Modeling of Three-Way-Catalyst Monolith Converters with

Ind. Eng. Chem. Res. 2004, 43, 4503-4510

4503

Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat Petr Kocˇ ı´,† Milan Kubı´cˇ ek,‡ and Milosˇ Marek*,† Departments of Chemical Engineering and of Mathematics, Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical Technology, Technicka´ 5, CZ-166 28 Prague, Czech Republic

Two models of catalytic monolith reactor with diffusion in the washcoat are described, employing the nonstationary kinetics of CO and hydrocarbon oxidation, NOx reduction, and oxygen storage with 23 reaction steps. The first model describes the dynamic behavior in a short monolith (recirculation reactor or CSTR), and the second one is a spatially two-dimensional nonstationary model of the monolith with plug flow. The models are used to demonstrate the qualitative agreement between the observed nonlinear dynamics of CO oxidation, including hysteresis and periodic and period-doubled oscillations, and earlier experiments. The effects of transport parameters within the washcoat on the monolith lightoff and on the outlet conversions are simulated. Computed spatiotemporal concentration patterns of reaction intermediates within the washcoat layer are used to discuss the oxidation and reduction functions of the three-waycatalyst monolith. 1. Introduction A large part of the newly produced and recycled noble metals (particularly platinum, palladium, and rhodium) is consumed in catalytic converters of automobile exhaust gases. The overall consumption increases as emissions regulations become more strict, but the use of Pt and Pd vary widely. For example, the reversal in Pt and Pd prices caused the consumption of Pt in catalytic converters of automobile exhaust to grow by 17% in 2002, but the Pd demand decreased in 2002 by approximately 40%.1 Large advances in the design of automobile catalysts have been made over the last 10 years, including the improvement of the thermal and chemical properties of the catalyst. The key enhancement was the addition of oxygen storage compounds (cerium and zirconium oxides) and NOx storage compounds (e.g., barium, lanthanum, or potassium oxides) to the washcoat. Thermal durability and stability at high temperatures of the ceramic and metallic supports as well as the catalytic washcoat layer have been improved. This enabled the use of catalysts with higher monolith cell densities and thinner walls, and smaller converters coupled close to the engine could thus be produced. The pollutants emitted before the catalyst reaches the lightoff account for the majority of the total emissions. Higher exhaust temperatures entering the close coupled catalyst enable one to reach the lightoff more rapidly because the reaction rates increase with temperature but also can increase the importance of transport effects within the washcoat. Optimization of engine operation parameters together with calibration of engine management systems enable one to tailor the catalyst to individual vehicle models and to reduce the loadings of expensive noble metals. * To whom correspondence should be addressed. Tel.: +420 22435 3104. Fax: +420 23333 7335. E-mail: milos.marek@ vscht.cz. † Department of Chemical Engineering. ‡ Department of Mathematics.

Mathematical modeling of catalytic monolith converters helps to speed up the development of catalysts. Versatile software for the construction of monolith models has been described and applied to various monolith arrangements.2-4 Until now, mostly semiempirical steady-state kinetics with kinetic parameters fitted to monolith experimental data were used in such models. However, because transient regimes before the lightoff are most important from the point of view of the amount of emitted pollutants, nonstationary kinetics should be properly used. A comprehensive set of microkinetic relations has been recently evaluated from nonstationary experiments for the set of reactions on a Pt/Ce/γAl2O3 three-way catalyst (TWC).5-8 Mukadi and Hayes9 used these kinetic expressions in the model of the TWC monolith converter. They pointed to the significance of the effects of washcoat diffusion and used a parallel computer for the solution of balance equations. A detailed microkinetic scheme was also used earlier in the simulations of partial oxidation of methane in a catalytic monolith but without consideration of diffusion in the washcoat.10 Ramanathan et al. in a recent publication11 have also stressed that an important process influencing the lightoff is washcoat diffusion. However, they performed their analysis for a single firstorder reaction. In this paper we present the results of simulations of the model of a TWC monolith reactor with nonstationary kinetics and diffusion in the washcoat for two arrangements. In the first one, we study the nonlinear dynamics in a well-stirred reactor (short monolith, recirculation reactor, or CSTR). Qualitative agreement between the results of simulations and earlier experiments confirms the robustness of the microkinetic model used. The second arrangement is a spatially two-dimensional model of the TWC monolith (plug-flow reactor, PFR). The analogy between the nonlinear behavior of CSTR and PFR is discussed. The effects of the internal diffusion in the washcoat are studied, and the computed spatiotemporal patterns of the reaction components in the washcoat along the monolith are used to discuss the functions of TWC.

10.1021/ie034137k CCC: $27.50 © 2004 American Chemical Society Published on Web 03/03/2004

4504 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 Table 1. Microkinetic Reaction Scheme Used in the Model of TWCa no.

reaction step

kinetic expression

1 2 3 4 5

CO + * h CO* O2 + 2* f 2O* CO* + O* f CO2 + 2* CO + O* h OCO* OCO* f CO2 + *

R1 ) - kb1LNMθCO* R2 ) 2 R3 ) k3LNMθCO*θO* f s R4 ) k4LNMcCOθO* - kb4LNMθOCO* R5 ) k5LNMθOCO*

6 7 8 9 10 11

C2H2 + * h C2H2* C2H2* + 2* h C2H2*** C2H2* + 3O* f 2CO* + H2O + 2* C2H2*** + 3O* f 2CO* + H2O + 4* C2H2 + O* h C2H2O* C2H2O* + 2O* f 2CO* + H2O + *

R6 ) kf6LNMcCs 2H2θ* - kb6LNMθC2H2* R7 ) kf7LNMθC2H2*θ*2 - kb7LNMθC2H2*** R8 ) k8LNMθC2H2*θO* R9 ) k9LNMθC2H2***θO* R10 ) kf10LNMcCs 2H2θO* - kb10LNMθC2H2O* R11 ) k11LNMθC2H2O*θO*

12 13 14

O2 + 2s f 2Os CO* + Os f CO2 + * + s C2H2* + 3Os + * f 2CO* + H2O + 3s

s R12 ) k12LOSCcO ξs 2 R13 ) k13LNMθCO*ξOs R14 ) k14LNMθC2H2*ξOs

15

CO2 + γ h CO2γ

s R15 ) kf15LSUPcCO χγ - kb15LSUPχCO2g 2

16 17 18 19 20 21 22 23

NO + * h NO* NO* + * f N* + O* NO* + N* f N2O* + * N2O* f N2O + * N2O* f N2 + O* N* + N* f N2 + 2* NO + O* h NO2* NO2* h NO2 + *

R16 ) kf16LNMcsNOθ* - kb16LNMθNO* R17 ) k17LNMθNO*θ* R18 ) k18LNMθNO*θN* R19 ) k19LNMθN2O* R20 ) k20LNMθN2O* R21 ) k21LNMθN*2 R22 ) kf22LNMcsNOθO* - kb22LNMθNO2* s θ* R23 ) kf23LNMθNO2* - kb23LNMcNO 2

kf1LNMcsCOθ* s k2LNMcO θ*

a The reaction subsystems for CO and C H oxidation on noble metal (*), O storage and release on ceria (s), CO storage on 2 2 2 2 γ-Al2O3 (γ), and NOx transformation on noble metal (*) are separated by empty lines. For values of the kinetic parameters, compare refs 5-9.

Extensive literature is devoted to the problem of the simulation of behavior of monolith reactors for automobile exhaust detoxification. However, TWC models including nonstationary kinetics with a detailed description of the reaction steps, internal diffusion within the washcoat, and axial heat dispersion have been formulated and solved only recently. The paper by Mukadi and Hayes9 is mostly devoted to the development of a parallelized algorithm for the solution of an extensive set of partial differential equations (PDEs) describing the model and gives just a few examples of the obtained solutions. Hence, the results presented here appear to be the first more detailed report on the transient behavior of TWC monoliths modeled with the use of microkinetics and diffusion in the washcoat layer.

the washcoat layer (eq 7). The appropriate boundary conditions are in the form of eqs 8 and 9.

kca dci(t) out ci + g (csi |r)δ - ci) ) uincin i - u dt  ∂csi (r,t)

)D

∂θk(r,t)

)

1

)

J

∑νi,jRj

sj)1

)

∑νk,jRj

(3)

J

1

1

νm,jRj ∑ j)1

(4)

J

νq,jRj ∑ j)1

(5)

LSUP

∂t

(2)

J

LOSC

∂t ∂χq(r,t)

1

+

LNMj)1

∂t ∂ξm(r,t)

∂2csi ∂r2

∂t

2. Model 2.1. CSTR. In a CSTR, spatially independent concentrations and temperature in the bulk gas phase can be assumed. Because the washcoat layer thickness is on the order of tens of micrometers, we can also consider that there are no temperature gradients within the washcoat.12 However, nonuniform concentration profiles may arise within the washcoat,9,12 where diffusion, surface deposition of the gaseous components, and catalyzed reactions take place simultaneously. Heatand mass-transfer coefficients are employed for the description of transport between the washcoat and the bulk gas. A spatially pseudo-1D, heterogeneous model of a wellmixed Pt/Ce/γ-Al2O3 TWC monolith is represented by the following ordinary differential equations (ODEs) and PDEs: mass balances in the bulk gas (eq 1), in the washcoat pores (eq 2), and on the catalyst surface (eqs 3-5), the combined overall mass and enthalpy balance for the bulk gas (eq 6), and the enthalpy balance for

eff

(1)

dT(t) T2 ) Tuout - inuin, dt T uout ) uin +

kha Rg(T s - T) (6) p gcg,m p

dT s(t) dt

)

kha Fscsp(1

g

(T - T s) -

-)

a

J

∫r)0∆HjRj dr ∑ g j)1

Fscsp(1 -  )

δ

(7)

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4505

D

eff

∂csi ) kc(ci - csi ) ∂r ∂csi )0 ∂r

at r ) δ

at r ) 0

(8)

(9)

Here Rj values are reaction rates defined together with the reaction scheme used in Table 1. Symbols θk, ξm, and χq denote fractions of the related components deposited on the noble metal (*), ceria (s), and γ-Al2O3 (γ) surface sites with the capacities LNM, LOSC, and LSUP, respectively (cf. Table 1). In the catalytic washcoat layer, r ) 0 corresponds to the wall and r ) δ means the external surface of the washcoat. The equations (6) result from the combination of the enthalpy and overall mass balance for the bulk gas under the assumptions of ideal gas, constant pressure, and constant molar heat capacity of the gas. 2.2. PFR. In a TWC monolith with plug flow, concentration and temperature gradients have to be considered in both axial (flow) and radial (transverse) directions. We can assume again that there are no temperature gradients in the radial direction within the washcoat layer and in the wall of the channel12 (cf. section 2.1). On the contrary, axial temperature gradients as well as concentration gradients can be large. Reaction and diffusion within the catalytic washcoat layer are described in a way similar to that in the model of the CSTR (cf. section 2.1). A spatially 2D, heterogeneous model of a Pt/Ce/γAl2O3 TWC monolith channel with plug flow is then represented by the following PDEs: mass balances in the flowing gas (eq 10), in the washcoat pores (eq 11), and on the catalyst surface (eqs 12-14), the enthalpy balance for the flowing gas (eq 15), and the enthalpy balance for the solid phase (eq 16). The appropriate boundary conditions are in the form of eqs 17-21.

∂(vci) kca s ∂ci(z,t) )+ g (ci |r)δ - ci) ∂t ∂z 

Table 2. Inlet Gas Composition (Molar Fractions, yin k ) Used in the Simulations (Balance N2)a component

molar fraction

component

molar fraction

CO C2H2 NO

1.20-1.22% 680 ppm 1000 ppm

O2 CO2

0.6-0.8% 12%

a If the range of concentrations is given here, the employed values can be found in the captions of individual figures.

Table 3. Values of Model Parameters Used in the Simulationsa parameter

value

parameter

value

a csp Deff l LNM LOSC LSUP

3000 m2‚m-3 1000 J‚kg-1‚K-1 (1-5) × 10-7 m2‚s-1 0.12 m 20-80 mol‚m-3 0-10 mol‚m-3 300 mol‚m-3

u δ g s λs Fs

40000 h-1 20-50 µm 0.77 0.7 5 W‚m-1‚K-1 2600 kg‚m-3

a If the range of parameter values is given here, the employed values can be found in the captions of individual figures.

Figure 1. Oscillatory behavior for CO oxidation: evolution of the outlet CO concentrations in the course of a slow temperature ramp (1 °C‚s-1). Isothermal CSTR, Pt/γ-Al2O3 catalyst, yin CO ) in 1.22%, yO ) 0.64%, LNM ) 40 mol‚m-3, δ ) 20 µm, and Deff ) 2 5 × 10-7 m2‚s-1.

∂T s(z,t) ∂t

)

λs ∂2T s Fscsp

∂z

k ha

+

Fscsp(1

2

(10)

)D

eff

)

)

∂t

1

1 

)

1

J

∫r)0∆HjRj dr ∑ g j)1 δ

-)

(16)

J

νi,jRj ∑ s j)1

T ) Tin

(11)

∂T s )0 ∂z

J

νk,jRj ∑ j)1

(12)

at z ) 0

(17)

at z ) 0 or l

(18)

ci ) cin i , i ) 1, ..., I

at z ) 0

(19)

∂csi ) kc(ci - csi ) ∂r

at r ) δ

(20)

J

∑νm,jRj

LOSCj)1

∂t ∂χq(z,r,t)

1 LNM

∂t ∂ξm(z,r,t)

+

∂r2

∂t ∂θk(z,r,t)

∂2csi

(T - T s) -

-)

a Fscsp(1

∂csi (z,r,t)

g

(13)

J

∑

LSUPj)1

νq,jRj

k ha ∂T(z,t) ∂T ) -v + g g,w g(T s - T) ∂t ∂z F c  p

(14)

(15)

Deff

∂csi )0 ∂r

at r ) 0

(21)

The values of mass- and heat-transfer coefficients along the monolith channel [kc(z) and kh(z), respectively] have been calculated from the correlations.13 Recently, a new set of correlations for heat and mass transfer have

4506 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 2. Oscillation regime of CO oxidation on the Pt/γ-Al2O3 catalyst: evolution diagrams in the inlet concentration of oxygen. The in ) 300 °C (adiabatic reactor). inlet concentration of O2 changes with constant rate 10-4%/s. Deff ) 5 × 10-7 m2‚s-1, yin CO ) 1.22%, and T CSTR: LNM ) 80 mol‚m-3, δ ) 20 µm. PFR: LNM ) 20 mol‚m-3, δ ) 50 µm.

been proposed.11 The comparison of different empirical and theoretical correlations with experimentally evaluated mass-transfer coefficients is given in the paper.14 Different theoretical models applied to bimodal poresize distribution of the washcoat (macro- and nanopores) can give large variations of the Deff value. The values used in our simulations correspond to typical measured diffusivities in the γ-Al2O3-based washcoat of the catalytic monolith converter of automobile exhaust gases.15 Constant Deff has been used throughout the computations because the use of variable Deff does not bring a significant difference (because of similar molar weights of the components and a relatively weak temperature dependence of Knudsen diffusivity).16 2.3. Numerical Solution. In the case of the model of the CSTR, the method of lines has been used for the transformation of the system of PDEs (eqs 2-5) with a microkinetic scheme (cf. Table 1) to a system of ODEs. The LSODE implicit integration method for stiff systems17 has been used for dynamic simulations. The system of PDEs representing the model of the reactor with plug flow (eqs 10-16) has been solved by the finite difference method, using semiimplicit approximations of derivatives with respect to time. The values of the model parameters used in the simulations are given in Table 3.

Figure 3. Periodic regimes of CO oxidation: evolution of the outlet CO concentrations. Monolith PFR, Pt/γ-Al2O3 catalyst, yin CO ) 1.22%, LNM ) 20 mol‚m-3, δ ) 50 µm, and Deff ) 5 × 10-7 m2‚s-1. in in (a) yO ) 0.67%; (b) yO ) 0.65%. 2 2

3. Results 3.1. CO Oxidation. Experiments on individual catalytic Pt/γ-Al2O3 pellets with transport effects for CO oxidation on Pt/γ-Al2O3 were performed in our laboratory in the late 1980s. Both synchronous periodic and aperiodic oscillations of CO, CO2, and temperature on individual pellets were observed.18 A reproducible transition from simple periodic oscillations via a sequence of period-doubling bifurcations to deterministic chaos was also observed.19 Oscillations and period-doubled oscillations have been found in the above lumped (CSTR) spatially 1D model for higher temperatures, when only the kinetic relations for CO oxidation (reactions 1-5 in Table 1) are used. An example of such nonlinear behavior is shown in Figure 1, where the CO oxidation lightoff and then a switch from the stationary to the periodic (oscillatory) solution at higher temperature can be seen.

The range of oxygen inlet concentrations where stable oscillations arise is mapped in the evolution diagram in Figure 2a (the inlet O2 concentration to the reactor increases slowly with time). We can observe that with the increasing oxygen concentration the originally monotonic outlet CO concentration becomes oscillatory; then the frequency of oscillations increases, and at the inlet oxygen concentration approximately equal to 0.63%, the period-doubled oscillations break in. For oxygen concentrations higher than approximately 0.655, singleperiod oscillations are observed, and for oxygen concentrations higher than approximately 0.675%, again a monotonic regime of the CO outlet concentration at slightly lower conversion sets in. Transitions among different oscillatory patterns for CO oxidation with the increasing inlet oxygen concentration have also been observed for the model of a tubular PFR. The results of computation of an evolution

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4507

Figure 4. Periodic regime of CO oxidation: evolution of the surface O* concentrations within the washcoat layer. Monolith PFR, Pt/γin -3 eff ) 5 × 10-7 m2‚s-1. Al2O3 catalyst, yin CO ) 1.22%, yO2 ) 0.67%, LNM ) 20 mol‚m , δ ) 50 µm, and D

diagram are depicted in Figure 2b. The monotonic outlet CO concentration becomes oscillatory, and then smallamplitude oscillations appear within the original oscillations. These small-amplitude oscillations grow, for oxygen concentrations higher than approximately 0.655%, complex oscillations appear, and then again singleperiod oscillations arise. Finally monotonic outlet CO concentrations are observed. Thus, the above kinetic model based on nonstationary kinetics predicts a qualitatively similar evolution of outlet conversions as sequences of regimes observed in experiments.18,19 The outlet CO concentrations for two types of periodic regimes arising in the PFR at constant inlet oxygen concentrations are shown in Figure 3. For inlet O2 concentrations equal to 0.67%, a single periodic regime shown in Figure 3a is observed. In Figure 3b (inlet O2 concentrations equal to 0.65%) are then depicted alternating small- and large-amplitude oscillations with the period approximately doubled in comparison with the period of the oscillations in Figure 3a. The sequence of spatial concentration patterns of surface oxygen on the noble metal sites (O*) within the washcoat layer along the reactor during one period of oscillations is shown in Figure 4. We can observe that O* surface coverage is first very low in the front part of the reactor (t ) 0.0 s) and then an isolated rising peak of the O* starts to propagate along the reactor and from the surface of the washcoat to the wall (t ) 0.3-0.7 s). Finally, the moving peak reaches the region of constant high O* coverage in the rear part of the reactor (t ) 0.8

s) and merges with it (t ) 1.0 s). During the remaining time of the period, the region of high O* coverage shrinks slightly (compare parts f and a of Figure 4) until a new O* peak arises. The nonlinear behavior observed in the model results from the nonstationary kinetics used. This has been found from the bifurcation studies20 for the CSTR reactor without consideration of diffusion within the washcoat.21 Furthermore, it has been shown that the introduction of transport effects within the catalytic washcoat layer can lead to period doubling.21 Multiple steady states can exist in the isothermal PFR. This is also confirmed by the computed evolution diagram depicted in Figure 5, where the temperature of the isothermal PFR is being slowly increased/ decreased at a constant rate. Outlet concentrations for CO oxidation in the isothermal PFR form a hysteresis loop for temperatures between approximately 190 and 240 °C. The models with microkinetics and diffusion in the washcoat can be also used for the studies of the influence of transport parameters on the course of the lightoff (cf. Figure 6). The courses of the CO oxidation lightoff are similar for values of diffusion coefficient Deff equal to 5 × 10-7 m2‚s-1 and higher. For the given set of parameters, the complete CO conversion is reached for an inlet temperature of approximately 220 °C. For lower Deff values, the course of CO outlet conversion is different and the complete conversion is approached more slowly (at higher temperatures); i.e., the lightoff

4508 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 5. CO oxidation hysteresis: evolution of the outlet CO concentrations in the course of a slow temperature ramp ((1 °C/s). Isothermal monolith PFR, Pt/γ-Al2O3 catalyst, yin CO ) in -3 eff ) ) 0.61%, L 1.22%, yO NM ) 33 mol‚m , δ ) 30 µm, and D 2 5 × 10-7 m2‚s-1.

Figure 6. Influence of washcoat transport properties on the conversion of CO oxidation in the course of a slow temperature ramp. Adiabatic monolith PFR, Pt/γ-Al2O3 catalyst, 〈LNM〉 ) 20 in in ramp ) 1 mol‚m-3, yin CO ) 1.22%, yO2 ) 0.67%, δ ) 50 µm, and T °C‚s-1. For “top inert” cases, a 10 µm washcoat sublayer adjacent to gas is inert (no catalytic activity); the total noble metal loading is kept constant.

is significantly limited by the internal diffusion within the washcoat layer. For Deff ) 1 × 10-7 m2‚s-1, the inlet temperature corresponding to the total CO conversion is 300 °C (cf. Figure 6). The top inert layer of the washcoat is sometimes employed in the commercial TWCs to protect the active noble metals and to improve the durability of the catalyst. Simulation results for the arrangement, where the total noble metal loading within the washcoat layer has been kept constant, are also given in Figure 6. It can be seen that for Deff ) 5 × 10-7 m2‚s-1 the outlet CO conversions are lowered only slightly. (For lower temperatures, somewhat better conversions than those without the top inert layer can even be observed, probably thanks to a higher concentration of the noble metal sites in the active washcoat sublayer.) However, for Deff ) 1 × 10-7 m2‚s-1, the transport limitation caused by the introduction of the top inert layer becomes very important and the outlet CO conversion is significantly decreased. 3.2. TWC Operation. The computational results presented in Figures 2-6 dealt with the oxidation of CO and used the kinetic relations 1-5 in Table 1. In the studies of TWC monolith for automobile exhaust detoxification the full set of reactions for CO and hydrocarbons oxidation and NOx reduction (cf. Table 1) has to be used. The resulting set of PDEs is large and the numerical solution is time-consuming, particularly due to steep temperature and surface-concentration gradients for higher temperatures.

Figure 7. TWC cold start and lightoff: evolution of the outlet C2H2 and NOx concentrations in the course of a slow temperature ramp (1 °C/s). Adiabatic monolith PFR, Pt/Ce/γ-Al2O3 catalyst, in yin CO ) 1.2%, yO2 ) 0.72% (stoichiometric; for other concentrations, cf. Table 2), LNM ) 20 mol‚m-3, LOSC ) 10 mol‚m-3, δ ) 50 µm, and Deff ) 5 × 10-7 m2‚s-1.

The evolution of C2H2 and NOx concentrations in the course of the temperature ramp (the TWC cold start and lightoff) under the stoichiometric conditions is given in Figure 7. After the start at low temperature, we can first observe a period on the order of tens of seconds when the outlet C2H2 concentration gradually increases up to the level equal to the inlet concentration (t ) 0-50 s in Figure 7). After that period, the outlet C2H2 concentration is stabilized until the time corresponding to the inlet temperature of approximately 150 °C, when a minor increase of the C2H2 outlet concentration can be observed. After the ignition of oxidation reactions (T in of approximately 210 °C), the outlet C2H2 concentration sharply decreases and the regime of high hydrocarbon conversion is reached for the inlet temperature of approximately 250 °C. As can be seen in Figure 7, the outlet NOx concentrations start to fall at higher temperature, when most of the hydrocarbons are already converted. This course of the outlet concentrations can be well understood from the evolution of the respective surface concentrations within the washcoat. In Figure 8, C2H2* surface concentration profiles within the washcoat are shown for four characteristic times (i.e., inlet temperatures). In the first cold-start period (t ) 10 s; i.e., T in ) 10 °C; Figure 8a), adsorption of C2H2 takes place on the surface sites. The spatial profile is monotonic, with the highest concentrations at the inlet and surface of the washcoat, where the adsorption rate is highest. Almost full coverage of the surface with C2H2* is observed in Figure 8b. The situation for the increasing temperature in the front part of the reactor, where the desorption takes place (but only very slow reaction occurs), is depicted in Figure 8c (t ) 190 s; i.e., T in ) 190 °C). The situation after the lightoff is shown in Figure 8d (t ) 280 s; i.e., T in ) 280 °C). The reaction between C2H2* and O* takes place mainly in the front part of the monolith, and thus low C2H2* concentrations can be seen there. Higher C2H2* concentrations occur in the rear part of the reactor. This results from the lower available O* concentrations; O2 in the gas phase is depleted. The source of O* for C2H2* oxidation then can only be O* resulting from NO* dissociation in the course of NO reduction. This hypothesis is supported by the respective surface concentration profiles of the oxygen stored on the Ce sites (Os) and dissociated nitrogen atoms on the noble metal sites (N*) shown in Figure 9. They illustrate the oxidation-reduction function of the TWC. A high sur-

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4509

Figure 8. TWC cold start and lightoff: evolution of surface C2H2* concentrations within the washcoat layer in the course of a slow temperature ramp. Simulation parameters are taken from Figure 7 (the time in seconds corresponds to the inlet temperature in degrees Celsius).

Figure 10. Concentration profile of NO2 in the pores of the washcoat layer. T in ) 280 °C. Simulation parameters are taken from Figure 7.

4. Conclusions

Figure 9. Surface concentration profile of the oxygen stored on Ce sites (Os) and dissociated nitrogen atoms on noble metal sites (N*) within the washcoat layer. T in ) 280 °C. Simulation parameters are taken from Figure 7.

face oxygen concentration in the front part of the reactor determines oxidation conditions and thus fast conversion of CO and hydrocarbons; cf. Figure 9a. The concentration of dissociated nitrogen atoms (N*) here is low; cf. Figure 9b. The higher N* concentration in the rear part of the reactor and the lower concentrations of surface oxygen determine the conditions favorable for the NOx reduction and the production of N2. The spatial profiles of the NO2 concentration in the pores of the washcoat are shown in Figure 10. The concentration increases in the front part of the reactor (from zero at the inlet) as NO2 is formed via the reaction NO + O* (reaction 22 in Table 1) and then decreases as the oxygen in the gas becomes depleted and NOx is reduced to nitrogen.

The development of TWC converters occurred in the last 20 years mostly empirically, supported by extensive experimentation and by the use of semiempirical kinetic and reactor models. Now when nonstationary kinetics has become available, proper nonstationary models can become an effective tool in the further development of TWC converters. Qualitative agreement of the observed nonlinear behavior in the models and the earlier experiments, such as simple and period-doubled oscillations, supports the robustness of nonstationary kinetic modeling. The distributed model of the washcoat layer combined with microkinetics specific for particular types of active catalytic sites (e.g., Pt, Rh, and CeO2) enables the simulation and optimization of the operation of advanced, multilayered catalytic washcoats.16 The model can be used also for the studies of the effects of concentration oscillations at the inlet to the monolith. Computed spatiotemporal concentration patterns within the washcoat layer can significantly improve the understanding of dynamic processes that take place in the TWC monolith converter under transient conditions. Acknowledgment This work has been supported by Project MSM 223400007 of the Czech Ministry of Education.

4510 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Nomenclature a ) density of the external surface area, c ) concentration in the bulk gas, mol‚m-3 cs ) concentration in the washcoat pores, mol‚m-3 cg,m ) molar heat capacity of the gas, J‚mol-1‚K-1 p g,w cp ) specific heat capacity of the gas, J‚kg-1‚K-1 csp ) effective specific heat capacity of the solid phase, J‚kg-1‚K-1 eff D ) effective diffusion coefficient, m2‚s-1 I ) number of gas components J ) number of reactions k ) kinetic constant of the reaction (dimension depends on the reaction order) kc ) mass-transfer coefficient, m‚s-1 kh ) heat-transfer coefficient, J‚m-2‚K-1‚s-1 l ) length of the monolith, m L ) concentration of active sites in the washcoat, mol‚m-3 p ) pressure, Pa r ) radial coordinate in the washcoat layer, m R ) reaction rate, mol‚m-3‚s-1 Rg ) universal gas constant, 8.31434 J‚mol-1‚K-1 t ) time, s T ) temperature of the bulk gas, K T s ) temperature of the solid phase, K u ) space velocity, s-1 v ) linear velocity, m‚s-1 y ) molar fraction of the component, 1 z ) axial coordinate of the monolith, m m2‚m-3

Greek Letters δ ) thickness of the washcoat layer, m ∆Hr ) standard reaction enthalpy, J‚mol-1 g ) macroscopic porosity of the reactor s ) porosity of the washcoat χ ) coverage of support sites (γ-Al2O3), 1 λ ) effective heat conductivity, J‚m-1‚K-1‚s-1 ν ) stoichiometric coefficient F ) effective density, kg‚m-3 θ ) coverage of noble metal sites (Pt), 1 ξ ) coverage of oxygen storage sites (Ce), 1 Sub- and Superscripts b ) backward f ) forward g ) gas i ) index of the gaseous component in ) inlet j ) index of the reaction k ) index of the component deposited on noble metal sites m ) index of the component deposited on Ce sites m ) molar NM ) noble metals out ) outlet OSC ) oxygen storage capacity q ) index of the component deposited on γ-Al2O3 SUP ) support γ-Al2O3 s ) solid phase; also oxygen storage (Ce) site in the reaction scheme w ) weight

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Received for review September 18, 2003 Revised manuscript received December 5, 2003 Accepted December 11, 2003 IE034137K