Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer membranes

Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer membranes

Journal of Membrane Science 251 (2005) 29–41 Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer me...

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Journal of Membrane Science 251 (2005) 29–41

Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer membranes S.J. Metz, W.J.C. van de Ven, J. Potreck, M.H.V. Mulder, M. Wessling∗ Membrane Technology Group, Department of Science and Technology, University of Twente, P.O. Box 217, NL-7500 AE Enschede, The Netherlands Received 26 August 2004; accepted 26 August 2004 Available online 15 December 2004

Abstract This paper studies in detail the measurement of the permeation properties of highly permeable and highly selective polymers for water vapor/nitrogen gas mixtures. The analysis of the mass transport of a highly permeable polymer is complicated by the presence of stagnant boundary layers at feed and permeate side. Such resistances are generally specific to the permeation cell used and can be extracted from the measurement of the overall resistance of polymeric films having different thickness. Water vapor permeabilities of ethyl cellulose and polysulfone films are determined and corrected for the resistance in the stagnant boundary layer and measured values correspond to those in literature. Permeability values of even higher permeable and more selective poly(ethylene oxide) poly(butylene terephthalate) multi-block copolymer (PEO-PBT) are presented to illustrate the contribution of the stagnant boundary layer at various process conditions. The mixed gas nitrogen permeability remains constant with an increase of water vapor activity on the feed side of the membrane, but increases significantly when the sweep gas is humidified. The water vapor permeability shows a strong dependence on the feed pressure. An increase of the feed pressure results in a larger resistance of the stagnant feed boundary layer, thereby lowering the total water vapor flux. The mixed gas nitrogen permeability decreases slightly with an increase of pressure most likely due to the compaction of the material. © 2004 Elsevier B.V. All rights reserved. Keywords: Water vapor transport; Permeability measurement; Mixed gas measurement; Concentration polarization; PEO-PBT block copolymer; Effect of permeate pressure

1. Introduction Water vapor transport through polymeric barrier materials or membranes is of major industrial importance. Applications can be found in the drying of natural gas [1], drying of compressed air [2], protective apparel [3], packaging materials, roofing membranes, and the humidity control in closed spaces (air conditioning in buildings, aviation and space flight). Various polymers can be used as a selective membrane or barrier material for the transport of water vapor. Depending on the application, a high or low permeability or selectivity for water vapor is preferred. Generally, water permeates to a larger

∗ Corresponding author. Tel.: +31 53 489 2950/2951; fax: +31 53 489 4611. E-mail address: [email protected] (M. Wessling).

0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2004.08.036

extent than permanent gases due to the larger solubility and diffusivity of water. Fig. 1 and Table 1 summarize the water vapor and nitrogen permeability and selectivity for various polymers at 30 ◦ C. The permeability values and selectivities are obtained from literature. They are extrapolated to a water vapor activity of 0 to exclude any effect of feed water activity. It is well known for binary gas mixtures of permanent gases that a higher selectivity is accompanied by a lower permeability. This relationship is often referred to as a Robeson plot [11]. However, such a relation does not hold for the permeance of water vapor in a mixture with a permanent gas. Most of the highly selective polymers also possess a very high permeability [12]. For different polymers, the water vapor/nitrogen selectivity changes over 7 orders of magnitude and the water vapor permeability 5 orders of magnitude between the various polymers.

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This paper studies in detail the measurement of the permeability of a water vapor/nitrogen mixture through polymers in a newly developed experimental set-up. First, systematic experiments with membranes of various thickness at various feed and permeate flow rate allow the quantification of laminar boundary layer resistances. Only then we can systematically study the effect of process parameters such as water vapor activity, temperature and feed pressure. The effect of the process variables are demonstrated for a very high selective and very permeable block copolymer, composed of hydrophilic PEO blocks and impermeable PBT blocks.

2. Background Fig. 1. Water vapor permeability and water vapor/N2 selectivity for various polymers at 30 ◦ C.

2.1. Measurement of water vapor permeation

Many of the permeability and selectivity values are obtained from pure gas permeabilities by calculating the ratio of the permeabilities for each species. In real gas mixtures, water may swell the membrane and its effect on the transport of the slower species often remains unknown. Also the extraction of intrinsic polymer properties from the overall transport rate in mixed gas experiments is difficult: the high transport rate of water through the membrane compared to the slower diffusion in laminar boundary layers induces concentration polarization at the feed and permeate side of the membrane. To the surprise of the authors, there is hardly any literature available that systematically studies the effect of process conditions on the transport of water/gas mixtures. However, such measurements are not trivial and require an intricate experimental protocol.

The “cup method” is probably the most frequently used technique to determine the transport rate of water vapor through a polymeric material. This method consists of a polymeric film, covering a container with water or a dessicant. This container is placed in a humidity-controlled environment, and the permeability of water vapor through a polymeric film is determined by the rate of weight decrease of the container. The permeability determined by the cup method is affected by the presence of stagnant boundary layers on both sides of the polymeric film [13]. Moreover, the sealing of the film can give rise to errors, especially for low-permeable films [14]. More accurate results can be obtained with the variablepressure constant-volume method, where a vacuum is applied at the permeate side of the membrane and a water vapor is present at the feed side of the membrane. The water vapor

Table 1 Water vapor and N2 permeability and selectivity for various polymers at 30 ◦ C, extrapolated to 0 water vapor activity Polymer

Ethyl cellulose Cellulose acetate Natural rubber 1000PEO 56PBT 44 Polyacrylonitrile Polyamide 6 (Nylon 6) Polycarbonate Polydimethylsiloxane Polyethersulfone Polyethylene Polyimide (Kapton) Polyphenyleneoxide Polypropylene Polystyrene Polysulfone Polyvinylalcohol Polyvinylchloride Sulfonated polyetheretherketon Sulfonated polyethersulofon

Abbreviation

EC CA NR PEO-PBT PAN PA-6 PC PDMS PES PE PI PPO PP PS PSF PVA PVC SPEEK SPES

H2 O Permeability (Barrer)

20000 6000 2600 85500 300 275 1400 40000 2620 12 640 4060 68 970 2000 19 275 61000 15000

Selectivity (H2 O/N2 )

6061 24000 299 40500 1875000 11000 4667 143 10480 6 5333333 1068 227 388 8000 33333 12500 10166667 214286

Reference H2 O

N2

[4] [6] [8] This work [8] [8] [8] [7] [8] [6] [4] [4] [6] [6] [8] [6] [4] [10] [9]

[5] [7] [5] [8] [7] [7] [7] [9] [7] [7] [7] [7] [7] [5] [7] [7] [10] [9]

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Fig. 2. Schematic representation of the newly developed permeation equipment.

permeability is determined from the pressure increase in the calibrated permeate volume. However, corrections have to be made for adsorption of the permeated water vapor on the equipment [15]. For the aforementioned techniques, only the pure water vapor permeability can be determined and the simultaneous measurement of the permeability of both the gas as well as vapor is not possible. When both water vapor and gas permeabilities have to be measured, other methods can be used as well. The methods described below use a vapor/gas mixture flowing over the membrane. A vacuum in combination with a cold trap can be used in order to collect the permeated vapor [16,17]. This method has the disadvantage that only the vapor permeability is measured and not the gas permeability. This can be circumvented by measuring the flow rate and the composition of the permeate stream at a certain permeate pressure [18]. However, the total flux through the membrane has to be high enough to be able to determine a flow rate of the permeate stream. The mixed gas vapor permeability can also be measured, without the use of a vacuum if the feed-side vapor pressure is larger than the partial vapor pressure at permeate at atmospheric conditions. The permeability values can be calculated from the composition and the flow rate of the permeate stream. This paper describes a further sophistication of the last methods. We feel this to be necessary, in particular, for highly selective and highly permeable materials. Instead of a vacuum, we use a sweep gas to remove the water vapor and nitrogen at the permeate side of the membrane as depicted in Fig. 2. (Counter-permeation of the sweep gas does not influence the results, as we will show later.) The permeability of water vapor and nitrogen is measured simultaneously using dew-pointing mirrors measuring the water content and gas chromatography for nitrogen. A detailed description of the experimental method is presented in Section 3. 2.2. Mass transfer limitations For many polymers, the highly selective transport of water vapor, in contrast to mixtures of permanent gases, can cause concentration polarization phenomena [19]. This is schemat-

Fig. 3. Schematic representation of the chemical potential profiles for water vapor in the stagnant boundary layers and the membrane for a water vapor/N2 mixture.

ically depicted in Fig. 3. Concentration polarization occurs in gas/vapor mixtures if the diffusion of water vapor through a stagnant layer on the feed or permeate side of the membrane contributes to the overall transport rate. Measuring the overall mass transfer rate can give reliable values for intrinsic membrane properties only when the boundary resistances are known. The overall mass transfer coefficient (kov ) can be determined from the measured water vapor flux through the membrane and the concentration difference over the membrane: JH2 O = kov (Cf − Cp )

(1)

where JH2 O is the flux of water vapor through the membrane (mol/(m2 s)), and Cf and Cp the bulk concentration of water vapor on the feed and permeate side of the membrane (mol/m3 ), respectively. In Fig. 3, kf , km , and kp are the mass transfer coefficients in the feed boundary layer, the membrane, and the permeate boundary layer, respectively. The stagnant boundary layers on the feed and permeate side of the membrane represent an extra resistance. These resistances can mathematically be represented with the resistance in series model: 1 1 1 1 = + + kov kf km kp

(2)

where 1/kov is the overall resistance for water vapor permeation (s/m) and kov the overall mass transfer coefficient for water vapor (m/s). The mass transfer coefficients on the feed and permeate side of the membrane depend on the geometry and the hydrodynamic conditions of the system and are often described with Sherwood relations [20]: b

Sh = a Re Sc

c



L dh

d (3)

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where   kdh Sh = , D

3. Experimental  Re =

ρvdh η



 ,

Sc =

η ρD

 3.1. Mixed gas water vapor permeation set-up

and a, b, c and d are empirical constants depending on the geometry of the system. Sh is the Sherwood number (–), Re the Reynolds number (–), Sc the Schmidt number (–), k the mass transfer coefficient (m/s), dh the hydraulic diameter (m), ρ the density (kg/m3 ), η the viscosity (Pa s), L the length of the flow path (m), and D the diffusion coefficient of water vapor in the gas mixture (m2 /s). The diffusion coefficient of water vapor in nitrogen at various pressures and temperatures can be estimated with the following empirical relation derived by Massman [21]:  D = D0

p0 p



T T0

1.81 (4)

where D is the diffusion coefficient of water in nitrogen (m2 /s), D0 the diffusion coefficient of water in nitrogen at 105 Pa (1 bar) and 273 K (D0 = 2.19 × 10−5 m2 /s), p0 = 1.013 × 105 Pa (1.013 bar), p the pressure (bar), T the absolute temperature (K) and T0 = 273.15 K. In a water vapor/nitrogen mixture, the rapid transport of water vapor through the membrane is limited by the transport of water vapor from the bulk of the gas phase to the membrane interface and the diffusion of water vapor from the permeate side through a stagnant helium boundary layer. This goes along with a higher amount of nitrogen near the membrane surface than the bulk concentration. Frequently, the effect for nitrogen is negligible when the amount of water vapor in the feed is significantly smaller than the amount of nitrogen (T = 30 ◦ C, pH2 O =42 × 105 mPa (42 mbar), pN2 > 2 × 105 Pa (2 bar) in all the experiments). Therefore, concentration polarization phenomena will only affect the water vapor permeability to a significant extent.

Reliable intrinsic polymer permeability data for water vapor/gas mixtures at elevated pressure and temperature are necessary to design membrane gas separation processes. To the best of our knowledge only few studies report such data. In particular, for highly selective and highly permeable membrane materials, this task remains an experimental challenge. Fig. 4 shows the mixed gas water vapor permeation set-up designed for the simultaneous measurement of a vapor and mixed gas permeability, in the temperature range 20–80 ◦ C, and pressure range 1 × 105 –80 × 105 Pa (1–80 bar). A gas/vapor mixture is generated by flowing a gas through a bubble column (3), which is filled with water, and a demister (4). The latter separates the entrained liquid droplets from the gas stream. Both the bubble column (0.6 l) and demister (0.5 l) are double-walled and temperature-controlled with the use of a heating bath. The saturated wet gas stream is mixed with a dry gas stream to the desired humidity level and sent to the permeation cell. The water vapor concentration in this stream is controlled by adjusting the flow rates of the dry and wet streams with the mass flow controllers 1 and 2 (FC, Brooks 0154), respectively. The following parameters are measured in the feed stream to the membrane test cell: total pressure (PI, Druck PTX 1400), temperature (TI, thermocouple), and the water vapor dew point (TD, Michel instruments SD). This gas mixture flows over a polymeric film mounted in a membrane test cell and leaves the system via a backpressure (6, Go backpressure regulator), which controls the total pressure in the system. The flow rate of the stream leaving the membrane test cell is measured with a soap bubble meter (FI). Water vapor as well as gas permeate through the membrane material and are removed with a helium sweep gas. The flow rate of this sweep gas can be controlled with a mass flow controller 5 (FC, Brooks 0154). In the sweep gas stream leaving the permeate

Fig. 4. Mixed gas vapor permeation set-up for the measurement of gas/vapor mixtures in the temperature range 20–80 ◦ C and pressure range 1 × 105 –80 × 105 Pa (1–80 bar).

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side of the cell, the following parameters are analyzed: water vapor dew point (TD, Michel instruments SD), temperature (TI, thermocouple), flow rate (FI, soap bubble meter), and nitrogen concentration with a gas chromatograph (GS, Varian 3400, column: molecular sieve 13×). The whole set-up is insulated and temperature-controlled with the use of a heating bath, via heat exchangers and heating tape (Isopad heating tape and Winkler temperature control unit), which prevent condensation of water vapor in the tubing of the set-up. 3.2. Permeation cell Fig. 5 shows a schematic representation of the permeation cell. It is based on a modification of a permeation cell design used over a decade in our laboratory, which has recently been applied to high-pressure gas-separation experiments [22]. The feed gas mixture enters on top and through the center of the cell and flows radially over the membrane leaving the cell via 12 holes on the outer ring. The sweep gas helium enters the lower part of the permeation cell through the 12 holes and flows radially to the center where it leaves the cell. The membrane package comprises the polymeric film to be characterized (thickness from 20 to 300 ␮m), a filter paper, and a porous metallic support plate supporting the membrane. This permeate-side construction is necessary to guarantee mechanical strength for the high-pressure experiments. It will complicate the analysis, as we shall show later. The effective membrane area is 11.95 cm2 . The two compartments of the permeation cell are sealed with O-rings (Viton). The cell compartments are double-walled and heated with a heating bath.

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meate side according to Eq. (5): Ji =

Pi (pi,feed − pi,permeate ) l

(5)

where Ji is the flux of component i through the membrane package (cm3 (STP)/(cm2 s) = 0.01 m3 (STP)/(m2 s)), Pi the permeability expressed in Barrer (1 Barrer = 10−10 cm3 (STP) cm/(cm2 s cmHg) = 7.5187 × 10−15 m3 (STP) m/(m2 s kPa)), l the thickness of the material (cm), pi,feed and pi,permeate the partial pressures on the feed and permeate side of the material (1 cmHg = 1.33 kPa), respectively. Knowing the partial pressures directly at the membrane surface as well as the membrane thickness and measuring the flux allows to calculate the intrinsic material property. However, the partial pressures for water at the membrane surface are unknown and must be determined through an extensive procedure as described below. 3.3.1. Nitrogen and helium permeation The amount of helium permeating from the permeate side to the feed side of the membrane is very low. The helium permeability of 1000PEO 56PBT 44, the polymer with the highest helium permeability used in this article, is estimated to be 30 Barrer at 80 ◦ C resulting in a flow of 1.3 × 10−3 cm3 (STP)/s (0.2% of the total sweep gas stream of 0.67 cm3 /s with a pressure difference of helium between feed and permeate at 1 × 105 Pa (1 bar)). Therefore, we expect the effect of helium counter-permeation on the nitrogen and water vapor permeability to be negligible. The nitrogen permeability is determined from the amount of nitrogen present in the sweep gas as detected with the gas chromatograph, and the feed pressure of nitrogen. The flux of can be determined with Eq. (6): φv,tot FN2 A

3.3. Determination of the permeability values

JN2 =

Gas and vapor permeate through the membrane material due to a partial pressure difference between the feed and per-

where JN2 is the flux of nitrogen (cm3 (STP)/(cm2 s)), φv,tot the volume flow of the sweep gas (cm3 (STP)/s), FN2 the volume fraction of nitrogen present in the sweep gas, and A the effective membrane area (cm2 ). The nitrogen permeability is determined by using Eq. (5), where pi,feed is the nitrogen pressure in the feed (cmHg) and pi,permeate the amount of nitrogen in the sweep. The latter partial pressure is negligible compared to the nitrogen pressure in the feed (pfeed = 2–5 × 105 Pa (2–5 bar), ppermeate = 1 × 10−1 –3 × 10−2 Pa (1 × 10−4 –3 × 10−3 bar)).

Fig. 5. Schematic representation of the permeation cell.

(6)

3.3.2. Water vapor permeation The partial pressures of water vapor on the feed and permeate side of the material are obtained from the dew-point temperature of water vapor which are measured with dewpointing mirrors. These sensors detect the temperature at which water vapor condenses on a cooled mirror surface. This temperature relates to the water vapor pressure in the bulk gas mixture. Various relations can be used to relate the dew-point temperature with a water vapor pressure. An ex-

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(cm), pH2 O,feed and pH2 O,perm are the water vapor pressure on the feed and permeate side of the membrane, respectively. A mass balance can be made over a small part of the permeate with a thickness dr:     pH2 O,perm pH2 O,perm Φv,perm  − Φv,perm  Ptot Ptot r+dr r P + r dr (pH2 O,feed − pH2 O,perm ) = 0 l Fig. 6. Plug flow behavior at the permeate side of the membrane.

ample is the Antoine equation, which relates the water vapor pressure with the measured dew-point temperature [23]: log10 (pH2 O ) = 5.11564 −

1687.537 Tdew + 230.17

(7)

where pH2 O is the water vapor pressure (bar) and Tdew the dew-point temperature (◦ C). The water vapor flux permeating through the membrane can be determined from the vapor pressure and the flow rate of the sweep gas: JH2 O =

φv,tot pH2 O Vm γ RTA

(8)

where JH2 O is the water vapor flux (cm3 (STP)/(cm2 s)), φv,tot the flow rate of sweep gas (m3 /s) containing water vapor, pH2 O the water vapor pressure in the permeate stream (Pa), R the gas constant (8.314 J/(mol K)), T the temperature (K), A the membrane area (cm2 ), Vm the volume of 1 mol penetrant at standard temperature and pressure (22,414 cm3 /mol) and γ the activity coefficient. The latter one is considered to equal unity (γ = 1), because the sweep gas comprises mainly of helium at 1 × 105 Pa (1 bar) and behaves as an ideal gas mixture. For the determination of the permeability (Eq. (5)), one may assume that the feed and permeate are ideally mixed: the concentration of water vapor of the gas stream leaving the membrane cell equals the concentration at any position at permeate side of the membrane. This assumption holds for the feed side because the water vapor concentration remains nearly constant: the flow of water vapor through the membrane is negligibly small compared to the total feed flow. However for our cell, the flow pattern on the permeate side should rather be considered plug flow. This influences the driving force in Eq. (5) and a new relation has to be derived. The derivation of such a relation is schematically depicted in Fig. 6, assuming that the concentration of water vapor in the feed gas mixture remains constant. The amount of water vapor permeating through a ring with a thickness dr is P N = 2πr dr (pH2 O,feed − pH2 O,perm ) l

(9)

where N is the flow of water vapor through the membrane with an area of r dr (cm3 (STP)/s), r the radius of the cell

(10)

where Ptot is the total pressure at the permeate side of the membrane, pH2 O,perm /Ptot the fraction of water vapor in the permeate stream, and φv,perm the flow rate of the sweep gas in the permeate. This results in  pH O,perm =0 2 dpH2 O,perm (p H2 O,feed − pH2 O,perm ) pH2 O,perm =pH2 O,perm  r=rcell −Ptot 2πrP = dr (11) φv l r=0 where the water vapor concentration in the sweep gas entering the permeation cell at r = rcell is 0 (dry sweep gas) and pH2 O,perm the water vapor pressure in the sweep gas leaving the permeation cell at r = 0, which is measured with the dew-pointing mirror. Solving P/l from Eq. (11) results in φv ln(pH2 O,feed /(pH2 O,feed − pH2 O,perm )) P = l Ptot Acell

(12)

Combining Eq. (5) with Eq. (8) and using a logarithmic pressure difference results also in Eq. (12). 3.4. Materials and chemicals Bisphenol A polysulfone (PSf), type Udel® P3500 was obtained from Amoco Chemicals (Belgium), and ethyl cellulose (ethoxyl content 49%) was obtained from Acros. Chloroform (CHCl3 ), tetrahydrofuran (THF), dichloromethane (CH2 Cl2 ) and trifluoroacetic acid (TFA) were purchased from Merck (analytical grade) and used as solvents. For the gas permeation experiments, nitrogen (N2 ) and helium (He) were purchased from Hoekloos b.v. (The Netherlands). All the gases have a purity greater than 99.9%. Gas mixtures of helium and nitrogen (1000, 1500 and 2500 ppm), for the calibration of the thermal conductive detector (TCD) of the gas chromatograph (GC) were obtained from Praxair n.v. (Belgium). 3.5. PEO-PBT block copolymers PEO-PBT block copolymers were obtained from ISOTIS b.v. (The Netherlands) and were used without further purification. Fig. 7 shows the schematic structure of the PEO-PBT block copolymers. These multi-block copolymers consist of two segments: a hard hydrophobic rigid crystalline PBT segment (x) and a soft hydrophilic amorphous rubbery PEO segment (y). The following notation classifies the various block copolymers: mPEO yPBT x, where m is the molecular weight

S.J. Metz et al. / Journal of Membrane Science 251 (2005) 29–41

35

Fig. 7. Structure of PEO-PBT block copolymers.

of the PEO segment and y and x are the weight percentages of PEO and PBT phases, respectively. The PEO-PBT block copolymer used in this study is 1000PEO 56PBT 44. 3.6. Film preparation Polymeric solutions (5–15 wt.%) were prepared by dissolving1000PEO 56PBT 44 in CHCl3 , PSf in THF, and ethyl cellulose and polysulfone in CH2 Cl2 . Thin films with a thickness ranging from 30 to 300 ␮m were prepared by solution casting on a glass plate. The cast films were dried in a nitrogen atmosphere at room temperature for 24 h. The homogeneous dense films were removed from the glass plate with the help of a small amount of water and were further dried and stored in a vacuum oven at 30 ◦ C.

4. Results and discussion 4.1. Boundary layer resistance In the permeation equipment, the overall flux of water vapor is measured and normalized for the membrane thickness and the driving force (Eq. (5)) resulting in an apparent permeability. It must be called apparent, since it may also contain the transport resistance of the potential boundary layers on the feed and permeate side of the membrane. These resistances and their contribution to the overall transport rate are discussed in the following paragraphs. 4.1.1. Feed-side boundary layer resistance Fig. 8 illustrates an effect of the feed-side boundary layer on the apparent water vapor permeability for a highly permeable PEO-PBT block copolymer (1000PEO 56PBT 44) with a thickness of 106, 174 and 295 ␮m at feed flow rates ranging between 5 and 28 cm3 /s. If only the membrane resistance determines transport of water, one would expect a single “apparent permeability” value. However, Fig. 8 suggests an increasing permeability with increasing thickness and feed flow rate. This is only possible if the overall water vapor transport resistance comprises several resistances, only one of them being the membrane resistance. Also, the apparent water vapor permeability increases with an increase of feed flow rate. This increase may stem from: (1) significant depletion of the water content in the feed gas mixture at low feed flow rates or (2) concentration polarization on the feed side of the membrane. Depletion of the feed gas mixture occurs at low feed flow rates and high trans-membrane fluxes: the amount of water vapor permeating through the membrane lowers the concen-

tration of water vapor in the bulk phase above the membrane reducing the effective driving force at the feed side. An increase in feed flow rate compensates for the water removal, thereby keeping a high driving force, but it would cause the apparent permeability to decrease. At the chosen experimental conditions, the water vapor flux through the membrane is small compared to the amount of water vapor flowing over the membrane (low stage cut). The effect of stage cut results in a 4% lower partial pressure of water at the feed side of the membrane with a thickness of 106 ␮m for a flow rate of 5 cm3 /s compared to a flow rate of 27 cm3 /s. The experimentally found increase in permeability of 20% indicates a decrease in the overall transport resistance rather than the effect of stage-cut. The increase in permeability with feed flow rate must be attributed to concentration polarization and an increased mass transfer coefficient at higher flow rates. The stagnant feed boundary layer influences the apparent water vapor permeability, even for very thick membranes (295 ␮m) where the water permeability increases slightly at elevated feed flow rates. Fig. 8 also shows the mixed gas nitrogen permeability at feed flow rates between 5 and 28 cm3 /s. The nitrogen permeability remains constant with increasing feed flow rate and is equal to the nitrogen permeability determined for pure gas permeation (open circle). A constant-nitrogen-permeability indicates that the presence of a stagnant boundary layer for water vapor does not affect the nitrogen permeability. This is to be expected since a change in partial nitrogen pressure at the membrane/gas interface, due to less concentration polarization, is negligibly small compared to its absolute value.

Fig. 8. Apparent water vapor and N2 permeabilities of 1000PEO 56PBT 44 at various feed flow rates and film thickness (activity 0.41, φv,permeate 0.67 cm3 /s, temperature 50 ◦ C, pfeed = 3.5 × 105 Pa (3.5 bar)).

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Fig. 9. Overall mass transfer coefficient (kov ) as a function of the feed flow rate. The dotted lines at a feed flow rate of 45 cm3 /s represents the mass transfer coefficient of the membrane and permeate. The feed-side mass transfer coefficient at various feed flow rates is calculated from the difference between the mass transfer coefficients at 45 cm3 /s and the measured mass transfer coefficient, as is shown by the formula.

An estimate of the feed-side boundary layer mass transfer coefficient can be obtained by plotting the overall mass transfer coefficient as a function of the feed flow rate (Fig. 9). The overall mass transfer coefficient is determined from the flux of water vapor through the membrane (Eq. (8)) and a logarithmic concentration difference as follows: kov =

J H2 O cp ln((Cf − Cp )/Cf )

(13)

where Cf is the concentration of water vapor on the feed side of the membrane (mol/m3 ) and Cp the concentration of water vapor in the sweep gas stream leaving the membrane cell. Eq. (13) assumes that the concentration of the feed gas stream entering the cell equals the concentration of water vapor leaving the cell. The overall mass transfer coefficients shown in Fig. 9 do not increase significantly with feed flow rate greater than 18 cm3 /s. At these high feed flow rates, the contribution of the stagnant feed-side boundary layer is small compared to the overall resistance. The feed-side mass transfer coefficient at various feed flow rates can be determined by subtracting the mass transfer coefficient at infinite feed flow rate from the overall mass transfer coefficient (Eq. (1)). The mass transfer coefficient extrapolated to high feed flow rates (45 cm3 /s) represents the mass transfer coefficient of the membrane and the permeate boundary layer (km + kp ). Fig. 10 shows the feed-side mass transfer coefficient determined at various feed flow rates from the overall mass transfer coefficient in Fig. 9. The feed-side mass transfer coefficient increases linearly with an increase of feed flow rate and is equal for the membranes regardless of the membrane thickness. The relative contribution from the feedside resistance (1/kf ) for the membranes shown in Fig. 9 is listed in Table 2. The contribution from the feed-side bound-

Fig. 10. Mass transfer coefficient on the feed side of the membrane: () 106 ␮m, (♦) 174 ␮m, () 295 ␮m. Table 2 Relative contribution (%) from the feed-side resistance to the overall resistance Feed flow rate (cm3 /s)

Membrane thickness 106 (␮m)

174 (␮m)

295 (␮m)

5 10 18

14.6 2.8 1.5

10.0 2.1 1.2

3.5 1.5 0.8

ary layer is negligible for high feed flow rates (>10 cm3 /s) and thick polymeric films (>100 ␮m) at 3.5 × 105 Pa (3.5 bar) feed pressure. All further experiments were performed with polymeric films with a thickness >100 ␮m and feed flow rates >10 cm3 /s. 4.1.2. Permeate-side boundary layer resistance The permeate flow rate of the sweep gas is also varied to demonstrate concentration polarization effects on the permeate side of the membrane. Fig. 11 shows the apparent water vapor permeability of 1000PEO 56PBT 44 at 30 and 50 ◦ C assuming that the permeate is ideally mixed (open symbols calculated with Eq. (5)) or when the sweep gas flow pattern is plug flow (closed symbols calculated with Eq. (12)). The apparent water vapor permeability decreases at 30 ◦ C with an increase of permeate flow rate assuming an ideally mixed permeate. This decrease contradicts the expectation that the resistance decreases with increasing permeate flow rate. Probably, the assumption of ideal mixing on the permeate side of the membrane is not valid stemming from an erroneous estimation of the permeate pressure. Assuming that the flow pattern is plug flow, the apparent permeability increases with an increase of permeate flow rate, as one expects in the presence of a stagnant permeate boundary layer. The apparent water vapor permeability increases at 50 ◦ C for both calculation methods and the difference between the estimation methods is smaller. The fact that both methods predict the same trends at 50 ◦ C stems probably from a larger partial pressure difference over the membrane; when the partial

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37

Table 3 Feed and permeate pressure at 30 and 50 ◦ C 1000PEO 56PBT 44 30 ◦ C 1000PEO 56PBT 44 (50 ␮m)

50 ◦ C 1000PEO 56PBT 44 (112 ␮m)

φv,perm (cm3 /s)

pfeed (cmHg)

pperm (cmHg)

φv,perm (cm3 /s)

pfeed (cmHg)

pperm (cmHg)

0.71 0.80 1.39 1.85 3.17

1.64 1.68 1.72 1.68 1.63

0.96 0.96 0.71 0.54 0.34

0.67 0.91 1.18 1.43

3.19 3.19 3.19 3.19

1.09 0.88 0.74 0.64

pressure difference is small (e.g. at 30 ◦ C, Table 3) a deviation in the permeate pressure will have a large effect on the permeability. These deviations will be smaller when the partial pressure difference is larger, e.g. at 50 ◦ C. From Fig. 11 it is clear that also a stagnant permeate boundary layer influences the transport rate significantly. The sweep gas flow rate cannot be increased infinitely because otherwise the permeate vapor pressure is too small for experimental quantification giving rise to experimental errors. An estimate of the stagnant permeate boundary layer on the total permeability can be determined by plotting the overall resistance for various films versus their thickness, as discussed in the next section. 4.1.3. Membrane resistance Now that the presence of feed- and permeate-side boundary layers is identified and the magnitude of the feed-side resistance is quantified, we proceed with a description of extracting the magnitude of the intrinsic membrane resistance. The membrane resistance for water vapor transport can be determined by plotting the overall transport resistance as a function of membrane thickness as shown in Fig. 12. Fig. 12 shows that the transport resistance increases linearly with membrane thickness and crosses the y-axis at 2000, indicating that the transport resistance is not only located in the mem-

Fig. 12. Overall mass transfer resistance for various film thickness (1000PEO 56PBT 44, φv,feed 10 cm3 /s, φv,permeate 0.67 cm3 /s, pressure 3.5 × 105 Pa (3.5 bar), activity 0.34 and temperature 80 ◦ C).

brane but resistances on the permeate side of the membrane contribute to the total membrane resistance as well. These resistances originate from a stagnant permeate boundary layer and resistances in the support material on the permeate side of the membrane, as discussed in Section 4.1.2. (The feed flow rate is kept at sufficient high flow rates in order to minimize the contribution from the stagnant feed boundary layer). This procedure is repeated at 30, 50, and 80 ◦ C to quantify the stagnant boundary layer resistance at different temperatures. The results are summarized in Table 4. We take the boundary layer resistance as a specific characteristic for the measurement cell at the specific permeate flow rate. The membrane permeability can be determined as follows: (1) the overall mass transfer coefficient is determined as specified in Section 4.1. (2) The two boundary layer resistances (1/kb and 1/kf ) are subtracted from the overall resistance (1/kov ) resulting in the membrane mass transfer coefficient (km , Eq. (2)). (3) From the water vapor flux through the membrane and the mass transfer coefficient (km ) it is possible Table 4 Resistances in the stagnant boundary layers at 30, 50 and 80 ◦ C

Fig. 11. Apparent water vapor permeability of 1000PEO 56PBT 44 at 30 and 50 ◦ C for various permeate flow rates. Open symbols represent values calculated with Eq. (5) and closed symbols represent values calculated with Eq. (12).

Temperature (◦ C)

Resistance (1/kov ) (s/m)

30 50 80

1800 2000 2000

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S.J. Metz et al. / Journal of Membrane Science 251 (2005) 29–41

to calculate the effective driving force over the membrane: (CH2 O,membrane,feed − CH2 O,membrane,permeate ) =

JH2 O km

(14)

where JH2 O is the flux of water vapor through the material determined with Eq. (8) and CH2 O,feed and CH2 O,permeate are the effective concentration of water vapor in the feed and permeate stream, respectively. (4) These concentrations can be converted to an effective water vapor pressure. (5) The permeability of the material can now be calculated from the flux, normalized for effective partial pressure difference over the membrane and the thickness. 4.2. Validation of permeability values Experiments are performed with ethyl cellulose (at 25 ◦ C) and polysulfone (at 40 ◦ C) to validate the methodology described above. The obtained experimental results are compared with literature data in Fig. 13 as a function of the water vapor activity. The closed symbols represent literature data and the open symbols represent measured values with the equipment shown in Fig. 4. The measured water vapor permeability is corrected for the presence of stagnant boundary layers. The measured values, which differ one order of magnitude, are in good agreement with literature data, indicating that the experimental set-up and the analysis method give reliable results. The relative contribution of the correction term for the stagnant boundary layer to the overall resistance calculated for a film thickness of 100 ␮m amounts to 15% for ethyl cellulose and 3% for polysulfone at activity 0.5. Using thick films minimizes the influence of the stagnant boundary layer on the total permeability. The measured nitrogen permeability of polysulfone (at 40 ◦ C) and ethyl cellulose is in good agreement with literature values (e.g. polysulfone: literature:

Fig. 13. Water vapor permeabilities of ethyl cellulose at 25 ◦ C and polysulfone films at 40 ◦ C; open symbols represent measured values and closed symbols represent literature data. Literature data: ethyl cellulose 25 ◦ C; (䊉) Wellon and Stannet [24]; polysulfone 40 ◦ C, () Schult and Paul [15]; () Swinyard et al. [25].

PN2 = 0.25 Barrer at 35 ◦ C [5], measured: PN2 = 0.26 Barrer at 40 ◦ C). This also indicates that the nitrogen permeability in polysulfone and ethyl cellulose is not affected by the presence of water vapor.

4.3. Permeability and selectivity of PEO-PBT block copolymers PEO-PBT block copolymers are investigated for their water vapor permeability, since the PEO block shows a high solubility for water [26] enhancing the high water vapor permeability. The high solubility of the block copolymer stems from a high solubility of water vapor in the PEO block. PEO itself as a pure polymer is soluble in water [27], but the addition of a PBT segment in the block copolymer makes the block copolymer insoluble in water, but still enables a high solubility of water vapor in the PEO phase. Fig. 14 shows the corrected (open symbols) and uncorrected (closed symbols) water vapor permeability of 1000PEO 56PBT 44 at 30 ◦ C, versus the water vapor activity. The water vapor permeability at 30 ◦ C increases with an increase in activity stemming from a higher solubility of water vapor at higher activities [26]. The relative contribution of the correction term for the stagnant boundary layer to the overall resistance calculated for a PEO-PBT block copolymer amounts to 55% at an activity of 0.3 and increase to 70% at activity 0.85. This relative higher boundary layer resistance at higher activities originates from a higher water vapor permeability (lower resistance) of the PEO-PBT block copolymer. The boundary layer contribution is much higher for 1000PEO 56PBT 44 than for ethyl cellulose and polysulfone due to the higher water vapor permeability of 1000PEO 56PBT 44.

Fig. 14. Water vapor and mixed gas N2 permeability of 1000PEO 56PBT 44 at 30 ◦ C. φv,feed 10 cm3 /s, φv,permeate 0.67 cm3 /s, pressure 3.5 × 105 Pa (3.5 bar), film thickness 112 ␮m. () measured water vapor permeability without the correction of a stagnant boundary layer, () water vapor permeability corrected for the presence of a stagnant boundary layer, () mixed gas N2 permeability.

S.J. Metz et al. / Journal of Membrane Science 251 (2005) 29–41

4.3.1. Mixed gas nitrogen permeability The nitrogen permeability depicted in Fig. 14 remains constant over the whole activity range and is 1.9 Barrer. It corresponds well to the pure gas nitrogen permeability. This constant mixed gas permeability of nitrogen as a function of the feed water activity is also observed for other rubbery polymers in the presence of a highly soluble penetrant, e.g. acetone/N2 in PDMS [28], ethyl benzene/N2 in PDMS [29] and n-butane/CH4 in PDMS [30]. The constant nitrogen permeability and the increasing water vapor permeability cause a strong dependence of the water vapor/nitrogen selectivity as a function of water vapor activity. This selectivity is 40,000 at activity 0.3 and increases up to about 80,000 at activity 0.84, which makes it exceptionally selective compared to other polymers [6]. The mixed gas nitrogen permeability is however very sensitive to the water vapor activity on the permeate side. The effect of water vapor activity on the permeate side on the nitrogen permeability is shown in Fig. 15. It shows two situations: one with a dry sweep gas (activity 0.2) and a wet sweep gas completely saturated with water vapor equal to the feed activity of 0.6. (The dry sweep gas has an activity of 0.2 since it contains some of the permeated water vapor). The nitrogen permeability is very close to the pure gas permeability, but it increases when the sweep gas is completely saturated with water vapor by about 50%. One may have expected that the swelling of the polymer affects the nitrogen permeability to some extent. We need to explain why there is no effect of the swelling on the feed side but on the permeate side. For the sake of simplification, we consider the nitrogen permeating through either water or PEO. The real situation must then be considered as an intermediate between the two limits of permeation through water on one hand and through non-swollen PEO on the other hand. The solubility of nitrogen in the PEO-PBT block copolymer is estimated from an analogous Pebax block copoly-

Fig. 15. Effect of permeate pressure on the N2 permeance in 1000PEO 56PBT 44 at 30 ◦ C, activity feed 0.6.

39

mer containing 57 wt.% PEO and polyamide 6. It amounts to 1.9 × 10−4 cm3 (STP)/(cm3 polymer cmHg) (at 35 ◦ C, reproduced from Bondar et al. [31]). The solubility of nitrogen in water equals 1.8 × 10−4 cm3 (STP)/(cm3 water cmHg) (at 35 ◦ C, reproduced from Janssen and Warmoeskerken [32]). The solubility of nitrogen in the polymer and in water is of the same order of magnitude. If the nitrogen permeability increases for a swollen polymer, this must be based on an increased diffusion coefficient of nitrogen. The diffusivity of nitrogen in water is estimated to be 2 × 10−9 m2 /s (estimated via the Wilke and Chang method [23]). The diffusivity of nitrogen [33] in PEO is estimated to be in the order of 5 × 10−11 m2 /s. An increase in the amount of water in the swollen membrane therefore would increase the nitrogen diffusivity and as a result increases the nitrogen permeability. However, the nitrogen permeability is insensitive to variations in the feed water vapor activity because the permeate side remains dry and the low diffusivity of nitrogen on the permeate side determines the resistance of the membrane for nitrogen. As soon as the dry permeate side of the membrane renders swollen, the nitrogen diffusivity can increase relaxing this resistance and the permeability of nitrogen can even increase by more than 50%. It is important to know this effect of water vapor activity on the permeate side, particular in cases where it is undesired to have an increase in inert gas permeation: applications such as natural gas drying frequently suffer from the loss of methane and one needs to control the water vapor activity on the permeate-side channel of a membrane module. 4.3.2. Effect of feed pressure Also, natural gas dehydration with membranes operates at feed pressures as high as 80 × 105 Pa (80 bar). It is of utmost importance to quantify the effect of feed pressure on the transport properties characteristics of polymers. The effect of the feed pressure on the apparent permeability of water vapor is depicted in Fig. 16. This figure shows the apparent water vapor and nitrogen permeability at 50 ◦ C in the pressure range of

Fig. 16. Mixed gas water vapor and nitrogen permeability as a function of the feed pressure. (water vapor activity 0.27, φv,permeate 0.67 cm3 /s, temperature 50 ◦ C).

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S.J. Metz et al. / Journal of Membrane Science 251 (2005) 29–41

The results in Figs. 16 and 17 indicate that the decrease in water vapor permeability with increasing pressure are caused by an increasing resistance at the feed boundary layer with higher pressures. They also indicate that at high feed pressures (50 × 105 Pa (50 bar)) the mass transfer resistance is mainly situated in the stagnant feed boundary layer.

5. Conclusions

Fig. 17. Experimental mass transfer coefficients of water vapor as a function of pressure: () overall mass transfer coefficient; () feed-side mass transfer coefficient in comparison to the prediction of the feed-side mass transfer coefficient, which is represented with a line and calculated with Eq. (16).

3.5 × 105 –60 × 105 Pa (3.5–60 bar). The apparent water vapor permeability decreases 5 times when the feed pressure increase from 3.5 × 105 to 60 × 105 Pa (3.5 to 60 bar), whereas the nitrogen permeability decreases only slightly. The latter decrease may stem from a compression of the polymer matrix which decreases the free volume, thereby lowering the diffusivity of nitrogen [34,35]. However, the dramatic decrease in water vapor permeability is much larger and cannot be explained by the compression of the material. This decrease is further discussed in Fig. 17, where the overall and the feedside mass transfer coefficient of water vapor are plotted as a function of the total feed pressure. The feed-side mass transfer coefficient can be estimated from a Sherwood relation (Eq. (3)) or by dividing two Sherwood relations at different pressures a and b, resulting in     ka Db ρa va ηb b ηa ρb Db c = (15) kb Da ρ b v b ηa η b ρa D a where the subscript a indicates the reference state at a feed pressure of 3.5 × 105 Pa (3.5 bar) and the subscript b indicates the variables at the applied pressure. An increase of feed pressure in our experimental set-up is accompanied by a proportional decrease in feed flow rate. However, the gas density rises proportionally with an increase in pressure (the viscosity increases only slightly with pressure [36]) causing the first term on the right-hand side in Eq. (15) to be close to unity. Also the second term remains 1, due to an increase of ρb /ρa , which is accompanied by a proportional decrease of Db /Da with pressure. This simplifies Eq. (15) to ka Db =1 kb Da

(16)

The diffusion coefficients are calculated with Eq. (4), ka is the mass transfer coefficient at 3.5 × 105 Pa (3.5 bar), being equal to 1.1 × 10−3 m/s. The result of this procedure is shown as a line in Fig. 17.

Extracting the intrinsic water vapor permeation properties from permeation experiments requires a systematic approach. The apparent permeability values are significantly affected by the presence of a stagnant boundary layer. In the permeation cell described here, the resistance is situated mainly on the permeate side of the membrane for low feed pressures. This resistance can be quantified by plotting the overall mass transfer coefficient versus the film thickness. Subtracting this resistance from the overall transport resistance results in the membrane resistance. The water vapor permeability of ethyl cellulose and polysulfone are corrected for this resistance and identical to literature values. The water vapor permeability and selectivity of 1000PEO 56PBT 44 block copolymers are high compared to other polymers and the water vapor permeability increases significantly with the water vapor activity of the feed gas mixture, whereas the nitrogen permeability remains constant. This causes a strong dependence of the water vapor nitrogen selectivity on the water vapor activity. The mixed gas nitrogen permeability increases strongly with the permeate water vapor activity indicating that the complete swelling of the membrane enhances the mixed gas nitrogen permeability. The water vapor permeability shows a strong dependence on the absolute feed pressure. An increase of the total pressure results in a larger resistance in the stagnant feed boundary layer, thereby lowering the total water vapor flux.

Acknowledgements The European Union is kindly acknowledged for supporting this project: Brite Euram III, Contract No. BRPR-CT 98-0804.

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