

and bromate . We expect that one of these steps will be much slower than the other two, and hence will control the bromine flux.

We can determine which of these steps is the slowest from the experi- mental results given above. All three steps imply that the bromine flux should be proportional to the bromine concentration, so the results in Fig. 2 are no immediate help. However, if step (2) is the slowest, then changes in membrane properties should change the flux. This is inconsistent with the results in Table 1 and Table 4, where different membranes and even different fluids in the membrane have little effect on membrane flux. Thus step (2) cannot be the slowest.

If step (3) is the slowest, then the bromine flux should depend on the concentration of reactants in the basic solution. The key chemical reaction in the base is

3 Brz + 6 NaOH + 5 NaBr + NaBr03 + 3 Hz0 (3)

so the exact dependence is complex [8, 201. However, as the data in Table 2 show, the bromine flux does not vary with changes in base concentration. Thus step (3) cannot be the slowest.

As a result, we believe that step (l), bromine diffusion out of the brine, controls the bromine flux. To test this belief, we first turn to the magnitude of the mass transfer coefficient 12 in the results above. For the flat membrane experiments in Tables 1 and 2 and in Fig. 2, we find k close to 3 X 10s2 cm/set under all conditions. For the hollow fiber experiments in Tables 3 and 4, we find k to be around 2 X 10m3 cm/set. We can compare these values with that expected for mass transfer controlled by the membrane itself, i.e., by step (2). For this case, the coefficient k is given by [8].

eDH kc _

1 (4)

where H is a Henry’s law constant relating the gas-to-liquid concentrations (both in ppm). From values in the literature [22], H is 0.054; from the Knudsen theory of gases [23], D is 0.02 cm2/sec; from the membrane manufacturer, E is 29 X 10e4 cm and E is 0.4. Thus we expect that k will be

53

about 0.1 cm/set if step (2) is slowest. This is much faster than the meas- ured value.

We can get further support for the contention that brine diffusion con- trols membrane performance from the variation of the mass transfer coef- ficient k with brine velocity ZJ in the hollow fibers. For laminar flow in a tube, we expect that k should vary with the cube root of u [24] . That this is nearly true is shown in Fig. 4; mass transfer coefficients reported in Fig. 4 for the hollow fibers fit to the equation

l/3

(5)

in close agreement with the correlation for the related heat transfer prob- lem [4]. Again, these results for hollow fibers give strong support to the idea that bromine diffusion in brine, step (l), controls the flux.

This conclusion suggests why the flux across flat membranes varies with temperature as shown in Fig. 2. This variation cannot result from an in- creased bromine vapor pressure, for such an increase will influence only step (2), which is not important in determining the overall rate. The temperature dependence probably is the result of decreased viscosity and hence more rapid stirring and a larger diffusion coefficient. Both of these factors will increase step (1) [ 251.

2.5 3.0

C Velocity, ctr~/aecl”~

Fig. 4. Mass transfer coefficient vs. brine velocity. The circles and squares correspond to modules X20 and X10, respectively. The main difference between these modules is that the fibers of the former have twice the porosity of those of the latter. The variation of the mass transfer coefficient with the cube root of brine velocity is consistent with the hypothesis that diffusion in the brine feed controls the bromine flux.

54

The conclusion that bromine diffusion in brine is rate limiting has an im- portant implication for gas membrane design. It means that the key mem- brane property is the total area per volume available for diffusion. Pore size and membrane thickness are less important, because they affect step (2) and not step (1). This small dependence on membrane properties is also observed for iodine and ammonia separations using gas membranes, where the membrane was responsible for about 20% of the resistance to mass trans- fer [13,14].

We now turn from the focus on membrane mechanisms to the more general concern of large-scale bromine separations. Hollow fiber gas mem- branes are attractive because they potentially offer faster mass transfer. This speed comes less from large mass transfer coefficients than from a large surface area per volume. For example, from Table 3 we find that for our system the mass transfer coefficient is about 2 X 10e3 cm/see. In packed towers, we can estimate the mass transfer coefficient as the diffusion coef- ficient divided by the film thickness. The diffusion coefficient for bromine is 1.8 X lo-’ cm2/sec; a good guess for the film thickness is 0.01 cm, so the mass transfer coefficient is around 2 X low3 cm/set, about that in the fibers.

In contrast, the area per volume can be substantially larger in the fibers than in packed beds. In our experiments, the area per volume is about 500 m2/m3 (150 ft2/ft3). This is considerably less than optimum, for hollow fiber units can have areas seven to fifty times this large [3]. Even with our present unit, the area per volume exceeds almost all values for dumped packing, even for l/4 inch Rashig rings [l] . Such small packings are rarely used industrially because they flood so easily. Fiber units do not flood.

Thus, hollow fiber air membranes like those reported in this work behave like an absorption tower filled with very small packing but with a built-in prevention against flooding. The membranes have the following character- istics for bromine: (1) They can rapidly concentrate bromine over 1000 times from seawater. (2) They carry out both the stripping and the absorption steps simulta-

neously, in one unit. (3) Their speed is very nearly controlled by diffusion in the brine, and hence

is largely independent of membrane properties except membrane area per volume.

(4) They work better hot, but may be compromised by large pressure losses or by fiber plugging.

The unknown factor about these membranes is their cost, for their applica- tion to this type of problem would create a market far beyond that current- ly available for hollow fibers. We look forward to exploring this potential.

Acknowledgements

Robert J. Callahan, Joan M. Slep and Paul A. Sessa of the Celgard Busi- ness Unit, Celanese Corporation, provided the hollow fiber modules used

55

in this work. The work was supported by the National Science Foundation grants CPE 8207917 and CPE 8408999, and by the Celanese Corporation.

List of symbols

A

[Brdt)l D d J k L N t v VC V z

total membrane area bromine concentration at time t bromine diffusion coefficient (eqn. A8) diameter hollow fiber (eqn. Al) initial flux (eqn. 1) mass transfer coefficient (eqn. Al) fiber length (eqn. A4) number hollow fibers (eqn. A5) time volume of brine (eqn. 2) volume of one cell compartment (eqn. 1) velocity in hollow fiber (eqn. Al) position

Greek symbols E membrane porosity

References

1

2

3

4

5 6

7

8 9

10

11

12 13

14

R.E. Treybal, Mass Transfer Operations, 3rd ed., McGraw-Hill, New York, NY, 1980. H.K. Lonsdale, The growth of membrane technology, J. Membrane Sci., 10 (1982) 81. S.L. Matson, J. Lopez and J.A. Quinn, Separation of gases with synthetic mem- branes, Chem. Eng. Sci., 38 (1983) 503. C.E. Reineke, Bromine, in: M. Grayson (Ed.), Kirk-Othmer Encyclopedia of Chemi- cal Technology, Vol. 4, Wiley, New York, NY, 1978, p. 226. H.H. Dow, U.S. Patent 460,370, September 27, 1891. F.D. Snell and C.L. Hitton (Eds.), Encyclopedia of Industrial Chemical Analysis, Interscience, New York, NY, 1966. M.E. Duffey, D.F. Evans and E.L. Cussler, Simultaneous diffusion of ions and ion pairs across liquid membranes, J. Membrane Sci., 3 (1978) 1. E.L. Cussler, Diffusion, Cambridge University Press, London, 1984, p. 26. Toyo Soda Manufacturing Co., Recovery of bromine, Kokai Tokkyo Koho JP 58-41, 701, March 11, 1983. W.C. Babcock, R.W. Baker and J.W. Brook, Coupled transport membranes for metal recovery - phase II, final report, NTIS PB81-179947, 1980. D. Pearson, Supported liquid membranes for metal extraction from dilute solutions, in: D.S. Flett (Ed.), Ion Exchange Membranes, Ellis-Howard, London, 1983. H. Watanabe and T. Miyauchi, Kagaku Kogaku Ronbushu, 2 (1976) 262. T. Miyauchi, K. Morita, T. Kakegawa and H. Watanabe, Rep. Asahi Glass Found. Ind. Technol., 33 (1978) 295. M. Imai, S. Furusaki and T. Miyauchi, Separation of volatile materials by gas mem- branes, Ind. Eng. Chem., Process Des. Dev., 21 (1982) 421.

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21

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24 25

G. Astarita, D.W. Savage and A. Bisio, Gas Treating with Chemical Solvents, Wiley, New York, NY, 1983. J.H. Perry, Chemical Engineers Handbook, McGraw-Hill, New York, NY, 1950. J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, NY, 1954. E.N. Sieder and G.E. Tate, Ind. Eng. Chem., 28 (1936) 1429. AI. Johnson and C.J. Huang, Mass transfer studies in an agitated vessel, AIChE J., 2 (1956) 412.

26 Qi Zhang and E.L. Cussler, Hollow fiber gas membranes, AIChE J., (1985) accepted.

Appendix: Mass transfer in the hollow fiber module

In this section, we want to analyze the operation of the hollow fiber module used in the experiments reported above. This analysis involves three steps: mass balances on one fiber, mass balances on the total volume of feed solution, and estimates of mass transfer coefficients.

We begin with mass balances on the bromine contained in a differential length of hollow fiber. In writing this balance, we assume that the bromine concentration outside of the fiber is low. Thus,

[ bromine

transferred through fiber wall 1 d[Br21

0 -pu- dz

- ndk([Br2] - 0) (AlI

where d is the fiber diameter, u is the velocity of the solution flowing inside the fiber, [Br,] is the bromine concentration, and h is the mass transfer coefficient. This equation is subject to the boundary condition

z = 0, [BrJ = [Br,] 0 (-1 Integration is straightforward

Wr21 - = exp(-4kz/du) [BrAo

(A3)

We expect that each time the fluid flows through a fiber of length L, only a

small fraction of the bromine is removed. As a result, eqn. (A3) may be approximated by

[BrJ o - [B&=L = VW o (A4)

This gives the change in bromine concentration for each pass through the fibers.

In our case, we have a larger bundle of N fibers to be used in processing a reservoir of solution. If we make a mass balance on this volume, We have

(bromine depletion in volume V) = (amount removed via fibers)

$( FM oV) = - NC: d*u)( PW o - 13r21 z=d (A5)

where t is the time. Note that the bromine concentration [Br,] ,, is now allowed to vary slowly with time. To emphasize this, we replace [Br,] ,, with [Br2(t)] . However, we assumed above that this concentration was constant. These two assumptions are not contradictory if the fiber volume is much less than the total volume of solution, which is the case here [B] . Equation (A5) is subject to the initial condition

t = 0, [Brl(t)] = [Br,(t=O)]

Integrating,

(A6)

Wr&)l W2(t=W

= exp(-nNdLkt/V) (A7)

This equation is that used to calculate the mass transfer coefficients. A more general derivation with fewer assumptions is given elsewhere [26] .