This tutorial model presents a detailed description of how to set up a model of a catalytic reactor for exhaust gas treatment. The example shows an application of the modeling strategy, described in the section Chemical Reaction Engineering Simulations and demonstrates through a series of simulations how an understanding of the catalytic reactor and its system can be improved. To do this, it uses a number of the interfaces and features found in the Chemical Reaction Engineering Module. Transport and thermodynamic properties are provided by the Thermodynamics feature under Global Definitions.

The system to be modeled is the selective reduction of harmful nitrogen oxides NOx (NO and NO2) into nitrogen (N2) in an exhaust gas after-treatment system of a heavy-duty diesel truck. The nitrogen oxides are reduced by ammonia that is injected upstream of the after-treatment system consisting of a catalytic, monolithic reactor.

The reactor has two catalytic beds with two different catalysts. The upstream bed is a selective catalytic reduction (SCR) bed with the purpose of selectively convert NOx to nitrogen. The second bed is an ammonia-slip-catalyst (ASC). This bed should convert the remaining ammonia (NH3) to nitrogen.

In both of the beds there are unwanted side-reactions. In the first bed, NH3 may react with oxygen instead of reducing NOx. This means that the amount of injected ammonia must exceed the amount of NOx, while not being so excessive as to release NH3 to the atmosphere. In the second bed, ammonia should get oxidized into nitrogen, but may instead react to form NOx. This is another reason to try and keep the injected amount of ammonia to a minimum.

The goals of the simulations are to find the optimal dosing of NH3, and to investigate the influence of engine load on the system. The engine load affects the gas temperature, amount of NOx, and mass flow rate of the exhaust gas.

You may want to revisit the flowchart in Figure 1 to follow the modeling strategy for this model as described next.

Having a better understanding of the reaction kinetics aids in the development of a more complex model. So, in the next step, the reaction kinetics implemented in the Single Channel Model are exported to the space-dependent Monolith Reactor Model. Here, the effect of temperature variations in the bed on the reaction rate and fluid flow can be investigated. This more advanced model reveals the necessary NH3 dosing levels based on the working conditions of the catalytic reactor in the exhaust stream.

and the NO2 SCR reaction

Except for the homogeneous gas phase equilibrium reaction (4), all reactions are heterogeneous catalytic reactions with reaction rates that depend on surface coverage. The surface coverage of ammonia can be related to the fluid phase concentration by assuming that ammonia desorption and adsorption are in equilibrium. With a Langmuir-Hinshelwood mechanism, based on this assumption, global rate expressions can be derived. The following five rate expressions have been suggested in Ref. 1:

Here, KNH3 is the ammonia adsorption equilibrium constant, expressed with the pre-exponential factor KNH3,523, and the adsorption enthalpy ΔHads:

Correspondingly, the rate expression for the NO2-SCR reaction is:

The reversed reaction rate is derived from the forward reaction rate and the equilibrium constant Keq that is derived from thermodynamics laws:

The reaction rate for the undesired oxidation of ammonia into nitrogen monoxide also follows a Langmuir–Hinshelwood mechanism, and has been suggested to take this form Ref. 2:

Here, G is a variable that accounts for the inhibition effects caused by adsorption of other species on the surface:

where Ki (i=1-4) follows an Arrhenius-type expression

In the ammonia slip catalyst bed, there is one desired, two undesired reactions, and the homogeneous equilibrium reaction (4) that take place. The desired reaction is the oxidation of ammonia to form nitrogen:

Reaction 7 and 8 are the same chemical equations as Reaction 5 and 6, but since the catalyst is different, the kinetic parameters differ. The rate expressions are assumed the same though. The rate expression for Reaction 9 is:

The competing chemical reactions raise the issue of optimal dosing of NH3 to handle the reduction process in the first bed. Stoichiometry suggests a 1:1 ratio of NH3 to NO as a lower limit for the standard SCR reaction. Due to the undesired oxidation of ammonia it is likely that a stoichiometric excess of NH3 is necessary. The excess ammonia will be converted in the second ammonia-slip catalyst bed. The NOx forming side reactions in the second bed motivates as low ammonia injection as possible. This is also important for economic and pressure-drop reasons.

To find the minimal level of NH3 required to reduce the NOx present in the exhaust gas requires a reactor model accounting for changing reactant concentrations and system temperature.

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)).

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 the heat of reaction (SI unit: J/mol), and rj the reaction rate (SI unit: mol/(m3·s)). The Qext is set to zero, based on the assumption that the modeled channel is close to the center of the monolith, and that the reactor is well insulated.

In this model, several different aspects of the system is studied. First, the temperature operating window for the selective catalytic reduction bed, is investigated. This is achieved by solving Equation 11–Equation 14 for a range of inlet temperatures, keeping the ammonia-to-NOx ratio (ANR) equal to 1.3 at the inlet. A value of 1.3 is chosen since more than stoichiometric amounts of ammonia is needed.

The first study aimed at finding the operating window for the selective catalytic reduction catalyst. This was achieved by varying the inlet gas temperature, while keeping the NH3:NOx ratio equal to 1.3. The resulting NOx conversion along the reactor axis as a function of inlet temperature is seen in Figure 3.

Figure 4 shows the temperature increase in the first bed along the reactor axis. The exothermic reactions create a temperature increase. For the four highest temperatures the outlet temperature has decreased. This is a result of the different selectivity in the system at different temperatures,

The optimal temperature operating window, defined as the temperatures giving maximum conversion of NOx, is 620–720K for the SCR bed at an NH3:NOx ratio equal to 1.3. The conversion of NOx is close to complete at this temperature. This is seen in Figure 5.

Moving on to investigate the influence of both inlet temperature and ammonia-to-NOx ratio (ANR). Figure 6 shows that for an increased ANR, the operating window widens and shifts toward lower temperatures. In addition, the conversion of NOx increases for the investigated range.

The conversion of ammonia as a function of ANR and inlet gas temperature is seen in Figure 7. Complete conversion of ammonia is reached for all ANR at inlet gas temperatures above 750 K.

The results from the SCR-bed model revealed that the optimal conversion window for NOx is at a lower temperature than that of ammonia. We also saw that the ammonia-to-NOx ratio needs to be kept above 1.2 to reach complete conversion of NOx. Higher ammonia dosing gives more ammonia-slip. With an ammonia slip catalyst downstream of the first bed, the excess ammonia can be converted. This allows for higher ANR. The influence of ANR in the dual bed, single channel model is therefor investigated. Figure 8 shows the molar fraction of ammonia and NOx along a single monolith channel in each bed.

The molar fractions decrease rapidly early in the SCR catalyst bed, and for the highest ammonia concentration the conversion of NOx is complete halfway through the first bed. The unconverted ammonia is almost completely converted in the ASC bed, even for the highest dosing, but due to undesired side reactions in the ASC bed, the NOx concentration increases. Even though the conversion is close to complete, the molar fractions might still be too high to pass the emission standards. The conversion in the dual bed, single channel system is seen in Figure 9.

High engine load gives more NOx, higher gas flow rate, and higher temperature. The previous studies were all performed for an intermediate engine load. A low engine load will result in low flow rate, low gas temperature, and low NOx from the engine. Figure 10 shows the molar fraction for these three load cases, and an ANR of 1.3.

This figure reveals that the highest emissions of both NOx and ammonia result from the lowest engine load. This is a result of the low temperature, which decreases the reaction rate. Even though the incoming gas contains the lowest amount of NOx to start with, and the flow rate of gas is the lowest, the reaction rate is simply too low. This is also seen in Figure 3.

Figure 9 shows the conversion in the dual bed single channel system for each of the three engine load cases.

The single channel model with two beds have been modeled as adiabatic, assuming that the modeled channel is close to the monolith center, and that the reactor is well insulated. Figure 10 shows the temperature increase along the reactor for each of the three engine load cases.

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 space-dependent reactor model accounting for this variation is called for. Based on the single channel model simulations, a NH3:NOx ratio of 1.3 appears appropriate for the extended model.

It is clear from the Single Channel Model that temperature plays a central role in affecting the optimal dosing of NH3. As the temperature distribution is likely to vary from channel to channel in a catalytic converter, a full monolithic reactor model is required.

The chemical equations and rate expressions are the same as those in the Chemistry section for the Single Channel Model.

In Equation 15, Di denotes the diffusion coefficient (SI unit: m2/s), ci is the species concentration (SI unit: mol/m3), and u equals the velocity vector (SI unit: m/s). The term  Ri (SI unit: mol/(m3·s)) corresponds to the species’ rate expression.

Mass transport is only allowed in the direction of the channels, corresponding to direction of the z-axis in the 2D-axisymmetric geometry used in this example. For the diffusive transport, this is accomplished by setting the x and y-components of the diffusivity matrix to zero. The pressure-driven flow in the monolith is also defined in the direction of the z-axis, hereby restricting the convective mass transport to the channel direction as well. Each monolith channel thus behaves as a 1D plug flow model with included diffusion. These separate channel models are connected through the heat transfer equations for the reactor monolith.

The monolith is treated as a porous matrix with the effective permeability κ (SI unit: m2). Similarly to the diffusivity, the x- and y-components of the permeability matrix are set to zero. The density, ρ (SI unit: kg/m3), and viscosity, μ (SI unit: Pa·s), of the gas are assumed to be well represented by the temperature-dependent properties of nitrogen, as only relatively small concentrations of other gases are present.

where ρf (SI unit: kg/m3) is the fluid density, Cpf (SI unit: J/(kg·K)) is the fluid heat capacity, and keff (SI unit: W/(m·K)) is the equivalent thermal conductivity. Furthermore, u (SI unit: m/s) is the fluid velocity field derived by the fluid flow interface. Q (SI unit: W/m3) is the heat source due to exothermic chemical reactions:

Above, Hj (SI unit: J/(mol·K)) is the heat of reaction for reaction j, and rj is the reaction rate for said reaction.

The effective conductivity of the solid-fluid system, keff, is related to the conductivity of the solid, ks, and to the conductivity of the fluid, kf, by:

In Equation 21, Θs denotes the solid material’s volume fraction, which is related to the volume fraction of the fluid Θf by:

Equation 19 is the equation set up by the Heat Transfer interface for a fluid domain. For the solid monolith, only heat transfer by conduction applies:

where ks (SI unit: W/(m·K)) is the thermal conductivity for the solid walls. For the extruded monolith material, the thermal conductivity is anisotropic.

The heat transfer in the porous support mat is also described by Equation 19 and 23. Contrary to the monoliths, the support mat has isotropic thermal conductivity. The same is true for the solid metal walls in the reactor.

is used at the inlet of the first bed. ΔH (SI unit: J/(kg)) is the sensible enthalpy.

where h (SI unit: W/(m2·K)) denotes the heat transfer coefficient, and Tamb (K) equals the ambient temperature.

Accurate thermodynamic data is required as input to energy balance equations, both in the Single Channel Model (plug flow model, (Equation 14)) and the Monolith Reactor Model (Equation 19). In addition to thermodynamic properties, the model equations also require transport properties to describe the space-dependent reactor model.

The Thermodynamics feature provides all necessary properties for the simulation. Different models are available for thermal and transport property calculations (see Thermodynamic Models and Theory). In this system, thermodynamic properties are calculated based on the ideal gas law while transport properties such as diffusivity, viscosity, and thermal conductivity are calculated from Fuller–Schettler–Giddings, Brokaw, and Kinetic Theory, respectively.

The system conditions used in this monolith reactor model is the same as those used for the single channel model. Three Solid are investigated, with a fixed ammonia-to-NOx ratio of 1.3.

Figure 13 shows the molar fraction of NH3, NO, and NO2 in the two catalyst beds for the low engine load case. The effect of the radial temperature gradient is clearly visible as the conversion decreases close to the edge. The temperature for the low engine load case is below the optimal temperature for the SCR reactor, see Figure 5. The low temperature results in low conversion of both NOx and ammonia.

Figure 14 illustrates the result for the intermediate engine load case. At this increased temperature, the conversion increases in the reactor. Higher mass flow rate and higher heat source due to increased conversion, gives smaller radial temperature gradient.

Figure 15 shows the results for the high engine load case..

Figure 16 illustrates the gas velocity, pressure, and temperature in the beds for the highest engine load.

The effect of temperature on conversion is seen in Figure 17. In this figure, the conversion is plotted both along the central symmetry axis, and along the edge of the monoliths. For a high engine load, the conversion does not vary significantly with the position in the reactor, but for lower engine loads, the conversion differs significantly.

The temperature differences along the reactor axis, at the center of the reactor, and at the edge of the beds, are seen in Figure 18. Close to the inlet of the first bed, the temperature increases both at the center and along the SCR edge. This is due to the exothermic reactions. After the first rapid temperature increase, the increase in temperature is slower, and at the edge of the first bed, the temperature instead decreases due to heat flux to the surroundings. For the high and intermediate engine load cases, the slip of ammonia from the first bed creates a significant temperature increase when this ammonia is oxidized in the second bed. For the low engine case, the activity is too low to create a temperature increase. At the bed edge, the heat flux to the surrounding decreases the temperature in the first bed, decreasing the ammonia conversion rate, which creates an even larger temperature increased during ammonia oxidation in the second bed.

Finally, the average values of ammonia and NOx molar fractions were derived both along the outlet of the first bed, as well as along the outlet of the second bed. The values are found in Table 1.

From the results in Table 1 it is clear that for an ammonia-to-NOx ratio of 1.3, the exhaust gases from the truck will contain the least ammonia at high load, and the least NOx at intermediate load.

This study revealed that the ammonia-to-NOx ratio should be varied with engine load. A reactant ratio NH3:NO of approximately 1.3 is found to be close to optimal for an intermediate engine load, but at higher loads this ratio could be decreased. At low engine load, the temperature is too low to give acceptable NOx reduction.

As an option to first build the Single Channel Model, you can open the completed model file for the Single Channel Model and proceed directly with the setup of the Monolith Reactor Model. See Modeling Instructions: Monolith Reactor Model for further details.

Both the Single Channel Model and the Monolith Reactor Model are available in the Application Libraries, see monolith_kinetics.mph and monolith_reactor.mph, respectively.