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Modeling of porous membranes for molten carbonate fuel cells
Materials Chemistry and Physics 48 (1997) 199–206
Modeling of porous membranes for molten carbonate fuel cells S. Freni, G. Maggio, E. Passalacqua Istituto CNR-TAE, via Salita S. Lucia sopra Contesse 39, 98126 Santa Lucia, Messina, Italy
Received 29 January 1996; revised 11 June 1996; accepted 20 June 1996
Abstract
The use of porous membranes permeable to hydrogen in molten carbonate fuel cells to control the diffusion of electrolyte vapours has been investigated. For this purpose, a mathematical model has been developed to study the influence of the membrane properties on the hydrogen permeate flow and on the electrolyte diffusive flow. The results demonstrated that a porous membrane can be applied to prevent the poisoning of the internal reforming catalyst. Keywords:
Molten carbonate fuel cell; Porous membrane; Catalyst poisoning; Mathematical model
1. Introduction
For several years, researchers in the field of molten carbonate fuel cells (MCFCs) have concentrated their major efforts on the development of high technology demonstrative power plants [1,2]. Furthermore, it has been widely demonstrated that an MCFC can be supplied with reformed gas, if designed in accordance with the external reforming configuration (ER-MCFC) [3], or directly with a methane/water mixture in the case of internal reforming (DIR-MCFC) [4]. A higher performance and a better thermal distribution along the electrode surfaces are the typical advantages of the latter configuration, which has encouraged wider researches on this kind of fuel cell [5]. In general, the internal reforming configuration, as schematically reported in Fig. 1(a), is based on the principle of obtaining the reforming of a raw fuel (as methane) directly inside the anodic compartment of the cell where the hydrogen produced is readily converted by the electrochemical cell reaction [6]. The commercialization of DIR-MCFC pilot plants is slowed down by the difficulty of finding a reforming catalyst that can be active in the operative conditions of an MCFC without suffering any chemical or thermal damage or poisoning. In fact, intensive investigations in this field have demonstrated that one of the main mechanisms of catalyst deactivation is the KOH vapour diffusion effect [7,8]. The catalyst deactivation is mainly due to coverage of a large part of the catalyst surface and plugging of the pores by alkali compounds [8]. Some researchers [9] have proposed to solve this problem by designing an innovative cell geometry, like that shown in Fig. 1(b), based on the application of a
dense membrane that hinders the diffusion of KOH from the anode towards the reforming catalyst. Generally, for this specific application, dense membranes of palladium or Pd alloys have been proposed. These membranes are permeable to hydrogen but present some disadvantages, such as the high cost, the high pressure gradient needed for an acceptable flow rate of diffused hydrogen to supply the cell and the risk of embrittlment after a long exposure to the hydrogen sorption/ desorption cycles [10]. Dense membranes are not the only type of permeablemembranes, which because of their specific characteristics, can be used as barriers to prevent catalyst poisoning by alkali. In fact, there are some ceramic porous membranes, characterized by a structure with pore radius of 0.1–5 mm, that could be successfully applied for this purpose [11]. First, the ceramic porous membranes can be produced by a good choice of ceramic powders, like carbides or metallic
Fig. 1. Schematic views of DIR-MCFC configuration (a) without and (b) with hydrogen permeable membrane.
0254-0584/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S0254-0584(96)01853-6
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oxides, that are commercially available, cheap, resistant to chemical attack by alkali and stable at the cell temperature. Besides, the separation factor of these membranes, which is an index of their separation capability, can reach values comparable with those of the dense membranes, while the permeate flow rate depends on certain characteristics of the structure such as the thickness, the particle diameter, the average pore radius and the porosity. To evaluate the theoretical degree of reliability of the ceramic porous membranes to protect the reforming catalyst in an MCFC, a mathematical model based on the equations that describe the diffusion of a gas mixture through a porous structure, has been developed. The model has been applied to a molten carbonate fuel cell, considering operative conditions of a DIR-MCFC anode compartment, and provides significative indications on the influence of the main membrane structure characteristics on the examined diffusion process. 2. Model development
As described before, one of the main phenomena inducing the deactivation of the steam reforming anodic catalyst employed in a molten carbonate fuel cell is the poisoning due to alkali hydroxide vapours [11]. The objective of this work is to study the possibility to enhance the catalyst lifetime in MCFCs, through the introduction of a porous membrane in the anodic compartment of the cell between the steam reforming catalyst housing and the anode. The porous membrane must be selective to the alkali vapour flow and, at the same time, must allow a flow of hydrogen sufficient to sustain the electrochemical cell reaction. The capability of themembrane to limit the KOH vapour diffusion is strictly dependent on its physical properties, such as the porosity and the pore size. However, since the flow of hydrogen through the membrane is counter to that of the alkali vapours, the determination of the optimal values of the membrane characteristics isacritical aspect, whose solution requires an in-depth analysis. For this purpose, based on typical anodic operative conditions for a DIR-MCFC, a mathematical model that describes the diffusion mechanisms of gases in a porous medium has been developed. From a general point of view, the property of a porous inorganic membrane to allow selective permeation of a mixture of gases depends on various mechanisms, such as surface adsorption and diffusion, molecular size exclusion, Knudsen diffusion and capillary condensation [12]. Nevertheless, in the range of average pores radius of the porous inorganic membranes considered in this paper (between 0.1 and 5 mm), the surface adsorption and diffusion mechanism and the molecular size exclusion mechanism are insignificant. Furthermore, since capillary condensation occurs when the operative conditions of the porous structure are characterized by high pressure and low temperature, which is not the case examined here, we assume that the molecular gas diffusion (bulk and Knudsen) is the prevailing mechanism for such
membranes. The other model assumptions can be summarized as follows: (i) the physical diffusion of gas occurs through the porous structure and no chemical interactions between the gas molecules and the bulk material occur; (ii) only diffusive flow has been considered in the calculation of the alkali vapour transport in the porous structure; (iii) the amount of diffusing alkali vapour has been evaluated assuming a rapid migration of KOH into the membrane structure, so that the membrane optimization for less severe conditions is warranted; (iv) the concentration of the alkali vapour is constant in the anodic compartment. Based on these assumptions, the basic equations of the model, describing the diffusive and convective flow of gases through the porous structure, are given by the expressions: i i pi,1ypi,2 Gdif sD eff RTL
(1)
P21yP22 2amiRTGiconv 1 P1 2RT(Giconv)2Mi s q bq ln L xigc L P2 xigc
ž
/
(2)
where Gidif and Giconv are the gas flow rates through the membrane respectively due to the diffusive and convective phenomena (mol cmy2 sy1), D ieff is the effective diffusion coefficient (cm2 sy1), R the gas constant (82.0567 cm3 atm moly1 Ky1), T the absolute temperature (K), L the membrane thickness (cm), a the viscosity resistance coefficient (cmy2), b the inertial resistance coefficient (cmy1) and gc the acceleration due to gravity (980.665 cm sy2). In addition, mi, Mi and xi are the gas viscosity (poise), the molecular weight (g moly1) and the molar fraction of component i; pi and P are the partial and absolute pressures(atm), respectively, with indices 1 and 2 denoting the membrane upstream and downstream, respectively. Eq. (1) is a generalization of diffusive flow phenomena due to concentration gradient [13], and Eq. (2) describes the isothermal flow of an ideal gas through porous media [14]. Equations for ideal gases have been chosen because they are a sufficiently good approximation at low pressure, as well as in the examined case [14]. Eq. (2) can be arranged as a quadratic equation for the convective flow rate a1(Giconv)2qa2Giconvqa3s0
(3)
with a1s bLqln
ž
P1 Mi P2
/
(4a)
a2samiL
(4b)
xigc 2 a3sa4 (P2yP12) 2RT
(4c)
where the constant a4s1033.23 represents the conversion factor from atm to g cmy2. The viscosity and the inertial resistance coefficients appearing in Eqs. (4a) and (4b) have been determined by the Ergun definition [15]:
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as
150(1yu)2 u3(fdp)2
(5)
bs
1.75(1yu) u3(fdp)
(6)
where u is the porosity, dp the particle diameter (cm) and f the particle shape factor, which is equal to 0.874 for cylinders [15]. The diffusive and convective flow rates have been determined as a function of the membrane properties, considering as operative conditions (temperature, pressure, gas composition) those of the experiments carried out on a bench scale isothermal monocell operating under direct internal reforming configuration. In the case of a binary gas mixture, the ordinary (free) diffusion coefficient of component i in the mixture, taking into account both Knudsen and bulk diffusions, is given by the relationship 1 1 j D i,free s i, jq i Db Dk
ž
(7)
/
The Knudsen and bulk diffusions are respectively given by T Mi
(8)
0.001T 1.75x1/Miq1/Mj D i,b js 1/3 2 P[(8v)1/3 i q(8v)j ]
(9)
Diks9700r#
y
and
where r# is the average pore radius (cm) and (8v)i the diffusion volume of component i. In the case of a gas component diffusing through a mixture, the multicomponent bulk diffusion coefficient is related to the binary diffusion coefficients of the i component respect to each component of the mixture, according to the following equation 1yxi
D i,m b s
(10)
8 xj/Dij
j/1
This relationship represents a good approximation for the description of the diffusion of a single component in a mixture, while the analysis of the simultaneous diffusion of two or more components of a mixture is more complicated. The ordinary diffusion coefficient for a multicomponent mixture can be obtained from Eq. (7) by substituting the binary bulk diffusion coefficient, D ib, j, with the multicomponent one, D ib,m, given by Eq. (10). For a medium with porosity, the effective diffusion coefficient, which appears in Eq. (1), can be calculated from the ordinary diffusion, multiplying for the term u/t 1 1 D effs i,mq i Db Dk i
ž
y1
/
u t
(11)
where t is a factor which accounts both for tortuosity and variation of the pore cross section. Thus, it represents a correction factor for the irregularity of the shape of the pore, resulting in a decrease of the effective diffusion coefficient. For most materials t is between 2 and 8, usually around 4 [13], which is the value used here. Thus, the above equations take into account the influence of the membrane properties, through the parameters L, u, dp and r#, even if the particle diameter can be correlated to the porosity and the average pore radius, by the expression 3r#(1yu) dps u
(12)
derived from the following literature [16,17] relationships, that assume cylindrical pores of uniform size: r#s
2u , (1yu)rAs
6 dps rAs
where As is the specific surface area (cm2 gy1) and r the solid density (g cmy3). The values utilized for the diffusion volume of the gas components are 7.07 for H2, 12.7 for H2O, 18.9 for CO, 26.9 for CO2 and 18 for CH4, where this last value was determined on the basis of the atomic diffusion volumes of carbon and hydrogen. Substitution of these values in the Gilliland-type Eq. (9) provides the bulk diffusion coefficients. In particular, the bulk diffusion coefficient of the alkali vapours has been calculated as binary diffusion coefficient of KOH vapour in H2, since the hydrogen is the main component of gas mixture. It has been estimated through Eq. (9) by assuming the diffusion volume of KOH to be equal to that of CO2, as suggested by Berger [16]. The upstream vapour partial pressure was calculated as equilibrium KOH vapour pressure for the reaction K2CO3(l)qH2Os2KOH(g)qCO2 according to the following relationship relative to a molten mixture of 62% Li2CO3 and 38% K2CO3: pH O (pKOH)2s 2 0.381.93 pCO2
(13) with thermodynamic data reported in the literature [16] (e.g. at 923, the log Ki values are 12.93, 22.44, 49.77, 11.17 for KOH(g), CO2, K2CO3 and H2O, respectively). The downstream vapour partial pressure was assumed to be equal to zero. This means that there is rapid migration of KOH through the membrane and corresponds, with regard to catalyst poisoning, to the most severe conditions. In practice, the amount of vapour that really diffuses will be certainly less than the value calculated from Eq. (1) on this hypothesis, and then the membrane optimization is warranted. Indeed, under the initial conditions the downstream vapour concentration is equal to zero, but as the vapour begins to diffuse towards the opposite side of the membrane its concentration =10(2 log KKOH(g)qlog KCO2ylog KK2CO3ylog KH2O)
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Table 1 Coefficients for viscosity, extrapolated from literature data Gas H2 CH4 CO CO2 H2O
ai
4.44557
y5.43597
6.97481
y19.8421 y12.5925
Table 2 Model base-case input data
bi=10
ci=104
di=107
Parameter
Value
3.61313 4.6993 6.7871 6.68342 3.61238
y2.92135 y3.02085 y4.29479 y3.50231
1.25714 1.06961 1.53759 0.98655 0
Temperature Pressure gradient Reformed gas composition
923 K 10 cmH2O 59.9%H2, 18.5%H2O, 10.6%CO, 7.0%CO2, 4.0%CH4 0.5 mm 40% 0.5 mm 4 0.874
0.238096
increases and the vapour flow rate through the membrane decreases. The gas viscosities, expressed in micropoise, have been calculated as a function of the temperature, according to the following general relationship (14)
misaiqbiTqciT 2qdiT 3
utilizing for the coefficients the values listed in Table 1 obtained by an extrapolation of viscosity data reported in the literature [18]. The capability of these membranes to separate the component i from the gas mixture depends by the relative permeability of the gases through the membrane and can be measured by the separation factor defined, in terms of the upstream and downstream molar fractions, as: xi,2 1yxi,1 Sfis xi,1 1yxi,2
(15)
When the specified membrane characteristics are such that the flow rate of diffused hydrogen is sufficient to sustain the electrochemical reaction, only the capability to hinder the diffusion of KOH vapours allows us to discriminate between the membranes efficiencies. For this purpose, it is necessary to relate the diffusive flow rate of KOH through the membrane, calculated by Eq. (1), to the poisoning mechanism induced on the catalyst. Thus, the definition of catalyst lifetime in the presence of a membrane is introduced: WK dyL L tcats q KOH MKS[KOH]o DKOH D b eff
ž
/
(16)
where WK is the amount of potassium adsorbed on the reforming catalyst surface (g), MK the molecular weight of potassium (39.11 g moly1), S the total anode surface area (cm2), d the distance between anode and catalyst surface (cm), and [KOH]o the KOH concentration at the anode surface (mol cmy3). This equation, based on the assumptions that the alkali hydroxide is the main reason for the catalyst poisoning and its vapour pressure at the edge of the catalyst grains is zero, represents a generalization of the definition of catalyst lifetime given in literature [16] and reduces to this definition for KOH Ls0 or DKOH (i.e. in the absence of membrane). eff sDb The lifetime can be determined by Eq. (16) once the percentage amount of potassium that produces the total poisoning of the catalyst is known.
Membrane thickness Membrane porosity Average pore radius Tortuosity factor Particle shape factor
3. Model parameters and base-case conditions
The sensitivity analysis of the model results has been accomplished, considering as the base case the data reported in Table 2, and varying the characteristics of a membrane (thickness, porosity and average pore radius) operating into the anodic compartment in accordance with the configuration shown in Fig. 1(b). In particular, the parameters which have been considered in the course of this analysis are as follows. Temperature: the operative temperature of the overall system. This parameter influences the thermodynamic equilibrium of the steam reforming reaction and then the composition of the reformed gas. In the case studied it has been chosen as 973 K. Gas composition: considered to be the composition of the gas mixture to be permeate. It has been calculated by an appropriate mathematical model for the determination of the mass balance in a methane direct internal reforming molten carbonate fuel cell [19] and it corresponds to 59.9% H2, 18.5% H2O, 10.6% CO, 7.0% CO2, 4.0% CH4. Pressure gradient: difference between the upstream and downstream pressures through the membrane surfaces. At first, the influence of this operative parameter on the gas diffusion has been evaluated in the range from 0 to 100 cm H2O. Then, the constant value of 10 cm H2O has been considered. Membrane thickness: the total thickness of the porous structure. This parameter has been studied in the range from 0.10 mm to 1.00 mm. Membrane porosity: considered to be the total porosity of the membrane structure; its influence has been extensively studied in the range from 0.0% to 80.0%. Average pore radius: the parameters is paramount for diffusional gas problems and was varied in the range 0.00– 3.00 mm. 4. Model results and discussion
At first, the influence of the gradient pressure on the hydrogen flow permeate has been investigated. The results of these calculations are reported in Fig. 2, where the variation of the
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Fig. 2. Hydrogen permeate flow vs. pressure gradient, for base-case conditions.
hydrogen permeate flow as a function of this parameter is shown. In the range examined the flow rate of the permeate appears to be directly correlated to the value of the gradient pressure applied to the membrane, and it increases with a slope of about 40=10y8 mol sy1 cmy2 per decade of cm H2O. If we analyze the case of a membrane operating into a cell, with the base-case characteristics, it is necessary to consider that the fuel cell requires, at least, 2.074= 10y6 mol sy1 cmy2 of hydrogen flow rate to produce 200 mA cmy2, at a fuel utilisation of 50%. Then, it appears clear that a gradient pressure of about 53 cm H2O should be applied on the membrane to have the flow required to sustain the electrochemical cell activity. Moreover, a separation factor equal to 1.838, calculated for a membrane operating at base-case conditions, confirms that the membrane allows the flow of a permeate with hydrogen rich composition. As reported in Fig. 3, the variation of the permeate flow as a function of the membrane porosity has been determined, for a porous structure characterized by a thickness of 0.5 mm, average pore radius of 0.5 mm and gradient pressure of 10 cm H2O. In this case also, a direct dependence of the hydrogen permeate flow on the value of the porosity is evident. In fact, with a porosity of 30%, the permeate diffuses at a rate of 29.1=10y8 mol sy1 cmy2, which increases to 58.2= 10y8 mol sy1 cmy2 when the porosity doubles. Thus, for a
Fig. 3. Hydrogen permeate flow vs. membrane porosity.
convenient application it would be interesting to have membranes of high porosity, which allow a substantial flow of the permeate when a low gradient of pressure is applied to the membrane. Furthermore, the calculations demonstrated that the dependence of the hydrogen permeate flow on the values of the average pore radius is marked. This is justified, because the viscosity and the inertial resistances become predominant when the gas flows into very small pores. The trend of the curve representing the permeate flow as a function of the average pore radius is reported in Fig. 4. From the analysis of this curve, it is evident that a slight increment of the pore radius substantially improves the diffusional flow, which results directly from the proportionality of the flow to the square of the average pore radius; for instance, at r#s1 mm, the permeate flow corresponds to 155=10y8 mol sy1 cmy2, while, for r#s3 mm, it will be 1395=10y8 mol sy1 cmy2, with an increase of 9 times. The last parameter examined was the thickness of the porous structure, whose influence on the hydrogen permeate flow is reported in Fig. 5. From the analysis of this curve, it is evident that the permeation is strongly limited by the thickness. This limit appears to be stronger for thicknesses larger than 400 mm, where the flow is extremely low; in the region characterized by values less than 400 mm, the permeate flow improves greatly for a small reduction of thickness, making
Fig. 4. Hydrogen permeate flow vs. membrane average pore radius.
Fig. 5. Hydrogen permeate flow vs. membrane thickness.
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Table 3 Hydrogen permeate flow (108 mol sy1 cmy2) as a function of the average pore radius and porosity (the values of the other parameters are those of the base case) Porosity (%)
20 40 60
Average pore radius (mm) 0.1
0.5
1.0
1.5
2.0
2.5
3.0
0.775 1.55 2.33
19.4 38.8 58.2
77.5 155 233
174 349 523
310 620 931
485 969 1450
698 1395 2090
Table 4 Alkali hydroxide vapour flow (1012 mol sy1 cmy2) as a function of the average pore radius and porosity (the values of the other parameters are those of the base case) Porosity (%)
20 40 60
Average pore radius (mm) 0.1
0.5
1.0
1.5
2.0
2.5
3.0
1.41 2.82 4.23
5.15 10.3 15.4
7.69 15.4 23.1
9.21 18.4 27.6
10.2 20.4 30.7
10.9 21.9 32.8
11.5 23.0 34.4
the thicknesses belonging to this region the most interesting ones for practical uses. A more complete analysis of the membrane capability to permeate hydrogen comes out from the diagram reported in Fig. 6, where the combined effects of the average pore radius and of the porosity on the permeate flow are shown. This diagram can be divided into two different regions characterized by values of the average pore radius smaller or bigger than 1 mm, respectively, where the influence of the two examined parameters on the permeate flow presents a different behaviour. In fact, in the first region, the influence of the porosity is very small, while the average pore radius is the controlling factor. In the second region, the influence of the porosity becomes more evident and increases as well as r# grows. More detailed results about the permeate flow as a function of the average pore radius and of the porosity are shown in Table 3. This table reveals that similar flows of permeate can be obtained from membranes with different characteristics; in fact, if we analyze the behaviour of two membranes with 1.0 mm and 40% and 1.5 mm and 20% of average pore radius and porosity, it is interesting to note that the flows of permeate are 155=10y8 mol sy1 cmy2 and 174=10y8 mol sy1 cmy2, respectively. Therefore, by choosing appropriate values for these two structural parameters, it is possible to have enough flow of hydrogen to sustain the cell reaction, even if the applied pressure gradient and thickness are low. This allows the selection of a membrane to be used in a molten carbonate fuel cell and reduces the impact of the presence of this additional component on the cell hardware geometry. As described before, we assumed only diffusive flow in the calculation of the alkali vapour transport through the porous structure and so the capability of the porous membrane to limit this diffusion depends on its physical properties, such
as porosity and average pore radius. The results of the model demonstrated that the KOH diffusion is directly influenced by the porosity with a dependence similar to that found for the hydrogen permeate. An analogous behaviour to that of the hydrogen permeate flow has also been found for KOH diffused flow as function of the membrane thickness. Instead, from a comparison between Figs. 4 and 7, referred to a membrane with the same characteristics (see base-case), the influences of the average pore radius on the KOH diffused flow (Fig. 7) and on the hydrogen permeate flow (Fig. 4) are different. The flow of KOH that diffuses in a membrane, with 1.5 mm pore radius and 40% of porosity, corresponds to 18.4=10y12 mol sy1 cmy2; this value quickly decreases when the pore radius becomes smaller, while slight increases when this parameter grows. For example, at the same conditions, for r#s0.5 mm, the electrolyte diffusion corresponds to 10.3=10y12 mol sy1 cmy2, while for r#s2.5 mm, it is 21.9=10y12 mol sy1 cmy2.
Fig. 6. Coupled influence of the membrane porosity and average pore radius on the hydrogen permeate flow.
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Fig. 7. Electrolyte vapour flow vs. membrane average pore radius.
Fig. 8. Coupled influence of the membrane porosity and average pore radius on the electrolyte vapour flow.
The cumulative effect of average pore radius and porosity of a membrane on the electrolyte diffusion has been determined and is represented in Fig. 8, and these values are also summarized in Table 4. The value of porosity appears to be the determining factor in the mechanism examined, and its influence becomes greater when the average pore radius increases. The influence of the average pore radius is less marked for low porosity values, while it is more consistent when the porosity is higher than 40%. 5. Conclusions
The analysis performed gave indications on the reliability of the membranes to permeation of a hydrogen-rich gas mixture and to limit the diffusion of electrolyte vapours towards the internal reforming catalyst site. Furthermore, the correlations between the permeate flows of hydrogen and of KOH
205
vapours and the main operative parameters and characteristics of the membrane have been determined. It has been shown that the hydrogen permeate flow is directly correlated to the pressure gradient applied to the two faces of the membrane. In the case examined the lowest pressure gradient applicable to guarantee a cell current density of 200 mA cmy2, at a fuel utilisation of 50%, is about 53 cm H2O. The porosity and the average pore radius of the membrane structure were found to be the other parameters that strongly influence the diffusion process. In particular, when the membrane presents an average pore radius smallerthan1 mm, the influence of the porosity is very small, while the average pore radius appears to be the controlling factor. In fact, under this condition of flow, the viscosity and the inertialresistances greatly increase. For membranes with average pore radius greater than 1 mm, the influence of the porosity increases and becomes relevant at higher pore radii. The thickness of the membrane also influences the diffusion process, and in the region of low thicknesses the permeate flow changes greatly for a small variation of the thickness. As regards the electrolyte vapour diffusion, it has been seen that this process is also influenced by porosity, average pore radius and thickness. The porosity appears to be the determining factor for this process, and its influence becomes greater when the average pore radius increases. In conclusion, the model allows us to analyze the reliability of the porous ceramic membranes to protect the internal reforming catalyst, in a molten carbonate fuel cell. Future work will be devoted to determining whether the characteristics of the membranes which can be selected in the model comply with the hardware cell requirements and to evaluate the influence of the membranes on the overall cell performance. Emphasis will be placed on the comparison of the model results with the experimental ones. References
[1] C.L. Laursen and L.J. Christiansen, Proc. 1990 Fuel Cell Seminar, Phoenix, AZ, 1990, pp. 44–47. [2] T. O’Shea and A. Leo, Proc. 1994 Fuel Cell Seminar, San Diego, CA, 1994, pp. 462–465. [3] M. Miyazaki, T. Okada, H. Ide, S. Matsumoto and T. Shinoki, Proc. 27th IECE Conf., San Diego, CA, 1992, Vol. 3, pp. 287–292. [4] T. Tanaka, M. Matsumura, Y. Gonjo, C. Hirai, T. Okada and M. Miyazaki, Proc. 25th IECE Conference, Reno, NV, 1990, Vol. 3, pp. 201–206. [5] J.H. Hirschenhofer, D.B. Stauffer and R.R. Engleman, Fuel Cells: A Handbook, DOE/METC-94/1006, Morgantown, WV, 3rd edn., 1994. [6] M.A. Rosen, Int. J. Hydrogen Energy, 15 (1990) 267–274. [7] K. Sato, T. Tanaka and T. Muharashi, Proc. 1990 Fuel Cell Seminar, Phoenix, AZ, 1990, pp. 40–43. [8] S. Cavallaro, S. Freni, R. Cannistraci, M. Aquino and N. Giordano, Int. J. Hydrogen Energy, 3 (17) (1992) 181–186. [9] L.M. Marianowski, US Patent 4702973, Oct. 27, 1987. [10] V.M. Gryaznov, V.S. Smirnov and M.G. Slin’ko, Proc. 6th Int. Congr. on Catalysis of the Chemical Society, London, 1977, Vol. 2, p. 894.
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[11] H.P. Hsieh, Catalysis Rev., 33 (1–2) (1991) 1–70. [12] H.P. Hsieh, AIChE Symp. Ser., 268 (1989) 53–67. [13] C.N. Satterfield and T.K. Sherwood, The Role of Diffusion in Catalysis, Addison-Wesley, Reading, MA, 1963. [14] R.H. Perry and C.H. Chilton (eds.), Chemical Engineers’ Handbook, McGraw-Hill, New York, 5th edn., 1974, Section 5-54. [15] Rohsenow, J.P. Hartnett and E.N. Ganic, Handbook of Heat Transfer Application, McGraw-Hill, New York, 2nd edn., 1985.
[16] R.J. Berger, Nickel catalysts for internal reforming in molten carbonate fuel cells, Ph.D. Thesis, Twente University, 1992. [17] S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 2nd edn., 1982. [18] R.C. Weast (ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 62nd edn., 1982, Section F-50. [19] S. Freni, M. Aquino, N. Giordano and S. Cavallaro, J. Power Sources, 39 (1992) 203–214.
Journal: MAC (Materials Chemistry and Physics)
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Modeling of porous membranes for molten carbonate fuel cells S. Freni, G. Maggio, E. Passalacqua Istituto CNR-TAE, via Salita S. Lucia sopra Contesse 39, 98126 Santa Lucia, Messina, Italy
Received 29 January 1996; revised 11 June 1996; accepted 20 June 1996
Abstract
The use of porous membranes permeable to hydrogen in molten carbonate fuel cells to control the diffusion of electrolyte vapours has been investigated. For this purpose, a mathematical model has been developed to study the influence of the membrane properties on the hydrogen permeate flow and on the electrolyte diffusive flow. The results demonstrated that a porous membrane can be applied to prevent the poisoning of the internal reforming catalyst. Keywords:
Molten carbonate fuel cell; Porous membrane; Catalyst poisoning; Mathematical model
1. Introduction
For several years, researchers in the field of molten carbonate fuel cells (MCFCs) have concentrated their major efforts on the development of high technology demonstrative power plants [1,2]. Furthermore, it has been widely demonstrated that an MCFC can be supplied with reformed gas, if designed in accordance with the external reforming configuration (ER-MCFC) [3], or directly with a methane/water mixture in the case of internal reforming (DIR-MCFC) [4]. A higher performance and a better thermal distribution along the electrode surfaces are the typical advantages of the latter configuration, which has encouraged wider researches on this kind of fuel cell [5]. In general, the internal reforming configuration, as schematically reported in Fig. 1(a), is based on the principle of obtaining the reforming of a raw fuel (as methane) directly inside the anodic compartment of the cell where the hydrogen produced is readily converted by the electrochemical cell reaction [6]. The commercialization of DIR-MCFC pilot plants is slowed down by the difficulty of finding a reforming catalyst that can be active in the operative conditions of an MCFC without suffering any chemical or thermal damage or poisoning. In fact, intensive investigations in this field have demonstrated that one of the main mechanisms of catalyst deactivation is the KOH vapour diffusion effect [7,8]. The catalyst deactivation is mainly due to coverage of a large part of the catalyst surface and plugging of the pores by alkali compounds [8]. Some researchers [9] have proposed to solve this problem by designing an innovative cell geometry, like that shown in Fig. 1(b), based on the application of a
dense membrane that hinders the diffusion of KOH from the anode towards the reforming catalyst. Generally, for this specific application, dense membranes of palladium or Pd alloys have been proposed. These membranes are permeable to hydrogen but present some disadvantages, such as the high cost, the high pressure gradient needed for an acceptable flow rate of diffused hydrogen to supply the cell and the risk of embrittlment after a long exposure to the hydrogen sorption/ desorption cycles [10]. Dense membranes are not the only type of permeablemembranes, which because of their specific characteristics, can be used as barriers to prevent catalyst poisoning by alkali. In fact, there are some ceramic porous membranes, characterized by a structure with pore radius of 0.1–5 mm, that could be successfully applied for this purpose [11]. First, the ceramic porous membranes can be produced by a good choice of ceramic powders, like carbides or metallic
Fig. 1. Schematic views of DIR-MCFC configuration (a) without and (b) with hydrogen permeable membrane.
0254-0584/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S0254-0584(96)01853-6
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oxides, that are commercially available, cheap, resistant to chemical attack by alkali and stable at the cell temperature. Besides, the separation factor of these membranes, which is an index of their separation capability, can reach values comparable with those of the dense membranes, while the permeate flow rate depends on certain characteristics of the structure such as the thickness, the particle diameter, the average pore radius and the porosity. To evaluate the theoretical degree of reliability of the ceramic porous membranes to protect the reforming catalyst in an MCFC, a mathematical model based on the equations that describe the diffusion of a gas mixture through a porous structure, has been developed. The model has been applied to a molten carbonate fuel cell, considering operative conditions of a DIR-MCFC anode compartment, and provides significative indications on the influence of the main membrane structure characteristics on the examined diffusion process. 2. Model development
As described before, one of the main phenomena inducing the deactivation of the steam reforming anodic catalyst employed in a molten carbonate fuel cell is the poisoning due to alkali hydroxide vapours [11]. The objective of this work is to study the possibility to enhance the catalyst lifetime in MCFCs, through the introduction of a porous membrane in the anodic compartment of the cell between the steam reforming catalyst housing and the anode. The porous membrane must be selective to the alkali vapour flow and, at the same time, must allow a flow of hydrogen sufficient to sustain the electrochemical cell reaction. The capability of themembrane to limit the KOH vapour diffusion is strictly dependent on its physical properties, such as the porosity and the pore size. However, since the flow of hydrogen through the membrane is counter to that of the alkali vapours, the determination of the optimal values of the membrane characteristics isacritical aspect, whose solution requires an in-depth analysis. For this purpose, based on typical anodic operative conditions for a DIR-MCFC, a mathematical model that describes the diffusion mechanisms of gases in a porous medium has been developed. From a general point of view, the property of a porous inorganic membrane to allow selective permeation of a mixture of gases depends on various mechanisms, such as surface adsorption and diffusion, molecular size exclusion, Knudsen diffusion and capillary condensation [12]. Nevertheless, in the range of average pores radius of the porous inorganic membranes considered in this paper (between 0.1 and 5 mm), the surface adsorption and diffusion mechanism and the molecular size exclusion mechanism are insignificant. Furthermore, since capillary condensation occurs when the operative conditions of the porous structure are characterized by high pressure and low temperature, which is not the case examined here, we assume that the molecular gas diffusion (bulk and Knudsen) is the prevailing mechanism for such
membranes. The other model assumptions can be summarized as follows: (i) the physical diffusion of gas occurs through the porous structure and no chemical interactions between the gas molecules and the bulk material occur; (ii) only diffusive flow has been considered in the calculation of the alkali vapour transport in the porous structure; (iii) the amount of diffusing alkali vapour has been evaluated assuming a rapid migration of KOH into the membrane structure, so that the membrane optimization for less severe conditions is warranted; (iv) the concentration of the alkali vapour is constant in the anodic compartment. Based on these assumptions, the basic equations of the model, describing the diffusive and convective flow of gases through the porous structure, are given by the expressions: i i pi,1ypi,2 Gdif sD eff RTL
(1)
P21yP22 2amiRTGiconv 1 P1 2RT(Giconv)2Mi s q bq ln L xigc L P2 xigc
ž
/
(2)
where Gidif and Giconv are the gas flow rates through the membrane respectively due to the diffusive and convective phenomena (mol cmy2 sy1), D ieff is the effective diffusion coefficient (cm2 sy1), R the gas constant (82.0567 cm3 atm moly1 Ky1), T the absolute temperature (K), L the membrane thickness (cm), a the viscosity resistance coefficient (cmy2), b the inertial resistance coefficient (cmy1) and gc the acceleration due to gravity (980.665 cm sy2). In addition, mi, Mi and xi are the gas viscosity (poise), the molecular weight (g moly1) and the molar fraction of component i; pi and P are the partial and absolute pressures(atm), respectively, with indices 1 and 2 denoting the membrane upstream and downstream, respectively. Eq. (1) is a generalization of diffusive flow phenomena due to concentration gradient [13], and Eq. (2) describes the isothermal flow of an ideal gas through porous media [14]. Equations for ideal gases have been chosen because they are a sufficiently good approximation at low pressure, as well as in the examined case [14]. Eq. (2) can be arranged as a quadratic equation for the convective flow rate a1(Giconv)2qa2Giconvqa3s0
(3)
with a1s bLqln
ž
P1 Mi P2
/
(4a)
a2samiL
(4b)
xigc 2 a3sa4 (P2yP12) 2RT
(4c)
where the constant a4s1033.23 represents the conversion factor from atm to g cmy2. The viscosity and the inertial resistance coefficients appearing in Eqs. (4a) and (4b) have been determined by the Ergun definition [15]:
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as
150(1yu)2 u3(fdp)2
(5)
bs
1.75(1yu) u3(fdp)
(6)
where u is the porosity, dp the particle diameter (cm) and f the particle shape factor, which is equal to 0.874 for cylinders [15]. The diffusive and convective flow rates have been determined as a function of the membrane properties, considering as operative conditions (temperature, pressure, gas composition) those of the experiments carried out on a bench scale isothermal monocell operating under direct internal reforming configuration. In the case of a binary gas mixture, the ordinary (free) diffusion coefficient of component i in the mixture, taking into account both Knudsen and bulk diffusions, is given by the relationship 1 1 j D i,free s i, jq i Db Dk
ž
(7)
/
The Knudsen and bulk diffusions are respectively given by T Mi
(8)
0.001T 1.75x1/Miq1/Mj D i,b js 1/3 2 P[(8v)1/3 i q(8v)j ]
(9)
Diks9700r#
y
and
where r# is the average pore radius (cm) and (8v)i the diffusion volume of component i. In the case of a gas component diffusing through a mixture, the multicomponent bulk diffusion coefficient is related to the binary diffusion coefficients of the i component respect to each component of the mixture, according to the following equation 1yxi
D i,m b s
(10)
8 xj/Dij
j/1
This relationship represents a good approximation for the description of the diffusion of a single component in a mixture, while the analysis of the simultaneous diffusion of two or more components of a mixture is more complicated. The ordinary diffusion coefficient for a multicomponent mixture can be obtained from Eq. (7) by substituting the binary bulk diffusion coefficient, D ib, j, with the multicomponent one, D ib,m, given by Eq. (10). For a medium with porosity, the effective diffusion coefficient, which appears in Eq. (1), can be calculated from the ordinary diffusion, multiplying for the term u/t 1 1 D effs i,mq i Db Dk i
ž
y1
/
u t
(11)
where t is a factor which accounts both for tortuosity and variation of the pore cross section. Thus, it represents a correction factor for the irregularity of the shape of the pore, resulting in a decrease of the effective diffusion coefficient. For most materials t is between 2 and 8, usually around 4 [13], which is the value used here. Thus, the above equations take into account the influence of the membrane properties, through the parameters L, u, dp and r#, even if the particle diameter can be correlated to the porosity and the average pore radius, by the expression 3r#(1yu) dps u
(12)
derived from the following literature [16,17] relationships, that assume cylindrical pores of uniform size: r#s
2u , (1yu)rAs
6 dps rAs
where As is the specific surface area (cm2 gy1) and r the solid density (g cmy3). The values utilized for the diffusion volume of the gas components are 7.07 for H2, 12.7 for H2O, 18.9 for CO, 26.9 for CO2 and 18 for CH4, where this last value was determined on the basis of the atomic diffusion volumes of carbon and hydrogen. Substitution of these values in the Gilliland-type Eq. (9) provides the bulk diffusion coefficients. In particular, the bulk diffusion coefficient of the alkali vapours has been calculated as binary diffusion coefficient of KOH vapour in H2, since the hydrogen is the main component of gas mixture. It has been estimated through Eq. (9) by assuming the diffusion volume of KOH to be equal to that of CO2, as suggested by Berger [16]. The upstream vapour partial pressure was calculated as equilibrium KOH vapour pressure for the reaction K2CO3(l)qH2Os2KOH(g)qCO2 according to the following relationship relative to a molten mixture of 62% Li2CO3 and 38% K2CO3: pH O (pKOH)2s 2 0.381.93 pCO2
(13) with thermodynamic data reported in the literature [16] (e.g. at 923, the log Ki values are 12.93, 22.44, 49.77, 11.17 for KOH(g), CO2, K2CO3 and H2O, respectively). The downstream vapour partial pressure was assumed to be equal to zero. This means that there is rapid migration of KOH through the membrane and corresponds, with regard to catalyst poisoning, to the most severe conditions. In practice, the amount of vapour that really diffuses will be certainly less than the value calculated from Eq. (1) on this hypothesis, and then the membrane optimization is warranted. Indeed, under the initial conditions the downstream vapour concentration is equal to zero, but as the vapour begins to diffuse towards the opposite side of the membrane its concentration =10(2 log KKOH(g)qlog KCO2ylog KK2CO3ylog KH2O)
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Table 1 Coefficients for viscosity, extrapolated from literature data Gas H2 CH4 CO CO2 H2O
ai
4.44557
y5.43597
6.97481
y19.8421 y12.5925
Table 2 Model base-case input data
bi=10
ci=104
di=107
Parameter
Value
3.61313 4.6993 6.7871 6.68342 3.61238
y2.92135 y3.02085 y4.29479 y3.50231
1.25714 1.06961 1.53759 0.98655 0
Temperature Pressure gradient Reformed gas composition
923 K 10 cmH2O 59.9%H2, 18.5%H2O, 10.6%CO, 7.0%CO2, 4.0%CH4 0.5 mm 40% 0.5 mm 4 0.874
0.238096
increases and the vapour flow rate through the membrane decreases. The gas viscosities, expressed in micropoise, have been calculated as a function of the temperature, according to the following general relationship (14)
misaiqbiTqciT 2qdiT 3
utilizing for the coefficients the values listed in Table 1 obtained by an extrapolation of viscosity data reported in the literature [18]. The capability of these membranes to separate the component i from the gas mixture depends by the relative permeability of the gases through the membrane and can be measured by the separation factor defined, in terms of the upstream and downstream molar fractions, as: xi,2 1yxi,1 Sfis xi,1 1yxi,2
(15)
When the specified membrane characteristics are such that the flow rate of diffused hydrogen is sufficient to sustain the electrochemical reaction, only the capability to hinder the diffusion of KOH vapours allows us to discriminate between the membranes efficiencies. For this purpose, it is necessary to relate the diffusive flow rate of KOH through the membrane, calculated by Eq. (1), to the poisoning mechanism induced on the catalyst. Thus, the definition of catalyst lifetime in the presence of a membrane is introduced: WK dyL L tcats q KOH MKS[KOH]o DKOH D b eff
ž
/
(16)
where WK is the amount of potassium adsorbed on the reforming catalyst surface (g), MK the molecular weight of potassium (39.11 g moly1), S the total anode surface area (cm2), d the distance between anode and catalyst surface (cm), and [KOH]o the KOH concentration at the anode surface (mol cmy3). This equation, based on the assumptions that the alkali hydroxide is the main reason for the catalyst poisoning and its vapour pressure at the edge of the catalyst grains is zero, represents a generalization of the definition of catalyst lifetime given in literature [16] and reduces to this definition for KOH Ls0 or DKOH (i.e. in the absence of membrane). eff sDb The lifetime can be determined by Eq. (16) once the percentage amount of potassium that produces the total poisoning of the catalyst is known.
Membrane thickness Membrane porosity Average pore radius Tortuosity factor Particle shape factor
3. Model parameters and base-case conditions
The sensitivity analysis of the model results has been accomplished, considering as the base case the data reported in Table 2, and varying the characteristics of a membrane (thickness, porosity and average pore radius) operating into the anodic compartment in accordance with the configuration shown in Fig. 1(b). In particular, the parameters which have been considered in the course of this analysis are as follows. Temperature: the operative temperature of the overall system. This parameter influences the thermodynamic equilibrium of the steam reforming reaction and then the composition of the reformed gas. In the case studied it has been chosen as 973 K. Gas composition: considered to be the composition of the gas mixture to be permeate. It has been calculated by an appropriate mathematical model for the determination of the mass balance in a methane direct internal reforming molten carbonate fuel cell [19] and it corresponds to 59.9% H2, 18.5% H2O, 10.6% CO, 7.0% CO2, 4.0% CH4. Pressure gradient: difference between the upstream and downstream pressures through the membrane surfaces. At first, the influence of this operative parameter on the gas diffusion has been evaluated in the range from 0 to 100 cm H2O. Then, the constant value of 10 cm H2O has been considered. Membrane thickness: the total thickness of the porous structure. This parameter has been studied in the range from 0.10 mm to 1.00 mm. Membrane porosity: considered to be the total porosity of the membrane structure; its influence has been extensively studied in the range from 0.0% to 80.0%. Average pore radius: the parameters is paramount for diffusional gas problems and was varied in the range 0.00– 3.00 mm. 4. Model results and discussion
At first, the influence of the gradient pressure on the hydrogen flow permeate has been investigated. The results of these calculations are reported in Fig. 2, where the variation of the
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Fig. 2. Hydrogen permeate flow vs. pressure gradient, for base-case conditions.
hydrogen permeate flow as a function of this parameter is shown. In the range examined the flow rate of the permeate appears to be directly correlated to the value of the gradient pressure applied to the membrane, and it increases with a slope of about 40=10y8 mol sy1 cmy2 per decade of cm H2O. If we analyze the case of a membrane operating into a cell, with the base-case characteristics, it is necessary to consider that the fuel cell requires, at least, 2.074= 10y6 mol sy1 cmy2 of hydrogen flow rate to produce 200 mA cmy2, at a fuel utilisation of 50%. Then, it appears clear that a gradient pressure of about 53 cm H2O should be applied on the membrane to have the flow required to sustain the electrochemical cell activity. Moreover, a separation factor equal to 1.838, calculated for a membrane operating at base-case conditions, confirms that the membrane allows the flow of a permeate with hydrogen rich composition. As reported in Fig. 3, the variation of the permeate flow as a function of the membrane porosity has been determined, for a porous structure characterized by a thickness of 0.5 mm, average pore radius of 0.5 mm and gradient pressure of 10 cm H2O. In this case also, a direct dependence of the hydrogen permeate flow on the value of the porosity is evident. In fact, with a porosity of 30%, the permeate diffuses at a rate of 29.1=10y8 mol sy1 cmy2, which increases to 58.2= 10y8 mol sy1 cmy2 when the porosity doubles. Thus, for a
Fig. 3. Hydrogen permeate flow vs. membrane porosity.
convenient application it would be interesting to have membranes of high porosity, which allow a substantial flow of the permeate when a low gradient of pressure is applied to the membrane. Furthermore, the calculations demonstrated that the dependence of the hydrogen permeate flow on the values of the average pore radius is marked. This is justified, because the viscosity and the inertial resistances become predominant when the gas flows into very small pores. The trend of the curve representing the permeate flow as a function of the average pore radius is reported in Fig. 4. From the analysis of this curve, it is evident that a slight increment of the pore radius substantially improves the diffusional flow, which results directly from the proportionality of the flow to the square of the average pore radius; for instance, at r#s1 mm, the permeate flow corresponds to 155=10y8 mol sy1 cmy2, while, for r#s3 mm, it will be 1395=10y8 mol sy1 cmy2, with an increase of 9 times. The last parameter examined was the thickness of the porous structure, whose influence on the hydrogen permeate flow is reported in Fig. 5. From the analysis of this curve, it is evident that the permeation is strongly limited by the thickness. This limit appears to be stronger for thicknesses larger than 400 mm, where the flow is extremely low; in the region characterized by values less than 400 mm, the permeate flow improves greatly for a small reduction of thickness, making
Fig. 4. Hydrogen permeate flow vs. membrane average pore radius.
Fig. 5. Hydrogen permeate flow vs. membrane thickness.
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Table 3 Hydrogen permeate flow (108 mol sy1 cmy2) as a function of the average pore radius and porosity (the values of the other parameters are those of the base case) Porosity (%)
20 40 60
Average pore radius (mm) 0.1
0.5
1.0
1.5
2.0
2.5
3.0
0.775 1.55 2.33
19.4 38.8 58.2
77.5 155 233
174 349 523
310 620 931
485 969 1450
698 1395 2090
Table 4 Alkali hydroxide vapour flow (1012 mol sy1 cmy2) as a function of the average pore radius and porosity (the values of the other parameters are those of the base case) Porosity (%)
20 40 60
Average pore radius (mm) 0.1
0.5
1.0
1.5
2.0
2.5
3.0
1.41 2.82 4.23
5.15 10.3 15.4
7.69 15.4 23.1
9.21 18.4 27.6
10.2 20.4 30.7
10.9 21.9 32.8
11.5 23.0 34.4
the thicknesses belonging to this region the most interesting ones for practical uses. A more complete analysis of the membrane capability to permeate hydrogen comes out from the diagram reported in Fig. 6, where the combined effects of the average pore radius and of the porosity on the permeate flow are shown. This diagram can be divided into two different regions characterized by values of the average pore radius smaller or bigger than 1 mm, respectively, where the influence of the two examined parameters on the permeate flow presents a different behaviour. In fact, in the first region, the influence of the porosity is very small, while the average pore radius is the controlling factor. In the second region, the influence of the porosity becomes more evident and increases as well as r# grows. More detailed results about the permeate flow as a function of the average pore radius and of the porosity are shown in Table 3. This table reveals that similar flows of permeate can be obtained from membranes with different characteristics; in fact, if we analyze the behaviour of two membranes with 1.0 mm and 40% and 1.5 mm and 20% of average pore radius and porosity, it is interesting to note that the flows of permeate are 155=10y8 mol sy1 cmy2 and 174=10y8 mol sy1 cmy2, respectively. Therefore, by choosing appropriate values for these two structural parameters, it is possible to have enough flow of hydrogen to sustain the cell reaction, even if the applied pressure gradient and thickness are low. This allows the selection of a membrane to be used in a molten carbonate fuel cell and reduces the impact of the presence of this additional component on the cell hardware geometry. As described before, we assumed only diffusive flow in the calculation of the alkali vapour transport through the porous structure and so the capability of the porous membrane to limit this diffusion depends on its physical properties, such
as porosity and average pore radius. The results of the model demonstrated that the KOH diffusion is directly influenced by the porosity with a dependence similar to that found for the hydrogen permeate. An analogous behaviour to that of the hydrogen permeate flow has also been found for KOH diffused flow as function of the membrane thickness. Instead, from a comparison between Figs. 4 and 7, referred to a membrane with the same characteristics (see base-case), the influences of the average pore radius on the KOH diffused flow (Fig. 7) and on the hydrogen permeate flow (Fig. 4) are different. The flow of KOH that diffuses in a membrane, with 1.5 mm pore radius and 40% of porosity, corresponds to 18.4=10y12 mol sy1 cmy2; this value quickly decreases when the pore radius becomes smaller, while slight increases when this parameter grows. For example, at the same conditions, for r#s0.5 mm, the electrolyte diffusion corresponds to 10.3=10y12 mol sy1 cmy2, while for r#s2.5 mm, it is 21.9=10y12 mol sy1 cmy2.
Fig. 6. Coupled influence of the membrane porosity and average pore radius on the hydrogen permeate flow.
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Fig. 7. Electrolyte vapour flow vs. membrane average pore radius.
Fig. 8. Coupled influence of the membrane porosity and average pore radius on the electrolyte vapour flow.
The cumulative effect of average pore radius and porosity of a membrane on the electrolyte diffusion has been determined and is represented in Fig. 8, and these values are also summarized in Table 4. The value of porosity appears to be the determining factor in the mechanism examined, and its influence becomes greater when the average pore radius increases. The influence of the average pore radius is less marked for low porosity values, while it is more consistent when the porosity is higher than 40%. 5. Conclusions
The analysis performed gave indications on the reliability of the membranes to permeation of a hydrogen-rich gas mixture and to limit the diffusion of electrolyte vapours towards the internal reforming catalyst site. Furthermore, the correlations between the permeate flows of hydrogen and of KOH
205
vapours and the main operative parameters and characteristics of the membrane have been determined. It has been shown that the hydrogen permeate flow is directly correlated to the pressure gradient applied to the two faces of the membrane. In the case examined the lowest pressure gradient applicable to guarantee a cell current density of 200 mA cmy2, at a fuel utilisation of 50%, is about 53 cm H2O. The porosity and the average pore radius of the membrane structure were found to be the other parameters that strongly influence the diffusion process. In particular, when the membrane presents an average pore radius smallerthan1 mm, the influence of the porosity is very small, while the average pore radius appears to be the controlling factor. In fact, under this condition of flow, the viscosity and the inertialresistances greatly increase. For membranes with average pore radius greater than 1 mm, the influence of the porosity increases and becomes relevant at higher pore radii. The thickness of the membrane also influences the diffusion process, and in the region of low thicknesses the permeate flow changes greatly for a small variation of the thickness. As regards the electrolyte vapour diffusion, it has been seen that this process is also influenced by porosity, average pore radius and thickness. The porosity appears to be the determining factor for this process, and its influence becomes greater when the average pore radius increases. In conclusion, the model allows us to analyze the reliability of the porous ceramic membranes to protect the internal reforming catalyst, in a molten carbonate fuel cell. Future work will be devoted to determining whether the characteristics of the membranes which can be selected in the model comply with the hardware cell requirements and to evaluate the influence of the membranes on the overall cell performance. Emphasis will be placed on the comparison of the model results with the experimental ones. References
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[11] H.P. Hsieh, Catalysis Rev., 33 (1–2) (1991) 1–70. [12] H.P. Hsieh, AIChE Symp. Ser., 268 (1989) 53–67. [13] C.N. Satterfield and T.K. Sherwood, The Role of Diffusion in Catalysis, Addison-Wesley, Reading, MA, 1963. [14] R.H. Perry and C.H. Chilton (eds.), Chemical Engineers’ Handbook, McGraw-Hill, New York, 5th edn., 1974, Section 5-54. [15] Rohsenow, J.P. Hartnett and E.N. Ganic, Handbook of Heat Transfer Application, McGraw-Hill, New York, 2nd edn., 1985.
[16] R.J. Berger, Nickel catalysts for internal reforming in molten carbonate fuel cells, Ph.D. Thesis, Twente University, 1992. [17] S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 2nd edn., 1982. [18] R.C. Weast (ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 62nd edn., 1982, Section F-50. [19] S. Freni, M. Aquino, N. Giordano and S. Cavallaro, J. Power Sources, 39 (1992) 203–214.
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