Reaction Kinetics for the Selective Catalytic Reduction (SCR) Catalyst
Now define the chemical reactions. First, type in the global reaction formula for the standard SCR reaction. The Reaction feature will automatically interpret the chemical equation and suggest reaction rates based on the mass action law (stoichiometry).
(1) Standard SCR: 4 NH3 + 4 NO + O2 => 4 N2 + 6 H2O
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 4NH3+4NO+O2=>4N2+6H2O.
4
Click Apply to generate the Reaction node as well as one Species node for each of the species in the Reaction Formula.
Notice that, there being several ways to balance this formula, the button Balance is not applicable in this case.
In this example, replace the automatically generated reaction rate expression with the rate expression known from the literature. The variable K_NH3 is defined in a Variables feature.
5
Locate the Reaction Rate section. From the Reaction Rate list choose User defined.
6
In the rj text field, type re.kf_1*re.c_NO*re.c_O2*re.c_NH3/(1+K_NH3*re.c_NH3).
In the next step, update the reaction order for this global reaction rate expression.
7
Locate the Reaction Orders section. Find the Volumetric overall reaction order subsection. In the Forward text field, type 3.
8
Locate the Rate Constants section. Select the Use Arrhenius expressions checkbox.
9
In the Af text field, type A1_SCR.
10
In the Ef text field, type E1_SCR.
Finally, edit the label of the Reaction feature. This is optional.
11
In the Label text field, type (1) Standard SCR: 4 NH3 + 4 NO + O2 => 4 N2 + 6 H2O.
In the same fashion, now define the reactions for the fast SCR reaction, the NO2 SCR reaction, the oxidation of NO, and the two undesired NH3 consuming reactions.
(2) Fast SCR: 2 NH3 + NO + NO2 => 2 N2 + 3 H2O
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 2 NH3 + NO + NO2 => 2 N2 + 3 H2O.
4
In the Label text field, type (2) Fast SCR: 2 NH3 + NO + NO2 => 2 N2 + 3 H2O.
5
Locate the Reaction Rate section. From the list, choose User defined.
6
In the rj text field, type re.kf_2*re.c_NO2*re.c_NO*re.c_NH3/(1+K_NH3*re.c_NH3).
7
Locate the Rate Constants section. Select the Use Arrhenius expressions checkbox.
8
In the Af text field, type A2_SCR.
9
In the Ef text field, type E2_SCR.
10
Locate the Reaction Orders section. Find the Volumetric overall reaction order subsection. In the Forward text field, type 3.
(3) NO2 SCR: 8 NH3 + 6 NO2 => 7 N2 + 12 H2O
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 8 NH3 + 6 NO2 => 7 N2 + 12 H2O.
4
In the Label text field, type (3) NO2 SCR: 8 NH3 + 6 NO2 => 7 N2 + 12 H2O.
5
Locate the Reaction Rate section. From the list, choose User defined.
6
In the rj text field, type re.kf_3*re.c_NO2*re.c_NH3/(1+K_NH3*re.c_NH3).
7
Locate the Rate Constants section. Select the Use Arrhenius expressions checkbox.
8
In the Af text field, type A3_SCR.
9
In the Ef text field, type E3_SCR.
10
Locate the Reaction Orders section. Find the Volumetric overall reaction order subsection. In the Forward text field, type 2.
(4) Equilibrium: 2 NO + O2 <=> 2 NO2
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 2 NO + O2 <=> 2 NO2.
4
Click Apply.
5
Locate the Rate Constants section. Select the Specify equilibrium constant checkbox.
6
Select the Use Arrhenius expressions checkbox.
7
In the Af text field, type A4.
8
In the Ef text field, type E4.
We want to derive the equilibrium constant from thermodynamics, which means that we first need to connect (couple) the species in Reaction Engineering to those in the Thermodynamic System.
By adding these reactions, the required Species features have been added. Couple all species in Reaction Engineering to corresponding species in the created Thermodynamic System.
9
In the Model Builder window, click Reaction Engineering.
10
In the Settings window for Reaction Engineering, locate the Mixture Properties section.
11
Select the Thermodynamics checkbox.
12
Locate the Species Matching section. In the table, enter the following settings:
Species
From Thermodynamics
H2O
H2O
N2
N2
NH3
H3N
NO
NO
NO2
NO2
O2
O2
Now, Reaction Engineering is coupled to the Thermodynamic System, and the equilibrium constant for the fourth reaction is derived from thermodynamics. Continue to add the final two reactions.
13
In the Model Builder window, under Component 1 > Reaction Engineering click 4: 2 NO + O2 <=> 2 NO2.
14
In the Settings window for Reaction, type (4) Equilibrium: NO + O2 <=> 2 NO2 in the Label text field.
(5) Undesired Oxidation: 4 NH3 + 3 O2 => 2 N2 + 6 H2O
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 4 NH3 + 3 O2 => 2 N2 + 6 H2O.
4
In the Label text field, type (5) Undesired Oxidation: 4 NH3 + 3 O2 => 2 N2 + 6 H2O.
5
Locate the Reaction Rate section. From the list, choose User defined.
6
In the rj text field, type re.kf_5*(re.c_NH3*re.c_O2)/(1+K_NH3*re.c_NH3).
7
Locate the Rate Constants section. Select the Use Arrhenius expressions checkbox.
8
In the Af text field, type A5_SCR.
9
In the Ef text field, type E5_SCR.
10
Locate the Reaction Orders section. Find the Volumetric overall reaction order subsection. In the Forward text field, type 2.
(6) Undesired NO Formation: 4 NH3 + 5 O2 => 4 NO + 6 H2O
1
In the Reaction Engineering toolbar, click  Reaction.
2
In the Settings window for Reaction, locate the Reaction Formula section.
3
In the Formula text field, type 4 NH3 + 5 O2 => 4 NO + 6 H2O.
4
In the Label text field, type (6) Undesired NO Formation: 4 NH3 + 5 O2 => 4 NO + 6 H2O.
5
Locate the Reaction Rate section. From the list, choose User defined.
6
In the rj text field, type re.kf_6*re.c_O2*re.c_NH3/G.
7
Locate the Rate Constants section. Select the Use Arrhenius expressions checkbox.
8
In the Af text field, type A6_SCR.
9
In the Ef text field, type E6_SCR.
10
Locate the Reaction Orders section. Find the Volumetric overall reaction order subsection. In the Forward text field, type 2.
Now rename the interface to something descriptive.
11
In the Model Builder window, click Reaction Engineering.
12
In the Settings window for Reaction Engineering, type Selective Catalytic Reduction Catalyst (SCR) in the Label text field.
After setting up the reaction kinetics, define the suitable reactor model where the reactions take place. Using the Reaction Engineering node you can choose one of the predefined reactor types. Since you are planning to set up a single channel model, having chosen the Stationary Plug Flow study type previously, choose the Plug flow reactor.
13
Locate the Reactor section. From the Reactor type list, choose Plug flow.
Continue by defining the initial values for the reactor. Use the parameters previously loaded from files.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the General Parameters section.
3
In the T0,in text field, type T_gas_in.
4
Locate the Volumetric Species Initial Values section. In the table, enter the following settings:
Species
Molar flow rate (mol/s)
H2O
FH2O_in
N2
FN2_in
NH3
FNH3_in
NO
FNO_in
NO2
FNO2_in
O2
FO2_in
Now that the reactions and kinetics settings are set, use Equation View to check what variable names were generated. These variable names should be those used in the imported variable definitions under the Definitions node.
Equation View
1
In the Model Builder window, click Show More Options .
2
Under Physics, check Equation View checkbox. Click OK.
3
In the Model Builder window, expand the (1) Standard SCR: 4 NH3 + 4 NO + O2 => 4 N2 + 6 H2O node . Click Equation View. Scroll through the Variables list to see the generated variable names, expressions, units, and descriptions.
Add a second Reaction Engineering physics interface to define the ammonia slip catalyst.