Mogenesen found on a variety of samples [81]. The reported activation energies of the material from Ni/YSZ anodes used in the short- and long-term tests is in the range between 164-185 kJ mol-1 and they are close. However, the reported pre-exponential factor is in the range from 1.7 × 10-3 mol s-1 g-1 Pa-0.6 to 139 mol s-1 g-1 Pa-0.9. The materials used after long term and short-term tests differ remarkably, though the activation energies do not differ sufficiently. The large size of the nickel particles in the anode, giving a smaller surface area for the same nickel content and thus less active sites, will influence the reaction rate of the steam reforming [39]. In fact, the agglomeration of Ni toward to larger size has been observed in an Ar-H2(4%)-H2O(3%) atmosphere at 1000 °C with increasing exposure time, thus the change in the microstructure has been reported [95], which is coarsening Ni-supported solid oxide anode and is recognized as a major degradation phenomenon on the Ni/YSZ supported SOFC anodes [211].
Iwai et al. have conducted a derivation of the reaction kinetics on the various compositions of Ni/YSZ cermet samples, of which the Ni contents are 75 vol.%, 50 vol.% and 25 vol.% [151].
The investigated cermet material had a disk shape with a thickness of 30 µm, 6 mm and 13 mm of inner and outer diameter respectively. The high-temperature sintering process of the catalyst materials resulted in the various microstructure of test samples. Table 7.3 shows the detailed information about the composition and microstructure of the prepared samples and the determined steam reforming process kinetics [151]. The reaction orders and activation energies they found are very similar for various compositions of the catalysts, however, the values of the pre-exponential factors derived on the basis of the apparent surface area are inconsistent among the various compositions. On the other hand, the values of the modified pre-exponential factors based on the Ni-pore contact area becomes close to each other. It seems that the composition of Ni and YSZ does not affect the pre-exponential factor, nevertheless, the microstructure created by the different compositions gives significance on determining the pre-exponential factor [151].
A comparison of the derived reaction kinetics with the results obtained in this study is shown in Figs. 7.1 and 7.2 For the comparison, models from two concepts, ii) first order reaction [32,116] and iii) power-law expression [81,147,148,153], were used. In demonstrating the comparison, formula and the values of reaction orders a and b, and the activation energy E are directly based on the literature data. Additionally, the following assumptions were made:
• The measurement is conducted on the packed catalyst bed.
• The used catalyst is prepared in the form of fine powder of at least 0.85 µm to avoid the effect of mass transport phenomena on the reaction kinetics.
• The properties of the used catalyst, density, porosity and active area, are the same as the one used in the present study. Properties such as density, porosity, support material and general microstructure influence the catalytic behaviour of the catalytic material and finally define its active area and are included in the value of the pre-exponential factor.
• Thus, the microstructure of the used catalyst is assumed to be the same as the one used in the present study.
Based on those assumptions, the pre-exponential factor is recalculated for all the reaction models to be adjusted to the experimental conditions incorporated in this study – the value of pre-experimental factor A is determined so that the standard deviation of A based on the experimental results becomes minimal. All of the reported studies for deriving the reaction kinetics did not use the exact same methodology to describe measurements, and moreover did not follow the appropriate conditions to avoid the possible effects of mass transport [39].
Thus, the reported kinetics may be specific to the setup of their systems, and will probably fail to describe and represent other systems [39]. By postulating the above mentioned assumption and applying the preceded approach, all the models are now modified and constrained to certain specification that have been applied in the present measurement and the comparison of the proposed models can be considered as practical and meaningful.
Figures 7.1 and 7.2 present the results obtained in two exemplary experimental conditions with the theoretical fractional conversion of methane based on the literature data and the present study. The results show that the kinetic model proposed in this study is the most accurate for the various operational conditions. Some of the competitive kinetic equations presented in the literature approximate the experimental results well in the limited temperature range (Mogensen equation) or for specified SC conditions (Lee equation).
However, the overall accuracy of the model derived in this study exceeds the other models in the case of the analysed cases.
Table 7.1 The used formula for the steam/methane reaction and derived reaction kinetics found in the literatures [4,8,11-15,17-20,22,36,40-45]
Reference Material Ni
content Reaction rate formula Pre-exponential factor A Activation energy E [kJ mol-1] (i) General Langmuir-Hinshelwood kinetics
Xu and Froment
[37] Ni/MgAl2O4
r =k pCH
4
2.5 pCH
4pH
2O− pCOpH
2
3 K
( )
α2+k p′ CH
4
2.5 pCH
4pH
2O−pCOpH
2
3 K′
( )
α22 2
2 2
4 4
2
CO CO H H
H O H O CH CH
H
1 K p K p
K p K p
p α = + +
+ +
Bebelis et al.[193] Ni/YSZ 70 wt.% 4 2 4
2 2
H CH CH
H O H O
1 ad
ad
r
k p p r k p
k K p
⎛ ⎞
= ⎜⎜⎝ − ⎟⎟⎠
Nakagawa et al.
[210] Ni/YSZ/CeO
(
1 CHCH44 CHCH44 H O2H O2 H O2H O2)
2kK p K p
r= K p K p
+ +
Peters et al. [38] Ni/YSZ 50 wt.%
(
4 4 4 24 22 2 2 2)
CH CH H O H O
2
CH CH H O H O CO CO
1
kK p K p
r= K p K p K p
+ + +
Dicks et al. [212] Ni/ZrO2
(
1 H2 1/2H2 CH4S H O2 H2)
nr kp
K p K p p
= + +
Table 7.1 The used formula for the steam/methane reaction and derived reaction kinetics found in the literatures [4,8,11-15,17-20,22,36,40-45] – continuation
Reference Material Ni
content Reaction rate formula Pre-exponential factor A Activation energy E [kJ mol-1] (ii) Expression with first order kinetics respect to methane
Akers and Camp [209]
Ni-based
material r =kpCH4
King et al. [150] Ni/YSZ 50 wt.% r =kpCH4 113~124
Achenbach [116] r =kpCH4 4.274
×
10-2[mol s-1 m-2 Pa-1] 82Belyaev et al. [207] Ni/ZrO2/CeO2 r =kpCH4 2.57
×
10-2 [mol s-1 g-1 Pa-1] 82 Achenbach andRiensche [123] Ni/ZrO2 20 wt.% 4 2
4 2
3 CO H CH
CH H O
1
p
r kp p p
p p K
⎛ ⎞
= ⎜⎜⎝ − ⎟⎟⎠ 4.274
×
10-2[mol s-1 m-2 Pa-1] 82Wei and Iglesia [32] Ni/MgO 7 wt.% 4 2
4 2
3 CO H CH
CH H O
1
eq
r kp p p
p p K
⎛ ⎞
= ⎜⎜⎝ − ⎟⎟⎠ 2.5
×
102 [s-1 Pa-1] 102Table 7.1 The used formula for the steam/methane reaction and derived reaction kinetics found in the literatures [4,8,11-15,17-20,22,36,40-45] – continuation
Reference Material Ni
content Reaction rate formula Pre-exponential factor A
Activation energy E [kJ mol-1] (iii) Power-law expressions derived from data fitting
Yakabe et al. [113] Ni/YSZ r =k p
( ) ( )
CH4 1.3 pH O2 −1.2
191 Ahmed and Foger
[125] Ni/YSZ r =k p
( ) ( )
CH4 0.85 pH O2 −0.35 27.012[mol s-1 m-2 Pa-0.5] 95 Iwai et al.[151] Ni/YSZ 75 vol.%50 vol.%
25 vol.% r =k p
( ) ( )
CH4 0.82 pH O2 0.12 0.1324[mol s-1 m-2 Pa-0.96] 0.103[mol s-1 m-2 Pa-0.96] 0.07[mol s-1 m-2 Pa-0.96]89.7 87.0 89.3 Lee et al. [153] Ni/ZrO2 60 vol.% r =k p
( ) ( )
CH4 1.0 pH O2 −1.25 4.3~42[mol s-1 g-1 Pa0.25] 74~98 Odegard et al. [147] Ni/YSZ 60 vol.%CH4
r =kp1.2 1.73
×
10-6[mol s-1 g-1 Pa-1.2] 58Timmermann et al.
[152] Ni/CGO
CH4
r =kp1.19 4.05
×
10-5[mol s-1 m-2 Pa-0.9] 26Brus [148] Ni/YSZ 60 vol.% r =k p
( ) ( )
CH4 0.98 pH O2 −0.09 1.55×
10-3[mol s-1 g-1 Pa-0.89] 117Mogensen [81] Ni/YSZ r =k p
( ) ( )
CH4 0.8 pH O2 −0.2 1.7×
10-3[mol s-1 m-2 Pa-0.9] 183Table 7.2 The reaction kinetics of the methane steam reforming on various catalysts derived by power-law expression by Mogensen [81]
Description Reaction rate formula
Pre-exponential
factor A
Activation energy
E [kJ/mol]
Model anode material Ni composition: 42 wt.%, size of the particles: approx.
0.3mm
r =k pCH
( )
4 0.9( )
pH2O −0.2( )
pCO2 0.2 139 [mol s1 g-1 Pa-0.9] - 185 Industrial anode material r =k p( ) ( ) ( )
CH4 0.8 pH O2 −0.2 pCO2 0.2 23 [mol sg-1 Pa-0.8-1] 166Industrial stack anode material after short term test
(Material of anode crushed with electrolyte)
( ) ( )
CH4 0.8 H O2 0.2r =k p p − 1.7
×
10-3 [mol s-1 g-1Pa-0.6]
183 Industrial anode from stack
after long term test (Material of anode crushed with
electrolyte)
( )
CH4 0.8r =k p 15.3 [mol s
-1 g-1 Pa-0.8] 164
Table 7.3 Comparison of reaction kinetic parameters for various materials derived with respect to their microstructure by Iwai et al. [151]
Sample A Sample B Sample C Sample D Composition
of the catalyst
Ni [vol.%] 32 34.6 10.3 37.1
YSZ [vol.%] 9.8 31 29.8 39.4
Pore [vol.%] 58.2 34.4 59.9 39.4
Contact area density between Ni and
pore [µm2 µm-3] 0.740 0.785 0.388 0.283
Reaction kinetic parameters
a [-] 0.82 0.82 0.82 0.84
b [-] 0.14 0.14 0.14 0.11
E [kJ mol-1] 89.7 87.0 89.3 86.3 A based on apparent
surface area 0.132 0.103 0.07 0.036
A based on Ni-pore
contact area 0.126 0.111 0.116 0.108
Figure 7.1 The comparison of the obtained fractional conversion with ones obtained from the proposed reaction kinetics in the published literature [32,81,116,147,148,153] in the conditions of SC
= 3, NC = 3
Figure 7.2 The comparison of the obtained fractional conversion with the ones obtained from the proposed reaction kinetics in the published literature [32,81,116,147,148,153] in the conditions of
SC = 4, NC = 2