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Analysis of membranes used in external membrane humidification of PEM fuel cells
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 5
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Analysis of membranes used in external membrane humidification of PEM fuel cells T. Cahalan a,*, S. Rehfeldt a, M. Bauer b, M. Becker b, H. Klein a a
Institute of Plant and Process Technology, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, 85748 Garching, Germany b BMW Group, Taunusstr. 41, 80788 Munich, Germany
article info
abstract
Article history:
This paper presents experimental water vapour transfer results and model analysis, using
Received 27 January 2017
theory proposed within, of state of the art flat sheet membranes used in external mem-
Received in revised form
brane humidification of polymer electrolyte membrane (PEM) fuel cells. The membranes
24 March 2017
have been tested in an experimental set-up which simulates the dry inlet air and the highly
Accepted 31 March 2017
humidified exhaust air of a fuel cell stack. Five effects have been identified in order to fully
Available online xxx
characterise the membranes for all possible conditions that may occur in an automotive PEM fuel cell stack. These effects are the relative humidity (RH) gradient effect, pressure
Keywords:
gradient effect, temperature gradient effect, pressure effect, and temperature effect. Each
PEM Fuel Cells
effect has been tested with a varying channel Reynolds Number between approximately 80
Humidification
and 2100, therefore remaining in the laminar range. The models in this paper use a lumped
Membranes
parameter version of Fick's law of diffusion with an extra dimensionless function X, which
Diffusion
relates the partial vapour pressure of the bulk flow to the partial vapour pressure at
Boundary Layer
membrane surface, as well as the percentage of membrane area which is used due to the
Modelling
channel geometry of the membrane test module. Using this extra dimensionless function X allows a membrane specific parameter P0 to be calculated using experimental data to compare each membrane. This membrane specific parameter P0 can be applied to membranes without knowledge of all membrane properties. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Although research into the application of PEM fuel cells for automotive applications has been ongoing since the 1980's, several key challenges still remain. One of these challenges is fuel cell performance [1]. One of the main factors influencing fuel cell performance is the water content of the fuel cell membrane, as it is directly related to the proton conductivity of the membrane [2]. One method to maintain proper water
content of the fuel cell membrane is to humidify the cathode inlet air. This can be achieved by passing the cathode inlet air (dry side) and the highly humidified cathode exhaust air (wet side) through a membrane humidifier. By passing both air streams over opposite sides of a membrane, water vapour permeates through the membrane from the wet side to the dry side due to the concentration gradient present. There are many membranes available on the market and in development which have good water vapour transfer properties, and the aim of this paper is to analyse a selection of
* Corresponding author. Fax: þ49 89 289 16510. E-mail address: [email protected] (T. Cahalan). http://dx.doi.org/10.1016/j.ijhydene.2017.03.215 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Cahalan T, et al., Analysis of membranes used in external membrane humidification of PEM fuel cells, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.03.215
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these membranes. All the membranes analysed in this paper are of the dense polymeric type. For dense polymeric membranes, the well-known solution-diffusion model describes the mass transfer of the permeating substance through the membrane [3]. In terms of water vapour transfer through a membrane, the solutiondiffusion model describes how the water molecules adsorb to the surface of the membrane on the wet side, diffuse through the membrane and desorb from the surface on the dry side of the membrane. When the water molecules adsorb to the membrane, they create a water concentration on the membrane surface. The rate of adsorption of the water molecules to the membrane is a function of the solubility coefficient and the partial vapour pressure at the surface of the membrane. The rate of diffusion of water molecules through the membrane is a function of the diffusion coefficient and the gradient of water concentration between the two surfaces of the membrane. The rate of desorption is assumed to be the same as the rate of adsorption. Apart from diffusion and solubility influencing the rate of water vapour transfer through a membrane, another influencing phenomenon that occurs in gas separation is concentration polarisation. This occurs when the water vapour transfer through the membrane is greater than the water vapour transfer through the boundary layer. Concentration polarisation leads to a decrease in the available driving force of the preferentially permeating species across the membrane and an increase for the less permeable species [4]. There is a very limited amount of publications which consider the boundary layer resistance to be a limiting factor in water vapour transfer through membranes, due to the common assumption that the binary diffusion of vapour in air is much greater than the diffusion through the membrane. In order to analyse the water vapour transfer properties of membranes, two approaches can be taken. The first approach is to identify each of the mechanisms which influence the water vapour transfer through a membrane, as discussed above, and measure each of them individually. Examples of test set-ups which measure diffusion only can be seen by Koester et al. [5] and by Schult and Paul [6]. Examples of test set-ups which measure solubility only can be seen by Takata et al. [7] and Stamatialis et al. [8]. Some of the authors who investigated the effect of concentration polarisation in membrane gas separation are Koester et al. [9], Bhattacharya and Hwang [4], Metz et al. [10] and Wijmans et al. [11]. The second approach is to use a mixed gas experimental set-up, which is the set-up used in this paper [12], and directly measure the mass transfer of vapour through the membrane.
Material and transport mechanisms The membranes which are analysed in this paper are divided into four different categories. Each membrane consists of a selective layer and a support structure. The membranes are categorised based on the type of polymer of their selective layer. The membrane groups are as follows: Sulfonated fluorinated polymer (SF) Sulfonated non-fluorinated polymer (SNF)
Non-sulfonated non fluorinated polymer (NSNF) Blend of sulfonated non-fluorinated polymer and nonsulfonated non-fluorinated polymer (SNF/NSNF) Some very common SF membranes are perfluorosulfonic acid polymer (PFSA) membranes such as Nafion® or Fumion® F. In order for PEM fuel cell membranes to have good proton conductivity, they must have good water transfer properties. This has been shown by Zawodzinski et al. [2] for PFSA membranes. PFSA membranes are commonly used as the membrane in a PEM fuel cell due to their high proton conductivity. Some SNF membranes are sulfonated polyetheretherketone (PEEK) based membranes, sulfonated polystyrene (PS), sulfonated polysulfone and sulfonated polyphenylene sulphides (PPS). Some NSNF membranes which are used in gas separation applications consist of polyether based block copolymers with polybutylene terephthalate (PBT), polyamide (PA) and polyurethane (PU) [10,13]. The following two sub-sections describe how sulfonation and fluorination of polymer membranes affect the water transfer mechanisms such as solubility and diffusion.
Sulfonation effects on water vapour transfer Sulfonated polymers consist of a polymer backbone with side chains ending in a charged sulfonic acid site. Polymers can be sulfonated to different degrees. The degree of sulfonation can be described by the equivalent weight (EW) of the membrane. EW can be defined as mass of dry polymer per mole of acid group when the polymer is sulfonated in the Hþ-form. The lower the EW, the higher the density of acid sites in the membrane. The mechanism behind the adsorption process of sulfonated and non-sulfonated membranes is different. With nonsulfonated polymers the water molecules can be molecularly dispersed in the polymer matrix while with a sulfonated polymer the water molecules interact with specific sites of the polymer [14]. These specific sites are the sulfonated acid sites and can adsorb various amounts of water molecules which depend strongly on the activity of the water and temperature. For water in a vapour phase, the water activity aw is defined as aw ¼
pw psat
(1)
where pw is the partial vapour pressure and psat is the saturation pressure. Zawodzinski et al. [2] have shown that each acid site can adsorb (described as water content l for sulfonated membranes given as molH2 O =molSO3 H ) up to 14 water molecules in vapour phase and up to 22 in liquid phase for Nafion®. For other sulfonated polymer membranes, Watari et al. [15] have investigated water sorption characteristics for sulfonated polyimides which have been shown to be a promising low cost replacement to Nafion®.
Fluorination effects on water vapour transfer Fluorinated polymers are polymers where trifluoromethyl (eCF3) or hexafluoroisopropylidene (6F) groups have been
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introduced to the polymer backbone [16]. Incorporating fluorine into the polymer chain increases such properties as solubility, thermal stability and glass transition temperature, while also decreasing such properties as crystallinity and water absorption. In polymers where all the CeH bonds are replaced by CeF bonds, the polymers are known as perfluoropolymers (e.g. Teflon) [16]. Nafion® is an example of a perfluoropolymer with the addition of sulfonated acid groups. As fluorine, when introduced to polymer chains in the form of eCF3 and 6F, is highly hydrophobic, the transfer of water molecules through the fluorinated polymer cannot occur without the addition of a hydrophilic polymer or acid sites. Zhao et al. [17] have shown for Nafion® that, as water molecules adsorb to the acid sites, the acid sites are pushed apart. As more water is adsorbed to the acid sites, the acid sites expand and create a hydrophilic channel which allows for diffusion of the molecules from one acid site to another.
Membrane overview A selection of nine membranes were chosen from different companies. The membrane selection comprises four different types of membranes which have been described in section Material and transport mechanisms. The membrane details can be seen in Table 1. While the structure of the nine membranes varies, all of them contain a selective layer and a support structure. The aim of most membrane suppliers is to reduce the thickness of the selective layer as this reduces the resistance for water vapour transfer across the membrane. With such a thin selective layer, a support structure is generally needed to give mechanical stability to the membrane. The variations of the membrane structures can be seen in Fig. 1. Membrane structure a shows the selective layer sandwiched between two support structures, membrane structure b shows a support structure coated on both sides by the selective layer material and membrane structure c shows the support structure coated on one side by the selective layer material.
M1 is a symmetric composite membrane made by W. L. Gore & Associates. The selective layer is a type of perfluorosulfonic acid polymer (PFSA) identified as the PFSA used in GORE-SELECT membranes. It has a thickness of approximately 10 mm. It is supported on both sides by expanded polytetrafluoroethylene (ePTFE). The membrane structure for M1 has been simplified in Fig. 1. M2 is also a symmetric composite membrane made by W. L. Gore & Associates and is similar to M1 with the only difference being the thickness of the selective layer. The selective layer thickness of M2 is 5 mm. The membrane structure for M2 has been simplified in Fig. 1. M3 is also a symmetric composite membrane made by W. L. Gore & Associates. This membrane has a different structure. It has a support structure of ePTFE and this support structure is coated on both sides by the PFSA of the GORE-SELECT membranes. The membrane structure for M3 has been simplified in Fig. 1. M4 is an asymmetric composite membrane made by FUMATECH. The selective layer is also a type of PFSA known as fumion® F, which is a trademark of FUMATECH. It has a thickness of approximately 8 mm. It is supported on one side by ePTFE. M5, as M4, is an asymmetric composite membrane made by FUMATECH with the same selective layer material and thickness and support structure material and thickness. The only difference is the equivalent weight of the PFSA polymer. M6 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a sulfonated polymer which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M7 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a blend of a sulfonated polymer and a non-sulfonated polymer which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M8 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support
Table 1 e Details of all nine membranes tested.
M1 M2 M3 M4 M5 M6 M7 M8 M9 a b c d
Company
Membrane name
Membrane structurea
Selective layer material
Selective layer thickness
Goreb Goreb Goreb Fumatechc Fumatechc dPointd dPointd dPointd dPointd
Not disclosed Not disclosed M815.15 Fumapem F-920-rf Fumapem F-1020-rf Not Disclosed Not Disclosed MX4 Product [18] Not Disclosed
a a b c c c c c c
SF SF SF SF SF SNF SNF/NSNF NSNF NSNF
10 mm 5 mm 15 mm 8 mm 8 mm 1 mme5 1 mme5 1 mme5 1 mme5
mm mm mm mm
Support structure material ePTFE ePTFE ePTFE ePTFE ePTFE Porous Porous Porous Porous
polyolefin polyolefin polyolefin polyolefin
based based based based
Support structure thickness
Compressed DM thickness
Not disclosed Not disclosed Not disclosed 12 mm 12 mm 32 mm 32 mm 110 mm 32 mm
Not disclosed Not disclosed Not disclosed 90 mm 90 mm 83.5 mme81.5 mm 83.5 mme81.5 mm 44.5 mme42.5 mm 83.5 mme81.5 mm
Please see Fig. 1 for membrane structure. W. L. Gore & Associates. FUMATECH. dPoint Technologies.
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outlet air (known from here on in as wet side) of a PEM fuel cell. A simplified version of the experimental set-up flow diagram can be seen in Fig. 3. A more detailed description of the set-up is given in Ref. [12].
Overview
Fig. 1 e The various membrane structures as introduced in Table 1. structure. This support structure is coated on one side with a non-fluorinated, non-sulfonated copolymer based coating which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M9 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a non-fluorinated, non-sulfonated copolymer based coating which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. Each membrane was tested with a diffusion media (DM) placed on both sides of the membrane. The DM has two functions. The first function is for mechanical support of the membrane and the second is for utilisation of the whole membrane area. This will be explained in further detail in subsection Membrane module. The DM used is a nonwoven polyester spunbond sheet with a smooth surface and thermally bonded filaments produced by Johns Manville. The area weight of the DM used is 30 g/m2, the uncompressed thickness is 150 mm and the air permeability at 200 Pa is 6000 l/(m2 s). Fig. 2 shows a microscopic view of the DM with a magnification of 200. The nonwoven polyester filaments can be clearly seen with free spaces in between.
Experimental set-up The experimental set-up simulates both the dry inlet air (known from here on in as dry side) and the highly humidified
Fig. 2 e Nonwoven structure of the DM.
The wet side is humidified by an evaporator which requires both synthetic air, 1, and liquid water, 2. Within the evaporator, 3, the liquid water is injected into the air stream and then the air stream is heated. By controlling the evaporator temperature, air mass flow, and liquid mass flow, the dew point and the dry bulb temperature of the wet side air can be controlled. Before entering the membrane module the dry bulb temperature, 4, and dew point temperature, 5, are measured. The membrane module is of a counter flow configuration. On exiting the membrane module, absolute pressure, 7, the dry bulb temperature, 8, and the dew point temperature, 9, are measured. Finally, the pressure loss, 6, through the wet side membrane module is measured. Before entering the membrane module, the dry side air stream is heated and the dry bulb air temperature, 10, is measured. The mass flow of this air stream is also controlled. On exiting the membrane module, the absolute pressure, 12, the dry bulb temperature, 13, and the dew point temperature, 14, are measured. Finally, the pressure loss, 11, through the dry side membrane module is measured. The specific humidity of the synthetic air is constant at 0.17 gw/kgair and is measured on a regular basis.
Membrane module Fig. 4 shows one flow field of the membrane module. The membrane module comprises two flow fields, which are identical apart from the sealing groove, with the membrane sandwiched in between. The membrane area that is used in this module is 27.7 cm2. Each flow field consists of 26 channels. The channel width, height and length are 1.25 mm, 1 mm and 54 mm respectively. The distance between each channel is 0.75 mm. As briefly described in section Membrane overview, one of the functions of the DM is to utilise the whole membrane area. This utilises the whole membrane area by supplying air flow to sections of the membrane in between channels, known as landings. While the use of DM is advantageous for utilisation of membrane area, it can reduce the Reynolds Number at the surface of the membrane, hence increasing the effect of the boundary layer. Fig. 5 shows a cross section of the membrane module with a membrane sandwiched between two DM. A pocket of 100 mm has been machined out of each flow field in order to provide space for the DM and membrane. When the two flow fields are sealed together, the total space left for the DM and membrane is 200 mm. This can also be seen in Fig. 5. The fixed depth of 200 mm influences the water vapour transfer through the membrane due to the variation in the DM thickness. This in turn can change the permeability and therefore change the concentration polarisation effects on each side of the membrane. For example, if the DM with an
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Fig. 3 e Simplified flow sheet of membrane humidification test stand.
Fig. 4 e One of two flow fields of the flat sheet membrane module with detail of channel geometry. uncompressed thickness of 150 mm and the thinnest membrane, M4 (20 mm), from Table 1 are used in combination, this will result in a total uncompressed thickness of 320 mm. When fitted into a sealed membrane module, each DM will decrease
to a compressed thickness of 90 mm. This will therefore decrease the permeability of the DM. Using the thickest membrane from Table 1, M8 (111 mme115 mm) the DM thickness will decrease to between 42.5 mm and 44.5 mm. All DM compressed thickness's can be seen in Table 1. Although compression of the support structures of the membranes will take place and therefore influence the water vapour transfer, these calculations are made on the assumption that no compression takes place in the support structures of the membranes. This assumption can be made due to the amount of free space in the DM as can be seen in Fig. 2. The DM will generally compress first as the support structure within the membrane has a much higher density. Compression effects have been studied both experimentally and with simulation/modelling for the gas diffusion layer (GDL) in PEM fuel cells. The GDL in fuel cells plays a similar role to that of the DM with an additional function of conducting electrons from the catalyst layer on one side to the landing area of the bipolar plate on the other side. The compression of the GDL will affect the flow distribution of the reactant gases and hence will affect fuel cell performance. For example if one area of the cathode flow field has reduced flow, this can lead to oxygen starvation and hence a decrease in cell voltage or membrane damage [19]. Flow field distribution has been studied experimentally by Haase and Mueller [20] using the differential pressure method (DPM), where the pressure drop between a reference pressure and an array of pressure sensors placed throughout the flow field at the membrane surface has been measured. This experimental approach was then validated using CFD simulation [21] which also took into account GDL intrusion into the channel. Both the experimental and simulation approach could also be applied to membrane humidification to examine the compression effect of the DM. The compression effect of the DM will be studied further in ongoing research.
Theory of water vapour transfer Fig. 5 e Cross section of membrane module showing two channels on each flow field, the two diffusion media and the membrane.
In order to calculate the molar flux of vapour J through a membrane per unit area, the following well-known permeation equation, Equation (2), can be used [22].
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Fig. 6 e Segmented mass transfer Simulink® model.
J¼
Dw Sw psw1
psw2
l
(2)
where Dw is the diffusion coefficient of the selective layer, Sw is the solubility coefficient, psw1 and psw2 are the partial vapour pressures at the membrane surface of the wet side air stream and dry side air stream respectively, and l is the thickness of the membrane. Changing Equation (2) from a molar flux per unit area to a mass transfer, the equation can be changed to the following m_ w ¼
Dw Sw psw1 psw2 Mw A l
(3)
_ w is the water vapour transfer through the memwhere m brane, Mw is the molar mass of water vapour, and A is the area of the membrane. In some cases, due to the following unknowns, Equation (3) cannot be used to evaluate water vapour transfer properties of the membrane: The partial vapour pressures at the membrane surfaces, psw1 and psw2 , are not known as they cannot be measured in this experimental set-up. Only the bulk partial vapour pressures at each inlet and outlet of the membrane module can be calculated from the measured dew point temperatures. The variation between the bulk partial vapour pressure and the surface partial vapour pressure is due to boundary layer effects. The water vapour transfer through the area A of the membrane may not be distributed evenly. This may be due to the channel geometry shown in Figs. 3 and 4. Therefore greater water vapour transfer occurs in the membrane area directly in contact with the channels, while much smaller water vapour transfer occurs in the membrane area between the channels. Therefore, assuming all of the area of the membrane is used equally is a false assumption. There is limited theory available for the diffusion coefficient Dw and solubility coefficient Sw for some of the membranes. Even with the membranes where there is some theory available, it only applies to membranes with certain characteristics such as equivalent weight (for sulfonated polymer membranes). Also the empirical equations used in this theory have been found at certain temperatures and pressures which are not applicable to the test conditions used here. Some characteristics of the membrane are not known. Thickness may be one unknown characteristic. This may be due to the manufacturing process not being able to
guarantee a constant thickness or due to it not being disclosed by the manufacturer. Another unknown characteristic may be the exact material make-up of the membrane. Therefore, a lumped parameter model as introduced by Ref. [12], is best used to evaluate the membranes: m_ w ¼ Fm pw1 pw2 :
(4)
here Fm is a lumped parameter used to take into account all the unknowns as described above. Notwithstanding all the above, there is still a possibility to identify the effect of the boundary layer by relating the GORESELECT PFSA based membranes, M1eM3, to Nafion®. Ye and Wang [23] used a scaling factor to relate the diffusion coefficient of Nafion®, which was described by Springer et al. [24] and Yeo and Eisenberg [25], to GORE-SELECT PFSA. By using this relation, they also assumed the solubility coefficient described by Zawodzinski et al. [2] for Nafion® is also valid for GORE-SELECT PFSA. Therefore a function X can be introduced m_ w ¼ F Sw X pw1 pw2
(5)
where F combines the diffusion coefficient with the area A, the selective layer thickness l, and the molar mass of water vapour Mw as shown in Equation (6). Sw is the solubility coefficient, X is the parameter which describes the boundary layer effect and pw1 and pw2 are the bulk partial vapour pressures of the wet side and dry side respectively. F ¼ Dw
Mw A : l
(6)
X can then be expressed as a function of the Reynolds Number Re, absolute pressure p and temperature T: X ¼ c Rea1
T T0
a2 a3 p p0
(7)
where Re is the Reynolds Number of the dry side channel and c, a1, a2, and a3 are coefficients determined empirically. Even though there is a boundary layer present on both sides of the membrane, the dry side Reynolds Number can be used, as the ratio between the mass flow rates of both sides always remains the same. This is dictated by the excess oxygen ratio used in a fuel cell. The variation of the temperature T and pressure p between both sides is relatively small during testing, so therefore the mean temperature and mean pressure can be used. The reference temperature T0 and reference pressure p0 used in Equation (7) are 298 K and 101325 Pa respectively.
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The definition of permeability P is usually given as the product of the diffusion coefficient Dw and the solubility coefficient Sw. In this paper the permeability P has been introduced to combine the F coefficient and the solubility coefficient. Hence it is expressed as P ¼ F Sw :
(8)
Equations (7) and (8) are then substituted into Equation (5) giving the following equation. m_ w ¼ P c Rea1
T T0
a2 a3 p pw1 pw2 : p0
(9)
Due to the variation found in c which is shown in subsection Averaged model, Equation (9) can be further simplified by introducing a modified permeability P0 which combines the permeability P and the coefficient c: P0 ¼ c P:
(10)
Equation (9) is then defined as m_ w ¼ P0 Rea1
T T0
a2 a3 p pw1 pw2 : p0
(11)
The parameter P0 in Equation (11) can be used to evaluate all membranes. This parameter is only a function of the diffusion coefficient Dw and the solubility coefficient Sw and should only vary with changes in temperature and relative humidity. Therefore P0 should not change with the Reynolds Number as now the function X/c describes the boundary layer effect. The molar mass Mw, area A, and the membrane thickness l, are also included in P0 but are the same in all membranes tested so they will not change its value.
Modelling This section consists of three sub-sections. The first subsection describes how the coefficients c, a1, a2, and a3 required in Equation (9) were found using a segmented model with membranes where diffusion and solubility theory is available. The second sub-section explains how these coefficients were then used to find the modified permeability P0 for all membranes using an averaged model. The final subsection then shows the variation of both models with regard to experimental results.
Segmented model As previously described, some parameters of some membranes are not known, so in order to compare each membrane, a membrane specific parameter P0 was proposed in Theory of Water Vapour Transfer section. This parameter P0 is only a function of the diffusion coefficient Dw and the solubility coefficient Sw. There are other parameters included within P0 such as water vapour molar mass Mw, membrane area A and membrane thickness l. These are fixed parameters, and therefore do not influence P0 . As P0 is only a function of diffusion and solubility, it should only vary with RH and temperature as the diffusion coefficient Dw varies with membrane water content and membrane temperature. The
7
solubility coefficient Sw varies with temperature and RH (more specifically water activity aw) but the RH gradient between both sides is described using (pw1pw2), as shown in Equation (11). In order to determine the function X which is required to find P0 , a segmented MATLAB Simulink® model was used. This model uses 10 segments throughout the length of the membrane module. In other words, the membrane module is segmented in the direction of air flow. The total channel length is 5.4 cm, therefore each segment has a total length of 0.54 cm and a membrane area of 2.7 cm2. Fig. 6 shows an overview of the segmented model. To determine the number of segments used in this model, the total calculated water vapour transfer using varying numbers of segments was studied. When using less than 5 segments, significant differences between the calculated total water vapour transfer was noted. From approximately 6 segments, the water vapour transfer started to converge. Hence, 10 segments was decided upon in order to give accurate values while also using acceptable computational time. In each segment i ¼ 1 … 10 a mass balance is completed, with the water vapour transfer across the membrane for each segment calculated using Equation (9). In the membrane module, P and (pw1pw2) are known to vary through the channel length, and therefore will vary from one segment to another. P will vary due to the changing membrane water content in each segment. (pw1pw2) will also vary as the partial vapour pressure will be changing in both air streams due to vapour loss and vapour addition to the wet side and dry side respectively. This segmented model allows a different P and (pw1pw2) to be calculated in every segment which therefore _ w,1 to gives an accurate estimated water vapour transfer rate m _ w,10 for each of the segments. The sum of all water vapour m transfer rates in each segment is equal to the total water vapour transfer in the complete membrane module. m_ w;tot ¼
10 X
m_ w;i :
(12)
i¼1
In order to use Equation (9) to determine the coefficients c, a1, a2, and a3, the permeability P must be known. As Nafion® is the most studied material regarding water vapour transfer, the literature available for calculation of P was used in combination with the scaling factor for the three GORE-SELECT PFSA based membranes. The four coefficients c, a1, a2, and a3 were then found by using a tool available in Simulink®, called Simulink Design Optimization™. This tool compares the calculated water vapour transfer rates from the segmented model to the measured experimental results. The measured experimental results were that of the four most notable effects previously mentioned such as the RH gradient effect, pressure gradient effect, pressure effect and temperature effect. The tool compared 88 test points for M1 and 40 test points for both M2 and M3. By reducing the sum squared error (SSE) between the calculated and measured results to the smallest possible value, the best fitting values of c, a1, a2, and a3 were found. The coefficients for the three GORE-SELECT PFSA based membranes are shown in Table 2. The values shown in Table 2 for Equation (9) are for a Reynolds Number range from approximately 80 to 2100. The
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Table 2 e Fitted values of c, a1, a2, and a3 for all three GORE-SELECT PFSA based membranes.
M1 M2 M3
c
a1
a2
a3
0.0111 0.0047 0.0189
0.3210 0.3657 0.3220
8.0155 8.8809 8.3753
0.8917 1.0901 1.0334
A note of caution for the coefficient values presented in this paper must be given. The coefficients describe the boundary layer effect on the water vapour transfer across the membrane with a specific DM and membrane module geometry. Any variation in the DM and membrane module may change the coefficients.
Averaged model Reynolds Number coefficient a1 for this Reynolds Number range was averaged to be 0.33, the temperature coefficient a2 was averaged to be 8.42 and finally the pressure coefficient a3 was averaged to be 1.0. However, due to the large variation in the coefficient c, it was considered to be membrane specific and hence incorporated with P to give P0 as shown in Equation (10). Therefore, the three coefficients a1, a2, and a3 describe the boundary layer effect, which is only a function of the DM and the membrane module geometry, which are constant for all membranes, and therefore can be applied to all 9 membranes tested. However, using a Reynolds Number coefficient of 0.33, a constant value for P0 as a function of Reynolds Number was not found. Fig. 7 shows the variation of P’ as a function of Reynolds Number using a1 ¼ 0.54 and a1 ¼ 0.33. The best results were found using a Reynolds Number range between approximately 990 and 2100 where a1 ¼ 0.54. In this range the calculated results using the model were accurate, with little variation in P0 as a function of Reynolds Number. It should be noted that a Reynolds Number coefficient of 0.33 over the whole Reynolds Number range can give reasonably accurate water vapour transfer results, however it is necessary to be aware that at some Reynolds Numbers the error can be rather large. The same method as described above was used to find the Reynolds Number coefficient for this Reynolds Number range between approximately 990 and 2100. The pressure and temperature coefficients were fixed at 8.42 and 1.0 respectively. The new Reynolds Number coefficient for the three GORESELECT PFSA based membranes are shown in Table 3. The Reynolds Number coefficient was averaged to be 0.54.
As the function X has been determined for the Reynolds Number range from 990 to 2100, P0 was calculated for all membranes, M1eM9, using experimental results. This has been done by replacing (pw1pw2) with Dpw,log in Equation (11) and is shown as follows: a2 a3 T p Dpw;log : (13) m_ w;tot ¼ P0 Rea1 T0 p0 Dpw,log is defined as Dpw;log ¼
dry out
in pwet pw w
ln
dry in out pwet pw w :
in pdry out w out pdry in pwet w w
pwet w
By rearranging Equation (13), P0 can be calculated for all membranes: P0 ¼
Rea1
m_ w;tot a2 a3 : p T Dpw;log p0 T0
(15)
_ w,tot was from experiThe water vapour transfer rate m mental results and the coefficients a1, a2, and a3 in the function X were those determined in sub-section Segmented model. According to Fig. 6, Dpw,log was calculated using partial vapour pressures at the inlets and outlets which were calculated using the measured dew point temperatures in the experimental setup.
Validation of the models In order to validate the models, a root mean square error (RMSE) as seen in Equation (16) between the models and experimental results was calculated. Validation of the models was completed on four of the most notable effects therefore leaving out the temperature gradient effect. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Pn _ _ 1 mw;exp mw;mod : RMSE ¼ n
Fig. 7 e Variation of P0 as a function of Reynolds Number using a1 ¼ 0.54 and a1 ¼ 0.33.
(14)
(16)
Both the averaged model and segmented model used the Reynolds Number coefficient a1 of 0.54 for a Reynolds Number range between 990 and 2100. They also used a temperature coefficient a2 of 8.42 and the pressure coefficient a3 of 1.0. The only difference between the averaged model and segmented model was the P0 that was used. For the averaged model, P0 was that calculated from experimental data using Equation (15). This averaged model was applied to all membranes. For the segmented model, P0 as shown in Equation (10) was used where P was calculated using the theory available and c was taken from Table 2. This segmented model was only applied to membranes M1 to M3, where theory is available to calculate P as it is a function of membrane temperature and water content.
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Fig. 8 e Variation of water vapour transfer rates between the models, averaged and segmented, and experimental for membrane M1. Solid lines are used to guide the eye.
Fig. 8 shows the variation of water vapour transfer rates per meter squared of membrane area between model and experimental results for four of the most notable effects for membrane M1, namely, the RH gradient effect, pressure gradient effect, pressure effect and temperature effect. For each effect, the channel Reynolds Number was varied from approximately 990 to 2100. Fig. 9 shows the RMSE for the four most notable effects and the average RMSE for all test points completed for M1. For the averaged model both the RH gradient effect and temperature effect are below average and regarding the segmented model, all effects except for the RH gradient are below average. The RMSE for the segmented model is approximately 1.5 times
Table 3 e Recalculated values of a1 for all three GORESELECT PFSA based membranes for a Reynolds Number range between 990 and 2100. a1 M1 M2 M3
0.5398 0.5665 0.5241
greater than it is for the averaged model. This could be due to the P0 used in the segmented model being from theory and P0 in the averaged model being calculated from experimental results. Fig. 10 shows the RMSE of all test points using the averaged model for all membranes. With an average RMSE of 0.1175 g/(s m2) for all membranes, it can be concluded that the modified permeability P’ is an accurate parameter to use to model water vapour transfer in the membrane module shown in sub-section Membrane module.
Results and discussion The results and discussion section is divided into two different sub-sections. The first sub-section shows the experimental results of water vapour transfer for the above described membranes and compares and contrasts the above effects which have been explained in detail in Ref. [12]. The second sub-section shows the calculated modified permeability P0 , which was used in the averaged model for all membranes for a Reynolds Number range between 990 and 2100.
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Fig. 9 e Root mean square error between models and experimental results for membrane M1.
Water vapour transfer Fig. 11 shows the water vapour transfer results per meter squared of membrane area for membrane M1 and membrane M2. The results for M1 have been previously published [12] but are shown again in order to show result trends. The number of test points for M2 have been decreased and slightly changed to increase experimental efficiency. For example, the pressure gradient effect was increased to 500 mbar for M2 as no conclusions could be made from the results of M1 using a pressure gradient of up to 300 mbar. Also, no further testing was done regarding the temperature gradient due to the same reason. Fig. 11 shows the water vapour transfer for all five effects that have been tested. For each effect, the channel Reynolds Number is varied from approximately 80 to 2100. The first effect shown in Fig. 11a is the RH gradient effect. In this effect the temperature and absolute pressure of both air streams were maintained at 350 K and 2.5 bar respectively. Four different levels of the wet side RH were measured, namely 95%, 85%, 75%, and 65%, while the dry side RH was close to 0%.
Fig. 10 e Root mean square error between the averaged model and experimental water vapour transfer rates for all membranes.
The second effect shown in Fig. 11b is the pressure gradient effect where a pressure gradient was introduced between the two air streams. Both air streams were maintained at a temperature of 350 K. The wet side RH was maintained at 95%. In this test the dry side absolute pressure was either equal to, or greater than the wet side. The third effect shown in Fig. 11c is the temperature gradient effect where a temperature gradient was introduced between the two air streams. Both air streams were maintained at a temperature of 2.5 bar. The wet side RH was maintained at 95%. In this test the dry side temperature was either equal to, or less than the wet side. The fourth effect shown in Fig. 11d is the pressure effect where the absolute pressure of both sides varies. There was no pressure gradient present here. The temperatures of both air streams were maintained at 350 K and the wet side RH was maintained at 85%. The reason for maintaining the wet side RH at 85% and not 95% is due to test stand limitations at high mass flow rates and low pressure. The final effect shown in Fig. 11e is the temperature effect, where the temperature of both sides varies. There was no temperature gradient present here. The absolute pressure of both air streams was maintained at 2.5 bar and the wet side RH was maintained at 95%. For all membranes tested, similar trends can be observed with all four effects. The trends that can be observed are as follows: An increase in water vapour transfer with an increase in the flow rate. But there is a decrease in the Water Recovery Ratio (WRR) from approximately 40% at a dry channel Reynolds Number of 80 to approximately 7% at a dry channel Re of 2100 (values for membrane M1). WRR is defined as WRR ¼
m_ w;dry out m_ w;dry in : m_ w;wet in
(17)
An increase in water vapour transfer with an increase in RH gradient. No significant change in water vapour transfer with a pressure gradient of up to 300 mbar between the two streams as shown with results from M1. When the pressure gradient is increased to 500 mbar with M2, a difference in water vapour transfer can be seen. This shows that the lower the wet side pressure and therefore pressure gradient, the higher the water vapour transfer. No significant change in water vapour transfer with a temperature gradient between the two streams. An increase in water vapour transfer with a decrease in absolute pressure. An increase in water vapour transfer with an increase in temperature As shown in Table 1, four types of membranes have been tested. Generally speaking, SF membranes are the best performing membranes for water vapour transfer due to the high solubility properties and hydrophobic backbones, but the major disadvantage to them is their cost. Fig. 12 shows five different SF membranes, all of which are PFSA type. The test
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Fig. 11 e Water vapour transfer results for M1 and M2. Solid lines are used to guide the eye.
points have been completed with a wet side RH of 95%. The temperature and absolute pressure of both the wet and dry sides are 350 K and 2.5 bar respectively. M1, M2 and M3 are made by the same company, W. L. Gore & Associates, and have the same selective layer. The main differences with these three membranes are the selective layer thickness, the total membrane thickness and the
structure. M1 and M2 have quite similar structures but the selective layer is 5 mm in M2 while it is 10 mm in M1. According to Equation (2), one would expect M2 to have double the water vapour transfer of M1 due to the selective layer thickness. As can be seen in Fig. 12 this is not the case. This shows that diffusion through the selective layer is not the controlling mechanism. There are other resistances affecting water
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Fig. 12 e Water vapour transfer results of the SF membranes. Solid lines are used to guide the eye.
vapour transfer through the membrane such as the resistances of the support layers of the membrane and the boundary layers. M4 and M5 are also made by the same company, FUMATECH, and have the same selective layer, fumion® F. These membranes differ only in EW as they have the same selective layer thickness (8 mm), membrane thickness and structure. The EW of M4 is 900 gdry polymer/molSO3 H while the EW of M5 is 1000 gdry polymer/molSO3 H . GORE-SELECT PFSA and fumion® F are both PFSA polymers but vary mainly due to the reinforcement of the PFSA. The best performing PFSA membrane cannot be extrapolated from Fig. 12, as in order to do that, membranes with the same EW, selective layer and membrane thickness and structure would have to be measured, which is not the case with the membranes compared here. All of the membranes shown in Fig. 13 are SNF/NSNF membranes. M6 and M7 contain a sulfonated polymer and a blend of a sulfonated polymer and non-sulfonated polymer in their selective layer, respectively. However they differ in
selective layer material, as explained above, but the selective layer thickness is within the same range of 1 mme5 mm. The support structure material and thickness are the same, as both of them have a porous polyolefin based support structure with a thickness of 32 mm. From Fig. 13, the change of selective layer material does not seem to have a big influence in the water vapour transfer. M8 and M9 are non-sulfonated and have the same selective layer material with the same thickness range. The support structure material is the same class of polymer, polyolefin, but the thickness of these membranes differ, as M8 has a support structure thickness of 110 mm, and M9 has a support structure thickness of 32 mm. From Fig. 13 it can be seen that the water vapour transfer is very similar for both membranes even though M9 has a support structure thickness of less than one third than the support structure of M8. From this, it appears that the support structure does not have a strong influence on the water vapour transfer. However, as explained by the membrane manufacturer, without the exact details of the selective layer thickness and the pore structure of the support layer, no informed conclusion can be reached in determining the effect of the substrate layer on water vapour transfer results. Fig. 14 shows the average water vapour transfer rate of 14 test points completed for the RH Gradient effect from a Reynolds Number range between 160 and 2100 approximately for each membrane. The 14 test points include four test points at 95%, 3 test points at 85%, 3 test points at 75% and four test points at 65%. M1 to M5 are all SF membranes. M6 and M7 are SNF and a blend of SNF/NSNF membranes respectively. M8 and M9 are NSNF membranes. It can be seen that M2 is the membrane with the highest vapour transfer, which is a SF membrane produced by W. L. Gore & Associates with a GORE-SELECT PFSA as the selective layer material and with a selective layer thickness of 5 mm. The membrane with the lowest vapour transfer is M8 which is a NSNF membrane, it should be noted that this membrane and the other membranes of dPoint Technologies are designed for lower temperature humidity transport applications. The thickness of the selective layer is between 1 mm and 5 mm.
Model results
Fig. 13 e Water vapour transfer results of the SNF/NSNF membranes. Solid lines are used to guide the eye.
Figs. 15e18 show P0 for a Reynolds Number range between 990 and 2100. Fig. 15 shows the variation of P0 with a change in wet in RH for all SF membranes. All these test points have been completed at 350 K. It shows that M2 has the highest calculated P0 of SF membranes and M4 has the lowest calculated P0 of SF membranes. At the highest wet in RH, 95%, M4 performs approximately 42% less than M2. At a wet in RH of 65%, this value increases to approximately 60%. Fig. 16 shows the variation of P0 with a change in wet in RH for all SNF/NSNF membranes. All of these test points have been completed at 350 K. It shows that M6, which is a SNF membrane, has the highest calculated P0 . M8 and M9, which are NSNF membranes, have the lowest calculated P0 . An interesting observation between M6 and M7 is that as wet in RH decreases, the difference of P0 between the two membranes increases. This shows that the sulfonated membrane
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Fig. 14 e Average water vapour transfer rate of 14 test points in the RH effect.
Fig. 17 e P0 with a change in membrane temperature for SF membranes. Solid lines are used to guide the eye.
Fig. 15 e P0 with a change in wet inlet RH for SF membranes. Solid lines are used to guide the eye.
M6 performs better than the membrane with a blend of sulfonated and non-sulfonated polymer particularly when there is a decrease in wet in RH. From Figs. 15 and 16, it can be noted that P0 increases with an increase in RH. This could be explained by the sorption coefficient which increases with water activity aw and/or partial vapour pressure pw. For SF membranes, Nafion® to be exact, Zawodzinski et al. [2] showed that the increase of water content l as a function of water activity aw is described by a third order polynomial function. For NSNF membranes, Metz et al. [26] has shown that water concentration C for a polyethylene oxide (PEO) and PBT block copolymers increases linearly at low water activities (aw<0.4) and increases exponentially at higher water activities. Fig. 17 shows the variation of P0 with a change in membrane temperature for all SF membranes. All of these tests points were completed at a wet in RH of 95%. This figure shows a decrease in P’ with an increase in membrane temperature. Fig. 18 shows the variation of P0 with a change in membrane temperature for all SNF/NSNF membranes. All of these
0
Fig. 16 e P with a change in wet inlet RH for SNF/NSNF membranes. Solid lines are used to guide the eye.
Fig. 18 e P0 with a change in membrane temperature for SNF/NSNF membranes. Solid lines are used to guide the eye.
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tests points were completed at a wet in RH of 95%. Similar to Fig. 16, M6 has the highest calculated P0 . Only one temperature, 350 K, has been studied for membranes M4, M7, M8 and M9. Diffusion coefficients increase with temperature which is described by the Arrhenius-type equation as shown by Springer et al. [24] and solubility coefficients decrease with temperature as shown by Metz et al. [26] and Azher et al. [27] due to its exothermic nature. Figs. 17 and 18 would then suggest that solubility is the controlling mechanism of the two mechanisms described by P0 . This may be due to the selective layers of the membranes being very thin.
Conclusion A range of membranes were tested, and the measured water vapour transfer rates and theoretical water vapour transfer rates from the proposed model have been presented. The membranes that have been tested range across four different categories, namely, sulfonated fluorinated polymer membranes SF, sulfonated non-fluorinated polymer membranes SNF, non-sulfonated non fluorinated polymer membranes NSNF and membranes with a blend of sulfonated nonfluorinated polymers and non-sulfonated non-fluorinated polymers SNF/NSNF. A function X was introduced in order to separate the boundary layer effects that occur in gas separation, such as concentration polarisation, from the membrane properties such as diffusion and solubility. In separating these two, a membrane specific parameter P0 was calculated using experimental results. The parameter P0 was then used to compare all membranes. The theory proposed in this paper was applied to an averaged and segmented model. The averaged model used the parameter P0 which was calculated from experimental results. This was applied to all membranes within a Reynolds Number range between 990 and 2100. The average RMSE for the water vapour transfer rate between the averaged model and experimental results for all membranes was 0.1175 g/(s m2). The segmented model used a parameter P which was calculated using the theory available. This was only applied to three membranes in the same Reynolds Number range due to the lack of necessary information on the other membranes. The average RMSE for the water vapour transfer rate between the segmented model and experimental results for membranes M1eM3 was 0.2739 g/(s m2). Even though the RMSE for the water vapour transfer rate is greater for the segmented model, two of the advantages for this model are that the partial vapour pressure profile for both sides and the water vapour transfer in each segment can be calculated. When considering the RMSE for the water vapour transfer rate of both the averaged and segmented model, the smallest vapour transfer rate measured with M1 at a Reynolds Number of 990 was 0.81 g/(s m2) and the largest vapour transfer rate measured with M1 at a Reynolds Number of 2100 was 4.94 g/(s m2). The results show that, for both the water vapour transfer rates and model results, the membranes which transfer the most vapour are sulfonated fluorinated membranes. In saying
that, there is quite a large variation in the performance of these sulfonated fluorinated membranes. This is due to the difference in the selective layer polymer and the membrane structure. The membranes which transfer the least vapour have been shown to be the non-sulfonated non-fluorinated membranes.
Acknowledgements The authors of this paper would like to thank the membrane manufacturers, W. L. Gore & Associates, FUMATECH and dPoint Technologies for providing the membrane samples and also for their feedback and additional comments regarding this paper.
List of symbols A a1 a2 a3 aw C c Dw EW F Fm J l _w m Mw n P P0 p Re sw T X
Membrane area, cm2 Reynolds Number coefficient,Temperature coefficient,Pressure coefficient,Water vapour activity,Water concentration, cm3vapour/cm3polymer Coefficient of X function,Diffusion coefficient, cm2/s Equivalent weight, gdry polymer/molSO3 H Factor, (cm3 g)/(s mol) Membrane factor, g/(s Pa) Membrane flux, mol/(s cm2) Membrane thickness, cm Water vapour mass flow rate, g/s Water vapour molecular mass, g/mol Number of test points, e Permeability, g/(s Pa) Modified permeability, g/(s Pa) Pressure, Pa Reynolds Number, e Solubility coefficient, mol/(Pa cm3) Temperature, K Boundary layer function,-
Subscripts 1 Wet side 2 Dry side exp Experimental results i Segment number log Natural log m Membrane mod Model results sat Saturation tot Total w Water vapour Superscripts s Membrane surface Greek symbols D Difference l Water content, molH2 O =molSO3 H
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[1] Wang H, Li H, Yuan Xiao-Zi. PEM fuel cell failure mode analysis. CRC Press; 2012. [2] Zawodzinski T, Neeman M, Sillerud L, Gottesfeld S. Determination of water diffusion coefficients in perfluorosulfonate ionomeric membranes. J Phys Chem 1991;95:6040. [3] Wijmans J, Baker R. The solution-diffusion model: a review. J Membr Sci 1995;107:1. [4] Bhattacharya S, Hwang S-T. Concentration polarization, separation factor, and Peclet number in membrane process. J Membr Sci 1997;132:73. [5] Koester S, Roghmans F, Wessling M. Water vapor permeance: the interplay of feed and permeate activity. J Membr Sci 2015;485:69. [6] Schult K, Paul D. Techniques for measurement of water vapor sorption and permeation in polymer films. J Appl Polym Sci 1996;61:1865. [7] Takata H, Mizuno N, Nishikawa M, Fukada S, Yoshitake M. Adsorption properties of water vapor in sulfonate perfluoropolymer membranes. Int J Hydrogen Energy 2006;32:371. [8] Stamatialis D, Wessling M, Sanopoulou M, Strathmann H, Petropoulos J. Optical vs. direct sorption and swelling measurements for the study of stiff-chain polymerpenetrant interactions. J Membr Sci 1997;130:75. € lsberg J, Lutz L, Marten D, Wessling M. On [9] Koester S, Lo individual resistances of selective skin, porous support and diffusion boundary layer in water vapor permeation. J Membr Sci 2016;507:179. [10] Metz S, van de Ven W, Potreck J, Mulder M, Wessling M. Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer membranes. J Membr Sci 2005;251:29. [11] Wijmans J, Athayde A, Daniels R, Ly J, Kamaruddin H, Pinnau I. The role of boundary layers in the removal of volatile organic compounds from water by pervaporation. J Membr Sci 1996;109:135. [12] Cahalan T, Rehfeldt S, Bauer M, Becker M, Klein H. Experimental set-up for analysis fo membranes used in external membrane humidification of PEM fuel cells. Int J Hydrogen Energy 2016;41:13666.
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[13] Lin H, Thompson S, Serbanescu-Martin A, Wijmans J, Amo K, Lokhandwala K, et al. Dehydration of natural gas using membranes. Part I: composite membranes. J Membr Sci 2012;413:70. [14] Cotugno S, Mensitieri G, Musto P, Nicolais L. Water sorption and transport in polymers. In: Proceedings of the conference on nylon and ropes for mountaineering and caving, Torino; 2002. [15] Watari T, Wang H, Kuwahara K, Tanaka K, Kita H, Okamoto K-i. Water sorption and diffusion properties of sulfonated polyimide membranes. J Membr Sci 2003;219:137. [16] Banerjee S, Mistri EA. Handbook of specialty fluorinated polymers. Elsevier; 2015. [17] Zhao Q, Majsztrik P, Benziger J. Diffusion and interfacial transport of water in nafion. J Phys Chem 2011;115:2717. [18] R. N. Huizing, „Coated membranes for enthalpy exchange and other applications“. United States of America Patent US9255744 B2, 9 February 2016. [19] Zhang G, Shen S, Guo L, Liu H. Dynamic characteristics of local current densities and temperatures in proton exchange membrane fuel cells during reactant starvations. Int J Hydrogen Energy 2012;37:1884. [20] Haase S, Mueller S. Pressure distribution method for ex-situ evaluation of flow distribution in polymer electrolyte membrane fuel cells. J Power Sources 2015;280:612. [21] Haase S, Rauber M. Ex-situ gas diffusion layer intrusion effect determination of polymer electrolyte membrane fuel cell flow fields. J Power Sources 2015;291:246. [22] George SC, Thomas S. Transport phenomena through polymeric systems. Prog Polym Sci 2001;26:985. [23] Ye X, Wang C-Y. Measurement of water transport properties through membrane-electrode assemblies I. Membranes. J Electrochem Soc 2007;154:676. [24] Springer T, Zawodzinski T, Gottesfeld S. Polymer electrolyte fuel cell model. J Electrochem Soc 1991;138:2334. [25] Yeo S, Eisenberg A. Physical properties and supermolecular structure of perfluorinated ion-containing (nafion) polymers. J Appl Polym Sci 1977;21:875. [26] Metz S, van der Vegt N, Mulder M, Wessling M. Thermodynamics of water vapor sorption in poly(ethylene oxide) poly(butylene terephthalate) block copolymers. J Phys Chem 2003;107:13629. [27] Azher H, Scholes CA, Stevens GW, Kentish SE. Water permeation and sorption properties of Nafion 115 at elevated temperatures. J Membr Sci 2014;459:104.
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Analysis of membranes used in external membrane humidification of PEM fuel cells T. Cahalan a,*, S. Rehfeldt a, M. Bauer b, M. Becker b, H. Klein a a
Institute of Plant and Process Technology, Department of Mechanical Engineering, Technical University of Munich, Boltzmannstr. 15, 85748 Garching, Germany b BMW Group, Taunusstr. 41, 80788 Munich, Germany
article info
abstract
Article history:
This paper presents experimental water vapour transfer results and model analysis, using
Received 27 January 2017
theory proposed within, of state of the art flat sheet membranes used in external mem-
Received in revised form
brane humidification of polymer electrolyte membrane (PEM) fuel cells. The membranes
24 March 2017
have been tested in an experimental set-up which simulates the dry inlet air and the highly
Accepted 31 March 2017
humidified exhaust air of a fuel cell stack. Five effects have been identified in order to fully
Available online xxx
characterise the membranes for all possible conditions that may occur in an automotive PEM fuel cell stack. These effects are the relative humidity (RH) gradient effect, pressure
Keywords:
gradient effect, temperature gradient effect, pressure effect, and temperature effect. Each
PEM Fuel Cells
effect has been tested with a varying channel Reynolds Number between approximately 80
Humidification
and 2100, therefore remaining in the laminar range. The models in this paper use a lumped
Membranes
parameter version of Fick's law of diffusion with an extra dimensionless function X, which
Diffusion
relates the partial vapour pressure of the bulk flow to the partial vapour pressure at
Boundary Layer
membrane surface, as well as the percentage of membrane area which is used due to the
Modelling
channel geometry of the membrane test module. Using this extra dimensionless function X allows a membrane specific parameter P0 to be calculated using experimental data to compare each membrane. This membrane specific parameter P0 can be applied to membranes without knowledge of all membrane properties. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Although research into the application of PEM fuel cells for automotive applications has been ongoing since the 1980's, several key challenges still remain. One of these challenges is fuel cell performance [1]. One of the main factors influencing fuel cell performance is the water content of the fuel cell membrane, as it is directly related to the proton conductivity of the membrane [2]. One method to maintain proper water
content of the fuel cell membrane is to humidify the cathode inlet air. This can be achieved by passing the cathode inlet air (dry side) and the highly humidified cathode exhaust air (wet side) through a membrane humidifier. By passing both air streams over opposite sides of a membrane, water vapour permeates through the membrane from the wet side to the dry side due to the concentration gradient present. There are many membranes available on the market and in development which have good water vapour transfer properties, and the aim of this paper is to analyse a selection of
* Corresponding author. Fax: þ49 89 289 16510. E-mail address: [email protected] (T. Cahalan). http://dx.doi.org/10.1016/j.ijhydene.2017.03.215 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Cahalan T, et al., Analysis of membranes used in external membrane humidification of PEM fuel cells, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.03.215
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these membranes. All the membranes analysed in this paper are of the dense polymeric type. For dense polymeric membranes, the well-known solution-diffusion model describes the mass transfer of the permeating substance through the membrane [3]. In terms of water vapour transfer through a membrane, the solutiondiffusion model describes how the water molecules adsorb to the surface of the membrane on the wet side, diffuse through the membrane and desorb from the surface on the dry side of the membrane. When the water molecules adsorb to the membrane, they create a water concentration on the membrane surface. The rate of adsorption of the water molecules to the membrane is a function of the solubility coefficient and the partial vapour pressure at the surface of the membrane. The rate of diffusion of water molecules through the membrane is a function of the diffusion coefficient and the gradient of water concentration between the two surfaces of the membrane. The rate of desorption is assumed to be the same as the rate of adsorption. Apart from diffusion and solubility influencing the rate of water vapour transfer through a membrane, another influencing phenomenon that occurs in gas separation is concentration polarisation. This occurs when the water vapour transfer through the membrane is greater than the water vapour transfer through the boundary layer. Concentration polarisation leads to a decrease in the available driving force of the preferentially permeating species across the membrane and an increase for the less permeable species [4]. There is a very limited amount of publications which consider the boundary layer resistance to be a limiting factor in water vapour transfer through membranes, due to the common assumption that the binary diffusion of vapour in air is much greater than the diffusion through the membrane. In order to analyse the water vapour transfer properties of membranes, two approaches can be taken. The first approach is to identify each of the mechanisms which influence the water vapour transfer through a membrane, as discussed above, and measure each of them individually. Examples of test set-ups which measure diffusion only can be seen by Koester et al. [5] and by Schult and Paul [6]. Examples of test set-ups which measure solubility only can be seen by Takata et al. [7] and Stamatialis et al. [8]. Some of the authors who investigated the effect of concentration polarisation in membrane gas separation are Koester et al. [9], Bhattacharya and Hwang [4], Metz et al. [10] and Wijmans et al. [11]. The second approach is to use a mixed gas experimental set-up, which is the set-up used in this paper [12], and directly measure the mass transfer of vapour through the membrane.
Material and transport mechanisms The membranes which are analysed in this paper are divided into four different categories. Each membrane consists of a selective layer and a support structure. The membranes are categorised based on the type of polymer of their selective layer. The membrane groups are as follows: Sulfonated fluorinated polymer (SF) Sulfonated non-fluorinated polymer (SNF)
Non-sulfonated non fluorinated polymer (NSNF) Blend of sulfonated non-fluorinated polymer and nonsulfonated non-fluorinated polymer (SNF/NSNF) Some very common SF membranes are perfluorosulfonic acid polymer (PFSA) membranes such as Nafion® or Fumion® F. In order for PEM fuel cell membranes to have good proton conductivity, they must have good water transfer properties. This has been shown by Zawodzinski et al. [2] for PFSA membranes. PFSA membranes are commonly used as the membrane in a PEM fuel cell due to their high proton conductivity. Some SNF membranes are sulfonated polyetheretherketone (PEEK) based membranes, sulfonated polystyrene (PS), sulfonated polysulfone and sulfonated polyphenylene sulphides (PPS). Some NSNF membranes which are used in gas separation applications consist of polyether based block copolymers with polybutylene terephthalate (PBT), polyamide (PA) and polyurethane (PU) [10,13]. The following two sub-sections describe how sulfonation and fluorination of polymer membranes affect the water transfer mechanisms such as solubility and diffusion.
Sulfonation effects on water vapour transfer Sulfonated polymers consist of a polymer backbone with side chains ending in a charged sulfonic acid site. Polymers can be sulfonated to different degrees. The degree of sulfonation can be described by the equivalent weight (EW) of the membrane. EW can be defined as mass of dry polymer per mole of acid group when the polymer is sulfonated in the Hþ-form. The lower the EW, the higher the density of acid sites in the membrane. The mechanism behind the adsorption process of sulfonated and non-sulfonated membranes is different. With nonsulfonated polymers the water molecules can be molecularly dispersed in the polymer matrix while with a sulfonated polymer the water molecules interact with specific sites of the polymer [14]. These specific sites are the sulfonated acid sites and can adsorb various amounts of water molecules which depend strongly on the activity of the water and temperature. For water in a vapour phase, the water activity aw is defined as aw ¼
pw psat
(1)
where pw is the partial vapour pressure and psat is the saturation pressure. Zawodzinski et al. [2] have shown that each acid site can adsorb (described as water content l for sulfonated membranes given as molH2 O =molSO3 H ) up to 14 water molecules in vapour phase and up to 22 in liquid phase for Nafion®. For other sulfonated polymer membranes, Watari et al. [15] have investigated water sorption characteristics for sulfonated polyimides which have been shown to be a promising low cost replacement to Nafion®.
Fluorination effects on water vapour transfer Fluorinated polymers are polymers where trifluoromethyl (eCF3) or hexafluoroisopropylidene (6F) groups have been
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introduced to the polymer backbone [16]. Incorporating fluorine into the polymer chain increases such properties as solubility, thermal stability and glass transition temperature, while also decreasing such properties as crystallinity and water absorption. In polymers where all the CeH bonds are replaced by CeF bonds, the polymers are known as perfluoropolymers (e.g. Teflon) [16]. Nafion® is an example of a perfluoropolymer with the addition of sulfonated acid groups. As fluorine, when introduced to polymer chains in the form of eCF3 and 6F, is highly hydrophobic, the transfer of water molecules through the fluorinated polymer cannot occur without the addition of a hydrophilic polymer or acid sites. Zhao et al. [17] have shown for Nafion® that, as water molecules adsorb to the acid sites, the acid sites are pushed apart. As more water is adsorbed to the acid sites, the acid sites expand and create a hydrophilic channel which allows for diffusion of the molecules from one acid site to another.
Membrane overview A selection of nine membranes were chosen from different companies. The membrane selection comprises four different types of membranes which have been described in section Material and transport mechanisms. The membrane details can be seen in Table 1. While the structure of the nine membranes varies, all of them contain a selective layer and a support structure. The aim of most membrane suppliers is to reduce the thickness of the selective layer as this reduces the resistance for water vapour transfer across the membrane. With such a thin selective layer, a support structure is generally needed to give mechanical stability to the membrane. The variations of the membrane structures can be seen in Fig. 1. Membrane structure a shows the selective layer sandwiched between two support structures, membrane structure b shows a support structure coated on both sides by the selective layer material and membrane structure c shows the support structure coated on one side by the selective layer material.
M1 is a symmetric composite membrane made by W. L. Gore & Associates. The selective layer is a type of perfluorosulfonic acid polymer (PFSA) identified as the PFSA used in GORE-SELECT membranes. It has a thickness of approximately 10 mm. It is supported on both sides by expanded polytetrafluoroethylene (ePTFE). The membrane structure for M1 has been simplified in Fig. 1. M2 is also a symmetric composite membrane made by W. L. Gore & Associates and is similar to M1 with the only difference being the thickness of the selective layer. The selective layer thickness of M2 is 5 mm. The membrane structure for M2 has been simplified in Fig. 1. M3 is also a symmetric composite membrane made by W. L. Gore & Associates. This membrane has a different structure. It has a support structure of ePTFE and this support structure is coated on both sides by the PFSA of the GORE-SELECT membranes. The membrane structure for M3 has been simplified in Fig. 1. M4 is an asymmetric composite membrane made by FUMATECH. The selective layer is also a type of PFSA known as fumion® F, which is a trademark of FUMATECH. It has a thickness of approximately 8 mm. It is supported on one side by ePTFE. M5, as M4, is an asymmetric composite membrane made by FUMATECH with the same selective layer material and thickness and support structure material and thickness. The only difference is the equivalent weight of the PFSA polymer. M6 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a sulfonated polymer which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M7 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a blend of a sulfonated polymer and a non-sulfonated polymer which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M8 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support
Table 1 e Details of all nine membranes tested.
M1 M2 M3 M4 M5 M6 M7 M8 M9 a b c d
Company
Membrane name
Membrane structurea
Selective layer material
Selective layer thickness
Goreb Goreb Goreb Fumatechc Fumatechc dPointd dPointd dPointd dPointd
Not disclosed Not disclosed M815.15 Fumapem F-920-rf Fumapem F-1020-rf Not Disclosed Not Disclosed MX4 Product [18] Not Disclosed
a a b c c c c c c
SF SF SF SF SF SNF SNF/NSNF NSNF NSNF
10 mm 5 mm 15 mm 8 mm 8 mm 1 mme5 1 mme5 1 mme5 1 mme5
mm mm mm mm
Support structure material ePTFE ePTFE ePTFE ePTFE ePTFE Porous Porous Porous Porous
polyolefin polyolefin polyolefin polyolefin
based based based based
Support structure thickness
Compressed DM thickness
Not disclosed Not disclosed Not disclosed 12 mm 12 mm 32 mm 32 mm 110 mm 32 mm
Not disclosed Not disclosed Not disclosed 90 mm 90 mm 83.5 mme81.5 mm 83.5 mme81.5 mm 44.5 mme42.5 mm 83.5 mme81.5 mm
Please see Fig. 1 for membrane structure. W. L. Gore & Associates. FUMATECH. dPoint Technologies.
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outlet air (known from here on in as wet side) of a PEM fuel cell. A simplified version of the experimental set-up flow diagram can be seen in Fig. 3. A more detailed description of the set-up is given in Ref. [12].
Overview
Fig. 1 e The various membrane structures as introduced in Table 1. structure. This support structure is coated on one side with a non-fluorinated, non-sulfonated copolymer based coating which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. M9 is an asymmetric membrane made by dPoint Technologies. It consists of a porous polyolefin based support structure. This support structure is coated on one side by a non-fluorinated, non-sulfonated copolymer based coating which acts as the selective layer. The selective layer thickness is in the range between 1 mm and 5 mm. Each membrane was tested with a diffusion media (DM) placed on both sides of the membrane. The DM has two functions. The first function is for mechanical support of the membrane and the second is for utilisation of the whole membrane area. This will be explained in further detail in subsection Membrane module. The DM used is a nonwoven polyester spunbond sheet with a smooth surface and thermally bonded filaments produced by Johns Manville. The area weight of the DM used is 30 g/m2, the uncompressed thickness is 150 mm and the air permeability at 200 Pa is 6000 l/(m2 s). Fig. 2 shows a microscopic view of the DM with a magnification of 200. The nonwoven polyester filaments can be clearly seen with free spaces in between.
Experimental set-up The experimental set-up simulates both the dry inlet air (known from here on in as dry side) and the highly humidified
Fig. 2 e Nonwoven structure of the DM.
The wet side is humidified by an evaporator which requires both synthetic air, 1, and liquid water, 2. Within the evaporator, 3, the liquid water is injected into the air stream and then the air stream is heated. By controlling the evaporator temperature, air mass flow, and liquid mass flow, the dew point and the dry bulb temperature of the wet side air can be controlled. Before entering the membrane module the dry bulb temperature, 4, and dew point temperature, 5, are measured. The membrane module is of a counter flow configuration. On exiting the membrane module, absolute pressure, 7, the dry bulb temperature, 8, and the dew point temperature, 9, are measured. Finally, the pressure loss, 6, through the wet side membrane module is measured. Before entering the membrane module, the dry side air stream is heated and the dry bulb air temperature, 10, is measured. The mass flow of this air stream is also controlled. On exiting the membrane module, the absolute pressure, 12, the dry bulb temperature, 13, and the dew point temperature, 14, are measured. Finally, the pressure loss, 11, through the dry side membrane module is measured. The specific humidity of the synthetic air is constant at 0.17 gw/kgair and is measured on a regular basis.
Membrane module Fig. 4 shows one flow field of the membrane module. The membrane module comprises two flow fields, which are identical apart from the sealing groove, with the membrane sandwiched in between. The membrane area that is used in this module is 27.7 cm2. Each flow field consists of 26 channels. The channel width, height and length are 1.25 mm, 1 mm and 54 mm respectively. The distance between each channel is 0.75 mm. As briefly described in section Membrane overview, one of the functions of the DM is to utilise the whole membrane area. This utilises the whole membrane area by supplying air flow to sections of the membrane in between channels, known as landings. While the use of DM is advantageous for utilisation of membrane area, it can reduce the Reynolds Number at the surface of the membrane, hence increasing the effect of the boundary layer. Fig. 5 shows a cross section of the membrane module with a membrane sandwiched between two DM. A pocket of 100 mm has been machined out of each flow field in order to provide space for the DM and membrane. When the two flow fields are sealed together, the total space left for the DM and membrane is 200 mm. This can also be seen in Fig. 5. The fixed depth of 200 mm influences the water vapour transfer through the membrane due to the variation in the DM thickness. This in turn can change the permeability and therefore change the concentration polarisation effects on each side of the membrane. For example, if the DM with an
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Fig. 3 e Simplified flow sheet of membrane humidification test stand.
Fig. 4 e One of two flow fields of the flat sheet membrane module with detail of channel geometry. uncompressed thickness of 150 mm and the thinnest membrane, M4 (20 mm), from Table 1 are used in combination, this will result in a total uncompressed thickness of 320 mm. When fitted into a sealed membrane module, each DM will decrease
to a compressed thickness of 90 mm. This will therefore decrease the permeability of the DM. Using the thickest membrane from Table 1, M8 (111 mme115 mm) the DM thickness will decrease to between 42.5 mm and 44.5 mm. All DM compressed thickness's can be seen in Table 1. Although compression of the support structures of the membranes will take place and therefore influence the water vapour transfer, these calculations are made on the assumption that no compression takes place in the support structures of the membranes. This assumption can be made due to the amount of free space in the DM as can be seen in Fig. 2. The DM will generally compress first as the support structure within the membrane has a much higher density. Compression effects have been studied both experimentally and with simulation/modelling for the gas diffusion layer (GDL) in PEM fuel cells. The GDL in fuel cells plays a similar role to that of the DM with an additional function of conducting electrons from the catalyst layer on one side to the landing area of the bipolar plate on the other side. The compression of the GDL will affect the flow distribution of the reactant gases and hence will affect fuel cell performance. For example if one area of the cathode flow field has reduced flow, this can lead to oxygen starvation and hence a decrease in cell voltage or membrane damage [19]. Flow field distribution has been studied experimentally by Haase and Mueller [20] using the differential pressure method (DPM), where the pressure drop between a reference pressure and an array of pressure sensors placed throughout the flow field at the membrane surface has been measured. This experimental approach was then validated using CFD simulation [21] which also took into account GDL intrusion into the channel. Both the experimental and simulation approach could also be applied to membrane humidification to examine the compression effect of the DM. The compression effect of the DM will be studied further in ongoing research.
Theory of water vapour transfer Fig. 5 e Cross section of membrane module showing two channels on each flow field, the two diffusion media and the membrane.
In order to calculate the molar flux of vapour J through a membrane per unit area, the following well-known permeation equation, Equation (2), can be used [22].
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Fig. 6 e Segmented mass transfer Simulink® model.
J¼
Dw Sw psw1
psw2
l
(2)
where Dw is the diffusion coefficient of the selective layer, Sw is the solubility coefficient, psw1 and psw2 are the partial vapour pressures at the membrane surface of the wet side air stream and dry side air stream respectively, and l is the thickness of the membrane. Changing Equation (2) from a molar flux per unit area to a mass transfer, the equation can be changed to the following m_ w ¼
Dw Sw psw1 psw2 Mw A l
(3)
_ w is the water vapour transfer through the memwhere m brane, Mw is the molar mass of water vapour, and A is the area of the membrane. In some cases, due to the following unknowns, Equation (3) cannot be used to evaluate water vapour transfer properties of the membrane: The partial vapour pressures at the membrane surfaces, psw1 and psw2 , are not known as they cannot be measured in this experimental set-up. Only the bulk partial vapour pressures at each inlet and outlet of the membrane module can be calculated from the measured dew point temperatures. The variation between the bulk partial vapour pressure and the surface partial vapour pressure is due to boundary layer effects. The water vapour transfer through the area A of the membrane may not be distributed evenly. This may be due to the channel geometry shown in Figs. 3 and 4. Therefore greater water vapour transfer occurs in the membrane area directly in contact with the channels, while much smaller water vapour transfer occurs in the membrane area between the channels. Therefore, assuming all of the area of the membrane is used equally is a false assumption. There is limited theory available for the diffusion coefficient Dw and solubility coefficient Sw for some of the membranes. Even with the membranes where there is some theory available, it only applies to membranes with certain characteristics such as equivalent weight (for sulfonated polymer membranes). Also the empirical equations used in this theory have been found at certain temperatures and pressures which are not applicable to the test conditions used here. Some characteristics of the membrane are not known. Thickness may be one unknown characteristic. This may be due to the manufacturing process not being able to
guarantee a constant thickness or due to it not being disclosed by the manufacturer. Another unknown characteristic may be the exact material make-up of the membrane. Therefore, a lumped parameter model as introduced by Ref. [12], is best used to evaluate the membranes: m_ w ¼ Fm pw1 pw2 :
(4)
here Fm is a lumped parameter used to take into account all the unknowns as described above. Notwithstanding all the above, there is still a possibility to identify the effect of the boundary layer by relating the GORESELECT PFSA based membranes, M1eM3, to Nafion®. Ye and Wang [23] used a scaling factor to relate the diffusion coefficient of Nafion®, which was described by Springer et al. [24] and Yeo and Eisenberg [25], to GORE-SELECT PFSA. By using this relation, they also assumed the solubility coefficient described by Zawodzinski et al. [2] for Nafion® is also valid for GORE-SELECT PFSA. Therefore a function X can be introduced m_ w ¼ F Sw X pw1 pw2
(5)
where F combines the diffusion coefficient with the area A, the selective layer thickness l, and the molar mass of water vapour Mw as shown in Equation (6). Sw is the solubility coefficient, X is the parameter which describes the boundary layer effect and pw1 and pw2 are the bulk partial vapour pressures of the wet side and dry side respectively. F ¼ Dw
Mw A : l
(6)
X can then be expressed as a function of the Reynolds Number Re, absolute pressure p and temperature T: X ¼ c Rea1
T T0
a2 a3 p p0
(7)
where Re is the Reynolds Number of the dry side channel and c, a1, a2, and a3 are coefficients determined empirically. Even though there is a boundary layer present on both sides of the membrane, the dry side Reynolds Number can be used, as the ratio between the mass flow rates of both sides always remains the same. This is dictated by the excess oxygen ratio used in a fuel cell. The variation of the temperature T and pressure p between both sides is relatively small during testing, so therefore the mean temperature and mean pressure can be used. The reference temperature T0 and reference pressure p0 used in Equation (7) are 298 K and 101325 Pa respectively.
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The definition of permeability P is usually given as the product of the diffusion coefficient Dw and the solubility coefficient Sw. In this paper the permeability P has been introduced to combine the F coefficient and the solubility coefficient. Hence it is expressed as P ¼ F Sw :
(8)
Equations (7) and (8) are then substituted into Equation (5) giving the following equation. m_ w ¼ P c Rea1
T T0
a2 a3 p pw1 pw2 : p0
(9)
Due to the variation found in c which is shown in subsection Averaged model, Equation (9) can be further simplified by introducing a modified permeability P0 which combines the permeability P and the coefficient c: P0 ¼ c P:
(10)
Equation (9) is then defined as m_ w ¼ P0 Rea1
T T0
a2 a3 p pw1 pw2 : p0
(11)
The parameter P0 in Equation (11) can be used to evaluate all membranes. This parameter is only a function of the diffusion coefficient Dw and the solubility coefficient Sw and should only vary with changes in temperature and relative humidity. Therefore P0 should not change with the Reynolds Number as now the function X/c describes the boundary layer effect. The molar mass Mw, area A, and the membrane thickness l, are also included in P0 but are the same in all membranes tested so they will not change its value.
Modelling This section consists of three sub-sections. The first subsection describes how the coefficients c, a1, a2, and a3 required in Equation (9) were found using a segmented model with membranes where diffusion and solubility theory is available. The second sub-section explains how these coefficients were then used to find the modified permeability P0 for all membranes using an averaged model. The final subsection then shows the variation of both models with regard to experimental results.
Segmented model As previously described, some parameters of some membranes are not known, so in order to compare each membrane, a membrane specific parameter P0 was proposed in Theory of Water Vapour Transfer section. This parameter P0 is only a function of the diffusion coefficient Dw and the solubility coefficient Sw. There are other parameters included within P0 such as water vapour molar mass Mw, membrane area A and membrane thickness l. These are fixed parameters, and therefore do not influence P0 . As P0 is only a function of diffusion and solubility, it should only vary with RH and temperature as the diffusion coefficient Dw varies with membrane water content and membrane temperature. The
7
solubility coefficient Sw varies with temperature and RH (more specifically water activity aw) but the RH gradient between both sides is described using (pw1pw2), as shown in Equation (11). In order to determine the function X which is required to find P0 , a segmented MATLAB Simulink® model was used. This model uses 10 segments throughout the length of the membrane module. In other words, the membrane module is segmented in the direction of air flow. The total channel length is 5.4 cm, therefore each segment has a total length of 0.54 cm and a membrane area of 2.7 cm2. Fig. 6 shows an overview of the segmented model. To determine the number of segments used in this model, the total calculated water vapour transfer using varying numbers of segments was studied. When using less than 5 segments, significant differences between the calculated total water vapour transfer was noted. From approximately 6 segments, the water vapour transfer started to converge. Hence, 10 segments was decided upon in order to give accurate values while also using acceptable computational time. In each segment i ¼ 1 … 10 a mass balance is completed, with the water vapour transfer across the membrane for each segment calculated using Equation (9). In the membrane module, P and (pw1pw2) are known to vary through the channel length, and therefore will vary from one segment to another. P will vary due to the changing membrane water content in each segment. (pw1pw2) will also vary as the partial vapour pressure will be changing in both air streams due to vapour loss and vapour addition to the wet side and dry side respectively. This segmented model allows a different P and (pw1pw2) to be calculated in every segment which therefore _ w,1 to gives an accurate estimated water vapour transfer rate m _ w,10 for each of the segments. The sum of all water vapour m transfer rates in each segment is equal to the total water vapour transfer in the complete membrane module. m_ w;tot ¼
10 X
m_ w;i :
(12)
i¼1
In order to use Equation (9) to determine the coefficients c, a1, a2, and a3, the permeability P must be known. As Nafion® is the most studied material regarding water vapour transfer, the literature available for calculation of P was used in combination with the scaling factor for the three GORE-SELECT PFSA based membranes. The four coefficients c, a1, a2, and a3 were then found by using a tool available in Simulink®, called Simulink Design Optimization™. This tool compares the calculated water vapour transfer rates from the segmented model to the measured experimental results. The measured experimental results were that of the four most notable effects previously mentioned such as the RH gradient effect, pressure gradient effect, pressure effect and temperature effect. The tool compared 88 test points for M1 and 40 test points for both M2 and M3. By reducing the sum squared error (SSE) between the calculated and measured results to the smallest possible value, the best fitting values of c, a1, a2, and a3 were found. The coefficients for the three GORE-SELECT PFSA based membranes are shown in Table 2. The values shown in Table 2 for Equation (9) are for a Reynolds Number range from approximately 80 to 2100. The
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Table 2 e Fitted values of c, a1, a2, and a3 for all three GORE-SELECT PFSA based membranes.
M1 M2 M3
c
a1
a2
a3
0.0111 0.0047 0.0189
0.3210 0.3657 0.3220
8.0155 8.8809 8.3753
0.8917 1.0901 1.0334
A note of caution for the coefficient values presented in this paper must be given. The coefficients describe the boundary layer effect on the water vapour transfer across the membrane with a specific DM and membrane module geometry. Any variation in the DM and membrane module may change the coefficients.
Averaged model Reynolds Number coefficient a1 for this Reynolds Number range was averaged to be 0.33, the temperature coefficient a2 was averaged to be 8.42 and finally the pressure coefficient a3 was averaged to be 1.0. However, due to the large variation in the coefficient c, it was considered to be membrane specific and hence incorporated with P to give P0 as shown in Equation (10). Therefore, the three coefficients a1, a2, and a3 describe the boundary layer effect, which is only a function of the DM and the membrane module geometry, which are constant for all membranes, and therefore can be applied to all 9 membranes tested. However, using a Reynolds Number coefficient of 0.33, a constant value for P0 as a function of Reynolds Number was not found. Fig. 7 shows the variation of P’ as a function of Reynolds Number using a1 ¼ 0.54 and a1 ¼ 0.33. The best results were found using a Reynolds Number range between approximately 990 and 2100 where a1 ¼ 0.54. In this range the calculated results using the model were accurate, with little variation in P0 as a function of Reynolds Number. It should be noted that a Reynolds Number coefficient of 0.33 over the whole Reynolds Number range can give reasonably accurate water vapour transfer results, however it is necessary to be aware that at some Reynolds Numbers the error can be rather large. The same method as described above was used to find the Reynolds Number coefficient for this Reynolds Number range between approximately 990 and 2100. The pressure and temperature coefficients were fixed at 8.42 and 1.0 respectively. The new Reynolds Number coefficient for the three GORESELECT PFSA based membranes are shown in Table 3. The Reynolds Number coefficient was averaged to be 0.54.
As the function X has been determined for the Reynolds Number range from 990 to 2100, P0 was calculated for all membranes, M1eM9, using experimental results. This has been done by replacing (pw1pw2) with Dpw,log in Equation (11) and is shown as follows: a2 a3 T p Dpw;log : (13) m_ w;tot ¼ P0 Rea1 T0 p0 Dpw,log is defined as Dpw;log ¼
dry out
in pwet pw w
ln
dry in out pwet pw w :
in pdry out w out pdry in pwet w w
pwet w
By rearranging Equation (13), P0 can be calculated for all membranes: P0 ¼
Rea1
m_ w;tot a2 a3 : p T Dpw;log p0 T0
(15)
_ w,tot was from experiThe water vapour transfer rate m mental results and the coefficients a1, a2, and a3 in the function X were those determined in sub-section Segmented model. According to Fig. 6, Dpw,log was calculated using partial vapour pressures at the inlets and outlets which were calculated using the measured dew point temperatures in the experimental setup.
Validation of the models In order to validate the models, a root mean square error (RMSE) as seen in Equation (16) between the models and experimental results was calculated. Validation of the models was completed on four of the most notable effects therefore leaving out the temperature gradient effect. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Pn _ _ 1 mw;exp mw;mod : RMSE ¼ n
Fig. 7 e Variation of P0 as a function of Reynolds Number using a1 ¼ 0.54 and a1 ¼ 0.33.
(14)
(16)
Both the averaged model and segmented model used the Reynolds Number coefficient a1 of 0.54 for a Reynolds Number range between 990 and 2100. They also used a temperature coefficient a2 of 8.42 and the pressure coefficient a3 of 1.0. The only difference between the averaged model and segmented model was the P0 that was used. For the averaged model, P0 was that calculated from experimental data using Equation (15). This averaged model was applied to all membranes. For the segmented model, P0 as shown in Equation (10) was used where P was calculated using the theory available and c was taken from Table 2. This segmented model was only applied to membranes M1 to M3, where theory is available to calculate P as it is a function of membrane temperature and water content.
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Fig. 8 e Variation of water vapour transfer rates between the models, averaged and segmented, and experimental for membrane M1. Solid lines are used to guide the eye.
Fig. 8 shows the variation of water vapour transfer rates per meter squared of membrane area between model and experimental results for four of the most notable effects for membrane M1, namely, the RH gradient effect, pressure gradient effect, pressure effect and temperature effect. For each effect, the channel Reynolds Number was varied from approximately 990 to 2100. Fig. 9 shows the RMSE for the four most notable effects and the average RMSE for all test points completed for M1. For the averaged model both the RH gradient effect and temperature effect are below average and regarding the segmented model, all effects except for the RH gradient are below average. The RMSE for the segmented model is approximately 1.5 times
Table 3 e Recalculated values of a1 for all three GORESELECT PFSA based membranes for a Reynolds Number range between 990 and 2100. a1 M1 M2 M3
0.5398 0.5665 0.5241
greater than it is for the averaged model. This could be due to the P0 used in the segmented model being from theory and P0 in the averaged model being calculated from experimental results. Fig. 10 shows the RMSE of all test points using the averaged model for all membranes. With an average RMSE of 0.1175 g/(s m2) for all membranes, it can be concluded that the modified permeability P’ is an accurate parameter to use to model water vapour transfer in the membrane module shown in sub-section Membrane module.
Results and discussion The results and discussion section is divided into two different sub-sections. The first sub-section shows the experimental results of water vapour transfer for the above described membranes and compares and contrasts the above effects which have been explained in detail in Ref. [12]. The second sub-section shows the calculated modified permeability P0 , which was used in the averaged model for all membranes for a Reynolds Number range between 990 and 2100.
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Fig. 9 e Root mean square error between models and experimental results for membrane M1.
Water vapour transfer Fig. 11 shows the water vapour transfer results per meter squared of membrane area for membrane M1 and membrane M2. The results for M1 have been previously published [12] but are shown again in order to show result trends. The number of test points for M2 have been decreased and slightly changed to increase experimental efficiency. For example, the pressure gradient effect was increased to 500 mbar for M2 as no conclusions could be made from the results of M1 using a pressure gradient of up to 300 mbar. Also, no further testing was done regarding the temperature gradient due to the same reason. Fig. 11 shows the water vapour transfer for all five effects that have been tested. For each effect, the channel Reynolds Number is varied from approximately 80 to 2100. The first effect shown in Fig. 11a is the RH gradient effect. In this effect the temperature and absolute pressure of both air streams were maintained at 350 K and 2.5 bar respectively. Four different levels of the wet side RH were measured, namely 95%, 85%, 75%, and 65%, while the dry side RH was close to 0%.
Fig. 10 e Root mean square error between the averaged model and experimental water vapour transfer rates for all membranes.
The second effect shown in Fig. 11b is the pressure gradient effect where a pressure gradient was introduced between the two air streams. Both air streams were maintained at a temperature of 350 K. The wet side RH was maintained at 95%. In this test the dry side absolute pressure was either equal to, or greater than the wet side. The third effect shown in Fig. 11c is the temperature gradient effect where a temperature gradient was introduced between the two air streams. Both air streams were maintained at a temperature of 2.5 bar. The wet side RH was maintained at 95%. In this test the dry side temperature was either equal to, or less than the wet side. The fourth effect shown in Fig. 11d is the pressure effect where the absolute pressure of both sides varies. There was no pressure gradient present here. The temperatures of both air streams were maintained at 350 K and the wet side RH was maintained at 85%. The reason for maintaining the wet side RH at 85% and not 95% is due to test stand limitations at high mass flow rates and low pressure. The final effect shown in Fig. 11e is the temperature effect, where the temperature of both sides varies. There was no temperature gradient present here. The absolute pressure of both air streams was maintained at 2.5 bar and the wet side RH was maintained at 95%. For all membranes tested, similar trends can be observed with all four effects. The trends that can be observed are as follows: An increase in water vapour transfer with an increase in the flow rate. But there is a decrease in the Water Recovery Ratio (WRR) from approximately 40% at a dry channel Reynolds Number of 80 to approximately 7% at a dry channel Re of 2100 (values for membrane M1). WRR is defined as WRR ¼
m_ w;dry out m_ w;dry in : m_ w;wet in
(17)
An increase in water vapour transfer with an increase in RH gradient. No significant change in water vapour transfer with a pressure gradient of up to 300 mbar between the two streams as shown with results from M1. When the pressure gradient is increased to 500 mbar with M2, a difference in water vapour transfer can be seen. This shows that the lower the wet side pressure and therefore pressure gradient, the higher the water vapour transfer. No significant change in water vapour transfer with a temperature gradient between the two streams. An increase in water vapour transfer with a decrease in absolute pressure. An increase in water vapour transfer with an increase in temperature As shown in Table 1, four types of membranes have been tested. Generally speaking, SF membranes are the best performing membranes for water vapour transfer due to the high solubility properties and hydrophobic backbones, but the major disadvantage to them is their cost. Fig. 12 shows five different SF membranes, all of which are PFSA type. The test
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Fig. 11 e Water vapour transfer results for M1 and M2. Solid lines are used to guide the eye.
points have been completed with a wet side RH of 95%. The temperature and absolute pressure of both the wet and dry sides are 350 K and 2.5 bar respectively. M1, M2 and M3 are made by the same company, W. L. Gore & Associates, and have the same selective layer. The main differences with these three membranes are the selective layer thickness, the total membrane thickness and the
structure. M1 and M2 have quite similar structures but the selective layer is 5 mm in M2 while it is 10 mm in M1. According to Equation (2), one would expect M2 to have double the water vapour transfer of M1 due to the selective layer thickness. As can be seen in Fig. 12 this is not the case. This shows that diffusion through the selective layer is not the controlling mechanism. There are other resistances affecting water
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Fig. 12 e Water vapour transfer results of the SF membranes. Solid lines are used to guide the eye.
vapour transfer through the membrane such as the resistances of the support layers of the membrane and the boundary layers. M4 and M5 are also made by the same company, FUMATECH, and have the same selective layer, fumion® F. These membranes differ only in EW as they have the same selective layer thickness (8 mm), membrane thickness and structure. The EW of M4 is 900 gdry polymer/molSO3 H while the EW of M5 is 1000 gdry polymer/molSO3 H . GORE-SELECT PFSA and fumion® F are both PFSA polymers but vary mainly due to the reinforcement of the PFSA. The best performing PFSA membrane cannot be extrapolated from Fig. 12, as in order to do that, membranes with the same EW, selective layer and membrane thickness and structure would have to be measured, which is not the case with the membranes compared here. All of the membranes shown in Fig. 13 are SNF/NSNF membranes. M6 and M7 contain a sulfonated polymer and a blend of a sulfonated polymer and non-sulfonated polymer in their selective layer, respectively. However they differ in
selective layer material, as explained above, but the selective layer thickness is within the same range of 1 mme5 mm. The support structure material and thickness are the same, as both of them have a porous polyolefin based support structure with a thickness of 32 mm. From Fig. 13, the change of selective layer material does not seem to have a big influence in the water vapour transfer. M8 and M9 are non-sulfonated and have the same selective layer material with the same thickness range. The support structure material is the same class of polymer, polyolefin, but the thickness of these membranes differ, as M8 has a support structure thickness of 110 mm, and M9 has a support structure thickness of 32 mm. From Fig. 13 it can be seen that the water vapour transfer is very similar for both membranes even though M9 has a support structure thickness of less than one third than the support structure of M8. From this, it appears that the support structure does not have a strong influence on the water vapour transfer. However, as explained by the membrane manufacturer, without the exact details of the selective layer thickness and the pore structure of the support layer, no informed conclusion can be reached in determining the effect of the substrate layer on water vapour transfer results. Fig. 14 shows the average water vapour transfer rate of 14 test points completed for the RH Gradient effect from a Reynolds Number range between 160 and 2100 approximately for each membrane. The 14 test points include four test points at 95%, 3 test points at 85%, 3 test points at 75% and four test points at 65%. M1 to M5 are all SF membranes. M6 and M7 are SNF and a blend of SNF/NSNF membranes respectively. M8 and M9 are NSNF membranes. It can be seen that M2 is the membrane with the highest vapour transfer, which is a SF membrane produced by W. L. Gore & Associates with a GORE-SELECT PFSA as the selective layer material and with a selective layer thickness of 5 mm. The membrane with the lowest vapour transfer is M8 which is a NSNF membrane, it should be noted that this membrane and the other membranes of dPoint Technologies are designed for lower temperature humidity transport applications. The thickness of the selective layer is between 1 mm and 5 mm.
Model results
Fig. 13 e Water vapour transfer results of the SNF/NSNF membranes. Solid lines are used to guide the eye.
Figs. 15e18 show P0 for a Reynolds Number range between 990 and 2100. Fig. 15 shows the variation of P0 with a change in wet in RH for all SF membranes. All these test points have been completed at 350 K. It shows that M2 has the highest calculated P0 of SF membranes and M4 has the lowest calculated P0 of SF membranes. At the highest wet in RH, 95%, M4 performs approximately 42% less than M2. At a wet in RH of 65%, this value increases to approximately 60%. Fig. 16 shows the variation of P0 with a change in wet in RH for all SNF/NSNF membranes. All of these test points have been completed at 350 K. It shows that M6, which is a SNF membrane, has the highest calculated P0 . M8 and M9, which are NSNF membranes, have the lowest calculated P0 . An interesting observation between M6 and M7 is that as wet in RH decreases, the difference of P0 between the two membranes increases. This shows that the sulfonated membrane
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Fig. 14 e Average water vapour transfer rate of 14 test points in the RH effect.
Fig. 17 e P0 with a change in membrane temperature for SF membranes. Solid lines are used to guide the eye.
Fig. 15 e P0 with a change in wet inlet RH for SF membranes. Solid lines are used to guide the eye.
M6 performs better than the membrane with a blend of sulfonated and non-sulfonated polymer particularly when there is a decrease in wet in RH. From Figs. 15 and 16, it can be noted that P0 increases with an increase in RH. This could be explained by the sorption coefficient which increases with water activity aw and/or partial vapour pressure pw. For SF membranes, Nafion® to be exact, Zawodzinski et al. [2] showed that the increase of water content l as a function of water activity aw is described by a third order polynomial function. For NSNF membranes, Metz et al. [26] has shown that water concentration C for a polyethylene oxide (PEO) and PBT block copolymers increases linearly at low water activities (aw<0.4) and increases exponentially at higher water activities. Fig. 17 shows the variation of P0 with a change in membrane temperature for all SF membranes. All of these tests points were completed at a wet in RH of 95%. This figure shows a decrease in P’ with an increase in membrane temperature. Fig. 18 shows the variation of P0 with a change in membrane temperature for all SNF/NSNF membranes. All of these
0
Fig. 16 e P with a change in wet inlet RH for SNF/NSNF membranes. Solid lines are used to guide the eye.
Fig. 18 e P0 with a change in membrane temperature for SNF/NSNF membranes. Solid lines are used to guide the eye.
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tests points were completed at a wet in RH of 95%. Similar to Fig. 16, M6 has the highest calculated P0 . Only one temperature, 350 K, has been studied for membranes M4, M7, M8 and M9. Diffusion coefficients increase with temperature which is described by the Arrhenius-type equation as shown by Springer et al. [24] and solubility coefficients decrease with temperature as shown by Metz et al. [26] and Azher et al. [27] due to its exothermic nature. Figs. 17 and 18 would then suggest that solubility is the controlling mechanism of the two mechanisms described by P0 . This may be due to the selective layers of the membranes being very thin.
Conclusion A range of membranes were tested, and the measured water vapour transfer rates and theoretical water vapour transfer rates from the proposed model have been presented. The membranes that have been tested range across four different categories, namely, sulfonated fluorinated polymer membranes SF, sulfonated non-fluorinated polymer membranes SNF, non-sulfonated non fluorinated polymer membranes NSNF and membranes with a blend of sulfonated nonfluorinated polymers and non-sulfonated non-fluorinated polymers SNF/NSNF. A function X was introduced in order to separate the boundary layer effects that occur in gas separation, such as concentration polarisation, from the membrane properties such as diffusion and solubility. In separating these two, a membrane specific parameter P0 was calculated using experimental results. The parameter P0 was then used to compare all membranes. The theory proposed in this paper was applied to an averaged and segmented model. The averaged model used the parameter P0 which was calculated from experimental results. This was applied to all membranes within a Reynolds Number range between 990 and 2100. The average RMSE for the water vapour transfer rate between the averaged model and experimental results for all membranes was 0.1175 g/(s m2). The segmented model used a parameter P which was calculated using the theory available. This was only applied to three membranes in the same Reynolds Number range due to the lack of necessary information on the other membranes. The average RMSE for the water vapour transfer rate between the segmented model and experimental results for membranes M1eM3 was 0.2739 g/(s m2). Even though the RMSE for the water vapour transfer rate is greater for the segmented model, two of the advantages for this model are that the partial vapour pressure profile for both sides and the water vapour transfer in each segment can be calculated. When considering the RMSE for the water vapour transfer rate of both the averaged and segmented model, the smallest vapour transfer rate measured with M1 at a Reynolds Number of 990 was 0.81 g/(s m2) and the largest vapour transfer rate measured with M1 at a Reynolds Number of 2100 was 4.94 g/(s m2). The results show that, for both the water vapour transfer rates and model results, the membranes which transfer the most vapour are sulfonated fluorinated membranes. In saying
that, there is quite a large variation in the performance of these sulfonated fluorinated membranes. This is due to the difference in the selective layer polymer and the membrane structure. The membranes which transfer the least vapour have been shown to be the non-sulfonated non-fluorinated membranes.
Acknowledgements The authors of this paper would like to thank the membrane manufacturers, W. L. Gore & Associates, FUMATECH and dPoint Technologies for providing the membrane samples and also for their feedback and additional comments regarding this paper.
List of symbols A a1 a2 a3 aw C c Dw EW F Fm J l _w m Mw n P P0 p Re sw T X
Membrane area, cm2 Reynolds Number coefficient,Temperature coefficient,Pressure coefficient,Water vapour activity,Water concentration, cm3vapour/cm3polymer Coefficient of X function,Diffusion coefficient, cm2/s Equivalent weight, gdry polymer/molSO3 H Factor, (cm3 g)/(s mol) Membrane factor, g/(s Pa) Membrane flux, mol/(s cm2) Membrane thickness, cm Water vapour mass flow rate, g/s Water vapour molecular mass, g/mol Number of test points, e Permeability, g/(s Pa) Modified permeability, g/(s Pa) Pressure, Pa Reynolds Number, e Solubility coefficient, mol/(Pa cm3) Temperature, K Boundary layer function,-
Subscripts 1 Wet side 2 Dry side exp Experimental results i Segment number log Natural log m Membrane mod Model results sat Saturation tot Total w Water vapour Superscripts s Membrane surface Greek symbols D Difference l Water content, molH2 O =molSO3 H
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