Fuel Processing for Fuel Cells - Institut für Technische Chemie und ...

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Author's personal copy Fuel Processing for Fuel Cells 37 referred to references (Bird et al., 2001; Hayes and Kolaczkowski, 1997; Kee et al., 2003; Patankar, 1980; Warnatz et al., 1996) and (Deutschmann, 2008, 2011; Kee et al., 2003), respectively. In the remainder of this section, the individual physical and chemical processes and their coupling will be discussed, beginning with the reactions on the solid catalyst. 6.1 Modeling the rate of heterogeneous catalytic reactions The understanding of the catalytic cycle in fuel reformers is a crucial step in reformer design and optimization. The development of a reliable surface reaction mechanism is a complex process, which is today increasingly based on the elucidation of the molecular steps. A survey on stateof-the-art modeling of heterogeneously catalyzed gas-phase reactions can be found in Deutschmann (2011). The catalytic reaction cycle can be expressed by a heterogeneous reaction mechanism, which consists of a set of K s chemical reactions among N g gas-phase species, N s species adsorbed on the top catalyst layer, and N b bulk species absorbed by the catalyst particle; species name is denoted by A i : N g þN X s þN b i¼1 n 0 ikA i ! N gþN X s þN b i¼1 n 00 ikA i ; (27) with n 0 ik, n 00 ik being the stoichiometric coefficients. In technical systems, the mean-field (MF) approximation is the most frequently applied approach for calculating the chemical reaction rates of the individual reactions in the mechanism (Deutschmann, 2008). In this concept, the local reaction rate is related to the size of the computational grid in the flow field simulation, assuming that the local state of the active surface can be represented by mean values for the cells of the computational grid. Hence, this model does not resolve any spatial inhomogeneity in this cell on the catalytic surface as Monte-Carlo simulation would do. In the MF approximation, the state of the catalytic surface is described by the temperature T and a set of surface coverages y i , which is the fraction of the surface covered with surface species i. The surface temperature and the coverage depend on time and the macroscopic position in the reactor, but are averaged over microscopic local fluctuations. The local chemical source term, R i het , is derived from the molar net production rate, _s i ,by X K R het s i ¼ F cat=geo _s i M i ¼ F cat=geo M i k¼1 n ik k f k N gþN Y s þN b j¼1 c n0 jk j : (28)
Author's personal copy 38 Torsten Kaltschmitt and Olaf Deutschmann Here, K s is the number of surface reactions, c i are the species concentrations, which are given, for example, in mol m 2 for the N s adsorbed species and in mol m 3 for the N g and N b gaseous and bulk species. The molar net production rate of gas-phase species i, _s i , given in mol m 2 s 1 , refers to the actual catalytically active surface area, that is, the (crystal) surface of the catalyst particle, which usually has the size of 1–10 3 nm. These catalyst particles are usually dispersed in a certain structure, for instance, they may occur as dispersed particles on a flat or in a porous substrate or pellet. The simplest way to account for this structure and the total active catalytic surface area in a reactor simulation is the scaling of the intrinsic reaction rate at the fluid–solid interphase by two parameters. The first parameter, F cat/geo , represents the amount of the total active catalytic surface area in relation to the geometric surface area of the fluid–solid interphase. Recently, it has been shown that this ratio (F cat/geo ) can also serve as a parameter to describe the dependence of the overall reaction rate on catalyst loadings and on effects of hydrothermal aging for structure-insensitive catalysts (Boll et al., 2010). An alternate representation of the total catalytic surface area is the volume-specific catalyst surface area, which is related to the reactor or porous media volume. The simplest model to include the effect of internal mass transfer resistance for catalysts dispersed in a porous media is the effectiveness factor, i , based on the Thiele modulus (Hayes and Kolaczkowski, 1997; Papadias et al., 2000). In case of infinite fast diffusion of reactants and products in the porous structure, the effectiveness factor becomes unity. According to Equation (28) and the relation Y i ¼c i s i G 1 , the variations of surface coverage follow @Y i @t ¼ _s is i G : (29) Here, the coordination number s i gives the number of surface sites which are covered by the adsorbed species. Since the binding states of adsorption of all species vary with the surface coverage, the expression for the rate coefficient, k fk , is commonly extended by coverage-dependent parameters m ik and e ik (Coltrin et al., 1991; Kee et al., 2003): Y N s k f k ¼ A k T b k exp E ak RT i¼1 Y m i k i exp e i k Y i RT : (30) Here, A k is the pre-exponential factor, b k is the temperature exponent, and E ak is the activation energy. A crucial issue with many of the mechanisms published is thermodynamic (in)consistency. Even though most of the mechanisms lead to consistent enthalpy diagrams, many are not consistent regarding the entropy change in the overall reaction due to lack of knowledge of the
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