The separation of mixtures of organic liquids by hyperfiltration

Journal of Membrane Science, 13 (1983) 127-149 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

THE SEPARATION FILTRATION

OF MIXTURES

W.J. ADAM, B. LUKE*

and P. MEARES

Chemistry

The University

Department,

OF ORGANIC

of Aberdeen,

127

LIQUIDS BY HYPER-

Old Aberdeen

AB9 2UE (Scotland)

(Received July 30, 1982; accepted August 27, 1982)

Summary

Two solid-membrane methods exist for separating mixtures of organic liquids. They are pervaporation, in which the product phase is a vapour, and hyperfiltration in which feed and product phases are both liquid. Technically hyperfiltration is similar to reverse osmosis but, if that term is to be used at all, it should be restricted to dilute solutions of solutes to which the membrane is almost semi-permeable. The polymer membranes which have been found so far to give significant degrees of separation and fluxes with organic liquid mixtures have been crystalline polar polymers with high glass temperatures. The problems of membrane preparation are thus more severe than with almost amorphous, freely soluble polymers such as cellulose acetate. The absorption of liquids from a mixture by a polymer and their permeation in the polymer have received relatively little attention and it is not yet possible to infer the behaviour from that of the polymer towards each liquid alone. Nevertheless a theory of hyperflltration can be developed based on Henry’s and Fick’s laws and neglecting any direct coupling of flows. The equations which predict the separation and fluxes are useful in the first place to predict the thermodynamic restraints on any potentially useful separation process. It turns out that relatively large pressures are required, 100 atm or more, and hyperfiltration is better adapted to further purifying a relatively good product than to recovering a small amount of a valuable substance from a large volume of waste. The equations lend themselves to a direct experimental test. An apparatus for doing this has been constructed and two liquid mixtures and membranes have been studied. They are toluene + n-heptane with an asymmetric polyacrylonitrile membrane and methanol + isobutanol with a uniform cellulose membrane. The mixtures were chosen as being thermodynamically close to ideal because this simplifies the interpretation of the data. Their nonideality has been taken fully into account. The results show that the simple theory accounts very well for the observed facts. For the first system the selectivity coefficient was about 2 and for the second, about 15. The mechanism of transport is found to be the normal solution-diffusion mechanism for permeation of organic solvents in polymers. There is some positive frictional coupling between the two liquids as a result of which the improvements in separation to be expected from an increase in the applied pressure are not achieved quantitatively. The increasing absorption of liquid by the membrane as the mole fraction of the preferentially absorbed liquid in the mixture is increased increases its permeability to both components by about

*Present address: Flurstrasse 7, D-5800 Hagen, West Germany.

0376-7388/83/$03.00

o 1983 Elsevier Science Publishers B.V.

128 the same factor. As a result, the selectivity coefficient is found to be relatively insensitive to the mole fractions of the liquids in the feed. Selectivity is also relatively unaffected .by increase of temperature but higher pressures are needed to obtain the same degree of separation at higher temperature to offset the increased random thermal motion of the molecules.

Introduction The separation of mixtures of organic liquids is a problem of great technical importance. The most widely used method is distillation but problems arise when azeotropes are formed. Scope exists for the development of alternative methods especially as these demand less energy than the phase change methods such as distillation. The application of membrane transport processes to large-scale liquid separation has advanced greatly in the past fifteen years [ 11. The purification, especially the desalination, of water by reverse osmosis is a case of particular interest [ 21. The membranes used have consisted of thin films of organic polymers although a few inorganic materials such as porous glass also have been studied. In principle, reverse osmosis is applicable to liquid mixtures in general but there are special problems in the choice of membrane polymers suitable for use with organic liquids because they interact very differently with the membrane than do dilute aqueous solutions. The conventional distinction between solute and solvent loses its significance in the case of organic liquid mixtures and the notion of osmosis becomes inappropriate. The widely used term hyperfiltration will, throughout this paper, be used to refer to the process of forcing a liquid mixture through a non-porous membrane by the application of pressure at the upstream side. There is a related process called pervaporation which consists of applying a vacuum on the down-stream side and extracting the product as a vapour. Although pervaporation can generate the maximum thermodynamic driving force very easily [3] it is appropriate for use only with easily volatile liquids. Theoretical A full account of the phenomena which might be met in the hyperfiltration of non-ionic binary mixtures has been given by SchlSgl [4] who explored the consequences of various degrees of flow coupling. A simpler approach is adopted here in which the possibility of coupling is usually ignored [ 51. It will be demonstrated that only congruent flows were encountered in this work. The solution-diffusion model of transport is a suitable starting point. Consider two components of molar volumes V, and V, which are assumed to be constants at constant temperature. The absorption of each liquid by a polymer from a mixture at uniform pressure can be written Cl =

s1 al

(1)

129

c2

=s2a2

(2)

where a, and a, are activities in the liquid phase; c1 and c2 are the molar concentrations in the polymer phase. The distribution coefficients s1 and s2 may turn out in practice to vary with the composition of the liquid mixture. They will be treated as constants partly for want of definite information and partly because the composition difference generated across a membrane in a hyperfiltration experiment is not large. Flux equations will be written first assuming that a continuous pressure gradient exists within the membrane. For component 1 the flux density J, is given by J1

=_$, RT

!!b

(3)

dx

where D1 is the diffusion coefficient polymer. p1 can be expressed by Pl

and p1 the chemical

+pV,

=MI ’ +RTlnc,f,

potential

in the

(4)

in which f1 is the activity coefficient andp the pressure. On substituting eqns. (1) and (4) into (3), one obtains J1=--

DIS, RT

a1

RT---

d In al dx

dp

+ v, dx 3

(5)

Equation (5) has to be integrated over the distance coordinate x which varies across the membrane from 0 to 1. To perform the integration it will be assumed that D1 and f1 can be treated as constants over the range or concentration existing between the two faces of the membrane. The integration requires information on either the pressure or the concentration profile in the membrane . By assuming that a, in front of the square bracket can be represented after integration by some average value Q1 integration gives J,

=

3

(6)

where (0) or (1) after a symbol denotes the boundary values just within the faces of the membrane and Ap is the positive driving pressure p(0) - p(l). In order that eqn. (6) shall reduce to Fick’s first law in the absence of a driving pressure aI must be the logarithmic mean, viz. aI

= Aa,/A In a,

(7)

An alternative approach to the integration of eqn. (5) is to assume a linear pressure gradient within the membrane i.e. dp/dx = - Ap/l

(8)

130

The integration of eqn. (5) then gives

in which B 1 is used to represent VI ApIRT. A different approach has been adopted by Paul [6] who has argued that a membrane is too weak to support a pressure gradient. He has supposed that the membrane is uniformly at the higher pressure and that there is a discontinuous drop to the lower pressure at the supported face of the membrane. By assuming that there is thermodynamic equilibrium across this face between the polymer at high pressure and the down-stream solution at the low pressure he has calculated that the concentrations at the down-stream face of the membrane are lower than those at the up-stream face. The membrane fluxes are then regarded as a consequence of ordinary diffusion across the concentration interval so produced. The expression of thermodynamic equilibrium at the down-stream face is given by cl (0 = s1 al (1) exp (- 0 1 1

(10)

Introducing this into Fick’s steady state diffusion equation leads to Jl

+4_

14 (0) exp6 1

exp 0 l

(11)

aI (01

-

Equations (6), (9) and (11) represent three forms of the flux equation for flow across the membrane under a pressure and a concentration gradient \ depending on the assumptions made. Analogous equations, with exchanged subscripts, apply to component 2. The mole fractions x1 (I) and x2 (I) in the product stream are controlled only by the fluxes. Thus xi (0/x, (0 = JI /Jz

(12)

On dividing eqns. (6), (9) and (11) by their respective counterparts for component 2 gives

x,(0 -x2

(0

Xl

(0

(Aal + ;I 0 1) = ?I2 (Aaz +&e2)

-

Xl -=

(0

x2(Z)

em 0,) [a,(0) em e1 exp ed [a2(0) em e2 -

VI cl-

xz=ylz-V2

(13)

(I-

, exp e2 [aI (0) exp 8 1

?,lZexp e

1

b2 (0) ew 82

-

al (01 a2 WI

6 (01 a2 (Ul

(14)

(15)

131

In these equations r12, y i2 and y 12’ represent the selectivity coefficient of the membrane D1 si /D, s2 which would be evaluated by analysing experimental data according to each of the three approaches. The flux equation used to generate these results specifically disregarded interaction between the two components in the membrane. Such interaction might take two forms. The presence of one component in the membrane mighl influence the distribution and diffusion coefficients of the other. Quantitative data on this problem are lacking but it is less likely to be important in the hard crystalline polymers suitable for hyperfiltration of organic liquids than in softer amorphous polymers which would swell considerably. The other form of interaction would be coupling between the flows of the two liquids in the membrane. Flow can occur only in the amorphous regions of a crystalline polymer and the flux densities in these regions will be larger than the flux densities averaged over the whole surface of the membrane. Consequently even at low overall flux densities coupling of flows may be significant in the regions where flow is taking place. Flow coupling can be included formally by using a non-equilibrium thermodynamic formulation

JI = L~bu,

+-h,b,

Jz = Lzl API + L,, AI-Q

(16) (17)

in which the coefficients Lll and Lz2 can be identified with D1 s1 $I /lRT and D2 sz a2 /ZRT, respectively. Flow coupling is represented by the cross coefficients LIZ and Lzl which, if Onsager reciprocity holds under the conditions of the experiment, should be equal. It is pointless at this stage to pursue further this more complex formalism until the simpler equations ignoring coupling have been tested. Flow coupling normally downgrades separation. In extreme cases a component might be dragged against the gradient in its chemical potential. This is referred to as incongruent flow and can occur only for the component which is enriched in the product stream. The convention chosen here is to designate this as component 1. By equating p 1 (0) and p I (1) it is easily shown that for the flow of component 1 to be congruent the criterion Aa, < al (0) (exp Bi - 1)

(18)

must be satisfied. It is a simple matter to test this on an experimental separation graph of AX, versus x1 (0). Experimental Calculations have been carried out by using eqn. (14) on the separations that might be expected in various circumstances [ 51. They showed that useful effects are likely only when pV is at least comparable with RT. In order

132

to achieve this at ordinary temperatures pressures up to at least 20 MPa are required. Previous workers [ 7,8] have used only 4-6 MPa. A new apparatus capable of being used up to 30 MPa was built for the present study. 1. The hyperfiltration apparatus Figure 1 is an outline diagram of the hyperfiltration apparatus. The feed solution was stored in the reservoir 1 which was closed by fastening a polyethylene bag tightly around its neck in order to prevent evaporation. The feed passed via a filter 4 to the intensifier pumps 2 (Madan Junior Air-Hydro pumps) which were driven by compressed air. The feed proceeded through a second filter into the high-pressure line. The intensifier pumps were arranged in parallel and protected by non-return valves 3 to minimise pressure pulsing in the line. Pulses were further smoothed by the accumulator 5. The rubber bag in the accumulator was not suitable for direct contact with organic liquids. It was separated from the main feed line by the U-tube 6 filled with mercury. All main high-pressure lines were 9.5 mm bore stainless steel. Couplings and valves were also made of stainless steel. One of the biggest problems was the initial cleansing of the interior of the pipework. This was achieved by prolonged washing under reflux with boiling solvents. On its way to the

Fig. 1. The hyperfiltration apparatus. 1 feed reservoir, 2 intensifier pumps, 3 non-return valves, 4 filter, 5 pressure accumulator, 6 mercury-filled U-tube, 7 drainage cocks, 8 heat exchanger, 9 bleed valve, 10 transducer, 11 thermocouple, 12 hyperfiltration cell, 13 circulating pump, 14 needle valve, 15 measuring burette, 16 retentate holding flask, 17 differential refractometer, 18 Abbd refractometer, 19 PTFE valves, 20 magnetic stirrer, 21 common liquid level.

133

hyperfiltration cell the feed passed through the heat exchanger 8 through which flowed a supply of water from a Churchill thermo-circulator. The piping from the heat exchanger to the pressure cell was kept short and well lagged. The pressure of the feed was continuously monitored by the transducer 10 (Bell & Howell type 4-366 or Coutant type XT33). The liquid then passed into the pressure cell 12 which is shown more fully in Fig. 2. This stainless steel cell had been provided by AERE Harwell in connection with an earlier project [9] . The Perspex flow labyrinth in the original cell was replaced by a brass version so as to resist the organic liquids. The Neoprene O-rings used originally for sealing the membranes into the cell were replaced by PTFE. 1

Fig. 2. The hyperfiltration cell. 1 membrane, 2 product chamber, 3 stainless steel sinter, 4 upper half-cell, 5 product outlet, 6 PTFE O-rings, 7 retentate outlet, 8 lower half-cell, 9 brass feed flow labyrinth, 10 securing bolt hole, 11 feed inlet.

Water jackets were attached to the top and bottom faces of the cell and water from the Churchill thermo-circulator was passed through them. The cell and its jackets were enclosed in a well-lagged asbestos box which helped to provide excellent thermostatic control. The temperature of the cell was measured by a thermocouple embedded in its body. The feed mixture was continuously recycled through the upstream side of the hyperfiltration cell at constant pressure by the magneticallydriven, double acting, free-piston reciprocating pump 13 operating in a recirculation loop. Because the permeation fluxes were low a moderate flow through the cell labyrinth was sufficient to eliminate concentration polarization at the high pressure surface of the membrane. A small fraction of the retentate liquid, indicated by R in Fig. 1, was continuously withdrawn via the needle valve 14 for analysis on line. It was held temporarily in the small reservoir 16. The permeate liquid, indicated by P in Fig. 1, also passed to the analysis section of the apparatus. This consisted of an Abbe refractometer 18 modified by the attachment of a continuous flow cell in place of the lower prism, a differential continuous flow refractometer 17 (Labodur, Winopal Forschung, Hanover, modified to reduce its

134 sens#,iv&y by inserting a light filter) and a small, calibrated burette 15. Miniature valves 19, made of PTFE, enabled the streams to be directed as required. Finally, all liquids were returned to the feed reservoir so that by running the apparatus continuously for a sufficiently long time a truly steady state would be achieved. The permeate flux rate was measured by timing the rise of the meniscus in the burette. The permeate composition was measured by comparison with a standard mixture in the differential refractometer, The retentate composition was also measured with the differential refractometer and, independently, the absolute value was obtained with the Abbe refractometer. This enabled the calibration of the differential refractometer to be checked without interrupting the experiment. Experiments could be run continuously at constant temperature and pressure indefinitely. Usually it took several days to reach steady conditions of permeate and retentate composition. This delay was due primarily to the time required to flush fully with permeate the stainless steel frit supporting the membrane.

2. Liquid mixtures Among the mixtures that might be most valuably treated in practice by membrane separation are azeotropes [7] but, by their nature, these deviate widely from ideal behaviour. Often the activities of the components change only slightly over a wide range of the mole fraction scale. Such mixtures are unsuitable for testing the theoretical equations. The interpretation of data is greatly simplified when nearly ideal mixtures are studied. l-i

1 1

3r^

00

02

0.4

x2 Fig, 3. Activity coefficients

06

08

10

o-o

0.2

04

06

0.8

x2

7, dnd y2 of toluene 1 + n-heptane 2 versus mole fraction

x2 at 25°C. Fig. 4. Activity coefficients 7, rind ya of methanol 1 + isobutanol 2 versus mole fraction x2 at 25°C.

IO

135

Two mixtures were selected from the many possible choices. They were toluene and heptane, and methanol and isobutanol. Both mixtures have been studied thermodynamically and reliable vapour pressure data are available [ 10,111. Figures 3 and 4 give plots of activity coefficient versus mole fraction at 25°C for both mixtures. In both cases the refractive indexes of the components differed sufficiently to permit an accurate determination of mixture composition by refractive index measurement. The calibration curves, which were not linear on the mole fraction scale, are shown in Fig. 5.

”

l-32' 00

I 02

I

I

I

0.4

0.6

0.8

1.0

"2

Fig. 5. Refractive indexes versus mole fraction for mixtures of toluene 1 + n-heptane 2 (curve 1) and methanol 1 + isobutanol 2 (curve 2).

3. Membranes The selection of membranes was a major problem. To obtain values of specific permeabihties of membrane materials as well as to measure selectivity factors it was desirable to use homogeneous films. It has been found already that useful separations are most frequently obtained when films of crystalline polar polymers are used [ 81. Unfortunately these have low permeabilities and have been studied only as asymmetric membranes. A number of commerci ally available thin films were obtained and tested but it was found that all gave fluxes too low to be studied in a reasonable time in our apparatus. Two types of membrane were selected for further study: asymmetric poly(acrylonitrile) (PAN) and a specially treated cellulose paper which gave an effectively homogeneous film. The PAN membrane was prepared by casting a solution of 18 g powdered polymer in 57 g dimethyl sulphoxide and 25 g acetone on a clean glass plate

136

to a thickness of about 0.3 mm. It was allowed to evaporate at room temperature for 1 minute before being placed into water at 0-4°C. The fully precipitated membrane, when released from the plate, was annealed in water at 55” C for 3 minutes [ 81. It was stored, handled and mounted in the way normal for Loeb-Sourirajan asymmetric membranes. The cellulose membrane consisted of fine paper which had been treated with solvent under pressure to swell and bond the cellulose fibres and thus produce an impervious, linter-free surface. Although supplied to us by I.C.I. Plastics Division, it was not made by them and its origin could not be traced. The membrane was 5.7 pm thick. Its density, found by flotation in caesium chloride solutions, was 1.632 kg m3. It dissolved slowly in boiling dimethyl sulphoxide but was insoluble in cold solvents. Scanning electron micrographs [ 121 showed clear evidence of the original fibrous nature of the material, A repeat examination of a membrane after 6 weeks use in the hyperfiltration cell showed no alteration in this structure. A transmission infrared absorption spectrum corresponded with the known spectrum of crystalline cellulose. A X-ray diffraction spectrum was dominated by peaks from crystalline cellulose and showed also some amorphous scattering. Some exploratory experiments were carried out to determine the solubility s and diffusion D coefficients of methanol and isobutanol in this membrane. It was attempted to determine s by soaking a weighed specimen of dry membrane in each of the solvents followed.by blotting and reweighing. The absorption of isobutanol amounted to about 1% by weight. It was too small to determine accurately. Appreciable amounts of methanol were absorbed but the rapid evaporation of methanol required that a series of weights be recorded at noted times t. Extrapolation to zero time was then made on a plot of weight versus t”. The solubility or partition coefficient of methanol s1 was found from these measurements to be 3060 mol ni3 at 25”C, i.e. the polymer absorbed about 6% by weight of methanol. No measurements were attempted with mixtures of methanol and isobutanol. It was not possible to estimate D from the plots of weight versus tlh because these were not linear. Evaporation was taking place into an atmosphere adjacent to the polymer surface that was increasingly contaminated with methanol. Instead the permeability coefficient was studied by the cup method [ 131. A glass vessel was made with a tightly fitting ring around its neck so that a membrane could be clamped without leakage over the mouth of the vessel of area about 12 cm2 . Methanol was placed in the vessel to a measured depth d below the lip and the membrane clamped in place. The vessel was weighed and then placed in a thermostatted dry box through which pure nitrogen was flowed. The vessel was reweighed at intervals and the steady rate of weight loss determined. It was in the region of a few mg per minute. The experiment was repeated for several different values of the vapour gap d. A plot of the reciprocal of the rate of weight loss versus d was linear. It was extrapolated to d = 0 to estimate the rate of loss in the absence of any diffusion resistance in the vapour phase below the membrane. The permeation of isobutanol was too slow to be studied by this method.

137

4. Results The mixture toluene and n-heptane was studied using the asymmetric PAN membrane primarily as a means of testing the hyperfiltration system. Two sets of data were collected. In the first the degree of separation Ax, was measured as a function of the composition of the feed r,(O) while using a constant pressure Ap. In the second Ax, was measured at constant feed composition while varying the pressure. Although the fluxes were recorded during these runs they are of no absolute significance because the thickness of the active layer of the PAN membrane was unknown. Furthermore, as is usual with asymmetric membranes under high pressure, progressive compaction of the porous layer during the experiments led to a continuous decrease in flux with time. Despite this, a steady state of retentate and permeate compositions could be established and the degree of separation data were consistent and repeatable. The results are shown in Figs. 6 and 7.

0.0

02

0.4 “1

06

(0)

08

10

0

10

20

Ap/MPa

Fig. 6. Separation Ax, Versus mole fraction in the feed tl (0) for toluene 1 + n-heptane 2 in PAN at 25°C and 13.6 MPa. The curve is theoretical and calculated from eqn. (14) with y,> = 2.27. The line Ax,(max) shows the upper limit of separation for congruent flow of component 1. Fig. 7. Separation AX% Versus applied pressure for toluene 1 + n-heptane 2 in PAN at 25°C. The feed composition was held constant at x, (0) = 0.443. The curve is the theoretical one drawn with yiz ‘- 2.50.

The mixture methanol and isobutanol was studied using the cellulose membrane. Plots of Ax 1 versus x 1 (0) at constant pressure and Ax 1 versus Ap at constant feed composition appear in Figs. 8 and 9. The corresponding plots of the fluxes of the components are shown in Figs. 10 and 11. The fluxes were steady and repeatable although rather small. It was found that about two days were required to reestablish a steady state in the apparatus after each change in the experimental conditions.

138 od

o-o

02

O-4 “7 (01

0 6

o-a

10

I 0

10

20

Ap/MPa Fig. 8. Separation Ax, versus mole fraction in the feed x, (0) for methanol 1 + isobutanol 2 in cellulose at 25” C and 15.5 MPa. The curve is theoretical and calculated from eqn. (14) with ylz i 12.3. The line Ax, (r&x) shows the upper limit of separation for congruent flow of component 1. Fig. 9. Separation Ax, versus applied pressure for methanol 1 + isobutanol 2 in cellulose at 25°C. The feed composition was held constant at xI (0) = 0.583. The curve is the theoretical one drawn with rrz ‘- 16.5.

20 I

Fig. 10. Fluxes of methanol 5, and isobutanol J, in cellulose at 25” C and 15.5 MPa versus feed composition x, (0). 0 J,, q J,.

139

-1,0

2

-i-

7 VI ‘;” E a

m

T-

E

7j

-k 7‘

-0 5

1

10

0

E ,”

20

Ap / MPa

Fig. 11. Fluxes of methanol J1 and isobutanol J, in cellulose at 25°C and constant feed composition x1 (0) = 0.583 versus applied pressure. o J,, d J,. -0.14

o-30-

O-IO16

I 20

I

I

I

I

24

20

32

36

temperature

/

0 -10 40

‘C

Fig. 12. Temperature dependence of volume flux (0) and separation ( n ) for methanol 1 + isobutanol 2 in cellulose at feed composition LX,(0) = 0.572 and applied pressure 17.1 MPa.

The fluxes of methanol and isobutanol were also measured at several temperatures for a single feed composition and pressure. The results of these measurements are plotted in Fig. 12. They and all other data are analysed in the Discussion.

140

Discussion 1. Toluene + n-heptane in PAN The only aspect of the data suitable for significant comparison of theory and experiment in the case of the asymmetric PAN membrane was the variations of the degree of separation with changes of pressure and feed composition. The progressive reduction of flux as a result of membrane compaction should not affect the separation unless compaction resulted in either a change of morphology in the active layer or the sealing of imperfections in the active layer of the membrane. Considering first the series of experiments carried out at constant pressure while varying the feed composition, for each set of experimental values of retentate and permeate composition a value of y ,1 can be calculated by using eqn. (14) and y12’ by using eqn. (15). In fact

Yl2’ =

712

Vl km C-e,) - 11

(19)

V2 [ew(-0 d - 11

holds so that y 12’ 1s ’ proportional to yiz at constant pressure. Table 1 shows ylz versus 3c1(0). It is seen that there is no systematic trend in y 12 with increasing x1 (0) although in this, and the second system studied, the point at the lowest value of z, (0) was significantly lower than the others. The theoretical separation curve in Fig. 6 was plotted by setting y 12 = 2.27. Apart from the point at 3c1(0) = 0.7, the fit of the theoretical curve with the experimental points is within reasonable expectation bearing in mind the difficulty of establishing absolutely steady conditions in the apparatus. The upper limit of Ax, for congruent flow, as calculated from eqn. (18), is indicated by a line on Fig. 6. Clearly there is no doubt that flow was congruent at all values of x1 (0). Equation (13) can be used in place of eqn. (14) to generate a set of values of ?I2 from the data. yj2 also is shown in Table 1; the values differ insignificantly from y12 and all are larger than y12’. From eqn. (19), when 712 = 2.27, y 12’ = 2.04. TABLE

1

Selectivity coefficients defined by eqns. (13), (14) and (15) at various feed compositions xt (0). Toluene and n-heptane in PAN at 25’C and 13.6 MPa. xt (0)

712

712

712

0.100 0.218 0.355 0.440 0.552 0.695 0.821

1.86 2.26 2.13 2.23 2.32 2.59 2.23

1.89 2.30 2.16 2.26 2.35 2.62 2.24

1.70 2.07 1.95 2.04 2.12 2.36 2.02

141

Equations (13), (14) and (15) can be used also to explore the effects of pressure on separation. When pressure is varied the relation between ylz and ylz’is no longer one of simple proportionality, Figure 13 shows these selectivity coefficients versus pressure with 3c1(0) held constant at 0.44. It is seen that the selectivity coefficients appear to decline as pressure was increased. The least variation was noted with y Iz derived from the linear pressure profile model. A decline of selectivity coefficient with increasing pressure is the behaviour expected if positive coupling occurred between the fluxes of the two components. In Fig. 7 a theoretical curve is included, calculated by setting y 12 = 2.50, to indicate the extent of the divergence between the behaviour predicted by the simple theory in which coupling was ignored and the experimental data.

1

8’ 5

I

I

I

10

15

20

Ap / MPa Fig. 13. Pressure dependence of selectivity coefficients ylz ('G),+,2 (0) and Y,~’ (a) for toluene + n-heptane in PAN at 25” C and x, (0) = 0.443.

The main conclusion to be reached in this analysis is that the simple theory of uncoupled flows given in this paper holds moderately well for the present system. Although the individual permeabilities may vary with composition their ratio scarcely varies so that at constant pressure y12 is independent of x1 (0). There is no significant difference between the values of ylz given by eqn. (13), in which no assumption is made about the pressure profile in the membrane, and that given by eqn. (14) in which a linear pressure profile is assumed. On the other hand Paul’s model, represented by eqn. (15), gives a very different value for, y 12. It appears that his approach although appropriate with a soft polymer such as rubber is not satisfactory in the case of a hard crystalline polymer such as PAN. Despite these comments, the simple theory which ignores the coupling of

142

flows predicts an improvement in separation with increasing pressure which is greater than that observed. Clearly the flows are only weakly coupled as the comparison with the congruency line in Fig. 6 shows but even weak coupling is sufficient to downgrade significantly the separation achievable in a hyperfiltration process. 2. Methanol + isobutanol in cellulose The theoretical curve drawn on Fig. 8 was generated by setting 7 ,2 or y 12 at 12.3 in eqns. (13) and (14) or by setting y12’ at 10.6 in eqn. (15). The line of Ax, (max) on Fig. 8 indicating the limits of congruent flow shows that in this case also the flow of both components is always congruent. In Table 2 the separation coefficients calculated from the data at constant Ap are tabulated against the retentate composition ~~(0). yi2’ is, as in the previous case examined, a little lower than either y 12 or ‘ylz. TABLE 2 Selectivity coefficients defined by eqns. (13), (14) and (15) at various feed compositions x, (0). Methanol + isobutanol in cellulose at 25°C and 15.6 MPa XI

(0)

0.275 0.425 0.470 0.578 0.578 0.590 0.600 0.600 0.620 0.718 0.858

YlZ

712

711

10.2 13.5 13.7 12.1 12.2 13.8 12.1 11.8 11.7 11.4 13.9

10.3 13.6 13.9 12.2 12.4 14.0 12.3 11.9 11.8 11.5 13.8

8.9 11.7 11.9 10.5 10.7 12.0 10.6 10.3 10.2 9.9 11.9

26r 22 h .; c

18-

ii u en ,4-n-;_::_

0 n

101 8

10

14

12 Ap

/

16

18

MPa

Fig. 14. Pressure dependence of selectivity coefficients y,2 and y,2 (0) and ylz’ (a) for methanol + isobutanol in cellulose at 25°C and x,(O) = 0.583.

143

Figure 14 shows y r2 versus Ap at constant composition 3tl (0) = 0.58. The curve plotted in Fig. 9 was generated by setting -ylz = 16.5. The pattern of behaviour shown by the mixtures of methanol and isobutanol in cellulose is qualitatively closely similar to that shown by toluene and heptane in PAN. In the present case, however, the use of a uniform cellulose membrane has permitted an analysis to be performed also on the flux data. The experimental measurements gave the volume flux j, and the composition by mole fractions of the permeate. Defining the molar volume v of the permeate by theoretical

V = VlX, (1) + V,X,(Z)

(20)

the molar flux densities can be calculated from

J, = Lx, WV;

J, =ivx, (O/v

(21)

Thus by using eqn. (9) each experimental flux can be used to find a value of D1 s1 /I or Dz s2 /I. The results are plotted in Fig. 15 as log(Ds/l) versus the arithmetic mean 3c1 of the mole fractions on the two sides of the membrane. Within experimental error log(Ds/l) for each component increases linearly with x1 . The plots appear to diverge slightly as 3ci increases which would imply some increase in y 12with increasing x1 (0). This was not obvious in the y 12 values themselves because they combined the errors in x1 (a) and x2 (I) thereby increasing the scatter in y 12. Although the extent of coupling of fluxes has not been quantified, it is nevertheless worthwhile to attempt a simple interpretation of the data in Fig. 15. The variation of the integral diffusion coefficient 6 of an organic

20-

o-o

02

0.4

06

0.8

I.0

%

Composition dependence of permeabilities of cellulose to methanol 1 and isobutanol 2 at 25°C. Permeability is represented by Ds/E, 3c1is the arithmetic mean of feed and permeate compositions. Fig. 15.

144

penetrant in a polymer has often been satisfactorily represented by D =D“expcrc

(22)

where D” would be the diffusion coefficient in the pure polymer and a is a complex function of the free volume characteristics of polymer and penetrant and of the free volume of activation for segmental rotation CJ*. In the case of a mixture of penetrants having small constant distribution coefficients si and sz , the specific free volume of the polymer plus penetrants, a, can be expressed approximately by @

=x1s141

+x2$2$2

(23)

+4p

where @i , G2 and @P are respectively the molar free volumes of the two penetrants and the specific free volume of the polymer. It is appropriate to write o= D” exp(a D/Q*)

(24)

where a is characteristic of the penetrant. Thus for the case of a mixture of two penetrants one finds lnDi=lnD”

+u~(s~@~ +c$J~)/@* +u~?,(s,c#J~ - s~$~)/@*

(25)

Here xl is the mean mole fraction over the composition range to which Di refers. Equation (25) shows that a plot of log@, s1 /Z) versus g1 should be linear and have slope a, (si $i - s2 ~~)/2.303 Q,*. Similarly log(D,sJZ) versus xl should have slope a, (sl $1 - s2 ~~)/2.303 @ *, Figure 15 shows that this general approach holds and that a, appears slightly greater than a,. Further, because the slopes are positive s1@I1 > s2 (p2. The truth of this latter statement can be verified as follows. The weight of methanol sorbed by the membrane exceeded by at least 6-fold the weight of isobutanol it absorbed. Thus on a molar basis s1 exceeded sz by a factor of at least 14. The coefficients of thermal expansion of methanol and isobutanol are very similar and one may surmise therefore that the free volume per mole of methanol is about half of that of isobutanol, Hence s1 C#J~ exceeds s2 I& probably by a factor of 5 or more. The two lines in Fig. 15 may be represented by the equation log(Diai/l) = log(D$i/Z ) + bir,,

i = 1,2

(26)

The mean diffusion coefficient D1 averaged over the full concentration range is related to Dt by (27) Using the D, defined in this way Di s1 /l may be compared with the effusion rate per unit area observed in the permeation cup experiment.

145

On combining eqns. (26) and (27) and carrying out the integration one obtains &sl

/1=D:sl

(lob1 - 1)/2.303 bl 1

(28)

/I can be read from the intercept on the left hand ordinate in Fig. 15 and b, is given by the slope of the line, The values are 7.55 X 1U3 mol m2 s* and 1.08 respectively. Whence D, s1 /I is found to be 33.5 X 1CJ3 mol me2 s-l. The value found in the permeation cup experiment was 3.2 X 10m3 mol me2 sl. It must be borne in mind that the left hand ordinate in Fig. 15 refers to the membrane saturated with isobutanol. It will have the effect of plasticizing the polymer and the value of DFsl /Zread from the ordinate will be greater than the value it would have in a “dry” membrane. The amount of isobutanol absorbed was about 1/6th by weight of the amount of pure methanol absorbed, If the free volume fractions of these two liquids were similar the plasticizing effects of the isobutanol might be corrected for, very approximately, by extrapolating the straight line to x1 =-0.17.Whenthisisdoneandfi,s1/1isrecalculated the value falls to 22 X 1(r3 mol ni* s-l. It can be seen that whether or not this correction is made the value of o1 s, /I from the pressure flow experiments exceeds by a factor of 6-10 the value from the permeation cup. This factor corresponds with the quantity g defined by Thau, Bloch and Kedem [ 141. (g - 1) is a measure of the extent to which direct frictional interaction between the permeant molecules in the membrane contributes to the flux. It is sometimes referred to as a convective contribution to the flow. No data exist with which to compare this value of g for methanol in cellulose membranes but values exist for water in a variety of membranes [ 151. Typical values are 3-4 in homogeneous cellulose acetate, 13 in polyvinyl alcohol, 40-80 in commercial cellulose films and 20-200 in hydrogels. The value 6-10 is clearly at the lower end of this range. This result suggests that the transport of methanol in this cellulose membrane is principally by diffusion occurring uniformly in the amorphous regions of the polymer. The volume fraction of methanol in these regions must be substantially larger than the overall volume fraction in the partly crystalline membrane. Consequently frictional encounters among permeant molecules in the amorphous regions may be expected to make an appreciable contribution to flux through direct momentum transfer. Because momentum could also be transferred from methanol to isobutanol molecules some positive coupling of their fluxes may be expected. It is for this reason that the theory which ignores coupling exaggerates the extent to which the separation factor Ax, should increase with increasing pressure at constant feed composition. Further information on the mechanism of permeation may be sought from the variation of the fluxes with change of temperature. The separation Ax, declined significantly and the volume flux increased as the temperature was increased at constant feed composition and pressure. The data, shown in

D,“sl

146

Fig. 12, can be analysed to give energies of activation for permeation of the two liquids. By disregarding the small extent of non-ideality of methanol and isobutanol, eqn. (6) can be reduced to

Di si

J, =-

1

VIAP -

-Ax,

RT

1 1

(29)

(30)

1

By using these equations the experimental data can be manipulated to produce plots of log(D1 sI /I) and log@ s2 /I) versus l/T. They are shown in Fig. 16. The number and precision of the points and the breadth of the temperature range covered are insufficient for detailed conclusions to be reached. It appears that, within experimental error, the plots can be represented by straight lines of equal slope. They give an Arrhenius activation energy for permeation of 30 i: 2 kJ mol’ . The activation energy for permeation is the sum of the enthalpy of sorption and the activation energy for diffusion. The former is likely to be much smaller than the latter. The apparent activation energies for viscous flow of methanol and isobutanol at 25’C are 10.6 and 22.5 kJ mol’, respectively. The observation that the energy of activation for permeation of both alcohols is the same and substantially greater than the energies of activation for viscous flow confirms the belief that transport through the membrane does not take place in micro-pores and frictional interaction between the polymer chain segments and the penetrant molecules is rate controlling.

0.01

I

I

3.2

3.3

34 103/T

Fig. 16. Logarithmicplot of permeability versus reciprocal of absolute temperaturefor methanol 1 + isobutanol 2 in cellulose with xI (0) = 0.572 and Ap = 17.1 MPa.

147

Summarizing, it can be said that on the basis of the limited data so far available, the separation of organic liquid mixtures by hyperfiltration in dense polymer membranes appears to be well described by a simple treatment of the solution-diffusion mechanism. The mechanism of transport in the membrane is not fundamentally different from that already elucidated through studies on the permeation of organic vapours through polymers. Nevertheless flow coupling appears to exert a significant influence on the degree of separation achieved and especially on its pressure dependence. An elementary and approximate attempt to estimate the extent of flow coupling can be made by considering the effect of pressure on the separation and fluxes shown in Figs. 9 and 11. Since Ax, varies with pressure over the range studied by only 0.05 it is fair to treat the phenomenological coefficents as constants and to seek the degree of coupling q via the definition

[=I

where Ril, Rzz and R,, are the resistance coefficients which appear when eqns. (16) and (17) are written in the reciprocal forms AP,

=RliJi +RnJz

Aclz =&J1

(32) (33)

+RzzJ,

and RI2 and RZ1 are treated as equal. Dividing eqn. (33) into (32) and rearranging gives

z-

Rzz

[ J1 ApI - JZApZ

I[ JI &I - J2b -

3

Thus by taking two sets of experimental values of J, , J, , Apl and A,uz the degree of coupling can be found. To do this the sets of data corresponding with the experimental points a, b, c and d in Fig. 9 have been used. The results are listed in Table 3. It is seen that a flow of one component drags the other in the same direction (R,Z negative and q positive) and the coupling is significant. If q were unity coupling would be complete and q is zero for uncoupled flows. RI1 is much smaller than R,, because the resistance to TABLE

3

Ratiosof resistance coefficients and degree of coupling of flows for methanol + isobutanol Datapoints

R,, /R22

R,,lR,,

9

iti a:d

0.078 0.070 0.089

-0.121 -0.089 -0.148

0.43 0.34 0.49

148

motion of methanol in the membrane is less than the resistance to motion of isobutanol. More thorough studies of flow coupling are needed if hyperfiltration is to be developed successfully as a technique for separating organic liquid mixtures [ 17 ] . Acknowledgements B. Luke gratefully acknowledges a scholarship from the NATO Science Fellowship Programme administered by the German Academic Service which made possible his participation in this work. The authors are grateful to Dr. R.P.C. Johnson of Aberdeen University Botany Department for preparing electron micrographs of the cellulose membrane and to Dr. J.D. Burnett of Imperial Chemical Industries, Plastics Division, for providing various thin films for testing as membranes. This paper is dedicated to Emeritus Professor R.M. Barrer, through whose inspiration the senior author first entered upon the study of transport in polymers. It is a pleasure to acknowledge with gratitude the encouragement which he received from Professor Barrer during his earliest researches in this field. Notation

ai ci d Di fi g

JV

Ji 1

L.zk! P i

R-zk Si

T

vi

V Xi

AXi

activity of i in liquid phase molar concentration of i in the membrane vapour gap thickness in permeation cup diffusion coefficient of i in the membrane activity coefficient of i in the membrane convective flow contribution from ref. [ 141 volume flux density molar flux density of i membrane thickness phenomenological permeability coefficients pressure degree of coupling of fluxes the gas constant phenomenological resistance coefficients distribution coefficient of i in the membrane absolute temperature molar volume of i molar volume of permeate mole fraction of i in liquid phase extent of separation

149

free volume

cr

function

in concentration

dependent

diffusion

coefficient

YlZ,

membrane

Yn, YlZ

ei Pi @i @P

*

’

selectivity

coefficients

Vi Ap/RT a dimensionless ratio chemical potential of i in the membrane molar free volume of i specific free volume of polymer specific free volume of polymer + penetrant

References 1 2 3

4 5

9

10 11

12 13 14 15 16 17

p. Meares, Membrane Separation Processes, Elsevier, Amsterdam,1976. S. Sourirajan, Reverse Osmosis, Logos Press, London, 1970. F.W. Greenlaw, W.D. Prince, R.A. Sheldon and E.V. Thompson, Dependence of diffusive permeation rates on upstream and downstream pressures, J. Membrane Sci., 2 (1977) 141. R. Schlogl, Stofftransport durch Membranen, Steinkopff Verlag, Darmstadt, 1964, Ch. 3. I.J. Brass and P. Meares, Some considerations regarding the hyperfiltration of mixtures of organic liquids, in: A.R. Cooper (Ed.) Polymeric Separation Media, Plenum, New York, 1982. D.R. Paul, The role of membrane pressure in reverse osmosis, J. Appl. Polym. Sci., 16 (1972) 771. U.F. Franck and J. Hungerhoff, Separation of azeotropic mixtures of solvents by means of ultrafiltration, Internat. Stand. Congr. Chem. Eng. (Proc.) Symp., IV (1974)l. J.H. Driessen, Zur Herstellung von permselectiven Membranen aus Polyamid und Polyacrylnitril, Dissertation, Rheinisch-Westfllischen Technischen Hochschule, Aachen, GFR, 1976. J.B. Craig, P. Meares and J. Webster, Diffusion and flow of water in cellulose acetate membranes, in: J, Sherwood (Ed,) Diffusion Processes, Gordon and Breach, London, 1970, Vol. 1. G. Arich, I. Kikic and P. Alessi, The liquid-liquid equilibrium for activity coefficient determination, Chem. Engng. Sci., 30 (1975) 187. J. Polak, S. Murakami, V.J. Lam, H.D. Pflug and G.C. Benson, Molar excess enthalpies, volumes, and Gibbs free energies of methanol-isomeric butanol systems at 25”C, Can. J. Chem., 48 (1970) 2457. Electron micrographs were obtained by Dr. R.P.C. Johnson, Botany Department, University of Aberdeen. J. Crank and G.S. Park, Diffusion in Polymers, Academic Press, London, 1968, Ch. 1. G. Thau, R. Bloch and 0. Kedem, Water transport in porous and non-porous membranes, Desalination, 1 (1966) 129. P. Meares, The mechanism of water transport in membranes, Phil. Trans. B. Royal Sot. (London), 278 (1977) 113. S.R. Caplan, The degree of coupling and efficiency of fuel cells and membranes, J. Phys. Chem., 69 (1965) 3801. P. Meares, Towards a molecular interpretation of material transport in polymers, Pure Appl. Chem., 39 (1974) 99.