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Laboratory experiments with hyperfiltration membranes
Desalination, 34 (1980) li-23 Elsevier Scientific Publishing
0
LABORATORY MEMBRANES”
WV.SCHNEIDER Institut
Amsterdam
- Printed in The Netherlands
EXPERIMENTS WITH HYPERFILTRATION
AND
fiir angewandte
(Received
Company,
February
0. BAUER physikalische
Chemie.
Universit&t Heidelberg
(West Germany)
7,198O)
SUMMARY
The operation properties of hyperfiltmtion membranes are representable by various model concepts. The different mathematical relationships that are based on the respective models correspond to the known phenomenological ones and are suitable for describing the throughput through these membranes as welI as their separation behaviour within a wide range of operation. Since those relationships are of the same analytical type, it is difficult to account for the mode ->f action of the membrane from these equations. Laboratory tests with RO membranes are reported with the aim of discussing experimental results which are not covered by the mathematical relationships or which deviate from them respectively. An analysis of these results seems to be helpful for extending the knowledge of the hyperfiltration process.
INTRODUCTION
Several mathematical relationships are applicable for characterizing the separation and the product llux of a hyperfiltration membrane. Some of these equations are purely phenomenological. and others are based on different models of the working mechanism of such a membrane. ln these models the membrane is regarded as a porous body whose free volume has the property of lowering the concentration and/or the mobility of included salt compared to that in the contiguous phases, eiid different physicochemical processes are discussed which cause this $~enomenon. Independent of the respective conception of those models, the density of the product flux (9 through the membrane may be divided into two parts,
*Presented at the Second Symposium Tiibingen, September 17-19, 1979.
on Synthetic
Membranes
in Science
and Industry,
W. SCHNEIDER
12
AND
0. BAUER
one of them containing pure water and being forced by the thermodynamic difference of (Ap - An): qa = a(Ap -An)
(1)
The second part refers to the imperfections of the membrane through which saline water passes convectively according to the mechanical difference Ap, gb = b
l
Ap
(2)
and the complete flux cpmay be written as cp = (a + b) -
(Ap ----O-A@ a+b
The coefficients a and b correspond to a respective model and the ratio a/(a + b) is equivalent to the so-called reflection coefficient C-J (1). The salt transport which may be formally attributed to the imperfections of the membrane is given by ‘ks = V’b
dc
. c-D’-
dx
where x stands for the coordinate in the direction of cpand c for the salt concentration at a respective level of x. D’ represents an effective diffusion coefficient of the salt within the imperfect spaces of the membrane. The essential equivalency of the different membrane models becomes apparent by the fact that their mathematical descriptions are of the same analytical type as Eqs. l-4 and therefore resulting in one common solution: 0)
= c(f)
‘Pb /P ’ exP(Vb /fl) Pb 19 -
1 + exP&b
/6)
(5)
where c(p) = concentration of the permeate, c(f) = concentration of the feed, and @ = effective salt transfer coefficient as the ratio of D’ over the pathlength across the membrane. Eqs. l-5 represent the fundamental keatment of the membrane process. For practical use, different simplifications may be applied to sufficiently characterize the process behaviour of RO membranes. For the reasons mentioned above, however, the applicability of those relationships is not a criterion that a special model or whose respective mechanism is true. A better understanding of these transport and separation mechanisms may be helpful for the improvement and development of membranes. The transport coefficients of RO membranes can be determined by measuring both the product and the salt fluxes as functions of the operating conditions [2]. If the coefficients are assumed to be constant, Eqs. (4) and (5) represent the ideal behaviour of a non-ideal membrane. In practice, how-
HYPERFILTRATION
MEMBRANES
13
ever, different deviations from the ideal behaviour are obsenred if the operating conditions are changed. These deviations rather than the absolute amounts of transport and separation may signify the respective mechanisms. The variation of the product flux coefficient with differing operating conditions is a perceptible example of the non-ideal behaviour of RO membranes. This phenomenon is collectively named compaction. Some more detailed measurements are presented here.
EXPERIMENTS
The membrane properties as a function of the operating conditions have been determined by experimental arrangements consisting of feed containers, pressure pumps, pressure shock absorbers, hyperfiltration units and back pressure reguiators. Feed pipings, hyperfiltration units and back pressure regulators have been thermostated. The experiments have been performed with overflow cells (type DH 120) by Berghof, Tiibingen and with CA membranes (type M 97 F-10-88) which had been obtained from this Throughput and separation of these membranes have been company. measured as functions of temperature, feed concentration and operating pressure. The effect of the operating pressure was studied, and effect of the sys+am pressure investigated by increasing the pressure on the product side of the membrane. Pure sodium chloride solution has been used as feed. During the first experiments the membrane properties were found to alternate slightly with time. From this experience the measurement devices have been appropriately automated in order to average numerous experimental data.
MECHANICAL
A.
COMPACTION
Irreversib Ze compaction
The compaction of a CA-membrane is affected by several parameters simultaneously, and sometimes it is difficult to evaluate the effect of a single parameter. Probably the best known kind of compaction is the decrease of the membrane properties with its working time. Fig. 1 shows the experimentally determined related fluxes $ as function of the working time at different operating pressures. The measurements of the related fluxes shown in Fig. 1 have been performed with pure water. The first section of the solid curve gives the fluxes at an original working of the membrane at 50 bars. When the operating pressure wa& increased up to 100 bars first an immediate drop of the related flux is observed which is followed by a further time dependent decrease approaching an amount that has been measured with a membrane
W. SCHNEIDER
14
AND 0. BAUER
p ( lO“P ] wc-bar
I
---
--
?--I---
100bar
50 bar
1 0
SOW
1 50
1 D
Ho&
Fig. 1. Related throughput through a CA membrane as a function of its working time. @ stands for the permeated volume per units of membrane area, time and pressure difference.
of the same kind but submitted to a pressure of 100 bars from the beginning of its working (lower broken curve). If afterwards the operating pressure was lowered to 50 bars again, the related flux increased jumplike again but without attaining the amount that has been observed during the initial period operating at 50 bars. After lowering of the operating pressure the membrane slowly recovered but at such an insignificant time constant that the time dependent compaction can be considered as irreversible compared to the immediatte variation of the related flux which is observed if the operating pressure is changed. As mentioned, the experimental results given in Fig. 1 have been obtained operating with pure water. If the membranes were fed with salt water, their time-dependent behaviour was similar to that of operating with pure water. The time-independent reversible variation of the related fluxes as a function of the pressure was increased with higher salt contents of the feed water. The measurement results will be given in the following chapter. The salt retention of the membranes investigated was lowered with time in the same way as the related throughput. B.
Reversible compaction For the measurement of the reversible part of the mechanical compaction, the membrane was first irreversibly compacted at a given pressure for about 200 hours. Afterwards the pressure dependence of the related flux was determined up to that pressure at which the irreversible compaction had been
HYPERFILTRATLON TABLE
MEMBRANES
15
I
SALT RETENTION OF A CA MEMBRANE AFTER DIFFERENT WORKING TIMES, OPERATED AT 70 BARS, 20°C AND AT A FEED CONCENTRATION OF 0.1 n NaCl. Working time (Days)
Salt rejection (lo)
12-14 35-37 74-76
97.3 96.3 95.0
performed. The procedure in this way was repeated by a stepwise increase of the pressures of the irreversible compaction. Fig. 2 gives the experimental results that were obtained operating with pure water. If the membrane was fed with salt water the reversible compaction proved to be additionally dependent on the feed concentration. In Fig. 3 such related fluxes are shown versus the operating pressure Ap. Measuring the related fluxes Q the respective effective pressures have been determined, i.e. the osmotic differences AX have been regarded. After irreversible compaction of the membrane at 60 bars with pure water the reversible compaction has been measured varying the feed concentration as noted in Fig. 3.
100
0
50
100
bar
Fig. 2. Pressure dependence of the related fluxes through a CA membrane after irreversible compaction at the noted pressures.
16
W. SCHNEIDER AND 0. BAUER
n NaCl
.. ... I LI
. SO
I !
0
I I 20
60
bar
Fig. 3. Pressure dependence of the related flux at different feed concentrations irreversible compaction of the membrane at 60 bars.
after
The lowering of the related fluxes with increasing feed concentration was found to be partially irreversible: If the salt concentration of the feed is increased and afterwards decreased again the previous fluxes are no longer attained. In the present example, after irreversible compaction of the membrane with pure water at 60 bars, at a first operation with 0.1 n sodium chloride solution the related fluxes have been measured that are given by the upper curve in Fig. 3. Then the feed concentration was increased up to 0.5 n NaCl with the result given by the lowest curve. After repeated lowering of the feed concentration to 0.1 n NaCl the fluxes have been determined that are given by the lower curve belonging to this concentration. Only after operating at low pressures for a considerable time the fluxes increased up to the previously obtained value. The compaction phenomena characterized above may be explained by the mechanical properties of the polymer membrane material. The irreversible variation of the related fluxes, i.e. the time dependent decrease of the mass transport coefficient, can be attributed to the fluidity of the polymer frarnework of the membrane. The reversible compaction represents the elastic fraction of the deformation of the membrane. Proceeding on this assumption efforts are made to reduce the compaction by a combination of a suited separating substance with a carrier material of a high rigidity.
HYPERFILTRATION
MEMBRANES
17
Concerning the related fluxes two observations seem to be worthy of note: For high pressures the related fluxes tend to final values exceeding zero. (The ordinates in Figs. l-3 are broken.) In Fig. 3 the related fluxes are given as a function of the operating pressures, i.e. it is suggested that the compaction of the membrane results from the mechanical pressure difference Ap only without an importance of the osmotic difference Ap - AX. Basing on this consideration the boundary value @, for vanishing operating pressure seems to be invariant of the feed concentration as well as it does not depend on the irreversible compaction (Fig. 2). For a given membrane, therefore, the boundary value &, may be regarded as a permeation constant which depends only on the temperature and the system pressure.
Temperature dependence of membrane properties Separation and transport properties of the CA membranes have been determined within the temperature range of 5OC up to 25OC. The measuring range was limited to this interval in order to avoid irreversible variations of the membranes that were provided for further investigations. The esperiments proved an exponential increase of the throughput with increasing temperature. Treating the measuring data by an Arrhenius relationship the virtual activation enthalpy of the throughput resulted in 20 kJ per mole of transported water. This amount is essentially the same as is reported for the intrinsic transport coefficients of pure water, self diffusion and reciprocal viscosity [ 31. Within the measuring accuracy this value was independent on the salt concentration of the feed. The salt retention of the membranes investigated was lowered with increasing temperature. Unlike the above characterized transport behaviour the temperature dependence of the salt rejection was changed with the former operating conditions: With increasing salt content of the feed the temperature dependent decline of the rejection was extended. Furthermore the temperature dependence of the separation behaviour varied with the specifications of a respective membrane specimen in a way that a membrane with a higher retention at given conditions showed a lower temperature dependence of its rejection. Table II gives the measuring results of membrane properties as a function of the temperature. TABLE
II
TEMPERATURE DEPENDENT BEHAVIOUR 70 BARS WITH 1 n NaCl SOLUTION AFTER Temp. (“C)
s&
Rejection (a)
5 10 15 20
1.40 1.65 1.87 2.16
92.1 91.4 90.8 90.1
OF A CA MEMBRANE OPERATED AT A WORKING PERIOD OF 54-58 DAYS.
18
W. SCHNEIDER
Transport properties
of CA membranes
AND
0.
BAUER
us a function of the system pressure
In hyperfiltration the applied pressure is a driving force. In order to determine the effect of the system’s pressure on the membrane properties independently of the operating pressure, separation and throughput have been measured at increased pressures on the product side of the membranes. To perform these measurements the experimental arrangement was supplemented by a back pressure regulator and a pressure measurement device in the permeate piping. While the separation did not change significantly with the system pressure, the effect on the throughput was evident. Fig. 4 gives the experimental results of the throughputs at different pressures on the product side of a CA membrane. The throughputs are related to the amount of &, as it is dealt with before; Ap stands for the difference of the pressures on the feed side and the product side of the membrane.
I2
%,
IO
I
I
I
Press& on the product side of, the membrane (bar)
.8
.6
50
7
v \
20
GIr Fig. 4. Throughput through a CA membrane as a function of the effective pressure and the system pressure. The operating pressure on the product side of the membrane is given by the sum of the effective pressure Ap and th$pressure on the product side of the membrane as parameter. The measurements have been performed with 0.1 n NaCl solution at 2o”c.
HYPERFILTRATION
MEMBRANES
19
Model systems The mode of action of a membrane may be suggested both from excessive transport phenomena and the thermodynamic behaviour of the ternary system water, salt and membrane material or such substances that have similar chemical properties to those of the membrane material. As such substances organic compounds with functional groups of that
kind are concerned which in aqueous mixtures interact with the protons of the water. Ternary systems of such substances with water and salts form two immiscible liquid phases and it is of interest in this connection that the separation of the phases is accompanied by a large depletion of the salt in the phase enriched with the compound containing the respective functional group. The mixing properties of different such systems have been investigated including esters and acetals with reference to the cellulose acetate. Many of these substances indeed are only partially miscible with water but by addition of salt the miscibility gaps are widened in such a way that the salt is left almost completely in the water enriched phase. This effect is not observed with functional groups which are proton donors themselves. In the system water-sodium chloride-ethanol e.g. the solubili:y of the salt is approximately proportional to the water content of this system. An ‘alcoholic’ membrane, therefore, is not expected to give a considerable separation. The salting out effect differs according to the respective salt in succession of the lyotropic series. The same gradation is observed in regard of the retention of these salts by CA-membranes. This fact may support the attempt to consider the mixing properties of the mentioned substances as a model of the chemical behaviour of the membrane material. The thermal properties of the aqueous mixtures of compounds with proton accepting groups indicate that the hydration of them is combined with a structuring of the hydrate water. At an appropriate arrangement of several functional groups within one molecule this effect is enlarged by overlapping of the structure. The structuring implies a loss of entropy that manifests itself by the temperature dependence of the mixing equilibria of such compounds that are partially miscible with water. Fig. 5 illustrates this behaviour by the example of the first oligomers of ethylene oxide, the aqueous mixture of the trimer having a lower consolute point which is significant for structuring in that system 143. Concept
of a structured
membmne
Transferring the properties of the model systems to the concept of the mode of action of a hyperfiltration membrane the accumulation of functional groups has no longer to be attached to each single molecule. As the
functional groups are locally fixed within the rigid spatial polymer framework of the membrane substance, also functional groups of different polymer chains may give a structure effective arrangement that establishes an
20
W. SCHNEIDER
AND
0.
BAUER
60
LO
20
0
0
20
10
60
Fig. 5. Miscibilities water as a function
100
80 Wmght .I.
of diethyl ether, glycol of the temperature.
t-l,0
diethyl
ether
and diglycol
diethyl
ether
with
overlapping hydration_ According to this concept the realization of overlapping structured sections results from the combined action of the chemical properties of the membrane material and the assembly of the membrane body. In analogy to the properties of the model systems the structured spheres are supposed to form a salt poor phase that is in equilibrium with salt water being contained within the residual interstices. The structure of water within the membrane is not known. For the linear arrangement of the functional groups in polyethylene oxide derivatives, a meandering-like structure is taken into consideration [ 51, but for the spatial arrangement of the functional groups in the membrane framework, an icelike structure may be presumed. For further consideration, however, this question is of no importance as the strength of the interaction of the water with the functional groups is not significant, i.e. whether the overlapping hydration is based on a primary hydrate or not. The structuring and the loss of entropy is rather due to the fact that the quantity of feasible orientations of the water is significantly reduced within the sphere of appropriately arranged functional groups. In manufacturing a membrane the arrangement of the functional groups is more or less random. Proceeding on the assumption that the membrane sub stance contains sufficient functional groups it may be defined by simplifica-
HYPERFILTRATION
MEMBRANES
21
tion that the frequency of overlapping hydrations is proportional to that quantity of pores in the membrane that do not exceed a certain cross section q*. In manufacturing the membrane, however, the pores are also not of uniform size but their cross sections are formed with a certain dispersion fi as illustrated in Fig. 6. According to Fig. 6 it is improbable that the separation is already performed at the surface of the membrane. In order to keep the shaded area in Fig. 6 sufficiently small the dispersion would have to be very low or the characteristic cross-section q* of the pores very large which is not to be expected for either. A reduction of the mean pore size Q would result in an over-proportional lowering of the throughput and therefore would be an unfavourable way to achieve a sufficient separation. The kurtosis of the pore sizes as shown in Fig. 6, however, corresponds to a differential dispersion, i.e. a dispersion of the cross-sections of the pores at the surface of the membrane or at any other level that is normal to the direction of the flow. To obtain a separation by overlapping of the hydration the respective cross-section Q* has to occur only once and according to a bottleneck principle the narrowest section of a pore is therefore effective for the separation rather than the mean cross-section. Passing through the membrane the probability of finding the characteristic cross-section Q* according-
1 g (q) = --exp p-I?7
I-
(q-C?) f12
Fig. 6. Differential dispersion of the pore cross sections of a membrane. The dispersion is based on a normal distribution where g(q) stands for the related frequency of a pore cross-section q, ij for the mean cross-section and q * for the maximum cross-section admitting an overlapping hydration. The coefficient 0 gives the range of the dispersion.
22
W. SCHNEIDER
AND 0. BAUER
ly corresponds to a distribution function as shown in Fig. 6 multiplied by some factor which is equivalent to the distance covered in passing through the membrane. At an extending mean cross-section of the pores j3, therefore, the separation takes place increasingly within the membrane. The above concept of the structure of a membrane may be illustrated by Fig. 7 which gives a hypothetical blow-up of the active layer of a membrane cut in the direction of flow. The black areas represent the polymer chains that are cut in the direction of flow. From the mode of the mechanical compaction it may be gathered that the membrane is of a quite loose structure, i.e. that the path length between two forkings of a pore is at most of the magnitude of the pore diameter. The shaded areas indicate the spheres of the pure or respectively salt poor water that is oriented to the functional groups of the membrane substance. The residual white area covers the volume remaining for the coexistent salt solution. In several places the shaded areas fill the space between the black ones indicating the fields of randomly overlapping hydration It should be noted that the water which is orientated to the functional groups is not fixed at these groups but is also mobile by means of a displacement mechanism. Analogous to the properties of the model systems the phases of the hydrated membrane substance and that of the feed solution are in equilibrium and similarly the extension of the ranges that are structured by orientation of the water to the functional groups depends on the salt content of the coexistent solution. According to this the probability of an overlapping hydra-
Fig. 7 _Hypothetical model of the structure of an hyperfiltration membrane.
HYPERFILTRATION
MEMBRANES
23
tion will be reduced with increasing salt content of the feed resulting in a decrease of the retention at higher feed concentrations. According to the above concept the water moving through the membrane from one oriented range to the next intermediately has to pass those interspaces where the salt is found. During this process, the intermolecular forces of salt and water become effective by lowering of the mobility of the water, which is apparent by a decrease of the related fluxes through the membrane at increasing salt contents of the feed water. Concentration polarization of the salt enriched within the free spaces of the membrane framework may give rise to an additional increase of the flow resistance of the membrane such as the partially irreversible compaction that has been observed after lowering of the feed concentration.
CONCLUSION
The concept of a structured membrane does not essentially differ from the models of an imperfect solution diffusion membrane such as e.g. suggested by Sherwood, Brian and Fisher 161. By tracing the separation to a combined action of the chemical properties of the membrane substance and the structure of the membrane body, however, the separation process is transferred from the surface of the membrane into its interior. Proceeding on this assumption, several phenomena of membrane behaviour can be explained. In investigating these membrane properties, it should be stressed that the excess properties which are considered to account for the mode of action of a hyperfiltration membrane should be analysed rather than the absolute amounts of transport and separation.
ACKNOWLEDGMENT
The experimental work has been supported by BMFT up to the end of 1978 and since 1979 by the Deutsche Forschungsgemeinschaft.
REFERENCES 1. A.J. Stavermann, Rec. Trav. Chim. Pays-Bas, 70 (1951) 344. 2. W. Pusch. Ber. Bunsenges., 81(9) (1977) 854. 3. D. Eisenberg and W. Kauzmann, The Structure and Properties of Water, Oxford University Press, 1969. 4. W. Schneider, R. Vogel and E. Mokhtari-Nejad, Ber. Bunsenges., 81( 10) (1977) 1076. 5. W. Luck, Naturwissenschaften, 52 (1965) 49. 6. T.K. Sherwood, P.L.T. Brian and R.E. Fisher, Ind. Eng. Chem Fundamentals, 6(l) (1967) 2.
0
LABORATORY MEMBRANES”
WV.SCHNEIDER Institut
Amsterdam
- Printed in The Netherlands
EXPERIMENTS WITH HYPERFILTRATION
AND
fiir angewandte
(Received
Company,
February
0. BAUER physikalische
Chemie.
Universit&t Heidelberg
(West Germany)
7,198O)
SUMMARY
The operation properties of hyperfiltmtion membranes are representable by various model concepts. The different mathematical relationships that are based on the respective models correspond to the known phenomenological ones and are suitable for describing the throughput through these membranes as welI as their separation behaviour within a wide range of operation. Since those relationships are of the same analytical type, it is difficult to account for the mode ->f action of the membrane from these equations. Laboratory tests with RO membranes are reported with the aim of discussing experimental results which are not covered by the mathematical relationships or which deviate from them respectively. An analysis of these results seems to be helpful for extending the knowledge of the hyperfiltration process.
INTRODUCTION
Several mathematical relationships are applicable for characterizing the separation and the product llux of a hyperfiltration membrane. Some of these equations are purely phenomenological. and others are based on different models of the working mechanism of such a membrane. ln these models the membrane is regarded as a porous body whose free volume has the property of lowering the concentration and/or the mobility of included salt compared to that in the contiguous phases, eiid different physicochemical processes are discussed which cause this $~enomenon. Independent of the respective conception of those models, the density of the product flux (9 through the membrane may be divided into two parts,
*Presented at the Second Symposium Tiibingen, September 17-19, 1979.
on Synthetic
Membranes
in Science
and Industry,
W. SCHNEIDER
12
AND
0. BAUER
one of them containing pure water and being forced by the thermodynamic difference of (Ap - An): qa = a(Ap -An)
(1)
The second part refers to the imperfections of the membrane through which saline water passes convectively according to the mechanical difference Ap, gb = b
l
Ap
(2)
and the complete flux cpmay be written as cp = (a + b) -
(Ap ----O-A@ a+b
The coefficients a and b correspond to a respective model and the ratio a/(a + b) is equivalent to the so-called reflection coefficient C-J (1). The salt transport which may be formally attributed to the imperfections of the membrane is given by ‘ks = V’b
dc
. c-D’-
dx
where x stands for the coordinate in the direction of cpand c for the salt concentration at a respective level of x. D’ represents an effective diffusion coefficient of the salt within the imperfect spaces of the membrane. The essential equivalency of the different membrane models becomes apparent by the fact that their mathematical descriptions are of the same analytical type as Eqs. l-4 and therefore resulting in one common solution: 0)
= c(f)
‘Pb /P ’ exP(Vb /fl) Pb 19 -
1 + exP&b
/6)
(5)
where c(p) = concentration of the permeate, c(f) = concentration of the feed, and @ = effective salt transfer coefficient as the ratio of D’ over the pathlength across the membrane. Eqs. l-5 represent the fundamental keatment of the membrane process. For practical use, different simplifications may be applied to sufficiently characterize the process behaviour of RO membranes. For the reasons mentioned above, however, the applicability of those relationships is not a criterion that a special model or whose respective mechanism is true. A better understanding of these transport and separation mechanisms may be helpful for the improvement and development of membranes. The transport coefficients of RO membranes can be determined by measuring both the product and the salt fluxes as functions of the operating conditions [2]. If the coefficients are assumed to be constant, Eqs. (4) and (5) represent the ideal behaviour of a non-ideal membrane. In practice, how-
HYPERFILTRATION
MEMBRANES
13
ever, different deviations from the ideal behaviour are obsenred if the operating conditions are changed. These deviations rather than the absolute amounts of transport and separation may signify the respective mechanisms. The variation of the product flux coefficient with differing operating conditions is a perceptible example of the non-ideal behaviour of RO membranes. This phenomenon is collectively named compaction. Some more detailed measurements are presented here.
EXPERIMENTS
The membrane properties as a function of the operating conditions have been determined by experimental arrangements consisting of feed containers, pressure pumps, pressure shock absorbers, hyperfiltration units and back pressure reguiators. Feed pipings, hyperfiltration units and back pressure regulators have been thermostated. The experiments have been performed with overflow cells (type DH 120) by Berghof, Tiibingen and with CA membranes (type M 97 F-10-88) which had been obtained from this Throughput and separation of these membranes have been company. measured as functions of temperature, feed concentration and operating pressure. The effect of the operating pressure was studied, and effect of the sys+am pressure investigated by increasing the pressure on the product side of the membrane. Pure sodium chloride solution has been used as feed. During the first experiments the membrane properties were found to alternate slightly with time. From this experience the measurement devices have been appropriately automated in order to average numerous experimental data.
MECHANICAL
A.
COMPACTION
Irreversib Ze compaction
The compaction of a CA-membrane is affected by several parameters simultaneously, and sometimes it is difficult to evaluate the effect of a single parameter. Probably the best known kind of compaction is the decrease of the membrane properties with its working time. Fig. 1 shows the experimentally determined related fluxes $ as function of the working time at different operating pressures. The measurements of the related fluxes shown in Fig. 1 have been performed with pure water. The first section of the solid curve gives the fluxes at an original working of the membrane at 50 bars. When the operating pressure wa& increased up to 100 bars first an immediate drop of the related flux is observed which is followed by a further time dependent decrease approaching an amount that has been measured with a membrane
W. SCHNEIDER
14
AND 0. BAUER
p ( lO“P ] wc-bar
I
---
--
?--I---
100bar
50 bar
1 0
SOW
1 50
1 D
Ho&
Fig. 1. Related throughput through a CA membrane as a function of its working time. @ stands for the permeated volume per units of membrane area, time and pressure difference.
of the same kind but submitted to a pressure of 100 bars from the beginning of its working (lower broken curve). If afterwards the operating pressure was lowered to 50 bars again, the related flux increased jumplike again but without attaining the amount that has been observed during the initial period operating at 50 bars. After lowering of the operating pressure the membrane slowly recovered but at such an insignificant time constant that the time dependent compaction can be considered as irreversible compared to the immediatte variation of the related flux which is observed if the operating pressure is changed. As mentioned, the experimental results given in Fig. 1 have been obtained operating with pure water. If the membranes were fed with salt water, their time-dependent behaviour was similar to that of operating with pure water. The time-independent reversible variation of the related fluxes as a function of the pressure was increased with higher salt contents of the feed water. The measurement results will be given in the following chapter. The salt retention of the membranes investigated was lowered with time in the same way as the related throughput. B.
Reversible compaction For the measurement of the reversible part of the mechanical compaction, the membrane was first irreversibly compacted at a given pressure for about 200 hours. Afterwards the pressure dependence of the related flux was determined up to that pressure at which the irreversible compaction had been
HYPERFILTRATLON TABLE
MEMBRANES
15
I
SALT RETENTION OF A CA MEMBRANE AFTER DIFFERENT WORKING TIMES, OPERATED AT 70 BARS, 20°C AND AT A FEED CONCENTRATION OF 0.1 n NaCl. Working time (Days)
Salt rejection (lo)
12-14 35-37 74-76
97.3 96.3 95.0
performed. The procedure in this way was repeated by a stepwise increase of the pressures of the irreversible compaction. Fig. 2 gives the experimental results that were obtained operating with pure water. If the membrane was fed with salt water the reversible compaction proved to be additionally dependent on the feed concentration. In Fig. 3 such related fluxes are shown versus the operating pressure Ap. Measuring the related fluxes Q the respective effective pressures have been determined, i.e. the osmotic differences AX have been regarded. After irreversible compaction of the membrane at 60 bars with pure water the reversible compaction has been measured varying the feed concentration as noted in Fig. 3.
100
0
50
100
bar
Fig. 2. Pressure dependence of the related fluxes through a CA membrane after irreversible compaction at the noted pressures.
16
W. SCHNEIDER AND 0. BAUER
n NaCl
.. ... I LI
. SO
I !
0
I I 20
60
bar
Fig. 3. Pressure dependence of the related flux at different feed concentrations irreversible compaction of the membrane at 60 bars.
after
The lowering of the related fluxes with increasing feed concentration was found to be partially irreversible: If the salt concentration of the feed is increased and afterwards decreased again the previous fluxes are no longer attained. In the present example, after irreversible compaction of the membrane with pure water at 60 bars, at a first operation with 0.1 n sodium chloride solution the related fluxes have been measured that are given by the upper curve in Fig. 3. Then the feed concentration was increased up to 0.5 n NaCl with the result given by the lowest curve. After repeated lowering of the feed concentration to 0.1 n NaCl the fluxes have been determined that are given by the lower curve belonging to this concentration. Only after operating at low pressures for a considerable time the fluxes increased up to the previously obtained value. The compaction phenomena characterized above may be explained by the mechanical properties of the polymer membrane material. The irreversible variation of the related fluxes, i.e. the time dependent decrease of the mass transport coefficient, can be attributed to the fluidity of the polymer frarnework of the membrane. The reversible compaction represents the elastic fraction of the deformation of the membrane. Proceeding on this assumption efforts are made to reduce the compaction by a combination of a suited separating substance with a carrier material of a high rigidity.
HYPERFILTRATION
MEMBRANES
17
Concerning the related fluxes two observations seem to be worthy of note: For high pressures the related fluxes tend to final values exceeding zero. (The ordinates in Figs. l-3 are broken.) In Fig. 3 the related fluxes are given as a function of the operating pressures, i.e. it is suggested that the compaction of the membrane results from the mechanical pressure difference Ap only without an importance of the osmotic difference Ap - AX. Basing on this consideration the boundary value @, for vanishing operating pressure seems to be invariant of the feed concentration as well as it does not depend on the irreversible compaction (Fig. 2). For a given membrane, therefore, the boundary value &, may be regarded as a permeation constant which depends only on the temperature and the system pressure.
Temperature dependence of membrane properties Separation and transport properties of the CA membranes have been determined within the temperature range of 5OC up to 25OC. The measuring range was limited to this interval in order to avoid irreversible variations of the membranes that were provided for further investigations. The esperiments proved an exponential increase of the throughput with increasing temperature. Treating the measuring data by an Arrhenius relationship the virtual activation enthalpy of the throughput resulted in 20 kJ per mole of transported water. This amount is essentially the same as is reported for the intrinsic transport coefficients of pure water, self diffusion and reciprocal viscosity [ 31. Within the measuring accuracy this value was independent on the salt concentration of the feed. The salt retention of the membranes investigated was lowered with increasing temperature. Unlike the above characterized transport behaviour the temperature dependence of the salt rejection was changed with the former operating conditions: With increasing salt content of the feed the temperature dependent decline of the rejection was extended. Furthermore the temperature dependence of the separation behaviour varied with the specifications of a respective membrane specimen in a way that a membrane with a higher retention at given conditions showed a lower temperature dependence of its rejection. Table II gives the measuring results of membrane properties as a function of the temperature. TABLE
II
TEMPERATURE DEPENDENT BEHAVIOUR 70 BARS WITH 1 n NaCl SOLUTION AFTER Temp. (“C)
s&
Rejection (a)
5 10 15 20
1.40 1.65 1.87 2.16
92.1 91.4 90.8 90.1
OF A CA MEMBRANE OPERATED AT A WORKING PERIOD OF 54-58 DAYS.
18
W. SCHNEIDER
Transport properties
of CA membranes
AND
0.
BAUER
us a function of the system pressure
In hyperfiltration the applied pressure is a driving force. In order to determine the effect of the system’s pressure on the membrane properties independently of the operating pressure, separation and throughput have been measured at increased pressures on the product side of the membranes. To perform these measurements the experimental arrangement was supplemented by a back pressure regulator and a pressure measurement device in the permeate piping. While the separation did not change significantly with the system pressure, the effect on the throughput was evident. Fig. 4 gives the experimental results of the throughputs at different pressures on the product side of a CA membrane. The throughputs are related to the amount of &, as it is dealt with before; Ap stands for the difference of the pressures on the feed side and the product side of the membrane.
I2
%,
IO
I
I
I
Press& on the product side of, the membrane (bar)
.8
.6
50
7
v \
20
GIr Fig. 4. Throughput through a CA membrane as a function of the effective pressure and the system pressure. The operating pressure on the product side of the membrane is given by the sum of the effective pressure Ap and th$pressure on the product side of the membrane as parameter. The measurements have been performed with 0.1 n NaCl solution at 2o”c.
HYPERFILTRATION
MEMBRANES
19
Model systems The mode of action of a membrane may be suggested both from excessive transport phenomena and the thermodynamic behaviour of the ternary system water, salt and membrane material or such substances that have similar chemical properties to those of the membrane material. As such substances organic compounds with functional groups of that
kind are concerned which in aqueous mixtures interact with the protons of the water. Ternary systems of such substances with water and salts form two immiscible liquid phases and it is of interest in this connection that the separation of the phases is accompanied by a large depletion of the salt in the phase enriched with the compound containing the respective functional group. The mixing properties of different such systems have been investigated including esters and acetals with reference to the cellulose acetate. Many of these substances indeed are only partially miscible with water but by addition of salt the miscibility gaps are widened in such a way that the salt is left almost completely in the water enriched phase. This effect is not observed with functional groups which are proton donors themselves. In the system water-sodium chloride-ethanol e.g. the solubili:y of the salt is approximately proportional to the water content of this system. An ‘alcoholic’ membrane, therefore, is not expected to give a considerable separation. The salting out effect differs according to the respective salt in succession of the lyotropic series. The same gradation is observed in regard of the retention of these salts by CA-membranes. This fact may support the attempt to consider the mixing properties of the mentioned substances as a model of the chemical behaviour of the membrane material. The thermal properties of the aqueous mixtures of compounds with proton accepting groups indicate that the hydration of them is combined with a structuring of the hydrate water. At an appropriate arrangement of several functional groups within one molecule this effect is enlarged by overlapping of the structure. The structuring implies a loss of entropy that manifests itself by the temperature dependence of the mixing equilibria of such compounds that are partially miscible with water. Fig. 5 illustrates this behaviour by the example of the first oligomers of ethylene oxide, the aqueous mixture of the trimer having a lower consolute point which is significant for structuring in that system 143. Concept
of a structured
membmne
Transferring the properties of the model systems to the concept of the mode of action of a hyperfiltration membrane the accumulation of functional groups has no longer to be attached to each single molecule. As the
functional groups are locally fixed within the rigid spatial polymer framework of the membrane substance, also functional groups of different polymer chains may give a structure effective arrangement that establishes an
20
W. SCHNEIDER
AND
0.
BAUER
60
LO
20
0
0
20
10
60
Fig. 5. Miscibilities water as a function
100
80 Wmght .I.
of diethyl ether, glycol of the temperature.
t-l,0
diethyl
ether
and diglycol
diethyl
ether
with
overlapping hydration_ According to this concept the realization of overlapping structured sections results from the combined action of the chemical properties of the membrane material and the assembly of the membrane body. In analogy to the properties of the model systems the structured spheres are supposed to form a salt poor phase that is in equilibrium with salt water being contained within the residual interstices. The structure of water within the membrane is not known. For the linear arrangement of the functional groups in polyethylene oxide derivatives, a meandering-like structure is taken into consideration [ 51, but for the spatial arrangement of the functional groups in the membrane framework, an icelike structure may be presumed. For further consideration, however, this question is of no importance as the strength of the interaction of the water with the functional groups is not significant, i.e. whether the overlapping hydration is based on a primary hydrate or not. The structuring and the loss of entropy is rather due to the fact that the quantity of feasible orientations of the water is significantly reduced within the sphere of appropriately arranged functional groups. In manufacturing a membrane the arrangement of the functional groups is more or less random. Proceeding on the assumption that the membrane sub stance contains sufficient functional groups it may be defined by simplifica-
HYPERFILTRATION
MEMBRANES
21
tion that the frequency of overlapping hydrations is proportional to that quantity of pores in the membrane that do not exceed a certain cross section q*. In manufacturing the membrane, however, the pores are also not of uniform size but their cross sections are formed with a certain dispersion fi as illustrated in Fig. 6. According to Fig. 6 it is improbable that the separation is already performed at the surface of the membrane. In order to keep the shaded area in Fig. 6 sufficiently small the dispersion would have to be very low or the characteristic cross-section q* of the pores very large which is not to be expected for either. A reduction of the mean pore size Q would result in an over-proportional lowering of the throughput and therefore would be an unfavourable way to achieve a sufficient separation. The kurtosis of the pore sizes as shown in Fig. 6, however, corresponds to a differential dispersion, i.e. a dispersion of the cross-sections of the pores at the surface of the membrane or at any other level that is normal to the direction of the flow. To obtain a separation by overlapping of the hydration the respective cross-section Q* has to occur only once and according to a bottleneck principle the narrowest section of a pore is therefore effective for the separation rather than the mean cross-section. Passing through the membrane the probability of finding the characteristic cross-section Q* according-
1 g (q) = --exp p-I?7
I-
(q-C?) f12
Fig. 6. Differential dispersion of the pore cross sections of a membrane. The dispersion is based on a normal distribution where g(q) stands for the related frequency of a pore cross-section q, ij for the mean cross-section and q * for the maximum cross-section admitting an overlapping hydration. The coefficient 0 gives the range of the dispersion.
22
W. SCHNEIDER
AND 0. BAUER
ly corresponds to a distribution function as shown in Fig. 6 multiplied by some factor which is equivalent to the distance covered in passing through the membrane. At an extending mean cross-section of the pores j3, therefore, the separation takes place increasingly within the membrane. The above concept of the structure of a membrane may be illustrated by Fig. 7 which gives a hypothetical blow-up of the active layer of a membrane cut in the direction of flow. The black areas represent the polymer chains that are cut in the direction of flow. From the mode of the mechanical compaction it may be gathered that the membrane is of a quite loose structure, i.e. that the path length between two forkings of a pore is at most of the magnitude of the pore diameter. The shaded areas indicate the spheres of the pure or respectively salt poor water that is oriented to the functional groups of the membrane substance. The residual white area covers the volume remaining for the coexistent salt solution. In several places the shaded areas fill the space between the black ones indicating the fields of randomly overlapping hydration It should be noted that the water which is orientated to the functional groups is not fixed at these groups but is also mobile by means of a displacement mechanism. Analogous to the properties of the model systems the phases of the hydrated membrane substance and that of the feed solution are in equilibrium and similarly the extension of the ranges that are structured by orientation of the water to the functional groups depends on the salt content of the coexistent solution. According to this the probability of an overlapping hydra-
Fig. 7 _Hypothetical model of the structure of an hyperfiltration membrane.
HYPERFILTRATION
MEMBRANES
23
tion will be reduced with increasing salt content of the feed resulting in a decrease of the retention at higher feed concentrations. According to the above concept the water moving through the membrane from one oriented range to the next intermediately has to pass those interspaces where the salt is found. During this process, the intermolecular forces of salt and water become effective by lowering of the mobility of the water, which is apparent by a decrease of the related fluxes through the membrane at increasing salt contents of the feed water. Concentration polarization of the salt enriched within the free spaces of the membrane framework may give rise to an additional increase of the flow resistance of the membrane such as the partially irreversible compaction that has been observed after lowering of the feed concentration.
CONCLUSION
The concept of a structured membrane does not essentially differ from the models of an imperfect solution diffusion membrane such as e.g. suggested by Sherwood, Brian and Fisher 161. By tracing the separation to a combined action of the chemical properties of the membrane substance and the structure of the membrane body, however, the separation process is transferred from the surface of the membrane into its interior. Proceeding on this assumption, several phenomena of membrane behaviour can be explained. In investigating these membrane properties, it should be stressed that the excess properties which are considered to account for the mode of action of a hyperfiltration membrane should be analysed rather than the absolute amounts of transport and separation.
ACKNOWLEDGMENT
The experimental work has been supported by BMFT up to the end of 1978 and since 1979 by the Deutsche Forschungsgemeinschaft.
REFERENCES 1. A.J. Stavermann, Rec. Trav. Chim. Pays-Bas, 70 (1951) 344. 2. W. Pusch. Ber. Bunsenges., 81(9) (1977) 854. 3. D. Eisenberg and W. Kauzmann, The Structure and Properties of Water, Oxford University Press, 1969. 4. W. Schneider, R. Vogel and E. Mokhtari-Nejad, Ber. Bunsenges., 81( 10) (1977) 1076. 5. W. Luck, Naturwissenschaften, 52 (1965) 49. 6. T.K. Sherwood, P.L.T. Brian and R.E. Fisher, Ind. Eng. Chem Fundamentals, 6(l) (1967) 2.