Axial distribution of permeance and selectivity of a porous cylindrical

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Axial distribution of permeance and selectivity of a porous cylindrical tube for binary gas mixtures (CO2/N2) Hussain NAJMI, Eddy El-Tabach, Nicolas Gascoin, Khaled Chetehouna, and Francois Falempin Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b06191 • Publication Date (Web): 31 Jan 2019 Downloaded from http://pubs.acs.org on January 31, 2019

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Industrial & Engineering Chemistry Research

Axial distribution of permeance and selectivity of a porous cylindrical tube for binary gas mixtures (CO2/N2) H. Najmi1, E. El-Tabach2, N. Gascoin1, K. Chetehouna1, F. Falempin3 1

INSA Centre Val de Loire, Univ. Orléans, PRISME EA 4229, F-18022 Bourges, France 2

Univ. Orléans, INSA-CVL, PRISME, EA 4229, F45072, Orléans, France. 3

MBDA, 1 avenue Réaumur 92358 Le Plessis-Robinson cedex, France

*

Address correspondance to Hussain NAJMI, 88 BD Lahitolle INSA Centre Val de Loire,

Univ. Orléans, PRISME EA 4229, F-18022 Bourges, France E-mail: [email protected] Phone: +33 752537470

Keywords: Regenerative cooling, separation process, fuel cell, porous stainless steel tube, process engineering

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Abstract In previous studies, the selectivity property of a porous stainless steel cylindrical tube showed different filtration rate of pure Carbon Dioxide (CO2) and of pure Nitrogen (N2) because of the effect of the dynamic boundary layer into the tube. In this study, a binary mixture of Carbon Dioxide (CO2) and of Nitrogen (N2) is considered under three different volumetric compositions (50/50%, 60/40% and 70/30%) in order to evaluate the separation property of a porous stainless steel tube (membrane effect). The pure gas permeability, the mixture permeability, the ideal selectivity and the separation selectivity of this tube are determined for a total mass flowrate ranging from 1 g.s-1 to 2.5 g.s-1 and for an inlet pressure varying from 2 bar to 3.5 bar accordingly. The factors affecting the distribution of CO2 and N2 inside the porous tube are qualified. It is found that both the ideal and separation selectivity value are close to each other for a 50/50% composition but the difference between the values increases for different compositions because of the effects of the partial and total pressures. Both ideal and separation selectivities decrease with an increase in the CO2 concentration. The mixed gas permeability of both gases vary in such a manner that the selectivity (N2/CO2) increases along the length of the tube for all the studied volumetric compositions. The concentration of CO2 in the main flow decreases along the length of the tube whereas the concentration of N2 increases. These findings will serve to design separation processes to be used in application like fuel cells or regenerative cooling on board high-speed flying vehicles. Nomenclature A L MM P R Re V 𝑉̇ X P.O S.O L ṁ θ

Area (m2) Length of tube (m) Molecular mass (g/mol) Pressure (Pa) Radius (m) Reynolds number Velocity (m/s)

Δp Partial pressure drop across the porous media Greek symbol Selectivity (Ҏi/Ҏj) 𝛼 k Darcy’s permeability (m2) µ Dynamic viscosity (Pa·s) ρ Fluid density (kg/m3) Ҏ Gas permeability ( m3(STP)·m/(m2·s·Pa))

Volumetric flowrate (m3/s) Volumetric Composition (%) Primary outlet Secondary Outlet Porous media thickness (m) Mass flowrate (g/s) Pressure ratio (PUP/PDN)

Subscripts e Entrance ext Exterior i 1st component of binary gas mixture j 2nd component of binary gas mixture mix Mixture STP Standard temperature pressure (T=293K, P=1 bar)

1. Introduction Fuel cells are among the cleanest sources of power generation [1]. They have some other advantages such as high efficiency and noise free operation. They convert chemical energy directly into electrical energy without any combustion process. This result in an 2 ACS Paragon Plus Environment

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independency from the thermodynamic laws like the Carnot efficiency associated with heat engines currently used in power generation [2]. The Solid Oxide Fuel Cell (SOFC) is among the commonly recognized technique for power generation in applications such as on board aircrafts [3]. To operate the fuel cell efficiently, the availability of high-purity hydrogen is essential. High gravimetric-based energy content and absence of greenhouse gas emissions make hydrogen a very unique contender in the area of green fuels. The absence of natural deposits of hydrogen enforces its production through different industrial techniques. There are mostly 15 different types of hydrogen production methods grouped into 4 main groups based on its input energy resources; see Table 1 [4]. Electrical Thermal

Hybrid

Biological

1. Plasma arc decomposition 2. Electrolysis 1. Thermolysis 2. Thermochemical water splitting 3. Biomass conversion 4. Steam reforming 5. Autothermal reforming 6. Gasification 1. Photo-electrochemical method 2. Hybrid thermochemical water splitting cycles 3. High temperature electrolysis 1. Dark Fermentation 2. Bio-photolysis 3. Photo-fermentation 4. Artificial photosynthesis

Table 1: Classification of hydrogen production techniques [4]. Nowadays, among the 15 above listed techniques, most of the hydrogen is produced through steam reforming of natural gas, which is also responsible for the production of a large amount of CO2 emission. Around 48% of Hydrogen demand is satisfied by natural gas, 30% by petroleum industry, 18% from the gasification of coal, 3.9% from electrolysis and the remaining 0.1% from other processes [5]. The presence of CO2, N2, CO etc. reduces the energy content of Hydrogen and thereby i) shortens the lifetime of a Fuel Cell, ii) decreases the efficiency and also iii) causes corrosion of pipelines [6-7]. It becomes thus very important to remove the unwanted gases from the Hydrogen to ensure efficient and long operational life of Fuel Cells.



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The six main technologies for gas separation are as follows: 1) pressure swing adsorption (PSA) [8-10], 2) solid adsorption [11, 12], 3) cryogenic distillation [13], 4) chemical looping [14-16], 5) gas hydrates [17, 18] and 6) selective permeation through a porous media [19-23]. Out of these methods, the selective permeation through a porous media has the advantages of low operational cost, small impact on environment, easy maintenance and less operation time compared to the others. The membrane used for selective permeation can be integrated in the fuel cell; which facilitates the on-board Hydrogen production, storage and efficient use. The separation efficiency of a membrane is often evaluated on the basis of two parameters: the first is the gas permeability and the second is the selectivity. Gas permeability and selectivity are determined experimentally using a porous media or a porous support of different shapes and geometry such as circular one [24, 25], rectangular one [26, 27] or tubes [28, 29]. Among the available studies, apart from the few ones in which a porous tube is used to study the H2 permeance as a support [1, 28, 29], most of them are related to flat configurations with one single main flow. For example, Korikov et al. (2005) studied the permeance of CO2 through a flat circular microporous media [24]. Sullivan-González et al (2017) studied methane permeance using a circular (90 mm) ionic liquid (RTIL) membranes at room temperature [25]. Wu et al. (2017) studied CO2 permeance using amine-containing membranes in a rectangular stainless steel cell with an effective area of 2.7 cm2 [26]. Vakharia et al. (2015) studied CO2/H2 selectivity using Amine-containing CO2-selective facilitated transport membranes in a rectangular gas permeation cell [27]. None of the researchers considered a tube configuration with one main flow (along the main direction) and one porous flow (perpendiculary to this main direction). However, this is required if a clear estimate of the distribution of selectivity along the length of the porous channel is required for some specific configuration [30]. The effect of the multispecies composition on the selectivity has also been investigated in open literature. Selectivity can either be determined using a single gas or using a gas mixture. Selectivity computed using a single gas is called the ideal selectivity and the selectivity determined using a gas mixture is known as the mixed selectivity or as the separation selectivity. Selectivity was determined for different volumetric compositions of a mixture by some authors [31-34]. Xiang et al. (2017) studied CO2/N2/CH4 permeance and selectivity using pure gases and gas mixtures with different volumetric compositions (50/50% 25/75%) in order to find the best conditions for extracting CO2. They found that in a mixed-gas permeation, both gas permeance and selectivity decrease with the increase in feeding 4 ACS Paragon Plus Environment

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pressure. In addition, they found that a higher concentration of CH4 or N2 result in a lower CO2 permeance [31]. Melendez et al. (2017) determined H2 permeance with binary mixtures containing CO2, N2 or CH4 (from 0% to 100% H2) using a porous tube. They found that for all the cases, the H2 permeance decreases with an increase in CO2, N2 or CH4 concentration [32]. Saberi et al. (2016) derived a mathematical model to determine the permeation of mixed gases (N2/CO2) in glassy polymers [33] and compared it with the experimental results of Visser et al. (2005) [34]. They vary the composition of CO2 in a binary mixture from 0 to 100% [33]. The obtained results suggest an increase in CO2 permeability with the decrease in a fraction of the second component in the feed [33, 34], which correlates the above mentioned conclusions from Xiang et al. In most of the above mentioned studies, the separation of gases is carried out on the basis of 1) Knudsen diffusion, 2) capillary condensation and 3) molecular sieving mechanisms [35]. Therefore, different types of coatings and membranes were used on porous stainless steel supports to enhance the adsorption properties and to improve the gas permeance and the selectivity of the material. There are now various CO2/H2 selective membranes for syngas purification [27, 36, 37]. Some inorganic palladium based membranes have an infinite selectivity but they suffer from Hydrogen embrittlement and sulphur poisoning [27]. It is also difficult to scale up the fabrication of palladium membranes that could be rolled into large robust modules for practical applications [27]. Thus, there is a need for a simpler way for the separation of gases. Present et al. [38] first accounted the separation phenomenon in 1949 by studying the binary gaseous flows through a long capillary. It was pointed out that a pressure gradient could result in a finite rarefaction effect wherein the different species of the mixture travel with different speeds in the channel due to their different molecular velocities which would lead to diffusion due to their tendency to separate. Further, it was discovered that the maximum separation degree depended on the molecular mass ratio. Further experiments have also been performed by researchers on gas separation effect, based on this theory [39, 40, 41, 42]. It is also noteworthy that change in density and viscosity can lead to separation in liquids also [43]. In light of the above studies, it is concluded that in a binary mixture of N2/CO2 where N2 is the lightest specie and CO2 is the heaviest one (based on molecular mass), gas molecules of both species would have different viscosity and density at the same temperature and pressure.



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Hence, different flow characteristics are to be noted; such as Reynolds number or linear and radial velocities. Thus, these properties can be used for separating the two gases present in a binary mixture as detailed in the following.

Figure 1: Illustrative principle of filtration from the main flow. Considering an application, a perpendicular flow (also called a porous flow, through-flow or permeate flow) occurs to the main one that flows into the pipe from the inlet to the main outlet of the tube (cf. Figure 1). As the fluid flows towards the so-called secondary outlet on Figure 1, the density, the viscosity, the main flow velocity and the temperature vary along the length of the channel due to a decrease in the pressure along this length. This may have a significant effect on the permeance and on the selectivity of gases that will be investigated in this work. The primary aim of this work is to investigate the effect of such tube configuration (Figure 1) on the gas separation without using special membrane coatings. Thanks to a dedicated permselectivity test bench, the change of density, viscosity, Reynold’s No. and velocity are investigated to understand their impact on gas permeance and on selectivity of gases. The Knudsen no. is determined to characterize the main flow inside the porous surface and the N2 and CO2 composition distribution profile is determined. 2. Materials and methods 2.1 Permselectivity test bench description and test methodology In this section, a short description of the developed test bench is given. Further details concerning the test bench, like the brand and models of each device, can be found in previous works [30, 44, 45]. The main sub-system of the bench (Figure 2) consists of a stainless steel (316L SS) tube that is supplied by Mottcorp USA. The physical and geometrical characteristics of the stainless steel porous tube are given in Table.2.


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Length

1m

Inner diameter

0.019 m

Outer diameter

0.025 m

Porosity

36%

Pore diameter

2 µm

Density

5040 kg.m-3

Table 2: Physical and geometrical characteristics of the stainless steel porous tube. This tube has one inlet and one main outlet. It has also another outlet because its wall is porous. This porous tube is placed inside 8 permeation cells that allow the monitoring of the spatial distribution of the permeate flow and its chemical composition along the axial direction. In order to measure the volumetric composition of the gases coming out of each cell line, a portable gas analyser (Biogas 5000) enables to track any composition change among the cells, that is to say along the tube. The pressure and the temperature inside each cell are measured and their signals are gathered by a data acquisition system with all other measures. A Coriolis mass flow meter is used to monitor the mass flowrate in each permeation cell. Coriolis and Thermal mass flow controllers (0 g.s -1 to 3 g.s-1) are placed at the inlet of CO2 and N2 respectively in order to control and to measure the mass flowrate of the fluids entering into the porous tube (to control the mixture composition). The data acquisition system is real-time controlled like the entire bench (opening/closing of valves, start/stop of equipments) by a LabView program (automated system control, data acquisition and safety control). Nitrogen and Carbon dioxide are supplied by Air Liquide France with purity of 99.99%.

Figure 2: Instrumentation of the permselectivity test bench composed of eight independent cells of monitoring the though-flow.



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In terms of the test methodology, the following automated sequence is used by LabVIEW. A vacuum pump is used to remove the traces of all the gases and to ensure that there are no foreign particles present inside the system before starting the experiments. Then, the gas flow is managed (either pure or in mixture). The experiments are performed for four different total mass flowrates (by varying the mass flowrates of the gases) and for three different volumetric compositions of binary gases CO2/N2 (50/50%, 60/40%, 70/30%) (Table 3). The case 1 roughly corresponds to a test at 1 g.s-1, case 2 at 1.5 g.s-1, case 3 at 2 g.s-1 and case 4 at 2.5 g.s-1 ; even if due to experimental uncertainties and manipulations, the effective total mass flowrate may vary (as seen in Table 3). Once the outlet flow rate is stabilized, the inlet flow rates of both gases are changed simultaneously in order to study the next case (a series of hydraulic plateau is considered to move for a given mixture composition from case 1 to case 4). The same process is repeated till case 4. In the present work, all the tests are performed at an ambient temperature. All the tests are performed three times in order to confirm the reliability of the results. The Standard Deviation (SD) in the calculation is so small that it makes it difficult to be presented in figures with the help of error bars. Therefore it is presented in a separated table attached to figures wherever it is feasible. 1st Composition Case CO2 N2 (50%) (50%) 1 (1g.s-1) 0.67±0.0011 0.39±0.0038 2 (1.5g.s-1) 0.94±0.0006 0.54±0.0019 3 (2g.s-1) 1.32±0.0004 0.75±0.0017 4 (2.5g.s-1) 1.52±0.0065 0.88±0.0009

2nd Composition CO2 N2 (60%) (40%) 0.87±0.0002 0.33±0.0011 1.05±0.0008 0.41±0.0005 1.55±0.0062 0.59±0.0013 1.84±0.0011 0.68±0.0010

3rd Composition CO2 N2 (70%) (30%) 1.09±0.0021 0.24±0.0008 1.27±0.0589 0.32±0.0213 1.70±0.0060 0.40±0.0004 2.06±0.0059 0.50±0.0022

Table 3: Inlet mass flowrates of gases resulting in different volumetric compositions. 2.2

Mathematical procedures for determining selectivity and permeance

Selectivity is the ratio of permeance of two different gases. It is commonly denoted by 𝛼 [45].

Ҏ𝑖 (1) Ҏ𝑗 Where Ҏ is the gas permeability, i is the 1st and j is the 2nd component of the binary gas 𝛼𝑗𝑖 =

mixture. In case of a permeate flow occurring in a radial direction (like present study) inside a porous tube, gas permeability is given by equations 2 and 3.

Ҏ=

1 𝜌𝑆𝑇𝑃 (𝑖)

𝑅𝑒𝑥𝑡 ] ṁ𝑖 𝑅 [ln 𝑅 [ ] 𝐴 · 𝛥𝑝𝑖

(2)


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Ҏ=

𝑘 · 𝜌𝑖 µ𝑖 · 𝜌𝑆𝑇𝑃 (𝑖)

(3)

The further description of the above equations can be found in previous work [45]. For Eq. 3, the density and viscosity of each specie (i.e. N2 and CO2) is determined on the basis of partial pressure of the respective specie. In this work (see section 3), gas permeability is determined using Eq. 2 as well as Eq. 3 and selectivity is determined using Eq. 1. Eq. 3 has already been validated for the pure gases in the previous work [45]. Hence using Eq. 3 in the present work will validate its applicability for multispecies mixture also. The density of the binary mixture is calculated using the following gas equation [46, 47]: [(𝑀𝑀𝑖 · 𝑋𝑖 ) + (𝑀𝑀𝑗 · 𝑋𝑗 )] · 𝑃𝑡𝑜𝑡𝑎𝑙 𝑅·𝑇 where, 𝑅 is the perfect gases constant. 𝜌𝑚𝑖𝑥 =

(4)

In order to facilitate the post-processing of the experimental data, the viscosity is determined upon the composition and the pressure by using the Wilke’s equation [48, 49]. This equation is verified by Kestin et al. for seven different binary gas mixtures of N2 and CO2 [50]. 𝑛

𝑥1 · µ𝑖 𝑛 ∑ 𝑥𝑗 · ф𝑖𝑗 𝑖=1 𝑗=1

µ𝑚𝑖𝑥 = ∑

ф𝑖𝑗 =

1 √8

1 − 2

· [1 +

𝑀𝑀𝑖 ] 𝑀𝑀𝑗

(5) 1 2

1 2 4

µ𝑖 𝑀𝑀𝑖 ] ] · [1 + [ ] [ µ𝑗 𝑀𝑀𝑗

(6)

The viscosity of the N2/CO2 mixture at the inlet of the tube (as plotted in Figure 3) is determined using Eq. 5 and 6. It decreases with the increase in the CO2 concentration and in fluid pressure. These results are in agreement with the literature data [50].



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Figure 3: Inlet viscosity of the N2 and CO2 mixture at different pressures for 3 different compositions. To understand the distribution of N2 and CO2 inside the pores of the porous tube along its length, the Knudsen number (Kn) is calculated using the following relation [51]: 𝜆 µ·𝜋·𝑉 (7) = 𝐷 4·𝑃·𝐷 Where λ is the mean free path and π is a constant. There are three types of flow regimes 𝐾𝑛 =

depending upon the Kn value which are as follows: i) Kn > 1 molecular flow, ii) 1 > Kn > 0.01 transition flow, iii) Kn < 0.01 continuum flow. In a molecular flow, the mean free path of the particles is much greater than the diameter of the tube. Therefore, the majority of the particles move along the straight trajectories until they hit a wall. Collisions between the particles occur very rarely, they move independently of each other. This type of flow is only caused by the kinetic energy of the particles [51]. However, in the case of a continuum flow, the mean free path of the particles is much smaller than the diameter of the tube. Hence collision of the gas particles is very frequent, resulting in a frequent exchange of momentum and energy. A continuum flow can either be turbulent or laminar viscous. A transition flow comes between the molecular flow and the continuum flow [51]. 3. Results and discussions Three different volumetric compositions 30-40-50% of N2 into CO2 (which is the major component) are studied for 4 different cases (total mass flowrates of 1 g.s -1, 1.5 g.s-1, 2 g.s-1, 2.5 g.s-1). The inlet pressure varies according to the total mass flowrate (roughly about 2.55 10 ACS Paragon Plus Environment

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bar, 2.73 bar, 3.16 bar and 3.47 bar respectively). As a consequence, it is important to note that both partial pressure of the compounds and the total pressure of the mixture are varying. It is seen that the flow at the entrance is in turbulent regime for all the studied cases of the three different compositions. It is transitional for case 1 (Re from 5100 at inlet to 3000 at outlet) and case 2 (Re from 6400 at inlet to 3700 at outlet). The flow is in turbulent regime for cases 3 and 4 (Re from 8500 or 11.000 at inlet to 5000 or 6000 at outlet). The Reynolds number decreases along the tube because of the decrease in pressure (Figure 4a) as well as of the mass loss due to the permeation process along the length of the porous tube [45]. Figure 4a presents the average pressure inside (upstream) and outside the porous tube (downstream) along the length. As discussed above, the variation in the pressure is mainly due to inlet mass flowrate and not so much due to the change in concentration. Hence the average pressure values for all three concentrations with respect to cases are presented in Figure 4a. The pressure inside the tube (upstream) decreases due to the continuous filtration along the length of the tube [45], while the pressure at primary outlets (downstream) remains more or less constant along the length of the tube (Figure 4a). This means the pressure ratio (PUP/PDN) decreases along the length of the tube. Similarly, the permeate flow also does not vary much with change in concentration. Therefore, its average value for all the three studied concentrations with respect to the cases is shown in Figure 4b. The primary outlet mass flowrate (permeate flow) for all the studied cases of the three different compositions increases from 4 to 5.5% (Figure 4b) along the length of the tube even though the pressure inside the main flow decreases (Figure 4a). This means that for a binary mixture, as seen in the pure gas study [45], the development of a viscous sublayer thickness is governing the primary flow along the length of the tube [45].

Figure 4: Average upstream and downstream pressure across the porous surface (left) and Average permeate flow expressed in relative weight compared to the main flow (right).



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3.1 Evidence on gas filtration of interactions between species in a binary mixture The mixed gas permeability of CO2 and of N2 is determined using Eq. 2 and 3. The permeability value obtained from both equations are the same; therefore, the results obtained from Eq. 2 are presented in Figure 5. This also confirms that the Eq. 3 can also be used for multispecies mixtures in case of porous stainless steel tube. For all compositions, moving from case 1 to 4 causes an increase in inlet mass flowrate of CO 2 and N2. Due to this, the porous flow increases and hence the mixed gas permeability of both the gases also increases. The pressure effect is the same for both CO2 and N2 (Figure 6a). However, the pressure rise is generated by a change in the respective partial pressures of N2 and CO2 (Figure 6b). Thus, the CO2 mixed gas permeability increases with the increase in CO2 concentration whereas the N2 mixed gas permeability decreases (because at the opposite, the N2 partial pressure decreases see Figure 5 secondary y-axis-) [32]. In addition, the mixed gas permeability profile along the length of the tube for all the three compositions seems to be constant on a global scale (Figure 5). This demonstrates that the main influencing parameter is the total pressure (case 1 to 4), the second is the partial pressure (composition) and only then, on third position, the spatial distribution may have an impact (as seen on the data on a closer view as it will be discussed below, based on Figure 6).


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Figure 5: Effects of total pressure (case 1 to 4), of partial pressure (composition of 50/50%, 60/40% and 70/30% of CO2/N2 mixture) and of spatial distribution on gas permeability. *filled symbols are for gas permeability and non-filled symbols are for partial pressure drop across the porous surface.

Figure 6: Average gas permeability (a), and partial pressure (b) variation with respect to total inlet pressure for different inlet composition of N2 and CO2. To understand the distribution of mixed gas permeability along the length of the tube, one test-case from each composition (the composition compared with pure gas study are marked in bold in Table 3) is considered and compared with the corresponding pure gas permeability (determined in a previous work [45]) obtained for similar mass flowrates (Figure 7). The N2 pure gas permeability increases for all the three compositions along the length of the tube, whereas the mixed gas permeability of N2 slightly increases or roughly remains constant for a 50/50% composition and decreases for the other two compositions (60/40% and 70/30%). Hence the increase in CO2 concentration reverses the trend of N2 gas permeability in case of a mixture. This is an important result because it demonstrates the fact that a competition between chemical species may happen in terms of filtration and this is the key principle that may govern the differentiated selectivity of materials. This observation does not apply to CO2 13 ACS Paragon Plus Environment


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gas permeability for which the pure and mixed gas permeabilities keep the same trend. This demonstrates that in case of a competition between species, the change is mostly observed for the minor compound and not for the major one.


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Figure 7: Change of trend for N2 permeability in a mixture compared to pure conditions when CO2 concentration is increased Table 4 shows the average values of the gas permeability and selectivity along the length of the tube for the respective cases. The difference between the separation selectivity and ideal selectivity values is 0.99% for 50/50% composition which is nearly the same compared to 18.9% and 39.9% obtained respectively for cases of 60/40% and 70/30%. As seen before, the ideal selectivity is very close to the separation selectivity for a 50/50% composition. The ideal selectivity and separation selectivity in a 60/40% and 70/30% composition are not the same due to the different partial pressures of the compounds [52]. The ideal selectivity (N2/CO2) decreases with an increase in CO2 concentration because the inlet mass flow rate of N2 for all the three compositions remains almost the same due to which the N2 gas permeability also remains constant. While in case of CO2, the pure CO2 gas permeability increases due to the increase in inlet MFR and hence the selectivity decreases. The separation selectivity (N2/CO2) decreases due to an increase in the CO2 mixture gas permeability caused by the higher CO2 content and partial pressure.



Inlet Composition % 100% 100% 100%

MFR (g/s) N2 CO2 0.54 0.94 0.59 1.50 0.50 2.06

Inlet Composition % 50/50 60/40 70/30

MFR (g/s) N2 CO2 0.54 0.94 0.59 1.50 0.50 2.06

Pure gas Permeability (m3(STP)·m/(m2·s·Pa)) N2 3.91×10-8 3.91×10-8 3.91×10-8

CO2 4.89×10-8 5.65×10-8 6.54×10-8

Mixture Permeability (m3(STP)·m/(m2·s·Pa))

N2 2.43×10-8 2.46×10-8 2.05×10-8

CO2 3.01×10-8 4.39×10-8 5.71×10-8

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Ideal selectivity N2/CO2 0.799 0.691 0.598 Separation selectivity N2/CO2 0.807 0.560 0.359

Table 4: Pure gas and mixture permeabilities and N2/CO2 selectivities for three different compositions (Pure gas permeability values are imported from [45]) 3.2 Investigation of the origin of multispecies interactions To understand the interactions between both gases, the concentrations of N2 and CO2 inside the porous tube for three different inlet compositions are determined (Figure 8). It can be seen that the CO2 concentration decreases and the N2 concentration increases inside the main flow along the length of the porous tube in all cases of the three different inlet compositions. This result is very important because it clearly demonstrates the ability of a tube configuration to filtrate preferably one chemical compound rather than another without use of any special membrane coating, even when mixed by equivalent mole composition (50/50).


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Figure 8: Distribution profiles of N2 and CO2 volumetric concentrations inside the porous tube along its length for 3 different inlet compositions (50/50%, 60/40% and 70/30%). The Kn value inside the porous surface is obtained using Eq. 7 for all the cases 1 to 4 and for the three different compositions (see Figure 9). The figure presents the average value of Knudsen number for the respective cases. It can be seen from Figure 9 that when the Knudsen number is greater than one, collisions between the particles occur very rarely and they move independently from each other.

Figure 9: Average Knudsen number variation along the length of the porous tube for 4 different cases. 17 ACS Paragon Plus Environment


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The average pressure of the mixture decreases along the length of the tube (Figure 4a) such that the mean Knudsen number increases (Figure 9). The momentum exchange between the light and heavy molecules is reduced [53]. Thus, the difference in the molecular velocities of different species is enhanced and more obvious gas separation tends to occur (Figure 8). The reason for this difference is that the larger molecular mass ratio brings about the larger velocity difference between the species in the N2–CO2 system, and thus enhances the quality of gas separation [53]. The separation selectivity (N2/CO2) increases along the flow (Figure 10) due to the effect of the boundary layer (as seen in previous work [40] and as seen in here through momentum consideration). In addition, the selectivity increases with the decrease of CO2 concentration (from 70/30 to 50/50 test cases). This is due to the CO2 partial pressure, which varies according to the CO2 concentration. However, one could have expected a decrease in the selectivity despite the fact that it is found to increase here. Indeed, the concentration of CO2 is decreasing and N2 is increasing inside the main flow; which means the filtrated CO2 content rises while the one of N2 decreases along the length of the tube. Hence, there should be a decrease in the selectivity along the length of the tube according to the equation of selectivity. However, an increase in selectivity is found (see Figure 9); which demonstrates that the effect of the decrease in partial pressure is of higher magnitude compared to the change of gas concentration. The decrease in volumetric concentration of CO2 and increase in N2 is not enough to affect the gas permeability which is mainly governed by the partial pressure (see Eq. 2). The change in concentration would have affected the gas permeability or selectivity if the pressure inside the tube would have remained constant along the length. This is because, on one hand, according to Dalton’s law, the partial pressure of any specie presents in a mixture is defined as 𝑃𝑖 = 𝑋𝑖 · 𝑃𝑡𝑜𝑡𝑎𝑙 and it varies according to the Xi (concentration of specie inside the main flow) if Ptotal (total pressure inside the main flow) is constant. Here the total pressure (Ptotal) inside the main flow decreases (Figure 4a) along the length of the tube due to the filtration (permeate flow) and to the fluid friction. Therefore, the partial pressure (Pi) of N2 and of CO2 also decrease (see Figure 5). Hence, the change in concentration does not affect the gas permeability.


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Figure 10: Effect of boundary layer on the separation selectivity (N2/CO2) distribution along the length of the porous tube for 3 different inlet compositions (50/50%, 60/40% and 70/30%).



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Conclusion The longitudinal separation ability of a stainless steel porous tube has been investigated through the estimation of gas permeability and selectivity of N2/CO2 mixtures. The ideal selectivity and the separation selectivity have been found to be different; which illustrates a matrix effect of the mixture for which the different viscosities of both species compete with each other and influence the filtration process of the other specie. The ideal and separation selectivity decreases with an increase in the CO2 concentration which shows that the major compounds has the main role, from far. This clear effect of selectivity has been shown corresponding to a larger filtration of CO2 (major compound) than of N2 compound (minor compound). For the three compositions under study, the concentration of N2 in the main flow increases from the inlet to the outlet. This demonstrates the ability of such a tube configuration to evacuate impurities like CO2 which are expected to be removed when considering applications like fuel cell. The increase in CO2 concentration also reverses the trend of N2 gas permeability in case of a mixture. In addition, the selectivity was found to vary along the tube length due to the dynamic boundary layer which plays a key role in this spatial separation process. The viscosity of the gas mixture is responsible for this change in the boundary layer and what changes the viscosity is the chemical composition of the mixture and the pressure mainly. Further studies will now focus on mixtures with Helium and CO 2 under enlarged operating conditions for mixtures from 50/50 to 01/99 compositions to get closer to the realistic operating conditions of fuel cells. Acknowledgments This work has been performed under the support of Airbus and MBDA Group.


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Figure: For Table of Contents Only


Axial distribution of permeance and selectivity of a porous cylindrical

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