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

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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