Separation of Hydrogen from Carbon Dioxide through Porous Ceramics

The gas permeability of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide porous ceramics toward H2, CO2, and H2–CO2 mixtures were investigated at room temperature. The permeation of H2 and CO2 single gases occurred above a critical pressure gradient, which was smaller for H2 gas than for CO2 gas. When the Knudsen number (λ/r ratio, λ: molecular mean free path, r: pore radius) of a single gas was larger than unity, Knudsen flow became the dominant gas transportation process. The H2 fraction for the mixed gas of (20%–80%) H2–(80%–20%) CO2 through porous Al2O3, YSZ, and SiC approached unity with decreasing pressure gradient. The high fraction of H2 gas was closely related to the difference in the critical pressure gradient values of H2 and CO2 single gas, the inlet mixed gas composition, and the gas flow mechanism of the mixed gas. Moisture in the atmosphere adsorbed easily on the porous ceramics and affected the critical pressure gradient, leading to the increased selectivity of H2 gas.

The reformed gas contains hydrogen and carbon dioxide. The byproduct, carbon dioxide, is usually removed by a pressure swing adsorption method or a cryogenic distillation method at a low temperature. However, the separation of hydrogen from carbon dioxide at high temperatures of 200-400 • C (i.e., the reaction temperature of Equation (2)) using a membrane separator is desirable from the point of view of reducing the energy consumption and costs associated with hydrogen refinement.
Polyimide membranes are well-known commercialized membranes for separating hydrogen gas at operating temperatures less than 200 • C [1,2]. In polymer membranes used to separate gases, the gas molecules are transported through the spaces of the polymer chain network. Hydrogen molecules, which are small, permeate through the polymer membrane more easily than other gases. For example, when a mixture of 10 vol % H 2 and 90 vol % CO 2 was fed at 0.4-0.6 MPa to a polyimide membrane with a thickness of approximately 50 µm [1], the H 2 selectivity (i.e., the ratio between the permeability coefficients of H 2 and CO 2 ) was 2.7, whereas the H 2 permeability coefficient was approximately 3 × 10 −15 mol·m/(m 2 ·s·Pa) [1].
where α is the permeability coefficient of gas (α = 2εrc/3RT for the Knudsen equation, α = εr 2 P/8RTη for the Poiseuille equation); ∆P/L is the pressure gradient between the inlet and outlet gases; ε and r are the open porosity and pore radius of a porous membrane, respectively; P is the average pressure between the inlet and outlet gases; η is the viscosity of the gas; c is the average velocity of gas molecules (c = √ 8RT/πM, where M is the molecular weight of the gas molecules); R is the gas constant; and T is the absolute temperature. The fraction (F) of hydrogen gas of the outlet gas for 50 vol % H 2 -50 vol % CO 2 mixed gas is calculated by Equations (4) and (5) for Knudsen and Poiseuille flow, respectively: The F value based on viscosities [12] of 8.73 µPa·s for H 2 gas and 14.53 µPa·s for CO 2 gas at 17 • C is 0.824 in Equation (4) and 0.611 in Equation (5). Note that the F value is related to the generally defined selectivity (i.e., the ratio between the permeability coefficients of the major and minor permeant gases) by Equation (6): The ratio of molecular mean free path to the pore size (i.e., the Knudsen number) determines the mechanism of gas flow. Figure 1 shows the molecular mean free paths (λ) of H 2 and CO 2 gases calculated by Equation (7) at 290 K [13].
Materials 2016, 9,930 3 of 20 The λ value increases with decreasing gas pressure and is larger for H 2 gas than for CO 2 gas. When the λ/r (pore radius) ratio is less than unity, Poiseuille flow becomes dominant. For instance, H 2 and CO 2 gases exhibit Knudsen and Poiseuille flow, respectively, in a pore with an 80-nm radius (Figure 1), thereby influencing the flux of transported gas.
One approach to enhancing the selectivity of a gas permeated through porous ceramics is to modify the surfaces of ceramic particles by an agent that interacts with a gas and suppresses the permeation of the other mixed gas (e.g., AlOOH [14] and silane coupling agents [15] interact with CO 2 gas). In this work, we used another approach to enhance the selectivity of a gas permeated through porous ceramics. In our previous study [16,17], the J-∆P/L relation for CO 2 gas was observed at pressures greater than a critical pressure gradient (∆P c /L), as shown in Figure 2. However, the critical pressure gradient of H 2 gas was closer to 0 MPa/m. This difference in critical pressure gradients can be exploited to separate H 2 gas from CO 2 gas in the ∆P/L range below the ∆P c /L for CO 2 gas. A large difference in the ∆P c /L values for two gases also favors an increase in the flux of a selected gas at a relatively low pressure. In this study, the selectivity of the H 2 -CO 2 mixed gas was investigated at room temperature using porous ceramics of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide.
Materials 2016, 9,930 3 of 20 The λ value increases with decreasing gas pressure and is larger for H2 gas than for CO2 gas. When the λ/r (pore radius) ratio is less than unity, Poiseuille flow becomes dominant. For instance, H2 and CO2 gases exhibit Knudsen and Poiseuille flow, respectively, in a pore with an 80-nm radius (Figure 1), thereby influencing the flux of transported gas.
One approach to enhancing the selectivity of a gas permeated through porous ceramics is to modify the surfaces of ceramic particles by an agent that interacts with a gas and suppresses the permeation of the other mixed gas (e.g., AlOOH [14] and silane coupling agents [15] interact with CO2 gas). In this work, we used another approach to enhance the selectivity of a gas permeated through porous ceramics. In our previous study [16,17], the J-ΔP/L relation for CO2 gas was observed at pressures greater than a critical pressure gradient (ΔPc/L), as shown in Figure 2. However, the critical pressure gradient of H2 gas was closer to 0 MPa/m. This difference in critical pressure gradients can be exploited to separate H2 gas from CO2 gas in the ΔP/L range below the ΔPc/L for CO2 gas. A large difference in the ΔPc/L values for two gases also favors an increase in the flux of a selected gas at a relatively low pressure. In this study, the selectivity of the H2-CO2 mixed gas was investigated at room temperature using porous ceramics of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide.   The λ value increases with decreasing gas pressure and is larger for H2 gas than for CO2 gas. When the λ/r (pore radius) ratio is less than unity, Poiseuille flow becomes dominant. For instance, H2 and CO2 gases exhibit Knudsen and Poiseuille flow, respectively, in a pore with an 80-nm radius (Figure 1), thereby influencing the flux of transported gas.
One approach to enhancing the selectivity of a gas permeated through porous ceramics is to modify the surfaces of ceramic particles by an agent that interacts with a gas and suppresses the permeation of the other mixed gas (e.g., AlOOH [14] and silane coupling agents [15] interact with CO2 gas). In this work, we used another approach to enhance the selectivity of a gas permeated through porous ceramics. In our previous study [16,17], the J-ΔP/L relation for CO2 gas was observed at pressures greater than a critical pressure gradient (ΔPc/L), as shown in Figure 2. However, the critical pressure gradient of H2 gas was closer to 0 MPa/m. This difference in critical pressure gradients can be exploited to separate H2 gas from CO2 gas in the ΔP/L range below the ΔPc/L for CO2 gas. A large difference in the ΔPc/L values for two gases also favors an increase in the flux of a selected gas at a relatively low pressure. In this study, the selectivity of the H2-CO2 mixed gas was investigated at room temperature using porous ceramics of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide.

Fabrication of Porous Ceramics
The employed powders were α-alumina (AKP50, specific surface area (S) 10.5 m 2 /g, equivalent diameter (D) 143 nm, isoelectric point (iep) pH 8.5, Sumitomo Chemical Co., Ltd., Tokyo, Japan), YSZ (TZ-8Y, 92 mol % ZrO 2 -8 mol % Y 2 O 3 , S = 14.9 m 2 /g, D = 68.3 nm, iep = pH 7.8, Tosoh Co., Tokyo, Japan) and SiC (impurity, mass%: SiO 2 0.66, C 0.37, Al 0.004 and Fe 0.013, S = 13.4 m 2 /g, D = 139 nm, iep = pH 2.5, Yakushima Electric Industry Co., Ltd., Tokyo, Japan). Each powder of Al 2 O 3 and YSZ was dispersed at a solid content of 30 vol % in double-distilled water adjusted with an HCl solution at pH 3 where the particles were charged positively to increase the electrostatic repulsive energy among the particles. After stirring for 24 h, the suspensions were consolidated by pressure filtration at pressures as high as 19 MPa and were dried at 100 • C in air for 24 h. The obtained Al 2 O 3 and YSZ compacts were sintered at 800 and 1100 • C, respectively, in air for 1 h. In the fabrication of porous SiC compacts, the sintering additives of α-alumina (AKP50) and yttria (purity > 99.9 mass%, S = 15.0 m 2 /g, D = 79.5 nm, iep = pH 7.5, Shin-Etsu Chemical Co., Ltd., Tokyo, Japan) were mixed in a mass ratio of SiC:Al 2 O 3 :Y 2 O 3 = 1:0.02:0.02. The aqueous suspension was prepared at a solid content of 30 vol % at pH 5, where the positively charged sintering additives were attracted to the negatively charged SiC particles to form heterocoagulated particle clusters. After stirring for 24 h, the suspension was consolidated over a gypsum board. The obtained compacts were hot-pressed at 1400, 1500, or 1700 • C under a pressure of 39 MPa in an argon atmosphere for 2 h. The densities of fabricated compacts were measured by the Archimedes method using double-distilled water. The microstructures were observed by field-emission scanning electron microscopy (FE-SEM, S-4100H, Hitachi High-Technologies Co., Tokyo, Japan); the pore size distributions were analyzed via an intercept method [18]. The two-dimensional pore size determined by the intercept method was converted into a three-dimensional pore size by multiplying by a factor of 1.56, where the pores were assumed to be spherical [19]. The pore size distributions were also measured by mercury porosimetry at the Saga Ceramics Research Laboratory in Japan (Arita-cho, Nishimatsuura-gun, Saga 844-0024, Saga, Japan).

Gas Permeation in Porous Ceramics
The Al 2 O 3 and YSZ samples were formed into disk shapes 20 mm in diameter and 3 mm in thickness. The diameter and thickness of the SiC disk sample were 10 and 3 mm, respectively. The side of each sample was sealed with phenolic resin. Before the gas separation experiments, each sample was dried at 100 • C for 24 h. The amount of moisture adsorbed on the dried sample was measured by a thermogravimetric/differential thermal analyzer (TG/DTA, Thermoplus, Rigaku, Tokyo, Japan). When the sample dried at 100 • C for 24 h was heated to 600 • C at the heating rate of 10 • C/min, the weight losses of Al 2 O 3 and YSZ porous ceramics were about 0.25% and 0.20%, respectively. In the Al 2 O 3 and YSZ samples dried at 300 • C for 24 h, the weight losses were about 0.25% and 0.10%, respectively. These results indicate that moisture in the atmosphere adsorbs easily on the present porous ceramics during the gas separation experiment. The sample to be measured was placed in a stainless steel holder, as shown in Figure 3. Rubber rings were placed in front of and behind the stainless spacers and were compressed by the stainless holder to avoid gas leakage. H 2 (>99.999% purity), CO 2 (>99.99% purity) and mixed gases with 20, 50, and 80 vol % H 2 were supplied at pressures as high as 0.199 MPa at room temperature. The pressure of the permeated gas was approximately constant at 0.101 MPa. The gas pressure was monitored using a pressure gauge (MJE-PPX No. 0003-81V, CKD Co., Ltd., Aichi, Japan). The flux of permeated gas was measured using a flow meter (Soapfilm Flow Meter, 3001-11002, GL Science Inc., Tokyo, Japan). The compositions of inlet and outlet gases were measured using a gas chromatograph equipped with an active carbon column and a thermal conductivity detector (GT7100T, J-ScienceLab Co., Ltd., Tokyo, Japan). The temperatures of the column and detector were 70 and 100 • C, respectively. The electric current supplied to the detector was 60 mA, and the carrier gas was argon.  Figure 4 shows the microstructures and pore size distributions of Al2O3 and YSZ compacts measured by mercury porosimetry. The relative density and the open and closed porosities were 62.7%, 36.2%, and 1.1%, respectively, for Al2O3 and 50.4%, 40.5%, and 9.1%, respectively, for YSZ. The median pore sizes of Al2O3 and YSZ were 45.3 and 115.8 nm, respectively. On the other hand, threedimensional pore size was also determined on the observed microstructures (Figure 4a,b) by multiplying the two-dimensional pore size by 1.56, as previously discussed [16,19]. The pore sizes at 10% and 90% of the cumulative frequency were 10.8 and 133.9 nm, respectively, in porous Al2O3 and 8.2 and 113.1 nm, respectively, in porous YSZ. The median sizes of the pores of Al2O3 and YSZ were 49.4 and 39.1 nm, respectively. Compared to the pore size measured by microscopic technique, the pore size of mercury porosimetry was almost the same for the Al2O3 compact but was three times larger for the YSZ compact. In this paper, the pore size measured by mercury porosimetry was used to discuss the flux and permeability coefficient of the gas permeated through the porous ceramics.    Figure 4 shows the microstructures and pore size distributions of Al 2 O 3 and YSZ compacts measured by mercury porosimetry. The relative density and the open and closed porosities were 62.7%, 36.2%, and 1.1%, respectively, for Al 2 O 3 and 50.4%, 40.5%, and 9.1%, respectively, for YSZ. The median pore sizes of Al 2 O 3 and YSZ were 45.3 and 115.8 nm, respectively. On the other hand, three-dimensional pore size was also determined on the observed microstructures (Figure 4a,b) by multiplying the two-dimensional pore size by 1.56, as previously discussed [16,19]. The pore sizes at 10% and 90% of the cumulative frequency were 10.8 and 133.9 nm, respectively, in porous Al 2 O 3 and 8.2 and 113.1 nm, respectively, in porous YSZ. The median sizes of the pores of Al 2 O 3 and YSZ were 49.4 and 39.1 nm, respectively. Compared to the pore size measured by microscopic technique, the pore size of mercury porosimetry was almost the same for the Al 2 O 3 compact but was three times larger for the YSZ compact. In this paper, the pore size measured by mercury porosimetry was used to discuss the flux and permeability coefficient of the gas permeated through the porous ceramics.  Figure 4 shows the microstructures and pore size distributions of Al2O3 and YSZ compacts measured by mercury porosimetry. The relative density and the open and closed porosities were 62.7%, 36.2%, and 1.1%, respectively, for Al2O3 and 50.4%, 40.5%, and 9.1%, respectively, for YSZ. The median pore sizes of Al2O3 and YSZ were 45.3 and 115.8 nm, respectively. On the other hand, threedimensional pore size was also determined on the observed microstructures (Figure 4a,b) by multiplying the two-dimensional pore size by 1.56, as previously discussed [16,19]. The pore sizes at 10% and 90% of the cumulative frequency were 10.8 and 133.9 nm, respectively, in porous Al2O3 and 8.2 and 113.1 nm, respectively, in porous YSZ. The median sizes of the pores of Al2O3 and YSZ were 49.4 and 39.1 nm, respectively. Compared to the pore size measured by microscopic technique, the pore size of mercury porosimetry was almost the same for the Al2O3 compact but was three times larger for the YSZ compact. In this paper, the pore size measured by mercury porosimetry was used to discuss the flux and permeability coefficient of the gas permeated through the porous ceramics.    Figure 5 shows the microstructures and pore size distributions of SiC samples hot-pressed at 1400, 1500, and 1700 • C. The relative density and the open and closed porosities of SiC samples were 61.1%, 36.1%, and 2.8%, respectively, at the hot-pressing temperature of 1400 • C, 69.3%, 28.1%, and 2.6%, respectively, at 1500 • C, and 75.4%, 17.9%, and 6.7%, respectively, at 1700 • C. The SiC samples densified through liquid-phase sintering consisted of bimodal particles smaller and larger than 1 µm. The fraction of larger particles increased at a higher hot-pressing temperature. Because the exact pore size distribution was difficult to measure on the basis of the scanning electron micrographs in Figure 5, the pore sizes were measured by mercury porosimetry. Figure 5d shows the cumulative pore volume of the porous SiC compacts. The median sizes of the cumulative pore volume were 111.9, 113.8, and 164.0 nm in the SiC samples hot-pressed at 1400, 1500, and 1700 • C, respectively. As a result, the pore size in the present experiment increased in the order Al 2 O 3 < SiC ≈ YSZ.

Microstructures of Porous Ceramics
Materials 2016, 9,930 6 of 20 Figure 5 shows the microstructures and pore size distributions of SiC samples hot-pressed at 1400, 1500, and 1700 °C. The relative density and the open and closed porosities of SiC samples were 61.1%, 36.1%, and 2.8%, respectively, at the hot-pressing temperature of 1400 °C, 69.3%, 28.1%, and 2.6%, respectively, at 1500 °C, and 75.4%, 17.9%, and 6.7%, respectively, at 1700 °C. The SiC samples densified through liquid-phase sintering consisted of bimodal particles smaller and larger than 1 μm. The fraction of larger particles increased at a higher hot-pressing temperature. Because the exact pore size distribution was difficult to measure on the basis of the scanning electron micrographs in Figure  5, the pore sizes were measured by mercury porosimetry. Figure 5d shows the cumulative pore volume of the porous SiC compacts. The median sizes of the cumulative pore volume were 111.9, 113.8, and 164.0 nm in the SiC samples hot-pressed at 1400, 1500, and 1700 °C, respectively. As a result, the pore size in the present experiment increased in the order Al2O3 < SiC ≈ YSZ.

Permeation of H2 and CO2 Gases through Porous Ceramics
Figures 6 and 7 show the single gas flux of H2 and CO2 through the Al2O3 and YSZ porous ceramics, respectively. The flux values for H2 and CO2 gases calculated via Equation (3) using the measured porosity and median pore size are also plotted in Figures 6 and 7. The permeation of CO2 gas in the porous Al2O3 and YSZ occurred above a critical pressure gradient. The gas flux then increased linearly with increasing pressure gradient. Compared with the flux and critical pressure gradient measured for CO2 gas, those measured for H2 were larger and smaller, respectively. The critical pressure gradient values of H2 and CO2 gases were 3.2 and 20.0 MPa/m, respectively, for Al2O3 and 1.1 and 11.4 MPa/m, respectively, for YSZ. The measured flux of H2 gas through the porous Al2O3 was similar to the calculated flux based on Knudsen flow (Equation (3)). The measured flux of CO2 gas was within the values calculated for Knudsen flow and Poiseuille flow. The Knudsen number (=λ/r, Figure 1) was calculated to be 3.32-4.19 for H2 gas and 1.19-1.30 for CO2 gas; the exact values depend on the gas pressure (i.e., variation of the molecular mean free path in Figure 1), supporting the agreement between the experimental and the calculated transport characteristics of both gases. In the porous YSZ, the measured flux of H2 gas was close to the flux calculated using the Knudsen equation. Furthermore, the measured CO2 flux was within the values of CO2 flux calculated using the Knudsen and Poiseuille equations.

Permeation of H 2 and CO 2 Gases through Porous Ceramics
Figures 6 and 7 show the single gas flux of H 2 and CO 2 through the Al 2 O 3 and YSZ porous ceramics, respectively. The flux values for H 2 and CO 2 gases calculated via Equation (3) using the measured porosity and median pore size are also plotted in Figures 6 and 7. The permeation of CO 2 gas in the porous Al 2 O 3 and YSZ occurred above a critical pressure gradient. The gas flux then increased linearly with increasing pressure gradient. Compared with the flux and critical pressure gradient measured for CO 2 gas, those measured for H 2 were larger and smaller, respectively. The critical pressure gradient values of H 2 and CO 2 gases were 3.2 and 20.0 MPa/m, respectively, for Al 2 O 3 and 1.1 and 11.4 MPa/m, respectively, for YSZ. The measured flux of H 2 gas through the porous Al 2 O 3 was similar to the calculated flux based on Knudsen flow (Equation (3)). The measured flux of CO 2 gas was within the values calculated for Knudsen flow and Poiseuille flow. The Knudsen number (=λ/r, Figure 1) was calculated to be 3.32-4.19 for H 2 gas and 1.19-1.30 for CO 2 gas; the exact values depend on the gas pressure (i.e., variation of the molecular mean free path in Figure 1), supporting the agreement between the experimental and the calculated transport characteristics of both gases. In the porous YSZ, the measured flux of H 2 gas was close to the flux calculated using the Knudsen equation. Furthermore, the measured CO 2 flux was within the values of CO 2 flux calculated using the Knudsen and Poiseuille equations.  Similarly, Figure 8 shows the relationship between the single-gas flux of H2 and CO2 and the pressure gradient in the SiC porous ceramics. A similar trend of ΔPc/L (critical pressure gradient) for H2 and CO2 gases was observed in the porous SiC ceramics. The critical pressure gradient of H2 and CO2 gases was 0.2 and 2.4 MPa/m, respectively, in the SiC hot-pressed at 1400 °C, 1.7 and 8.5 MPa/m, respectively, at 1500 °C, and 0.8 and 2.8 MPa/m, respectively, at 1700 °C. Figure 9 and Table 1 summarize the permeability coefficients of H2 and CO2 gases as a function of the Knudsen number. The permeability coefficient was determined by dividing the flux J by the effective pressure gradient (ΔP/L − ΔPc/L). Note that, because each J-ΔP/L plot for H2 and CO2 gases showed an intercept (i.e., a critical pressure gradient), the permeability coefficient was determined for the gas flow above the ΔPc/L value. The Knudsen number represents the molecular mean free path (λ) normalized by the pore radius (r). The molecular mean free path was calculated using Equation (7). The pore radii of the oxides and SiC were measured by mercury porosimetry, as described in Section 3.1. The measured permeability coefficients were compared with the permeability coefficients calculated using the Knudsen and Poiseuille equations. In the Al2O3 and YSZ porous ceramics, the permeability coefficients of both the H2 and CO2 gases were similar to those calculated using the Knudsen model. In the SiC  Similarly, Figure 8 shows the relationship between the single-gas flux of H2 and CO2 and the pressure gradient in the SiC porous ceramics. A similar trend of ΔPc/L (critical pressure gradient) for H2 and CO2 gases was observed in the porous SiC ceramics. The critical pressure gradient of H2 and CO2 gases was 0.2 and 2.4 MPa/m, respectively, in the SiC hot-pressed at 1400 °C, 1.7 and 8.5 MPa/m, respectively, at 1500 °C, and 0.8 and 2.8 MPa/m, respectively, at 1700 °C. Figure 9 and Table 1 summarize the permeability coefficients of H2 and CO2 gases as a function of the Knudsen number. The permeability coefficient was determined by dividing the flux J by the effective pressure gradient (ΔP/L − ΔPc/L). Note that, because each J-ΔP/L plot for H2 and CO2 gases showed an intercept (i.e., a critical pressure gradient), the permeability coefficient was determined for the gas flow above the ΔPc/L value. The Knudsen number represents the molecular mean free path (λ) normalized by the pore radius (r). The molecular mean free path was calculated using Equation (7). The pore radii of the oxides and SiC were measured by mercury porosimetry, as described in Section 3.1. The measured permeability coefficients were compared with the permeability coefficients calculated using the Knudsen and Poiseuille equations. In the Al2O3 and YSZ porous ceramics, the permeability coefficients of both the H2 and CO2 gases were similar to those calculated using the Knudsen model. In the SiC Similarly, Figure 8 shows the relationship between the single-gas flux of H 2 and CO 2 and the pressure gradient in the SiC porous ceramics. A similar trend of ∆P c /L (critical pressure gradient) for H 2 and CO 2 gases was observed in the porous SiC ceramics. The critical pressure gradient of H 2 and CO 2 gases was 0.2 and 2.4 MPa/m, respectively, in the SiC hot-pressed at 1400 • C, 1.7 and 8.5 MPa/m, respectively, at 1500 • C, and 0.8 and 2.8 MPa/m, respectively, at 1700 • C. Figure 9 and Table 1 summarize the permeability coefficients of H 2 and CO 2 gases as a function of the Knudsen number. The permeability coefficient was determined by dividing the flux J by the effective pressure gradient (∆P/L − ∆P c /L). Note that, because each J-∆P/L plot for H 2 and CO 2 gases showed an intercept (i.e., a critical pressure gradient), the permeability coefficient was determined for the gas flow above the ∆P c /L value. The Knudsen number represents the molecular mean free path (λ) normalized by the pore radius (r). The molecular mean free path was calculated using Equation (7). The pore radii of the oxides and SiC were measured by mercury porosimetry, as described in Section 3.1. The measured permeability coefficients were compared with the permeability coefficients calculated using the Knudsen and Poiseuille equations. In the Al 2 O 3 and YSZ porous ceramics, the permeability coefficients of both the H 2 and CO 2 gases were similar to those calculated using the Knudsen model. In the SiC porous ceramics, the measured permeability coefficient of H 2 gas is well explained by the Knudsen model. The permeability coefficient of CO 2 gas was within the values predicted by the Knudsen and Poiseuille models. When the Knudsen number (λ/r) is greater than unity, Knudsen flow becomes the dominant gas transportation process, which is the usual tendency. As observed in Figure 9, when the Knudsen number decreases to a smaller value (<1) in the SiC porous compacts, the influence of Poiseuille flow becomes larger in the case of CO 2 gas. porous ceramics, the measured permeability coefficient of H2 gas is well explained by the Knudsen model. The permeability coefficient of CO2 gas was within the values predicted by the Knudsen and Poiseuille models. When the Knudsen number (λ/r) is greater than unity, Knudsen flow becomes the dominant gas transportation process, which is the usual tendency. As observed in Figure 9, when the Knudsen number decreases to a smaller value (<1) in the SiC porous compacts, the influence of Poiseuille flow becomes larger in the case of CO2 gas.   Figure 10 shows the critical pressure gradient (ΔPc/L) as a function of the Knudsen number (λ/r ratio). The ΔPc/L value increases at a small Knudsen number. This result implies that the ΔPc/L value is greater for CO2 gas with a small λ value than for H2 gas with a large λ value (Figure 1) in the same pore size distribution. Another observation is that the decreased pore size (2r) for a specified gas   porous ceramics, the measured permeability coefficient of H2 gas is well explained by the Knudsen model. The permeability coefficient of CO2 gas was within the values predicted by the Knudsen and Poiseuille models. When the Knudsen number (λ/r) is greater than unity, Knudsen flow becomes the dominant gas transportation process, which is the usual tendency. As observed in Figure 9, when the Knudsen number decreases to a smaller value (<1) in the SiC porous compacts, the influence of Poiseuille flow becomes larger in the case of CO2 gas.   Figure 10 shows the critical pressure gradient (ΔPc/L) as a function of the Knudsen number (λ/r ratio). The ΔPc/L value increases at a small Knudsen number. This result implies that the ΔPc/L value is greater for CO2 gas with a small λ value than for H2 gas with a large λ value (Figure 1) in the same pore size distribution. Another observation is that the decreased pore size (2r) for a specified gas    Figure 10 shows the critical pressure gradient (∆P c /L) as a function of the Knudsen number (λ/r ratio). The ∆P c /L value increases at a small Knudsen number. This result implies that the ∆P c /L value is greater for CO 2 gas with a small λ value than for H 2 gas with a large λ value (Figure 1) in the same pore size distribution. Another observation is that the decreased pore size (2r) for a specified gas leads to an increase of the ∆P c /L value. That is, the ∆P c /L value increases in the case of Poiseuille flow giving a small flux of permeated gas rather than in the case of Knudsen flow giving a large flux of permeated gas (Figures 6 and 7). As evident in Figure 10a, the ∆P c /L value is more sensitive to the Knudsen number in the case of the alumina porous ceramics than in the case of the SiC or YSZ porous ceramics. That is, the pore size, chemical composition of porous ceramics, and shape of pores (in SiC compacts) affect the ∆P c /L value. The large difference in ∆P c /L values between H 2 and CO 2 gases is effective to separate H 2 gas from CO 2 gas. Table 1. Summary of permeability coefficients in Figure 9. leads to an increase of the ΔPc/L value. That is, the ΔPc/L value increases in the case of Poiseuille flow giving a small flux of permeated gas rather than in the case of Knudsen flow giving a large flux of permeated gas (Figures 6 and 7). As evident in Figure 10a, the ΔPc/L value is more sensitive to the Knudsen number in the case of the alumina porous ceramics than in the case of the SiC or YSZ porous ceramics. That is, the pore size, chemical composition of porous ceramics, and shape of pores (in SiC compacts) affect the ΔPc/L value. The large difference in ΔPc/L values between H2 and CO2 gases is effective to separate H2 gas from CO2 gas. Table 1. Summary of permeability coefficients in Figure 9.   Figure 11 shows the flux of H2 and CO2 gases for the mixed gas of 50 vol % H2 and 50 vol % CO2 in the Al2O3 and YSZ porous ceramics. For comparison, the flux values of H2 and CO2 single gases are also shown in Figure 11. In both of the porous ceramics, the flux of H2 gas was greater than that of CO2 gas. The flux of H2 gas in the mixed gas decreased substantially compared to that of single H2 gas. The critical pressure gradient (ΔPc/L) of CO2 gas in the mixed gas became smaller than that of single CO2 gas and approached that of single H2 gas. Figure 12 shows the flux of H2 and CO2 gases in the mixed gas permeated through the SiC porous ceramics. The flux values of H2 and CO2 gases were similar to each other and were similar in magnitude to the flux of single H2 gas. This tendency differs from the results shown in Figure 11. As previously mentioned, the H2 and CO2 single gases permeated through the Al2O3 or YSZ porous ceramics according to the Knudsen mechanism ( Figure 9, Table 1 Figure 11 shows the flux of H 2 and CO 2 gases for the mixed gas of 50 vol % H 2 and 50 vol % CO 2 in the Al 2 O 3 and YSZ porous ceramics. For comparison, the flux values of H 2 and CO 2 single gases are also shown in Figure 11. In both of the porous ceramics, the flux of H 2 gas was greater than that of CO 2 gas. The flux of H 2 gas in the mixed gas decreased substantially compared to that of single H 2 gas. The critical pressure gradient (∆P c /L) of CO 2 gas in the mixed gas became smaller than that of single CO 2 gas and approached that of single H 2 gas. Figure 12 shows the flux of H 2 and CO 2 gases in the mixed gas permeated through the SiC porous ceramics. The flux values of H 2 and CO 2 gases were similar to each other and were similar in magnitude to the flux of single H 2 gas. This tendency differs from the results shown in Figure 11. As previously mentioned, the H 2 and CO 2 single gases permeated through the Al 2 O 3 or YSZ porous ceramics according to the Knudsen mechanism ( Figure 9, Table 1).

Permeation of H 2 -CO 2 Mixed Gas in Porous Ceramics
One factor used to interpret the permeation of the mixed gas is the interaction between pore walls and gas species, which is not expressed in the Knudsen equation (Equation (3)). The oxide porous ceramics have ionic bonds, and CO 2 molecules are polarized between their carbon atom (delta plus) and oxygen atoms (delta minus) because of their different electronegativities. The attractive interaction between pore walls of porous oxide ceramics and CO 2 molecules is expected to be strong compared to the interaction between pore walls and H 2 molecules. The adsorption of CO 2 molecules of the mixed gas on the pore walls of oxide ceramics may be interrupted by the collision between pore walls and H 2 molecules, leading to a decrease in the critical pressure gradient of CO 2 gas in the mixed gas.
On the basis of the data in Figures 11 and 12, Figure 13 shows the fraction of H 2 gas in the outlet gas and the H 2 fractions predicted by the Knudsen and Poiseuille models. In the Al 2 O 3 and YSZ porous ceramics, the H 2 fraction was higher than that of the supplied gas. When the pressure gradient decreased, the H 2 fraction increased, reaching 0.966 at 6.16 MPa/m in the porous Al 2 O 3 and 0.844 at 3.13 MPa/m in the porous YSZ, which exceeded the fraction of H 2 predicted by the Knudsen equation. In the SiC porous ceramics, the H 2 fraction was approximately the same value as in the supplied gas at pressure gradients greater than 10 MPa/m. In the lower pressure-gradient range, the H 2 fraction increased drastically. Within the detection limit of gas concentration (approximately 0.1% in this study), the H 2 fraction reached almost unity at 1.36 MPa/m. One factor used to interpret the permeation of the mixed gas is the interaction between pore walls and gas species, which is not expressed in the Knudsen equation (Equation (3)). The oxide porous ceramics have ionic bonds, and CO2 molecules are polarized between their carbon atom (delta plus) and oxygen atoms (delta minus) because of their different electronegativities. The attractive interaction between pore walls of porous oxide ceramics and CO2 molecules is expected to be strong compared to the interaction between pore walls and H2 molecules. The adsorption of CO2 molecules of the mixed gas on the pore walls of oxide ceramics may be interrupted by the collision between pore walls and H2 molecules, leading to a decrease in the critical pressure gradient of CO2 gas in the mixed gas.
On the basis of the data in Figures 11 and 12, Figure 13 shows the fraction of H2 gas in the outlet gas and the H2 fractions predicted by the Knudsen and Poiseuille models. In the Al2O3 and YSZ porous ceramics, the H2 fraction was higher than that of the supplied gas. When the pressure gradient decreased, the H2 fraction increased, reaching 0.966 at 6.16 MPa/m in the porous Al2O3 and 0.844 at 3.13 MPa/m in the porous YSZ, which exceeded the fraction of H2 predicted by the Knudsen equation. In the SiC porous ceramics, the H2 fraction was approximately the same value as in the supplied gas at pressure gradients greater than 10 MPa/m. In the lower pressure-gradient range, the H2 fraction increased drastically. Within the detection limit of gas concentration (approximately 0.1% in this study), the H2 fraction reached almost unity at 1.36 MPa/m.  Figures 14 and 15 show the H2 fraction for 20 vol % H2-80 vol % CO2 mixed gas and 80 vol % H2-20 vol % CO2 mixed gas, respectively. A similar increase of H2 fraction was measured at a low pressure gradient. In the case of 20% H2-80% CO2 mixed gas (Figure 14), the H2 fraction was 0.972 at 6.88 MPa/m in Al2O3, 0.504 at 8.04 MPa/m in YSZ, and 0.999 at 3.40 MPa/m in SiC, respectively. When 80% H2-20% CO2 mixed gas was permeated (Figure 15), the H2 fraction was 0.976 at 7.61 MPa/m in Al2O3, 0.936 at 3.13 MPa/m in YSZ, and 0.987 at 3.06 MPa/m in SiC, respectively. These results are further discussed in a later section.
The selectivity is defined generally by Equation (6) in the Introduction; the selectivity for 50% H2-50% CO2 mixed gas is included in Figure 16. The selectivity of all samples increased with decreasing pressure gradient. The selectivity of Al2O3 reached 28.8 at 6.16 MPa/m, which is The selectivity is defined generally by Equation (6) in the Introduction; the selectivity for 50% H 2 -50% CO 2 mixed gas is included in Figure 16. The selectivity of all samples increased with decreasing pressure gradient. The selectivity of Al 2 O 3 reached 28.8 at 6.16 MPa/m, which is significantly higher than the reported selectivity of 3.9 at ∆P = 0.1 MPa and 100 • C in the case of an amorphous silica membrane with a thickness of 30 nm [6].
Materials 2016, 9, 930 11 of 20 significantly higher than the reported selectivity of 3.9 at ΔP = 0.1 MPa and 100 °C in the case of an amorphous silica membrane with a thickness of 30 nm [6].   significantly higher than the reported selectivity of 3.9 at ΔP = 0.1 MPa and 100 °C in the case of an amorphous silica membrane with a thickness of 30 nm [6].

Separation Model
In the present porous ceramics, the critical pressure gradient was measured in the single-gas H2 and CO2 gas flows ( Figure 10). This property is affected by the attractive interaction between the pore walls and the polarized gas molecules. Furthermore, the critical pressure gradient is closely related to the tortuous pore structure in the porous ceramics, which interrupts the smooth transportation of gas molecules [17]. In the Knudsen and Poiseuille models, straight pores parallel to the direction of gas flow are assumed to transport the inlet gas molecules. The flux of the H2 gas of the mixed gas in the Knudsen model was modified by Equation (8) using the critical pressure gradient (∆Pc/L) of single H2 gas flow: where ∆P(mix) is the pressure gradient of mixed gas, ) (H 2 c is the velocity of H2 molecules, and x is the H2 gas fraction of the supplied mixed gas. This equation indicates that J(H2) becomes 0 mol/s m 2 at x = 0 or ∆P(mix) = ∆Pc(H2). Similarly, Equation (9) represents the flux of CO2 molecules of the mixed gas in the modified Knudsen model: The H2 fraction is then expressed by Equation (10):

Separation Model
In the present porous ceramics, the critical pressure gradient was measured in the single-gas H 2 and CO 2 gas flows ( Figure 10). This property is affected by the attractive interaction between the pore walls and the polarized gas molecules. Furthermore, the critical pressure gradient is closely related to the tortuous pore structure in the porous ceramics, which interrupts the smooth transportation of gas molecules [17]. In the Knudsen and Poiseuille models, straight pores parallel to the direction of gas flow are assumed to transport the inlet gas molecules. The flux of the H 2 gas of the mixed gas in the Knudsen model was modified by Equation (8) using the critical pressure gradient (∆P c /L) of single H 2 gas flow: where ∆P(mix) is the pressure gradient of mixed gas, c(H 2 ) is the velocity of H 2 molecules, and x is the H 2 gas fraction of the supplied mixed gas. This equation indicates that J(H 2 ) becomes 0 mol/s m 2 at x = 0 or ∆P(mix) = ∆P c (H 2 ). Similarly, Equation (9) represents the flux of CO 2 molecules of the mixed gas in the modified Knudsen model: The H 2 fraction is then expressed by Equation (10): Equation (10) indicates that F(H 2 ) approaches unity at x = 1 and ∆P(mix) = ∆P c (CO 2 ). The flux values of H 2 and CO 2 molecules of the mixed gas in Poiseuille flow are modified by Equations (11) and (12), respectively: In Equations (11) and (12), P(mix) is the average pressure between the inlet and outlet mixed gases, η(mix) is the viscosity of the mixed gas, and ∆P(mix)/L is the pressure gradient between the inlet and outlet mixed gases. The H 2 fraction in the Poiseuille model is given by Equation (13): Equation (13) approaches unity at x = 1 and ∆P(mix) = ∆P c (CO 2 ) and is similar to Equation (10).
A specified pore provides different gas flow mechanisms for H 2 and CO 2 gases, as is evident in Figures 1 and 9. H 2 gas with λ/r > 1 and CO 2 gas with λ/r < 1 in a specified pore are treated as Knudsen and Poiseuille flows, respectively. The H 2 fraction of the mixed gas in this pore is derived from Equations (8) and (12) and is expressed by Equation (14): A commonality among Equations (10), (13) and (14) is the increase in the F(H 2 ) value at a small ratio of J(CO 2 )/J(H 2 ). This is discussed in the introduction and is seen in the calculated gas flux in Figure 6 or Figure 7. The theoretical H 2 fraction increases in the order of Equation (13) (Poiseuille model) < Equation (10) (Knudsen model) < Equation (14) (Knudsen model for H 2 gas, Poiseuille model for CO 2 gas). That is, the specified pore giving Equation (14) exerts a kind of sieving effect for CO 2 gas in the mixed gas. The previous discussion indicates that the following factors are key to increasing the H 2 selectivity: (1) a large difference of ∆P c for H 2 and CO 2 gases (∆P c (CO 2 ) >> ∆P c (H 2 )), which is closely related to the tortuous pore structure, chemical composition of material, and Knudsen number ( Figure 10); (2) a specified pore giving Knudsen flow for H 2 gas and Poiseuille flow for CO 2 gas (Figures 1 and 9); and (3) attractive interactions between the pore walls and the specified gas molecules (CO 2 ). In this paper, Factor (3) is not examined with sufficient experimental data. Figures 17 and 18 show comparisons between measured and calculated H 2 fractions in the Al 2 O 3 porous ceramics and SiC porous ceramics, respectively. In the calculation of Equation (14), η(mix) is approximated by η(H 2 )x + η(CO 2 )(1 − x). As is evident in Figures 17 and 18, the calculated F(H 2 ) lines for Equations (10), (13) and (14) increase in the order Equation (13) < Equation (10) < Equation (14) with decreasing pressure gradient. The three calculated F(H 2 ) lines of the mixed gas explain the general tendency of the experimental results. The discrepancy of ∆P/L values at F(H 2 ) = 1 between the calculation and experiment in Figure 17 is related to the decrease of ∆P c (CO 2 ) for the mixed gas as compared with single CO 2 gas (Figure 11). The condition of ∆P c (CO 2 ) ≈ ∆P c (H 2 ) in Equations (10), (13) and (14) implies no dependence of F(H 2 ) on ∆P(mix) and gives a constant F(H 2 ) value that depends on the gas flow mechanism and the inlet gas composition (e.g., F(H 2 ) = 0.5 in Equation (13), F(H 2 ) = 0.824 in Equation (10), and F(H 2 ) = 0.967 in Equation (14) for x = 0.5). The measured range of the H 2 fraction for a constant x value in Figure 17 or Figure 18 was almost in agreement with the range calculated via Equation (13). This similarity suggests that (1) the mixed gas in the Al 2 O 3 or SiC porous ceramics flows via the Poiseuille mechanism; (2) the flow mechanism of the mixed gas is controlled by CO 2 gas with a small Knudsen number ( Figure 9); and (3) the Knudsen flow of single H 2 gas with a high Knudsen number is greatly influenced in the mixed gas by the coexisting CO 2 molecules with a short molecular mean free path. Therefore, the molecular mean free path of H 2 molecules is reduced by mixed CO 2 molecules. That is, Equation (13) is able to explain the H 2 fraction of the mixed gas under Poiseuille flow.
Materials 2016, 9,930 15 of 20 by CO2 gas with a small Knudsen number ( Figure 9); and (3) the Knudsen flow of single H2 gas with a high Knudsen number is greatly influenced in the mixed gas by the coexisting CO2 molecules with a short molecular mean free path. Therefore, the molecular mean free path of H2 molecules is reduced by mixed CO2 molecules. That is, Equation (13) is able to explain the H2 fraction of the mixed gas under Poiseuille flow.

Reliability of Experiment
To demonstrate the reproducibility of the gas separation experiment, the experiments were repeated for another three Al2O3 samples with 59.3%-61.2% relative densities, which were sintered at 800 °C for 1 h. Figure 19 shows the typical flux values of the H2 and CO2 gases through the porous Al2O3 compact of 60.9% relative density (sample No. 4 in Figure 20) for the 50% H2-50% CO2 mixed inlet gas with and without moisture (3 vol % H2O). The humidification of the supplied gas was carried out by bubbling the mixed gas in distilled water at 25 °C. When the dried gas was supplied, the flux of H2 gas decreased by mixing as compared with the flux of single H2 gas. However, the CO2 gas flux of the mixed gas was not affected by coexisting H2 gas. These results were similar to the result shown in Figure 11. The critical pressure gradient of CO2 gas depended on the Al2O3 sample used. In 70% of the total 20 experiments using the different four Al2O3 samples, including the sample in Section 3, for several supplied gas compositions, the critical pressure gradient was observed for H2 and CO2 gases. Figure 20 shows the fraction of H2 gas permeated through the different four Al2O3 samples sintered at 800 °C. In two samples (Nos. 1 and 2), the H2 fraction increased with a decrease in the pressure gradient. The other two samples (Nos. 3 and 4) exhibited no dependence of H2 fraction on pressure gradient, but the H2 fraction of sample No. 3 was 10%-25% higher than that of the supplied gas.

Reliability of Experiment
To demonstrate the reproducibility of the gas separation experiment, the experiments were repeated for another three Al 2 O 3 samples with 59.3%-61.2% relative densities, which were sintered at 800 • C for 1 h. Figure 19 shows the typical flux values of the H 2 and CO 2 gases through the porous Al 2 O 3 compact of 60.9% relative density (sample No. 4 in Figure 20) for the 50% H 2 -50% CO 2 mixed inlet gas with and without moisture (3 vol % H 2 O). The humidification of the supplied gas was carried out by bubbling the mixed gas in distilled water at 25 • C. When the dried gas was supplied, the flux of H 2 gas decreased by mixing as compared with the flux of single H 2 gas. However, the CO 2 gas flux of the mixed gas was not affected by coexisting H 2 gas. These results were similar to the result shown in Figure 11. The critical pressure gradient of CO 2 gas depended on the Al 2 O 3 sample used. In 70% of the total 20 experiments using the different four Al 2 O 3 samples, including the sample in Section 3, for several supplied gas compositions, the critical pressure gradient was observed for H 2 and CO 2 gases. Figure 20 shows the fraction of H 2 gas permeated through the different four Al 2 O 3 samples sintered at 800 • C. In two samples (Nos. 1 and 2), the H 2 fraction increased with a decrease in the pressure gradient. The other two samples (Nos. 3 and 4) exhibited no dependence of H 2 fraction on pressure gradient, but the H 2 fraction of sample No. 3 was 10%-25% higher than that of the supplied gas. Therefore, in 75% of the experiments with the different four samples and several supplied gas compositions, the fraction of permeated H 2 gas increased up to 16%-76% from the H 2 fraction of the supplied gas. The influence of moisture in the porous compact or in the H 2 -CO 2 mixed gas was investigated using sample No. 4, Al 2 O 3 (60.9% relative density) in Figures 19 and 21. When the humidified H 2 -CO 2 mixed gas was supplied to sample No. 4, Al 2 O 3 , the dependence of the CO 2 gas flux on the pressure gradient (Figure 19b) was similar to the trend described in Section 3.3 ( Figure 11). That is, the CO 2 gas flux decreased rapidly with decreasing pressure gradient. In the dried gas condition, the H 2 fraction was almost the same as that of supplied gas in the pressure gradient range from 2.0 to 37.8 MPa/m (Figure 21). In the humidified condition, the fraction of H 2 gas, which was measured 2-6 times at each pressure gradient, was significantly scattered but the H 2 fraction was apparently enhanced as compared to the dried gas condition. The maximum H 2 fraction was 0.331, 0.905, and 0.986 when the supplied gas contained 20%, 50%, and 80% H 2 , respectively. Therefore, the moisture in the experimental condition adsorbs easily on the present porous ceramics, as described in the experimental section, and affects the selectivity of the supplied H 2 -CO 2 mixed gas. After the experiment with the humidified gas in Figure 21, a slight weight gain of 0.034% was measured. That is, the scattered data of the gas separation in Figure 21 are caused by the structure of porous ceramics (tortuosity and size distribution of pores, and porosity) and interaction between gas molecules and pore wall (i.e., ceramics particles), which is affected by the moisture adsorbed on the porous ceramics or included in the supplied gas.
Therefore, in 75% of the experiments with the different four samples and several supplied gas compositions, the fraction of permeated H2 gas increased up to 16%-76% from the H2 fraction of the supplied gas. The influence of moisture in the porous compact or in the H2-CO2 mixed gas was investigated using sample No. 4, Al2O3 (60.9% relative density) in Figures 19 and 21. When the humidified H2-CO2 mixed gas was supplied to sample No. 4, Al2O3, the dependence of the CO2 gas flux on the pressure gradient (Figure 19b) was similar to the trend described in Section 3.3 ( Figure  11). That is, the CO2 gas flux decreased rapidly with decreasing pressure gradient. In the dried gas condition, the H2 fraction was almost the same as that of supplied gas in the pressure gradient range from 2.0 to 37.8 MPa/m (Figure 21). In the humidified condition, the fraction of H2 gas, which was measured 2-6 times at each pressure gradient, was significantly scattered but the H2 fraction was apparently enhanced as compared to the dried gas condition. The maximum H2 fraction was 0.331, 0.905, and 0.986 when the supplied gas contained 20%, 50%, and 80% H2, respectively. Therefore, the moisture in the experimental condition adsorbs easily on the present porous ceramics, as described in the experimental section, and affects the selectivity of the supplied H2-CO2 mixed gas. After the experiment with the humidified gas in Figure 21, a slight weight gain of 0.034% was measured. That is, the scattered data of the gas separation in Figure 21 are caused by the structure of porous ceramics (tortuosity and size distribution of pores, and porosity) and interaction between gas molecules and pore wall (i.e., ceramics particles), which is affected by the moisture adsorbed on the porous ceramics or included in the supplied gas.

Conclusions
Porous ceramics of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide were fabricated, and their permeability toward hydrogen, carbon dioxide, and hydrogen-carbon dioxide mixtures was investigated. The open porosity and median pore size of the fabricated porous ceramics were 36.2% and 45.3 nm for Al2O3, 40.5% and 115.8 nm for YSZ, and 17.9%-36.1% and 111.9-164.0 nm for SiC samples hot-pressed at 1400-1700 °C, respectively. The permeation of single H2 or CO2 gas occurred above a critical pressure gradient and increased linearly with an increasing pressure gradient. A higher flux and a lower critical pressure gradient were measured for H2 gas than for CO2 gas. In the Al2O3 and YSZ porous ceramics, the permeability coefficients of both H2 and CO2 gases were similar to those predicted by the Knudsen model. In the SiC porous ceramics, the measured permeability coefficient of H2 gas was explained by the Knudsen model, and the permeability coefficient of CO2 gas was within the range based on values calculated by the Knudsen and Poiseuille models. The aforementioned results are explained by the Knudsen number (λ/r ratio, λ: molecular mean free path of gas molecules, r: pore radius). When the Knudsen number is larger than unity, Knudsen flow becomes a dominant gas transportation process. In the nanometer-sized tortuous pore structure, the composition of material and the Knudsen number (λ/r ratio) affect the critical pressure gradient of a single gas of H2 or CO2. The critical pressure gradient increases more with decreasing Knudsen number in the case of Al2O3 than in the case of SiC.
In the permeation of the mixed gas of 50 vol % H2-50 vol % CO2, the H2 flux value in Al2O3 or YSZ became smaller than that of single H2 gas and approached that of single CO2 gas. By contrast, the CO2 flux in the mixed gas through SiC ceramics became larger than that of single CO2 gas and approached the flux of single H2 gas. The fraction of H2 gas through the Al2O3 and YSZ compacts became higher than the mixing ratio of the supplied gas and increased with decreasing pressure gradient, reaching 0.966 at 6.16 MPa/m in Al2O3 and 0.844 at 3.13 MPa/m in YSZ. These values of H2 fraction exceeded the fraction calculated using the Knudsen equation (0.824). In porous SiC, the H2 fraction increased at a lower pressure gradient (<10 MPa/m) and reached 0.999 at 1.4 MPa/m of pressure gradient. A similar trend of the dependence of the H2 fraction on the pressure gradient was also observed for the mixed gases with different inlet gas compositions of 20 vol % H2-80 vol % CO2  Figure 20).

Conclusions
Porous ceramics of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide were fabricated, and their permeability toward hydrogen, carbon dioxide, and hydrogen-carbon dioxide mixtures was investigated. The open porosity and median pore size of the fabricated porous ceramics were 36.2% and 45.3 nm for Al 2 O 3 , 40.5% and 115.8 nm for YSZ, and 17.9%-36.1% and 111.9-164.0 nm for SiC samples hot-pressed at 1400-1700 • C, respectively. The permeation of single H 2 or CO 2 gas occurred above a critical pressure gradient and increased linearly with an increasing pressure gradient. A higher flux and a lower critical pressure gradient were measured for H 2 gas than for CO 2 gas. In the Al 2 O 3 and YSZ porous ceramics, the permeability coefficients of both H 2 and CO 2 gases were similar to those predicted by the Knudsen model. In the SiC porous ceramics, the measured permeability coefficient of H 2 gas was explained by the Knudsen model, and the permeability coefficient of CO 2 gas was within the range based on values calculated by the Knudsen and Poiseuille models. The aforementioned results are explained by the Knudsen number (λ/r ratio, λ: molecular mean free path of gas molecules, r: pore radius). When the Knudsen number is larger than unity, Knudsen flow becomes a dominant gas transportation process. In the nanometer-sized tortuous pore structure, the composition of material and the Knudsen number (λ/r ratio) affect the critical pressure gradient of a single gas of H 2 or CO 2 . The critical pressure gradient increases more with decreasing Knudsen number in the case of Al 2 O 3 than in the case of SiC.
In the permeation of the mixed gas of 50 vol % H 2 -50 vol % CO 2 , the H 2 flux value in Al 2 O 3 or YSZ became smaller than that of single H 2 gas and approached that of single CO 2 gas. By contrast, the CO 2 flux in the mixed gas through SiC ceramics became larger than that of single CO 2 gas and approached the flux of single H 2 gas. The fraction of H 2 gas through the Al 2 O 3 and YSZ compacts became higher than the mixing ratio of the supplied gas and increased with decreasing pressure gradient, reaching 0.966 at 6.16 MPa/m in Al 2 O 3 and 0.844 at 3.13 MPa/m in YSZ. These values of H 2 fraction exceeded the fraction calculated using the Knudsen equation (0.824). In porous SiC, the H 2 fraction increased at a lower pressure gradient (<10 MPa/m) and reached 0.999 at 1.4 MPa/m of pressure gradient. A similar trend of the dependence of the H 2 fraction on the pressure gradient was also observed for the mixed gases with different inlet gas compositions of 20 vol % H 2 -80 vol % CO 2 and 80 vol % H 2 -20 vol % CO 2 . When 80% H 2 -20% CO 2 mixed gas was permeated, the H 2 fraction was 0.976 at 7.61 MPa/m in Al 2 O 3 , 0.936 at 3.13 MPa/m in YSZ, and 0.987 at 3.06 MPa/m in SiC, respectively. In the case of 20% H 2 -80% CO 2 mixed gas, the H 2 fraction was 0.972 at 6.88 MPa/m in Al 2 O 3 , 0.504 at 8.04 MPa/m in YSZ and 0.999 at 3.40 MPa/m in SiC, respectively. The aforementioned high fraction of H 2 gas was closely related to the difference in the critical pressure gradient values for H 2 and CO 2 single gases, the inlet mixed gas composition, and the gas flow mechanism of the mixed gas. A gas flow of CO 2 molecules with a small Knudsen number and the collision between H 2 and CO 2 molecules control the gas flow mechanism (Poiseuille flow) of the mixed gas. The calculated H 2 fraction derived from the modified Poiseuille equations of H 2 and CO 2 gases explained well the measured H 2 fraction as a function of pressure gradient of the mixed gas in Al 2 O 3 and SiC porous ceramics. In the present experimental conditions, moisture in atmosphere adsorbed easily on the porous ceramics and affected the critical pressure gradient, leading to the increased selectivity of H 2 gas.