Analysis of NOx Reaction Kinetics

This example looks at the reduction of NO by ammonia. The reaction is critical to purify vehicle exhaust gases from NO. In these cases, the reaction usually takes place within the channels of a monolithic reactor situated within the exhaust system.

Central for the monolithic reactor is that NH3 is present in amounts that do not limit the NO reduction reaction. At the same time, excess NH3 at the outlet of the reactor leads to undesirable waste. The situation is complicated by the fact that ammonia can be depleted by oxidation, a reaction that is parallel to the NO reduction, and that the rates of the two competing reactions are affected by temperature as well as composition.

This tutorial aims at getting a primary understanding of the monolithic reactor. It concentrates on the investigation of the selectivity of the reactions by solving the model with the Plug Flow ideal reactor type in the Reaction Engineering interface.

Model Definition

Chemical Reactions

NO reduction by ammonia can be summarized by the following reaction:

(1)

However, ammonia can at the same time undergo oxidation:

(2)

The heterogeneous catalytic conversion of NO to N2 is described by an Eley-Rideal mechanism. A key reaction step involves the reaction of gas-phase NO with surface-adsorbed NH3. The following rate equation (SI unit: mol/(m3·s)) has been suggested in Ref. 1 for Equation 1:

where

and

For Equation 2, the reaction rate (SI unit: mol/(m3·s)) is given by

(3)

where

The competing chemical reactions raise the issue of optimal dosing of NH3 to handle the reduction process. Stoichiometry suggests a 1:1 ratio of NH3 to NO as a lower limit. It is likely that a stoichiometric excess of NH3 is necessary but, at the same time, we want to avoid unnecessarily high levels of NH3 in the gas stream leaving the catalytic converter.

SINGLE CHANNEL MODEL

To find the minimal level of NH3 required to reduce the NO present in the exhaust gas requires a reactor model accounting for changing reactant compositions and system temperature. From a mass transfer point of view, channels of the reactor monolith can be considered to be uncoupled to one another. Therefore, it is reasonable to perform simulations where a single reactive channel, modeled by nonisothermal plug flow equations, represents the monolith reactor. These equations are available within the Plug-flow reactor type in the Reaction Engineering interface.

Model Equations

Assuming steady state, the mass balance equation for a plug-flow reactor is:

(4)

where Fi is the species molar flow rate (SI unit: mol/s), V represents the reactor volume (SI unit: m3), and Ri is the species net reaction rate (SI unit: mol/(m3·s)). The molar flow rate is related to the species concentrations, ci (SI unit: mol/m3), through the volumetric flow rate, v (SI unit: m3/s):

(5)

where the volumetric flow rate is given by the average flow velocity, u (SI unit: m/s), multiplied by the reactor cross-section A (SI unit: m2):

(6)

The energy balance for the ideal reacting gas is:

(7)

where Cp,i is the species molar heat capacity (SI unit: J/(mol·K)), and Qext is the heat added to the system per unit volume (SI unit: J/(m3·s)). Q denotes the heat due to chemical reaction (SI unit: J/(m3·s))

where Hj is the heat of reaction (SI unit: J/mol) for reaction j, and rj the reaction rate (SI unit: mol/(m3·s)).

The model is first solved with Equation 4, Equation 5, and Equation 6 for several different ratios of reactant concentrations (NH3:NO) and with a temperature ramp along the reactor. The molar flow rates of NH3 and NO are kept constant throughout the reactor to investigate the temperature impact alone. Thereafter, Equation 7 is included; that is, nonisothermal conditions due to heat of reaction are studied.

Results and Discussion

REACTION KINETICs ANALYSIS

Analyzing the kinetics can help narrow down a proper NH3:NO ratio. A first study looks at the reaction rates of the reduction and oxidation reactions, for fixed molar flow rates of NH3 and NO, as function of temperature and relative amounts of reactants. Figure 1 shows the reaction rates for the reduction reaction (reaction 1 above). The curves represent a set of NH3:NO ratios (X0) ranging from 1 to 2. The concentration of NO in the exhaust gas entering the catalytic converter is known to be 0.0411 mol/m3.

Figure 1: Reaction rates of the NO reduction reaction (r1) as a function of temperature. The NH3:NO ratio ranges from 1 to 2 and the molar flow rates of NH3 and NO are kept constant throughout the reactor.

The rate of NO reduction goes through a maximum and falls off at higher temperatures. The maximum shifts toward higher temperatures as the ratio NH3:NO increases. This behavior is explained by the desorption rate of NH3 from the catalyst surface becoming faster than the reaction of adsorbed NH3 with gas-phase NO.

According to Equation 3, the oxidation rate increases with increased temperature and NH3 concentration. This is seen in Figure 2, plotting the selectivity parameter S as a function of reactant ratio and temperature. S is defined as the ratio of reaction rates:

An S-value greater than one means that NO reduction is favored.

Figure 2: Selectivity parameter (r1/r2) as a function of temperature. The NH3:NO ratio ranges from 1 to 2.

The kinetic analysis suggests that preferred working conditions involve moderate temperatures and relatively low ratios of NH3:NO.

SINGLE CHANNEL Model

To find the minimal level of NH3 required to reduce the NO present in the exhaust gas requires a reactor model accounting for changing reactant concentrations and system temperature. For this purpose, a nonisothermal plug-flow reactor serves to simulate the behavior of a reactive channel.

For an exhaust gas containing 41.1 mmol/m3 of NO, with a temperature of 523 K, passing through the monolith at 0.3 m/s, the plug-flow model suggests a NH3:NO ratio higher than 1.2 to guarantee that NH3 is available as a reductive agent throughout the entire length of the reactive channel, see Figure 3. The reactor is 0.36 m long and has a volume of 45e-5 m3.

Figure 3: Molar flow rate of NH3 as function of channel volume.

A plot of the selectivity parameter (Figure 4) confirms that the NO reduction chemistry is favored in the monolith reactor at NH3:NO ratios ranging from 1.3 to 1.5.

Figure 4: Selectivity parameter (r1/r2) as a function of channel volume. The NH3:NO ratio ranges from 1.3 to 1.5.

Finally, Figure 5 shows the temperature, as well as the conversion of NO, throughout the single channel reactor. The maximum values for these properties are included. The highest temperature in the reactor is 532K for X0 = 1.3, and 533 K for X0 = 1.5. The conversion of NO is practically 1 (99%) for both X0 values.

Figure 5: Temperature and conversion as a function of channel volume.

It is clear that temperature plays a central role in affecting the optimal dosing of NH3. Since the temperature distribution is likely to vary from channel to channel in a monolith reactor, a full 3D reactor model is called for. Based on the single channel model simulations, a NH3:NO ratio between 1.3 and 1.4 appears appropriate for the 3D model.

For details on the full 3D model of the reactor monolith, see the example monolith_3d.mph in the Chemical Reaction Engineering Module’s Application Libraries.

Chemical_Reaction_Engineering_Module/Tutorials/monolith_kinetics

Reference

1. G. Schaub, D. Unruh, J. Wang, and T. Turek, “Kinetic analysis of selective catalytic NOx reduction (SCR) in a catalytic filter,” Chemical Engineering and Processing, vol. 42, no. 3, pp. 365–371, 2003.

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

Start by reading in a set of global parameters defining the process conditions for the monolith reactor, including the dimensions of the reactive channels, the flow rate of the reacting gas, and the temperature conditions.

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file monolith_kinetics_parameters.txt.

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
S	re.r_1/re.r_2		Selectivity
a	a0exp(-E0/(R_constre.T))	m³/mol	Concentration correction

Reaction Engineering (re)

Next, create a Thermodynamic System that includes all thermodynamic properties (such as enthalpy, entropy, and so on) needed in the simulation of the reacting system. The thermodynamic properties are automatically coupled to the Reaction Engineering interface.

In the toolbar, click

and choose .

Select System

Go to the window.

Click in the window toolbar.

Select Species

Go to the window.

In the list, select .

Click

In the list, select .

Click

In the list, select .

Click

In the list, select .

Click

In the list, select .

Click

Click in the window toolbar.

Select Thermodynamic Model

Go to the window.

Click in the window toolbar.

Reaction Engineering (re)

Now define the chemical reactions. First, type in the reaction formula for NO reduction. The will automatically interpret the reaction formula and suggest reaction rates based on the mass action law.

Reaction 1

In the window, under right-click and choose .

In the window for , locate the section.

In the text field, type 4NO+4NH3+O2=>4N2+6H2O.

Notice that, there being several ways to balance this formula, the button is not applicable in this case.

In this example, replace the automatically generated expression with the rate expression known from the literature. Use the in the denominator of the rate expression to avoid negative concentrations.

Locate the section. From the list, choose .

In the rj text field, type re.kf_1*re.c_NO*a*re.c_NH3/(1+a*max(re.c_NH3,0[M])).

In the next step, update the reaction order.

Find the subsection. In the text field, type 1.

Locate the section. Select the check box.

In the Af text field, type A1.

In the Ef text field, type E1.

In the same fashion, now define the reaction for NH3 oxidation.

Reaction 2

In the toolbar, click

In the window for , locate the section.

In the text field, type NH3+O2=>N2+H2O.

Click in the upper-right corner of the section.

This reaction can be balanced with since there is only one solution to the balancing problem.

Locate the section. From the list, choose .

In the rj text field, type re.kf_2*re.c_NH3.

Continue by updating the reaction order so that it matches with the rate expression.

Find the subsection. In the text field, type 1.

Locate the section. Select the check box.

In the Af text field, type A2.

In the Ef text field, type E2.

Now choose reactor type.

In the window, click .

In the window for , locate the section.

From the list, choose .

Couple all species in to corresponding species in the created .

Locate the section. Select the check box.

Locate the section. In the table, enter the following settings:


Species	From Thermodynamics
H2O	H2O
N2	N2
NH3	H3N
NO	NO
O2	O2

Isolate the effect of temperature and reactant ratios by keeping the volumetric flow rate constant. Therefore, select to compute pressure from the ideal gas law.

Locate the section. From the list, choose .

The following steps allow you to study the reaction rate for fixed reactant concentrations, solely as a function of temperature. First, use the independent variable V (reactor volume, written re.Vr) to set up a temperature ramp between 500 K and 750 K. Then, after defining initial values, lock the concentrations of reactant NO and NH3 and add a feature.

Locate the section. From the list, choose .

In the T text field, type 500[K]+250[K/m^3]*re.Vr.

Locate the section. Find the subsection. In the v text field, type vrate.

Initial Values 1

Enter the initial values.

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Species	Molar flow rate (mol/s)
H2O	F_H2O_in
N2	F_N2_in
NH3	F_NH3_in
NO	F_NO_in
O2	F_O2_in

Lock the reactant concentrations in the following way.

Species: NO

In the window, click .

In the window for , click to expand the section.

Select the check box.

Species: NH3

In the window, click .

In the window for , locate the section.

Select the check box.

Now add a feature to solve the model for a set of NH3:NO ratios.

Study 1

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

From the list in the column, choose .

Click

In the dialog box, type 1 in the text field.

In the text field, type 0.2.

In the text field, type 2.

Click .

Solution 1 (sol1)

In the toolbar, click

It is good practice to tighten the default solver tolerances and make sure that the solution plots do not change between consecutive test runs. Both the relative and absolute tolerance should be tightened. In this case the relative tolerance needs to be reduced to 10−7.

Step 1: Stationary Plug Flow

In the window, click .

In the window for , locate the section.

From the list, choose .

In the text field, type 1e-7.

In the toolbar, click

All the solutions generated by pressing in the interface are saved and can be copied and modified. This enable easy postprocessing of the results, since several different case studies, within the same study, can be saved and compared.

Parametric Solutions 1 (sol2)

In the window, right-click and choose .

Kinetics