Global Kinetic Model for Lean NOx Traps - Industrial & Engineering

Ind. Eng. Chem. Res. 2005, 44, 3021-3032

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Global Kinetic Model for Lean NOx Traps Louise Olsson,*,† Richard J. Blint,‡ and Erik Fridell† Competence Centre for Catalysis, Chalmers University of Technology, SE-412 96 Go¨ teborg, Sweden, and Chemical and Environmental Sciences Laboratory, General Motors Research and Development Center, 30500 Mound Road, Warren, Michigan 48090-9055

Modeling and flow reactor experiments are used to investigate the global kinetics for lean NOx traps (LNTs). Experiments were conducted with a Pt/Rh/BaO/Al2O3 model catalyst, and the inlet feed gas was switched between lean and rich periods. It has previously been observed that NO oxidation to NO2 is important for NOx storage, and therefore a global mechanism for NO oxidation on Pt/Al2O3 is developed. This is then used in the NOx trap model, after the parameters had been adjusted to match the NO and NO2 concentrations from experiments on the Pt/Rh/BaO/ Al2O3 catalyst. The mass transport of NO and NO2 inside the particles is described by a shrinkingcore model. Further, it is found that two global reaction steps are needed for storage in order to explain the experimental observations: one step for the formation of barium nitrates and the other step for the formation of loosely bound barium nitrites. Reaction steps were added to the model for regeneration of the trap with C3H6. The model is tuned based on six experiments at three different temperatures and two different NO concentration levels. The model is able to adequately describe NOx storage during the lean period, the NO reduction during the regeneration period, the NOx breakthrough peaks observed initially in the rich period, and the relation between the measured NO and NO2 concentrations. Experimentally, we have observed that only a fraction of the barium is used for storage in our model catalysts. In the simulations, only 7% of the barium is used for NOx storage. In addition, TEM experiments have shown that our barium particles are large, and therefore a model is evaluated using an inert core in the center of the particle, which resulted in an equally good fit. However, when using catalysts with small particles, which probably is the case in commercial catalysts, a model without an inert core in barium particles seems to be the most realistic one. The model with an inert core is validated with three additional experiments not included in the fitting procedure. In these experiments the oxygen concentration was lowered to 4% during the lean period, compared to 8% O2 in the experiments used when adjusting the kinetic parameters. The model can simulate the experimental features of these experiments well. 1. Introduction Gasoline lean burn engines and diesel engines have a lower fuel consumption compared with stoichiometric gasoline engines. There is, however, a major problem connected with using excess oxygen during the combustion, i.e., that the conventional three-way catalyst is no longer capable of reducing the nitrogen oxides (NOx) effectively. One possible technology for removing NOx is lean NOx traps (LNTs),1-3 which are used in combination with mixed lean operation, where the air-to-fuel ratio is altered between lean (oxygen excess) and rich (fuel excess) mixtures. During the relatively long lean periods, NOx is adsorbed on a storage component, e.g., barium. During short rich periods, the storage material is regenerated and the released NOx reacts with the hydrocarbons and CO to produce CO2, H2O, and N2 over the noble metal sites. Different types of simulations/modeling of NOx storage catalysts have been reported in the literature. A detailed kinetic model was developed by Olsson et al.4,5 that could describe flow reactor experiments for model NOx storage catalysts. First-principles calculations based * To whom correspondence should be addressed. Fax: +4631-772 3035. E-mail: [email protected]. † Chalmers University of Technology. ‡ General Motors Research and Development Center.

on density functional theory have been performed by Broqvist et al.,6 giving the energetics for Ba(NO3)2 formation. Thermodynamic calculations for different storage components, including barium, were performed by Kobayashi et al.7 Global mechanisms and different control-oriented models are also presented in the literature.8-15 Hepburn et al.8,9 developed a global kinetic model, which included a shrinking-core description of the mass transport in the barium particles. This model was validated with both laboratory experiments and vehicle test data. In this work, we construct a global kinetic model for NOx storage and regeneration, based on a shrinkingcore model. The model parameters are determined from experiments using a Pt/Rh/BaO/Al2O3 model monolith catalyst with the feed gas cycled between lean and rich mixtures. 2. Experimental Section Two model catalysts are used in this study: a Pt/Rh/ BaO/Al2O3 catalyst (2 wt % Pt, 1 wt % Rh, and 20 wt % BaO) and a Pt/Al2O3 catalyst (2 wt % Pt). The catalysts are prepared using wet-impregnation techniques, which are described elsewhere.3 The catalysts are monoliths with washcoat weights of about 200 mg. The samples were 15 mm in length and 12 mm in diameter (69 square channels). The reactor system used was de-

10.1021/ie0494059 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/15/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005

scribed in more detail previously.3 Briefly, the catalyst is placed in a quartz tube, with one thermocouple inside the catalyst and one about 10 mm in front of the sample (for detecting the gas temperature). The quartz tube is placed in an oven for heating and temperature control. Gas is supplied to the reactor using several mass flow controllers. The NO and NO2 concentrations are analyzed using a chemiluminescence detector (Tecan CLD 700 EL ht). The NO oxidation activity is investigated using the Pt/Al2O3 catalyst. The catalyst is then exposed to 600 ppm NO and 8% O2 during a temperature ramp between 25 and 500 °C, at a heating rate of 5 °C/min with a total feed flow rate of 2600 mL/min, giving a space velocity of 92 000 h-1. For the NOx storage experiments, the Pt/Rh/BaO/ Al2O3 catalyst is used and the inlet gas was cycled between lean (240 s) and rich periods (60 s) with a total feed flow rate of 1500 mL/min, yielding a space velocity of 53 000 h-1. The concentrations in the respective periods are as follows. Lean period: ∼450 ppm NO, 900 ppm C3H6, 8% O2. Rich period: ∼450 ppm NO, 900 ppm C3H6. The experiment is also repeated with a higher NO concentration (∼900 ppm NO). The experiment is conducted at three different temperatures, 320, 380, and 440 °C (measured in the inlet gas). For validation of the model, three additional experiments are used, with 4% O2 in the lean period (lean period, ∼900 ppm NO, 900 ppm C3H6, 4% O2; rich period, ∼900 ppm NO, 900 ppm C3H6). These experiments are also conducted at 320, 380, and 440 °C (measured in the inlet gas). 3. Kinetic Model In this work, a tank-in-series model is used to describe the monolith, and the transient material balances and heat balance are solved numerically. The flow is relatively high; the monolith can be viewed as a plug-flow reactor, and it is sufficient to use 20 elements in the model. The temperatures measured in the gas phase before the catalyst and inside the catalyst reveal that there are heat losses in the experimental setup. The following equation is used to describe these losses:

Q ) -h(Tcatalyst - Tambient)

(1)

where h is the heat-transfer coefficient. Tambient is the temperature outside the catalyst, which is the same as the gas temperature before the catalyst because both the gas and catalyst are heated in the oven. It is difficult to know the exact location of the thermocouple inside the catalyst. In the NOx storage experiment with a temperature of 440 °C in the inlet feed gas, the temperature inside the sample is measured to be 476 °C, which is lower than what the temperature would be if the reactor was adiabatic, considering the heat release from C3H6 oxidation. However, at this high temperature, it is expected that the NO2 concentration after the catalyst is at the thermodynamic equilibrium level. Assuming NO-NO2 equilibrium for the 440 °C experiments, the simulation gives 476 °C in element number 7 out of 20. Therefore, we assume that the thermocouple was placed in this position, i.e., 5 mm from the front of the catalyst. The values for h were tuned until the calculated temperature in the catalyst matched the

measured temperature, and the resulting values for h for the experiments at 320, 380, and 440 °C can be found in the appendix. Global reaction steps are used for modeling of NOx storage and regeneration, and the different steps are described in the following three sections. The Arrhenius equation is used for the rate constants k:

k ) Ae-EA/RT

(2)

where A is the pre-exponential factor, EA the activation energy (J/mol), R the gas constant (8.314 J/mol‚K), and T the temperature (K). 3.1. Oxidation Reactions. 3.1.1. C3H6 Oxidation. C3H6 oxidation on the noble metal can be described by the following global mechanism:

C3H6 + 9/2O2 w 3CO2 + 3H2O

(3)

The rate expression used for this reaction is the one derived by Volz et al.,16 which has been used in a number of studies:17-20

rC3H6,ox ) kC3H6,oxCC3H6CO2/G

(4)

where

G ) T(1 + K1CCO + K2CC3H6)2(1 + K3CCO2CC3H62)(1 + K4CNO0.7) (5) 3.1.2. NO Oxidation. It has been shown in many previous studies1,7,21,22 that oxidation of NO to NO2 on the noble metal sites is an important reaction step in the NOx storage mechanism. It has also been suggested that NO oxidation is the rate-determining step for NOx storage at low temperatures.21 The following reversible global reaction was used for NO oxidation:

NO + 1/2O2 S NO2

(6)

with the corresponding global reaction rate

rNO,ox ) kNO,oxCNOCO21/2 -

kNO,ox C Keq,NO,ox NO2

(7)

Keq,NO,ox is the equilibrium constant that can be calculated from the change in Gibbs free energy ∆G based on the relationship

Kp ) e-∆G/RT

(8)

∆G ) ∆H - T∆S

(9)

where

The value for the enthalpy change for the reaction is -58 kJ/mol and that for the entropy change -76.1 J/mol‚K.23 3.2. NOx Storage. The formation of barium nitrates has been experimentally observed by Fourier transform infrared (FTIR) by several groups.24,25 Detailed kinetic modeling4 has shown that formation of Ba(NO3)2 can describe the stoichiometry between NO and NO2 observed in experiments where a BaO/Al2O3 catalyst was exposed to NO2. In addition, first-principles calculations6 showed that it was beneficial to have two NOx species on each BaO. In this modeling, NOx storage is

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r ) rf - rb

(11)

r)r1 r)r1 CO21/4θBaCO3,m ) k/f CNO θ (12) rf ) kfCNO 2 2 BaCO3,m

rb ) kbCCO21/2θBa(NO3)2,m ) k/bθBa(NO3)2,m

Figure 1. Schematic picture of Ba(NO3)2 formation in a BaCO3 particle, with the shrinking-core model (model 1).

mainly described by the following reaction between BaCO3 and NO2 to form barium nitrate:

r)r1 where CNO is the concentration of NO2 at the reaction 2 front (r ) r1) and θBaCO3,m and θBa(NO3)2,m are the mean coverages of barium carbonate and barium nitrate, respectively. O2 and CO2 are in excess and therefore assumed to be constant. The rate of diffusion, Rdiff, at any radial position r (within the shell) is constant and can be expressed as

Rdiff ) D(4πr2)

1

/2BaCO3 + NO2 + 1/4O2 S 1/2Ba(NO3)2 + 1/2CO2 (10)

Internal mass transport within the particles of the NOx storage material has been included in some NOx storage simulations. Kojima et al.10 explain their experimental results by mass transport in the washcoat and include a simple mathematical expression for describing this. Hepburn et al.8,9 assume that there are mass-transport limitations in the barium particles and use a shrinking-core model to account for this. Theis et al.26 also explain their experimental results with a shrinking-core model. The form of the kinetic rate expression when including mass transfer has the potential to describe the storage process, with an initial rapid storage followed by a slow breakthrough of NOx. It is difficult to distinguish whether there are masstransfer limitations in the washcoat or in the barium particles or a combination of the two. Both methods give similar mathematical expressions for the rate, when using a shrinking-core description. Judat and Kind27 investigated the morphology and internal structure of barium sulfate using transmission electron microscopy (TEM). They found that barium sulfate has a porous structure, which arises from aggregation of crystallites. We have chosen to implement a shrinking-core model for describing mass transport in the particles. Figure 1 gives a schematic description of the shrinking-core model, where nitrates start to form on the external surface and penetrate into the particle. rtot is the radius of the particle and l the thickness of the nitrate layer. In a pure shrinking-core model, the reaction rates are dependent only on the gas-phase concentrations8 and the coverage of free sites at the reaction front at radius r1 is always 1 (θBaCO3 ) 1); see Figure 1. Thus, all sites at a radius larger than r1 are occupied before adsorption can occur deeper into the particle. However, in the beginning of the storage phase, the surface sites are used and the coverage on the surface is likely very important. Thus, several models include a coverage dependence in the reaction rates.10-12 It is possible to use two reaction rates, one coverage-dependent rate for the surface reaction and another rate for penetration into the particles. This would give additional rate parameters, which would be difficult to determine, and there would also be a large correlation between the parameters. We have therefore chosen to use only one reaction rate, which is dependent on the mean coverage in the particle. The following rate expression has been used in the simulations:

(13)

dc dr

(14)

where D is the diffusivity. Integrating eq 14 between r1 and rtot, with the corresponding NO2 concentrations r)r1 r)rtot CNO and CNO , results in 2 2

Rdiff )

4πD r)rtot r)r1 (CNO2 - CNO )r1rtot 2 l

(15)

At the interface (r ) r1), the rate of diffusion is equal to the rate of reaction, which gives

4πD r)rtot r)r1 r)r1 )r1rtot ) 4πrtot2(k/f CNO θ (CNO2 - CNO 2 2 BaCO3,m l k/bθBa(NO3)2,m) (16) Equation 16 gives the following expression for the concentration of NO2 at the reaction front:

l r1 r)rtot + kb θ CNO 2 D rtot Ba(NO3)2,m r)r1 CNO2 ) l r1 1 + kf θ D rtot BaCO3,m

(17)

Inserting eqs 12, 13, and 17 into eq 11 gives

r)

kf r)rtot CNO CO21/4θBaCO3,m 2 l r1 1 + kf θ D rtot BaCO3,m kb CCO21/2θBa(NO3)2,m (18) l r1 1 + kf θ D rtot BaCO3,m

and from this equation, the bulk rate constant can be defined as

kbulk )

kf l r1 1 + kf θ D rtot BaCO3,m

(19)

When nitrates are formed, the thickness of the nitrate layer (l) increases, which causes the rate constant to decrease. However, at the same time, the mean coverage of BaCO3 will decrease, which has the opposite effect on kbulk. This results in a complex behavior of the rate constant, where k first decreases, reaches a minimum, and then increases. In the shrinking-core concept, the

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To calculate the depth of the diffusion, l, at a given point, an expression for the barium nitrate was derived for model 2 (with an inactive core):

θBa(NO3)2,m )

VBa(NO3)2 Vtotal

)

rtot3 - r13

(23)

rtot3 - r03

Figure 2. Schematic picture of Ba(NO3)2 formation in a BaCO3 particle, with the shrinking-core model and assuming an inactive core in the center of the particle (model 2).

where VBa(NO3)2 is the volume of Ba(NO3)2 and Vtotal the total volume of the particle. Rearranging eq 23 gives the following expressions for the thickness of the Ba(NO3)2 layer (l ) rtot - r1) and the ratio of r1/rtot:

coverage of BaCO3 at the reaction front is always 1 (see Figure 1), and setting θBaCO3,m ) 1 in eq 19 gives

l ) rtot - [rtot3 - θBa(NO3)2,m(rtot3 - r03)]1/3

kbulk,* )

kf l r1 1 + kf D rtot

(20)

This form of the rate expression has a more natural behavior when the nitrate concentration increases. However, as discussed above, it is important to have a coverage-dependent reaction rate, and therefore the rates in eqs 11-13 are used unchanged. The coveragedependent reaction rate gives a smooth decrease in storage for higher temperatures, which is seen experimentally. In summary, the following reaction rates have been used in the simulations: bulk,/ C C 1/4θBaCO3,m rNO2-Ba ) kNO 2-Ba,f NO2 O2 bulk,/ kNO C 1/2θBa(NO3)2,m (21) 2-Ba,b CO2

bulk,/ kNO 2-Ba,f

)

kNO2-Ba,f l r1 1 + kNO2-Ba,f D rtot bulk,/ ) kNO 2-Ba,b

and

kNO2-Ba,b l r1 1 + kNO2-Ba,f D rtot

[

(22)

For low nitrate coverages, r1 ≈ rtot, which gives the same form of the bulk rate constant as that used by Hepburn et al.8,9 When a comparison of the total amount of stored NOx, in experiments where saturation of the catalyst was reached, with the amount of barium in the catalyst, it was observed that only a fraction of the barium sites in the model catalysts are used for NOx storage. There are many possible explanations for why some of the barium is not available. Prinetto et al.28 measured a decrease in the Brunauer-Emmett-Teller surface area as well as the pore volume when comparing Pt/Al2O3 and Pt/ BaO/Al2O3 samples (Pt/Al2O3, ∼200 m2/g, 1.1 cm3/g; Pt/ BaO/Al2O3, 160 m2/g, 0.63 cm3/g). It is possible that there is blocking of some pores, which hinders the gas from reaching the barium sites. Further, TEM measurements have shown that our particles are large, about 100 nm. It is thus possible that the inner part of the particles is not accessible for the gas, and we therefore also investigated a second shrinking-core model (model 2), with the inclusion of an inactive core. The schematic description of this model is shown in Figure 2.

( )

]

r1 r0 3 ) 1 - θBa(NO3)2,m + θ rtot rtot Ba(NO3)2,m

(24)

1/3

(25)

For model 1 (without an inactive core), the expressions in eqs 24 and 25 can be used with r0 set equal to 0. It has been experimentally observed by FTIR24,25 that when a barium and platinum containing catalyst is exposed to NO + O2, nitrites are initially observed, but after longer exposure, nitrates are dominant. NO will also adsorb on the catalyst,24 forming mainly nitrites. Despite the fact that the Pt/Rh/BaO/Al2O3 model catalyst has a low NO oxidation activity, NOx conversion in the storage phase is observed to be high initially. We suggest that this high initial conversion is due to formation of low coverages of barium nitrites, and the following reaction step was therefore added: 1

/2BaCO3 + NO + 1/4O2 S 1/2Ba(NO2)2 + 1/2CO2 (26)

In the model, this step will be important only when the NO oxidation rate is low. The nitrites are loosely bound and are in the model replaced by the more stable nitrates after continued exposure to NO + O2. We use the same form of the reaction rate for barium nitrite formation as that for barium nitrate formation: bulk,/ rNO-Ba ) kNO-Ba,f CNOCO21/4θBaCO3,m bulk,/ CCO21/2θBa(NO2)2,m (27) kNO-Ba,b

The nitrites can probably be further oxidized to nitrates by NO2.4,22 This step was not crucial for simulating the experiments used in the fitting procedure and was therefore not included. However, it is possible that this step may be important for other reaction conditions. 3.3. NOx Regeneration and NOx Reduction. Montreuil et al.29 presented a kinetic model for three-way converters, including a large set of reactions, which has also been used by Shamim et al.18 Montreuil et al. used different kinetics for some of the reactions (e.g., NO reduction) depending on the stoichiometry of the exhaust gas. This was achieved by using a weight function β1 (see eqs 28-31) to switch between lean and rich kinetics, where β1 is a function of the λ value. A similar approach to model LNT regeneration has been adopted by Kim et al.11 and Kojima et al.10 Kim et al.11 described the rate for release of NOx as a function of the λ value [λ ) (air/fuel)actual/(air/fuel)stoich.]. Kojima et al.10 turned off the regeneration reactions during lean conditions. In this study, we use β1,29 for the reactions involving regeneration of the storage component and for the NO + C3H6 reaction. This gives a smooth transition to the


Figure 3. Temperature ramp for the Pt/Al2O3 catalyst, with the feed gas containing 600 ppm NO and 8% O2 in Ar: (a) experimental concentrations (solid lines) and thermodynamic equilibrium levels (dash-dotted lines); (b) experimental (solid lines) and simulated concentrations (dashed lines).

regeneration phase and hinders NOx reduction and regeneration of the storage component during the lean period, even if the catalyst has a low oxidation activity, resulting in incomplete combustion of the hydrocarbons. The function R1, eq 29, is adapted for the gases that are present in our experiments.

β1 ) 2500R1 + 0.5

(28)

R1 ) 9yC3H6 - 2yO2 - yNO - 2yNO2

(29)

if β1 < 0, set β1 ) 0

(30)

if β1 > 1, set β1 ) 1

(31)

where yi is the molar fraction of species i. The NO + C3H6 reaction on Pt is described by the following global reaction and reaction rate:

NO + 1/9C3H6 w 1/2N2 + 1/3CO2 + 1/3H2O (32) rNO-C3H6 ) β1kNO-C3H6CNO0.13CC3H6

(33)

The concentration dependence on NO is assumed to be the same as that for the NO + CO reaction (CNO0.13), as was found by Subramanian and Varma.30 The global reaction and the corresponding rate for LNT regeneration by C3H6 are 1

/2Ba(NO3)2 + 1/6C3H6 w 1/2BaCO3 + NO + 1/2H2O (34) rnitrate-C3H6 ) β1knitrate-C3H6CC3H6θBa(NO3)2,m0.5 (35)

We can describe the size of the NOx breakthrough peaks, observed when switching from lean to rich conditions (see below), more accurately when using an exponent lower than 1 for the coverage of barium nitrate, and this is the reason for using an exponent of 0.5. The reaction rate for regeneration of barium nitrite was assumed to have the same form as that for regeneration of barium nitrate: 1

/2Ba(NO2)2 + 1/18C3H6 + 1/3CO2 w 1

/2BaCO3 + NO + 1/6H2O (36)

rnitrite-C3H6 ) β1knitrite-C3H6CC3H6θBa(NO2)2,m0.5 (37) 4. Results and Discussion 4.1. NO Oxidation. The activity for NO oxidation on platinum is investigated using the Pt/Al2O3 catalyst.

Figure 4. Measured NO, NO2, and NOx concentrations at the catalyst outlet for one NOx storage cycle over the Pt/Rh/BaO/Al2O3 catalyst at 320 °C.

The NO, NO2, and NOx concentrations measured at the catalyst outlet during a temperature ramp while exposing the catalyst to 600 ppm NO and 8% O2 are shown in Figure 3a. Also shown in the figure are the thermodynamic levels of NO and NO2. It can be seen that at higher temperatures the formation of NO2 is limited by thermodynamics but at lower temperatures the conversion is limited by kinetics. The oxidation of NO to NO2 is modeled using a global reaction rate, which includes the forward and reverse reactions (see eq 7). The rate constant for the reverse reaction is determined by thermodynamics. The preexponential factor and activation energy for the forward rate are adjusted to minimize the least-squares error. 4.2. NOx Storage. NOx storage is investigated using the Pt/Rh/BaO/Al2O3 catalyst with the feed cycled between lean (240 s) and rich (60 s) conditions. The inlet gas during the lean period contained 450 (or 900) ppm NO, 8% O2, and 900 ppm C3H6, and the rich period was obtained by shutting off the O2 feed. The experiments were conducted at three temperatures, 320, 380, and 440 °C. Figure 4 shows the NO, NO2, and NOx concentrations measured at the catalyst outlet from one NOx storage cycle. During the rich period, there is a complete reduction of NOx, and during the lean period, there is storage of NOx, with the NOx storage amount marked by the gray area in the figure. There is also a NOx breakthrough peak seen at the early phase of the rich period. 4.2.1. NOx Storage, Model 1 (without an Inactive Core). The data from the six NOx storage experiments described previously (two inlet NO concentrations and three temperatures) are used for calibrating the global

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Figure 5. Catalyst-out NO, NO2, and NOx concentrations for experiments (solid lines) and simulations (dashed lines) for a NOx storage cycle at 320 °C, using the Pt/Rh/BaO/Al2O3 catalyst. Results from two inlet NO concentrations are shown: ∼450 ppm NO (a) and ∼900 ppm NO (b). Magnifications of the switches to rich conditions in parts a and b are shown in part c. Model 1 (without an inert core) is used for the simulations.

kinetic model. For NO oxidation, the same activation energy that is used in Figure 3 for Pt/Al2O3 (see section 4.1) is adopted. The pre-exponential factor is adjusted (decreased) to fit the NOx storage experiments on Pt/ Rh/BaO/Al2O3. This is in accordance with previous results, which showed that the addition of barium give a negative effect for the NO oxidation reaction over platinum.4 It has also been observed that the more alkaline the support is, the more the activity for hydrocarbon oxidation on platinum is lowered.31 Thus, an alkaline support decreases the activity for oxidizing both NO and hydrocarbons. The first NOx storage model (model 1) does not include an inactive core. However, experimentally it is observed that only a fraction of the barium sites in the catalyst could be used in the storage process. To describe the experiments, the number of active barium storage sites in the model must be reduced compared to the total amount in the sample (120 mol/m3 monolith, corresponding to 20 wt % barium). This is achieved by treating the number of sites as an adjustable parameter, which results in 7.77 mol of barium/m3 of monolith. The rich period of 60 s is long enough to completely regenerate the catalyst, and for the initial conditions in the simulations, it is therefore assumed that all barium is in the form of BaCO3. The rate constants for the reverse reactions in the NOx storage mechanism (kNO2,Ba,b, eq 22, and kNO,Ba,b, eq 27) are calculated from ∆H and ∆S of the respective reactions. For the reaction where Ba(NO3)2 is formed from BaCO3, thermodynamic data give an enthalpy change of -114 kJ/mol and an entropy change of -125 J/mol‚K.23 BaCO3 is favored thermodynamically over

Ba(NO3)2 at 400 °C and higher. However, it is wellknown experimentally3,32,33 that barium stores NOx at 400 °C and at higher temperatures as well. The reason for this discrepancy can be that at least some of the nitrates formed are surface species, which may have different enthalpies and entropies from those for bulk barium nitrate. Therefore, ∆S for the reaction is adjusted by fitting, as was also done in the study by Hepburn et al.9 The enthalpy for the reaction is kept fixed to the thermodynamic value for bulk barium nitrate because there are no thermodynamic data available for surface species. The same procedure is used for the reaction where barium nitrites are formed (∆H ) -63.8 kJ/mol23,34). Figures 5-7 show the results from the simulations (dashed lines) together with the measured concentrations (solid lines) for the six experiments included in the fitting procedure. In the figures, the maximum heights for the NOx breakthrough peaks observed at the start of the rich period, as well as the NOx levels in the rich period, are indicated with arrows. Magnifications of the switch to rich conditions are shown in part c of each of the figures. It should also be pointed out that the scales on the y axes are different in the figures. The height of the NOx peak is quite similar for the two different inlet NO concentrations; at 380 °C, for example, 450 ppm inlet NO resulted in a peak of 320 ppm (above the inlet concentrations) and 900 ppm inlet NO gave a peak of 340 ppm. There is a large difference between the different temperatures, with the peak height increasing with the temperature. With 900 ppm NO in the feed gas, the NOx peak heights are 140 ppm at 320 °C, 340 ppm at 380 °C, and 615 ppm at 440 °C



(peak heights above the inlet concentrations). The model is able to adequately describe NOx storage in the lean periods, NO conversion to NO2, and the catalyst-out NOx concentrations during the regeneration period. The parameters for the model can be found in the appendix. Two reaction steps for NOx storage are used in the model, as described in section 3.2: one step for barium nitrate formation from NO2 and another step for barium nitrite formation from NO. FTIR measurements24,25 have shown that in experiments with NO and O2 in the gas feed there are initially nitrites formed but after longer exposure nitrates dominate. Simulations were first performed with only the nitrate reaction, but because of the low NO oxidation activity of the sample, the model could then not adequately describe the high NOx storage rate in the beginning of the lean period. After the inclusion of the nitrite step, the model is able to describe the NOx storage rate as well as NO2 formation. Fridell et al.3 performed NOx storage experiments on a similar Pt/Rh/BaO/Al2O3 catalyst comparing the amount of stored NOx using NO or NO2 in the feed for experiments at temperatures between 300 and 450 °C. The amount of NOx stored was similar with either NO or NO2 in the feed gas for the temperatures examined. This catalyst also showed a low NO oxidation activity, and this would indicate that at 300 °C and higher NO oxidation is not the critical step for NOx storage. This suggests an alternative storage process besides NO2 adsorption on barium, occurring at least initially, which our modeling accounts for by a global reaction scheme including the formation of barium nitrite from NO and O2. The nitrites are loosely bound and are in the model sequentially replaced with the more stable nitrates. However, it is also likely that

nitrites are oxidized into nitrates4,22 by NO2, but this step is not needed in order to model the six experiments used for calibrating the model, and therefore this step is not added to the model. In addition, the current model predicts low nitrite concentrations at the end of the lean period. This is in accordance with FTIR data,24,25 which also indicates that a nitrite to nitrate step is not necessary when simulating these experiments. The simulated coverages on the surface for a storage cycle at 380 °C are shown in Figure 8. The coverages are the mean values for the 20 elements (continuous stirred tank reactors) used in the simulation. It can be seen that when the lean storage cycle starts, there is an initial rapid formation of barium nitrites followed by a decrease in the coverage, while at the same time the barium nitrate coverage increases monotonically. At the end of the lean cycle, there is only a low coverage of barium nitrites, with barium nitrates dominating. 4.2.2. NOx Storage, Model 2 (with an Inactive Core). In the second model investigated, an inactive core is placed in the center of the barium particles to account for the experimental observation that only a fraction of the barium sites in the catalyst are used as storage sites. The model is described in section 3.2 and is schematically illustrated in Figure 2. The kinetic parameters from model 1 were readjusted and can be found in the appendix. Figure 9 shows the results for the low inlet NO concentration (∼450 ppm) in the feed gas and for three different temperatures: 320, 380, and 440 °C. Magnifications of the switches to rich conditions in Figure 9a-c are shown in Figure 9d. There is an equally good fit between this model and the experiments compared to that for model 1 described in the previous section. When the parameters for model

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Figure 8. Simulated coverages on the surface for a NOx storage cycle at 380 °C and with ∼900 ppm NO in the feed (see Figure 6b). Model 1 (without an inert core) is used for the simulation, and the coverage is the mean value over the 20 elements.

2 are readjusted, the most crucial parameter to change is the diffusivity within the particle. The diffusivity needs to be decreased by a factor of about 17 in order to correctly describe the experiments because the penetration depth is much smaller in this model. In both models, only about 7% of the barium sites are active storage sites. If the whole particle is used as in model 1, it is difficult to understand why only 7% of the particles are used. It is not likely that barium aluminates or blocking of the pores can account for the loss of 93% of the barium sites. However, when the barium particles are very large (100 nm), it is possible that the inner part of the barium particles is not accessible for the gas. We therefore suggest that model 2 (with an inert core) is more realistic for these large particles. However, when there are small particles, which prob-

ably is the case for commercial samples, model 1 could be a better description. 4.2.3. Validation of the NOx Storage Model (Model 2). The LNT model with an inert core (model 2) is validated using three separate experiments not included in the fitting procedure. The Pt/Rh/BaO/Al2O3 catalyst is used, and the gas feed cycled between lean (240 s) and rich (60 s) conditions. The inlet gas during the lean period contains 900 ppm NO, 900 ppm C3H6, and 8% O2, and the rich period is obtained by shutting off the O2 feed. The sequence is then repeated using 4% O2 during the lean period. The experiments are conducted at three temperatures, 320, 380, and 440 °C. The first part of the experiment using 8% O2 is used in the fitting procedure. However, the second part of the measurement, with the low O2 concentration (4% O2), is not included when adjusting the parameters and is only simulated using the model. The resulting NO, NO2, and NOx concentrations from the experiment and the simulations are shown in Figure 10. Magnifications of the switches to rich conditions in Figure 10a-c are shown in Figure 10d,e. The model is able to simulate the lowering of both NO2 formation and NOx storage during the lean period when decreasing the oxygen concentration in the inlet feed gas. The model can also capture the decrease in the breakthrough peak when switching to rich conditions at 440 °C. There is a small discrepancy in the regeneration at 320 °C, where the simulations predict a higher NOx peak than that seen in the experiment. One possible explanation for this is that when using a lower oxygen concentration, there is less NO2 formed, resulting in higher nitrite formation and at the same time lower nitrate formation. The nitrites are loosly bound and decompose rapidly when starting


Figure 9. Catalyst-out NO, NO2, and NOx concentrations for experiments (solid lines) and simulations (dashed lines) for a NOx storage cycle using the Pt/Rh/BaO/Al2O3 catalyst. Data for three different temperatures are shown: 320 °C (a), 380 °C (b), and 440 °C (c) for an inlet NO concentration of 450 ppm. Magnifications of the switches to rich conditions in parts a-c are shown in part d. Model 2 (with an inert core) is used for the simulations. Table 1. Kinetic Parameters for Model 1 (without an Inert Core) rate constant

pre-exponential factor

activation energy (kJ/mol)

kC3H6,ox kNO,ox kNO2-Ba kNO-Ba kNO-C3H6 knitrate-C3H6 knitrite-C3H6

3.0 × 1011 7.51 × 10-2 4.67 × 107 1.80 × 102 12.94 2.09 × 108 3.74 × 105

105.0 39.2 83.7 20.0 60.0 100.3 60.3

the rich period, resulting in a large NOx breakthrough peak. The addition of a reaction step to the model, where nitrites are oxidized to nitrates, may give a lower NOx peak at 320 °C. 5. Concluding Remarks In this work, a global kinetic model for LNT is developed and the kinetic parameters are calibrated based on the results of the flow reactor experiments with a Pt/Rh/BaO/Al2O3 model catalyst. A global mechanism for NO oxidation is developed for a Pt/Al2O3 catalyst because NO oxidation to NO2, catalyzed by platinum, is an important step in the NOx storage process. The NO oxidation activity is found to be lower for platinum supported on BaO/Al2O3 compared to Pt/Al2O3, which is in line with previously published results.4 Therefore, the pre-exponential factor for NO oxidation is adjusted to match the NO and NO2 levels on the Pt/Rh/BaO/Al2O3 catalyst. The main global reaction step used for NOx storage is the formation of Ba(NO3)2 from BaCO3 and NO2. The

Table 2. Additional Parameters for Model 1 (without an Inert Core) parameter rtot D ∆HBa(NO3)2 ∆SBa(NO3)2 ∆HBa(NO2)2 ∆SBa(NO2)2

K1 K2 K3 K4 h(320 °C) h(380 °C) h(440 °C)

description radius of the barium particle (nm) diffusivity (m2/s) enthalpy from thermodynamic table (kJ/mol) entropy (fitted) (kJ/mol) enthalpy from thermodynamic table (kJ/mol) entropy (fitted) (kJ/mol) NOx storage capacity (mol/m3 monolith) fraction of barium that is active (%) equilibrium constant equilibrium constant equilibrium constant equilibrium constant number of elements heat losses for the 320 °C expt (J/s‚K) heat losses for the 380 °C expt (J/s‚K) heat losses for the 440 °C expt (J/s‚K)

value 100 6.13 × 10-8 -113.9 -95.0 -63.75 -60.41 7.77 6.5 65.6 exp(961/T) 2.08 × 103 exp(361/T) 3.98 exp(11611/T) 4.79 × 105 exp(-3733/T) 20 3.92 × 10-4 1.34 × 10-3 2.24 × 10-3

catalyst shows a low activity for NO oxidation, especially at 320 °C, but still the initial NOx storage is significant. To capture this feature, an additional reaction step was added where low coverages of loosely bound barium nitrites are initially formed from BaCO3 and NO, in accordance with previous FTIR studies.24,25

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Figure 10. Catalyst-out NO, NO2, and NOx concentrations for experiments (solid lines) and simulations (dashed lines) for two NOx storage cycles with 8 and 4% O2, respectively, during the lean period for the Pt/Rh/BaO/Al2O3 catalyst. Results for three different temperatures are shown: 320 °C (a), 380 °C (b), and 440 °C (c). Magnifications of the switches to rich conditions in parts a-c are shown in parts d and e. Model 2 (with an inert core) is used for the simulations.

A shrinking-core model is used for describing internal mass transfer in the barium particles. It has been observed in experiments that, for the model catalysts used here, only a fraction of the barium particles are used in the storage process. There are different possible explanations for why some of the barium is not accessible, e.g., blocking of the pores, which hinders the gas from reaching the particles. Further, TEM measurements have shown that the barium particles in our model catalysts are large, about 100 nm. It is possible that the inner cores of the particles are not exposed to the gas. Two different models are tested in this work. In the first model, the number of active sites is fitted to the experimental data, resulting in a lowering of the

barium sites compared to the total amount of barium in the sample. In the second model, an inactive core is placed in the inner part of the particles. Global reaction steps for regeneration of the NOx trap with C3H6 are also incorporated into the model. The two models are calibrated based on the results of experiments at three different temperatures (320, 380, and 440 °C) and two different NO concentrations. The models are able to adequately describe NOx storage during the lean period, NO reduction during the regeneration period, the NOx breakthrough peaks observed initially in the rich period, and the measured ratio between NO and NO2. The fit is equally good with both models. However, to capture the experiments, the

Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 3031 Table 3. Kinetic Parameters for Model 2 (with and Inert Core)a rate constant

pre-exponential factor

activation energy (kJ/mol)

kNO2-Ba kNO-Ba kNO-C3H6 knitrate-C3H6 knitrite-C3H6

1.61 × 107 1.88 × 102 13.62 2.10 × 108 3.78 × 105

80.3 20.0 60.0 100.1 60.3

a

Only parameters that differ from model 1 are given.

Table 4. Additional Parameters for Model 2 (with an Inert Core)a parameter

description

value

r0 D

radius of the inert core (nm) diffusivity (m2/s) NOx storage capacity (mol/m3 monolith) fraction of barium that is active (%)

97.7 3.63 × 10-9 8.04 6.7

a

Only parameters that differ from model 1 are given.

amount of active sites is adjusted, which results in the use of only about 7% of the barium in the catalyst. A possible explanation is that the inner core of these large particles (100 nm) is not used, which is the case of model 2. However, when using catalysts with small barium particles, which is probably the case for commercial catalysts, model 1 (without an inert core) seems to be more realistic. Model 2 (with an inert core) is validated with three NOx storage experiments not included in the fitting procedure. In these experiments, 4% oxygen is used in the lean period, compared to 8% oxygen previously used. The model is able to adequately describe the validation experiments. Acknowledgment The authors acknowledge helpful discussions with Se Oh, Ed Bissett, Yongsheng He, David Monroe, and Wei Li of the General Motors Research and Development Center. We also greatly acknowledge the General Motors Research and Development Center for their financial support. Appendix The kinetic parameters used in the two models are given in Tables 1-4. Literature Cited (1) Miyoshi, N.; Matsumoto, S.; Katoh, K.; Tanaka, T.; Harada, J.; Takahashi, N.; Yokota, K.; Sugiura, M.; Kasahara, K. Development of new concept three-way catalyst for automotive lean-burn engines. SAE Tech. Pap. Ser. 1995, 950809. (2) Bo¨gner, W.; Kra¨mer, M.; Krutzsch, B.; Pischinger, S.; Voigtla¨nder, D.; Wenninger, G.; Wirbeleit, F.; Brogan, M. S.; Brisley, R. J.; Webster, D. E. Removal of nitrogen oxides from the exhaust of a lean-tune gasoline engine. Appl. Catal. B 1995, 7, 153. (3) Fridell, E.; Skoglundh, M.; Westerberg, B.; Johansson, S.; Smedler, G. NOx storage in barium-containing catalysts. J. Catal. 1999, 183, 196. (4) Olsson, L.; Persson, H.; Fridell, E.; Skoglundh, M.; Andersson, B. A kinetic study of NO oxidation and NOx storage on Pt/ Al2O3 and Pt/BaO/Al2O3. J. Phys. Chem. B 2001, 105, 6895. (5) Olsson, L.; Fridell, E.; Skoglundh, M.; Andersson, B. Mean Field Modelling of NOx Storage on Pt/BaO/Al2O3. Catal. Today 2002, 73, 263.

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Received for review July 7, 2004 Revised manuscript received January 19, 2005 Accepted February 4, 2005 IE0494059

Global Kinetic Model for Lean NOx Traps - Industrial & Engineering

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