Supplementary material (S1)
Nomenclature list
𝐴𝑖
𝑐𝑘
𝑐𝑘𝐵
𝑑ℎ𝑦𝑑
𝐷𝑘,𝑔
𝐸𝑎,𝑖
𝐺𝑆𝐴
∆𝐻
𝑘𝑘,𝑚
𝐾
𝑘𝑖
𝑀𝐺𝑘,𝑔
𝑟𝑖
𝑅
∆𝑆
Sh
𝑊
𝑍𝐵𝑟,1
𝑍𝐵𝑟,2
𝐹𝑒𝑀,1
𝐹𝑒𝑀,2
𝐹𝑒𝐷
𝐹𝑒𝑃
𝑇𝑠
𝑡
𝑣𝑘,𝑖
𝑣𝑔
𝑤𝑘,𝑔
𝑧
Pre-exponential factor for reaction i. Depends on the rate expression
Mole fraction at the reaction layer of species k (-)
Mole fraction in the gas bulk of species k (-)
Hydraulic diameter of the channel (m)
Diffusion coefficient of species k in the gas bulk
Activation energy for reaction i (J/mol)
Geometric surface area per reactor volume (m-1)
Enthalpy change (kJ/mol)
Mass transfer coefficient of species k (mol/ m2 s)
Equilibrium constant (-)
Rate constant for reaction i. Depends on the rate expression
Molar mass of gas phase species k (kg/kmol)
Reaction rate for reaction i (kmol/s m3wash-coat)
Gas constant (J/mol K)
Entropy change (J/mol K)
Sherwood number (-)
Weak zeolite adsorption site
Brønsted zeolite site, 1
Brønsted zeolite site, 2
Monomeric iron site, 1
Monomeric iron site, 2
Dimeric iron site
Iron particle site
Temperature at catalyst surface (K)
Time (s)
Stoichiometric coefficient of species k in reaction i
Gas velocity (m/s)
Mass fraction of species k in gas phase (-)
Spatial coordinate in axial direction (m)
Greek letters
𝛼𝑘,𝑖
𝜀𝑔
𝜃𝑘
𝜌𝑔
Θ𝑗
Coverage dependence for species k in reaction i (-)
Volume fraction of gas phase in entire system (-)
Coverage of species k (-)
Density of the gas phase (kmol/ m3)
Surface site density of storage site j (mol/ m2)
The kinetic model
The main governing equation for the gas phase species for a single channel model is [1]:
εg
∂ρg ∙ wk,g
∂t
= εg
∂ρg ∙ wk,g ∙ vg
∂z
+ MGk,g ∑nr
i vi,k ∙ ri (ck , Ts , θk )
(Eq.1)
The coverage of component k on the surface is solved by [1]:
∂θk
(Θ
∂t
∙ GSA) = ∑nr
i vi,k ∙ ri (ck , Ts , θk )
(Eq.2)
The geometric surface area per unit reactor volume, GSA, in Eq. (2) is given by [1]:
GSA
dhyd
= 4 × (cell density)
(Eq.3)
Furthermore, mass-transport from gas bulk to the catalytic surface and vice versa is included. Under
quasi steady-state conditions, the rates of the surface reactions balance the diffusive transport from the
gas bulk to the surface. The molar surface concentration (ck) of component k is evaluated using [1],
GSA ∙ k k,m ∙ (ck − ckB ) = ∑nr
i vi,k ∙ ri (ck , Ts , θk )
(Eq.4)
where ckB is the concentration of species k in the gas bulk and k k,m is the mass transfer coefficient of
the individual species calculated according to [1]:
k k,m =
Sh∙ Dk,g
dhyd
(Eq. 5)
where Dk,g is the diffusion coefficient of species k in the gas mixture and the Sherwood number is
calculated according to the Sieder/Tate relationship [2].
Table 1:
Reactions and rate expressions for NH3 and NO adsorption and desorption (W represents sites for
weakly bound ammonia. ZBr and FeM represent Brønsted and monomeric iron sites, respectively)
Reaction number
Reaction
Reaction rate
1
𝑁𝐻3 + 𝑊 ⇔ 𝑁𝐻3 − 𝑊
𝑟1 = 𝑘1,𝑓 𝑐𝑁𝐻3 𝜃𝑊−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘1,𝑏 𝜃𝑁𝐻3−𝑊
2
𝑁𝐻3 + 𝑍𝐵𝑟,1 ⇔ 𝑁𝐻3 − 𝑍𝐵𝑟,1
𝑟2 = 𝑘2,𝑓 𝑐𝑁𝐻3 𝜃𝑍𝐵𝑟,1−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘2,𝑏 𝜃𝑁𝐻3−𝑍𝐵𝑟,1
3
𝑁𝐻3 + 𝑍𝐵𝑟,2 ⇔ 𝑁𝐻3 − 𝑍𝐵𝑟,2
𝑟3 = 𝑘3,𝑓 𝑐𝑁𝐻3 𝜃𝑍𝐵𝑟,2−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘3,𝑏 𝜃𝑁𝐻3−𝑍𝐵𝑟,2
4
𝑁𝐻3 + 𝐹𝑒𝑀,1 ⇔ 𝑁𝐻3 − 𝐹𝑒𝑀,1
𝑟4 = 𝑘4,𝑓 𝑐𝑁𝐻3 𝜃𝐹𝑒𝑀,1−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘4,𝑏 𝜃𝑁𝐻3−𝐹𝑒𝑀,1
5
𝑁𝐻3 + 𝐹𝑒𝑀,2 ⇔ 𝑁𝐻3 − 𝐹𝑒𝑀,2
𝑟5 = 𝑘5,𝑓 𝑐𝑁𝐻3 𝜃𝐹𝑒𝑀,2−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘5,𝑏 𝜃𝑁𝐻3−𝐹𝑒𝑀,2
𝑁𝐻3 − 𝑍𝐵𝑟,1 + 𝐹𝑒𝑀,1 ⇔ 𝑍𝐵𝑟,1 + 𝑁𝐻3 − 𝐹𝑒𝑀,1
𝑟6 = 𝑘6,𝑓 𝜃𝑁𝐻3−𝑍𝐵𝑟,1 𝜃𝐹𝑒𝑀,1−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘6,𝑏 𝜃𝑍𝐵𝑟,1−𝑣𝑎𝑐𝑎𝑛𝑡 𝜃𝑁𝐻3−𝐹𝑒𝑀,1
7
𝑁𝑂 + 𝑍𝐵𝑟,2 ⇔ 𝑁𝑂 − 𝑍𝐵𝑟,2
𝑟7 = 𝑘7,𝑓 𝑐𝑁𝑂 𝜃𝑍𝐵𝑟,2−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘7,𝑏 𝜃𝑁𝑂−𝑍𝐵𝑟,2
8
𝑁𝑂 + 𝐹𝑒𝑀,2 ⇔ 𝑁𝑂 − 𝐹𝑒𝑀,2
𝑟8 = 𝑘8,𝑓 𝑐𝑁𝑂 𝜃𝐹𝑒𝑀,2−𝑣𝑎𝑐𝑎𝑛𝑡 − 𝑘8,𝑏 𝜃𝑁𝑂−𝐹𝑒𝑀,2
6a,b
a
b
– Thermodynamically restricted (cf. 3.2.1).
– Reaction rate is independent of the corresponding site densities.
Table 2:
Reactions and rate expressions for NH3 and NO oxidation.
Reaction number
9a
10b
11c,e
12d,e
Reaction
Reaction rate
4𝑁𝐻3 + 3𝑂2 ⇒ 2𝑁2 + 6𝐻2 𝑂
𝑟9 = 𝑘9 𝑐𝑁𝐻3 𝑐𝑂2
4𝑁𝐻3 + 3𝑂2 ⇒ 2𝑁2 + 6𝐻2 𝑂
𝑟10 = 𝑘10 𝑐𝑁𝐻3 𝑐𝑂2
2𝑁𝑂 + 𝑂2 ⇔ 2𝑁𝑂2
2𝑁𝑂 + 𝑂2 ⇔ 2𝑁𝑂2
proceeds over site 𝑍𝐵𝑟,2 (Θ𝑍𝐵𝑟,2 ).
𝑟11 = 𝑘11,𝑓 𝑐𝑁𝑂 𝑐𝑂0.5
− 𝑘11,𝑏 𝑐𝑁𝑂2
2
𝑟12 = 𝑘12,𝑓 𝑐𝑁𝑂 𝑐𝑂0.5
− 𝑘12,𝑏 𝑐𝑁𝑂2
2
– Reaction rate (r9)
– Reaction rate (r10) proceeds over site 𝐹𝑒𝐷 (Θ𝐹𝑒𝐷 )
c
– Reaction rate (r11) proceeds over site 𝑍𝐵𝑟,2 (Θ𝑍𝐵𝑟,2 ).
d
– Reaction rate (r12) proceeds over site 𝐹𝑒𝑃 (Θ𝐹𝑒𝑃 ).
e
– 𝑘11,𝑏 and 𝑘12,𝑏 are calculated from the thermodynamic restrictions (∆𝐻 = 58.3 kJ/mol and
∆𝑆 = -76.1 J/mol K) [3]
a
b
Table 3:
Reactions and rate expressions for NH3-SCR (ZBr and FeM represents Brønsted and monomeric iron
sites, respectively).
Reaction number
Reaction
Reaction rate
13
4𝑁𝐻3 − 𝑍𝐵𝑟,1 + 4𝑁𝑂 − 𝑍𝐵𝑟,2 +𝑂2 ⇒ 4𝑁2 + 6𝐻2 𝑂 + 4𝑍𝐵𝑟,1 + 4𝑍𝐵𝑟,2
𝑟13 = 𝑘13 𝑐𝑂2 𝜃𝑁𝐻3−𝑍𝐵𝑟,1 𝜃𝑁𝑂−𝑍𝐵𝑟,2
14
4𝑁𝐻3 − 𝐹𝑒𝑀,1 + 4𝑁𝑂 − 𝐹𝑒𝑀,2 +𝑂2 ⇒ 4𝑁2 + 6𝐻2 𝑂 + 4𝐹𝑒𝑀,1 + 4𝐹𝑒𝑀,2
𝑟14 = 𝑘14 𝑐𝑂2 𝜃𝑁𝐻3−𝐹𝑒𝑀,1 𝜃𝑁𝑂−𝐹𝑒𝑀,2
4𝑁𝐻3 + 4𝑁𝑂 +𝑂2 ⇒ 4𝑁2 + 6𝐻2 𝑂
𝑟15 = 𝑘15 𝑐𝑂2 𝑐𝑁𝐻3 𝑐𝑁𝑂
15a
a
– Reaction rate (r15) proceeds over the dimeric iron sites (Θ𝐹𝑒𝐷 ).
Table 4:
Kinetic parameters for NH3 and NO adsorption and desorption.
Rate
NH3 adsorption (𝑟1,𝑓 )
NH3 desorption (𝑟1,𝑏 )
Rate constants
𝑘1,𝑓 a
𝑘1,𝑏 a
Pre-exponential factor
1.76x102
2.44 x104
Activation energy (kJ/mol)
0
53.23
Coverage dependence(𝛼)
0
0.98
NH3 adsorption (𝑟2,𝑓 )
NH3 desorption (𝑟2,𝑏 )
𝑘2,𝑓 a
𝑘2,𝑏 a
2.05x102
2.97 x105
0
79.59
0
0.066
NH3 adsorption (𝑟3,𝑓 )
NH3 desorption (𝑟3,𝑏 )
𝑘3,𝑓 a
𝑘3,𝑏 a
3.4882x104
5.05 x107
0
79.59
0
0.066
NH3 adsorption (𝑟4,𝑓 )
NH3 desorption (𝑟4,𝑏 )
𝑘4,𝑓 a
𝑘4,𝑏 a
3.29x102
5.01x102
0
72.98
0
0.07
NH3 adsorption (𝑟5,𝑓 )
NH3 desorption (𝑟5,𝑏 )
𝑘5,𝑓 a
𝑘5,𝑏 a
3.23x103
2.07 x106
0
72.98
0.07
NH3 spillover (𝑟6,𝑓 )
𝑘6,𝑓 b
2.18x103
65.75
0
NO adsorption (𝑟7,𝑓 )
NO desorption (𝑟7,𝑏 )
𝑘7,𝑓 a
𝑘7,𝑏 a
7.94x103
6.32 x105
0
105.81
0
NO adsorption (𝑟8,𝑓 )
NO desorption (𝑟8,𝑏 )
𝑘8,𝑓 a
𝑘8,𝑏 a
2.78x103
7.6 x105
0
65.29
0
a
b
– Unit: 1/(s m)
– Unit: m/(kmol s)
Table 5:
Kinetic parameters for NH3 and NO oxidation.
Rate
NH3 oxidation (𝑟9 )
NH3 oxidation (𝑟10 )
Rate constants
𝑘9 a
𝑘10 a
NO oxidation (𝑟11,𝑓 )
NO oxidation (𝑟12,𝑓 )
a
Pre-exponential factor
8.76x106
9.22 x1014
Activation energy (kJ/mol)
83.14
166.14
8.32x103
8.07 x104
𝑘11,𝑓 a
𝑘12,𝑓 a
8.71
20.03
– Unit: 1/(s m)
Table 6:
Kinetic parameters for NH3 SCR.
Rate
Standard SCR, zeolite (𝑟13 )
Standard SCR, monomeric (𝑟14 )
Standard SCR, dimeric (𝑟15 )
Rate constants
𝑘13 a
𝑘14 a
𝑘15 b
Pre-exponential factor
4.16x109
– Unit: m/(kmol s)
– Unit: 1/(s m)
c
– Parameter fixed from Brandenberger et al. [4]
a
b
2.89x108
2.65 x1015
Activation energy (kJ/mol)
85.7
36.2c
93c
Molecular size of phosphoric acid
Y. Huang, X. Dong, M. Li, M. Zhang, Y. Yu, RSC Advances 4 (2014) 14573-14581
References
[1]AVL BOOST Aftertreatment manual, AVL, www.avl.com, 2011.
[2]J.R. Welty, C.E. Wicks, R.E. Wilson, G. Rorrer, Fundamentals of Momentum, Heat, and Mass
Transfer, John Wiley & Sons, Inc, USA, 2001.
[3]A. Lindholm, N.W. Currier, J.H. Li, A. Yezerets, L. Olsson, J. Catal. 258 (2008) 273-288.
[4]S. Brandenberger, O. Kröcher, A. Tissler, R. Althoff, Applied Catalysis B: Environmental 95 (2010)
348-357.
Supplementary material (S2)
Figure 1. Schematic summary of the active sites and their corresponding reactions in the kinetic
deactivation model for Fe-BEA.
Figure 2. NH3 uptake and desorption profiles for the studied catalysts. (a) Catalysts exposed to 10
ppm H3PO4 for 14, 24 and 48 h compared to a fresh sample. (b) Measured and calculated NH3 outlet
concentration during NH3-TPD for the fresh Fe-BEA sample. The red dashed line shows the
calculated concentration and the solid black line show the measured concentration. The samples were
exposed to 400 ppm NH3 and 5% H2O for 40 min at 1500C, followed by exposure to 5% H2O for 30
min at 1500C where after the temperature was increased linearly (100C/min) to 5000C. The total flow
rate was 3500 ml/min and Ar was used as balance.
Figure 3. Measured and calculated outlet NH3 concentrations from the NH3-TPD experiments for all
samples exposed to 10 ppm of H3PO4. The red dashed line shows the calculated concentration and the
solid black line show the measured concentration.
Figure 4. Evolution of NH3 concentration during NH3 oxidation experiments. (a) Catalysts exposed to
10 ppm H3PO4 for 14, 24 and 48 h compared to a fresh sample. (b) Measured and calculated NH3
outlet concentration during NH3 oxidation for the fresh Fe-BEA sample. The red dashed line shows
the calculated concentration and the solid black line shows the measured concentration. The samples
were exposed to 400 ppm NH3, 8% O2 and 5% H2O at 150, 200, 250, 300, 400 and 5000C. The total
flow rate was 3500 ml/min and Ar was used as balance.
Figure 5. Measured and calculated outlet NH3 concentrations during NH3 oxidation experiments for
all samples exposed to 10 ppm of H3PO4. The red dashed line shows the calculated concentration and
the solid black line shows the measured concentration.
Figure 6. Evolution of NO concentration during NO oxidation experiments. (a) Catalysts exposed to
10 ppm H3PO4 for 14, 24 and 48 h compared to a fresh sample. (b) Measured and calculated NO
outlet concentration during NO oxidation for the fresh Fe-BEA sample. The red dashed line shows the
calculated concentration and the solid black line shows the measured concentration. The samples
were exposed to 400 ppm NO, 8% O2 and 5% H2O at 150, 200, 250, 300, 400 and 5000C. The total
flow rate was 3500 ml/min and Ar was used as balance.
Figure 7. Measured and calculated outlet NO concentrations during NO oxidation experiments for all
samples exposed to 10 ppm of H3PO4. The red dashed line shows the calculated concentration and the
solid black line shows the measured concentration.