Low Temperature Dynamic Characteristics of a Three-Way Catalytic Converter

Copyright @ IFAC Advances in Automotive Control, Karlsruhe, Gennany, 2001

LOW TEMPERATURE DYNAMIC CHARACTERISTICS OF A THREE-WAY CATALYTIC CONVERTER M. Balenovic ',1 J .M.A. Harmsen ",1 J .H.B.J. Hoebink" A.C.P.M. Backx'

• Department of Electrical Engineering, Eindhoven University of Technology •• Laboratory of Chemical Reactor Engineering, Eindhoven University of Technology

Abstract : A mathematical model of a three-way catalytic converter based on a detailed chemical kinetic model has been created mainly to analyze the converter's dynamic behavior at low temperatures. The light-off process of the converter is analyzed in detail. Competition of species for empty noble metal surface determines the light-off characteristic, as inhibition processes increase light-off temperatures of some exhaust gas components in the complete exhaust mixture. Perturbations of the exhaust gas mixture around stoichiometry can in certain conditions decrease the effect of inhibition and lower the light-off temperature for some exhaust components. Copyright ©2001

IFAC. Keywords: Automotive emissions, dynamic modeling, physical models, nonlinear systems, finite element computation.

cheap tool to design an exhaust emiSSion controller (if the converter model is coupled with an engine model).

1. INTRODUCTION After the introduction of strict exhaust emission regulations, the catalytic converter has become a standard part of almost every exhaust aftertreatment system. With the regulations getting constantly more stringent the need for optimization of the complete exhaust after-treatment system arises. Engine and catalytic converter should both be considered when designing an emission control system. The catalytic converter has a quite complex nonlinear dynamic behavior, however, with many features only being observed but not fully explained . A mathematical model can therefore help to the optimize design of a catalytic converter, explain important processes that take place but are mostly unobservable to the measuring equipment , and serve as a convenient and

As the vast majority of harmful exhaust emissions occurs at low temperatures, usually after the cold start of the engine, reducing the needed time for the converter light-off becomes one of the main issues in the exhaust emission control. This can be achieved by additional measures for a rapid increase of the converter temperature such as converter heating and secondary air injection (Balenovic et al., 1999) . Many authors (Taylor and Sinkevitch, 1983; Silverston, 1995; Tagliaferri et al. , 1999) have reported that oscillations of the inlet gas composition around stoichiometry can sometimes lead to a faster light-off. This conversion enhancement is attractive because it does not imply any physical changes in the exhaust aftertreatment system. The only necessary condition is that the controller can achieve desired amplitude

1 This work has been financially supported by the Dutch Technology Foundation STW.

313

2.1 ReactoT model

and frequency of the oscillations. Moreover, due to a standard relay-type lambda sensor characteristic and delays in the control loop, a typical lambda controller induces exhaust gas oscillations around stoichiometry.

The reactor model is briefly presented here , while a detailed model description can be found in (Balenovic et al., 1999; Nievergeld et al., 1997). The monolithic reactor is modeled as one dimensional adiabatic reactor with one channel as the representative for the whole converter. The reactor model is a set of partial differential equations which includes continuity equations for the species in the bulk gas and solid phase as well as adsorbed on the noble metal or ceria surface (equations (1),(2),(3)) , and energy equations in the gas and solid phase (equations (4), (5)) :

This paper presents a mathematical model of a catalytic converter, which enables a thorough analysis of the converter dynamics. The model is based on a detailed elementary step kinetic model which includes oxidation of carbon monoxide and hydrocarbons (acetylene and ethylene) submodels as well as a nitric oxide reduction submodel. The oxidation submodels have been obtained by transient kinetic modeling of elementary reactions over a single Pt/Rhh-AI203/Ce02 catalyst (Nibbelke et al., 1998; Harmsen et al., 2000 ; Harmsen et al., 1999) . The NO reduction kinetic submodel is based on the available literature data (Oh et al. , 1986) . Typical converter models (Oh and Cavendish, 1982; Koltsakis et al., 1997; Evans et al. , 1999) usually comprise steady state kinetics, which is a reasonable approximation at higher temperatures where reactions become very fast, but fails to explain competition for empty noble metal surface at low temperatures, which mainly determines the light-off characteristic of the catalytic converter. By analyzing the noble metal surface dynamics one can find conditions at which an oscillating feed improves the converter's conversion. These conditions should then be recognized during the converter operation so that an optimal control strategy could be applied.

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where Cf,s are concentrations in gas and solid phase, 0 fractional noble metal surface coverage, Tf ,s gas and solid phase temperature,h .. 9(p) vector of converter 's physical parameters, Ta ,d,r,gl adsorption , desorption , reaction and global reaction rates , Leap capacity of catalyst phase (noble metal or oxygen storage), (6.. r H) reaction enthalpy, CP~P superficial mass flow , P density and cps solid phase specific heat.

2. MATHEMATICAL MODEL The components used to represent the exhaust gas are carbon monoxide , hydrocarbons (acetylene and ethylene), oxygen , nitric oxide, carbon dioxide and water. As there are many hydrocarbons in the exhaust, selection of the representatives to be modeled is not straightforward. Ethylene is found in considerable quantities in the exhaust (Impens, 1987; Kubo et al. , 1993) , and is set to represent majority of the hydrocarbons which are relatively easily oxidized . Acetylene , on the other hand , represents hydrocarbons which are difficult to be oxidized but easily access the empty noble metal surface. Acetylene is known to influence the light-off of carbon monoxide (Mabilon et al., 1995) and is also found in considerable amounts in the exhaust(Impens, 1987; Kubo et al., 1993), especially at lower temperatures. Hydrogen was not explicitly modeled, but it was accounted for by increasing the reaction enthalpy of the carbon monoxide oxidation .

2.2 Kinetic model

The core of the converter model is the underlying kinetic model consisting of elementary steps of individual global reactions. Adsorption and desorption of the species to and from the noble metal and oxygen storage surface are given by (0* is empty fraction of the noble metal surface): Ta ,; = ka,;LcapC;O Td ,; = kd ,; L capO; 314

*

(6) (7)

The rates of the surface reactions depend on the surface coverages of involved species (x,y), e.g. for Langmuir-Hinshelwood equations, typically in the following manner:

Table 1. Physical parameters of the simulated reactor. Substrate length Substrate width Cell density Wall thickness Wash coat loading Washcoat surface area Noble metal capacity Oxygen storage capacity

(8) The adsorption rate coefficients do not severely change with temperature, while des or pt ion and reaction rates mostly have Arrhenius temperature dependence:

ka i = ka iOVT

k d(r) ,i = A d(r),iexp ( - EaC,d(r)'i) RT

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from Oh et al. (Oh et al., 1986) , with some of its kinetic parameters adapted to describe measured data during an European test cycle (Hoebink et

(9)

al., 2000).

(10) 2.3 Numerical methods

In some cases reaction is not an activated process and the reaction rate coefficient is then given by a constant. The above given equations are only typical relations used in the model. There are some special cases not presented here .

The system to be solved is a system of nonlinear, partial differential equations (PDE), which is quite a complex task. To relax the problem complexity the method of lines with discretization in the axial direction has been applied to transform the system into a larger set of ordinary differential equations (ODE), which is then solved using Backward Differentiation Formulae (BDF) with variable order and variable size (NAG , 1991) . The Jacobian of the system has analytically been calculated to achieve a better numeric stability and speed up the calculation.

The reaction mechanism is given in the appendix. It comprises elementary steps from various global reactions. It has been shown (Harmsen et al., 2000; Harmsen et al. , 1999) that by combining elementary steps from single global reactions one can predict converter behavior with complex mixtures. Consider the CO oxidation submodel, which is given by steps 1 to 5,22 and 23 in the appendix. Steps 1 and 2 represent adsorption and desorption of O 2 and CO to and from the noble metal surface (equations (6) a nd (7)) . Surface reaction is given by step 3, with its rate calculated by equation (8). A CO molecule can adsorb on the noble metal surface already covered by an oxygen adatom (Eley-Rideal-like step) and subsequently oxidize to CO 2 . Steps 4 and 5 describe this reaction path. Accompanying rate equations are similar, but slightly different than those for steps 1-3. Another possible path for the CO oxidation is through a reaction of CO adsorbed on the noble metal surface and oxygen adsorbed on the ceria surface (steps 22 and 23). The presence of ceria is extremely important during a dynamic operation of the converter as it can store oxygen when the inlet feed is lean and release it to oxidize CO and hydrocarbons when the inlet feed becomes rich (shortage of oxygen). Somewhat more complex are the elementary steps for the oxidation of hydrocarbons ethylene and acetylene (steps 1022, 24 and 25). All kinetic rate parameters for the oxidation processes were obtained by transient kinetic modeling on the same catalyst (Nibbelke et al., 1998; Harmsen et al., 2000; Harmsen et al. , 1999) . The modeling studies showed that when hydrocarbons are present in the feed a fraction of the noble metal surface may not be accessible to oxygen. This fraction was set to 30% in this study. The NO reduction submodel was adopted

3. SIMULATION Dynamic simulations presented here were performed with the converter model whose main parameters are given in table 1. As light-off with different inlet feeds is of main concern in this paper, the inlet temperature in all simulations increases from 300K to 550K linearly in lOOs and then remains at that temperature. This is an approximation of the cold start of an engine. The exhaust mass flow was kept constant at 0.015 kg/ so This approximation is less realistic but simplifies the analysis. The inlet gas concentrations are taken as non linear static functions of the inlet lambda signal. In case of the stoichiometric feed these concentrations are: CO 0.6 vol%, O 2 0.53 vol% , NO 1200 ppm, HC 1000 ppm , CO 2 12 vol% and H 2 0 10 vol% .

3.1 Steady inlet feed

Light-off characteristics of the reactor with steady, stoichiometric (A= 1), rich (A=O. 96) and lean (A=1.04) feeds are presented in figure 1. Acetylene represents 30% of total hydrocarbons. Carbon monoxide , nitric oxide and acetylene light off in a very narrow time interval when stoichiometric 315

feed is applied, while the light-off of ethylene occurs about 20 seconds later. Lean feed benefits the light-off of carbon monoxide and acetylene while rich feed improves the NO conversion. Interestingly, though the conversion of ethylene starts earlier with the lean feed, the light-off time is increased. The conversion reaches 100% eventually (not shown in the figure) , but at much slower rate . The reason for this is competition for the empty noble metal surface between ethylene and oxygen, as will thoroughly be discussed later in the text . Figure 2 shows the normalized gas concentrations and the noble metal surface coverage at the position 6.5 cm from the reactor inlet in the case of the stoichiometric feed. Gas phase concentrations resemble the responses shown in figure l. At low temperatures acetylene covers most of the noble metal surface because it has a strong ability to access the surface but difficulties to be oxidized . Acetylene therefore inhibits the conversion of other components as they can hardly reach the noble metal surface, e.g. CO light-off temperature increases by more than lOOK in the presence of hydrocarbon inhibiting species, mostly acetylene (Evans et al. , 1999; Mabilon et al., 1995; Harmsen et al. , 1999) . The accumulation of NO on the noble metal surface starts after 50s leading to a partial desorption of acetylene from the surface (negative conversion) . Nitric oxide is also known to increase the light-off temperature of carbon monoxide (Evans et al., 1999) . There is no larger accumulation of CO on the noble metal surface because it has difficulties to reach the surface with the inhibitors present, and can easily be oxidized with the help of oxygen stored on the ceria surface if no oxygen is available on the noble metal surface. Adsorbed NO needs extra vacant sites for its dissociation , thus first only NO notably covers the surface. With the catalyst temperature further increasing, sites become available for the dissociation of NO leading to the accumulation of N adatoms on the noble metal. This is favorable for the NO conversion as one possible path for N2 creation is the reaction between adsorbed NO and N adatoms (appendix, step 8). As dissociation becomes faster with the increasing temperature, N adatoms outnumber NO species and accumulate on the noble metal surface. Since the other path for the creation of N2, via recombination of two N adatoms (appendix, step 9) , activates at higher temperatures, the dip in the NO conversion occurs around 115s with the stoichiometric feed . With increased NO dissociation and conversion, space on the surface becomes available for oxygen which begins to accumulate after lOOs. The rapid conversion of ethylene starts only after almost all other components have been converted. Ethylene can easily be oxidized but has difficulties to reach the noble metal surface at low temperatures. There is practically no accumulation of ethylene species on

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3.2 Oscillating inlet feed A standard air-fuel ratio control system produces oscillations of the converter inlet lambda signal around stoichiometry due to a relay-type lambda sensor and considerable system delays. These oscillations are sometimes found to be beneficial for the converter performance, but sometimes not . The influence, and possible benefits of an oscillating feed are analyzed here. 316

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Fig. 4. Light-off characteristics with steady, stoichiometric, and oscillating feeds of different amplitudes and frequencies.

Fig. 3. Warming up test with the stoichiometric feed. Acetylene represents 30%, 10%, 5% and 0.1% of the total hydrocarbon amount.

a time interval when feed oscillations improve the conversion , are shown for the stoichiometric and oscillating (A=0.02 , f=0 ,67Hz) feed. The main difference, which also leads to the ethylene conversion improvement, lies in the noble metal surface coverage by oxygen. While with the stoichiometric feed oxygen accumulates on the surface because it has a stronger affinity to reach the surface than ethylene, the oscillating feed leads to the interchanging of oxygen and ethylene on the surface during lean and rich periods. The conversion maximum occurs at the interchange between rich and lean feed when both components have the access to the noble metal surface. This is generally the case when an oscillating feed can improve the conversion: if one component has a stronger ability to reach the surface when the feed is lean, while another component occupies the surface when the feed becomes rich, an oscillating feed can help both components to reach the surface and improve the rate of conversion, see equation (8). The light-off of other components is not improved by oscillating the feed because the inhibiting species, C2 H 2 and NO on the noble metal surface, are not affected by oscillations and do not let other species access the surface.

The oscillations in the exhaust gas lambda value, induced by a standard control system, typically have an amplitude around 0.02 with a frequency in the range 0,5-2Hz. Table 2 compares the lightoff times of all components in the cases of steady, stoichiometric feed , and oscillating feeds. The influence of acetylene fraction in the total amount of hydrocarbons on the light-off times is given. Lightoff is defined as the moment when the conversion of a certain component reaches 50%. Oscillations clearly do not improve the light-off characteristics of carbon monoxide, nitric oxide and acetylene. Ethylene conversion, on the other hand, starts earlier when the inlet feed oscillates. The improvement is more profound with the decreased amount of acetylene in the feed. Further analysis is done with acetylene representing 10% of hydrocarbons , to emphasize the oscillating effects but keep the assumptions realistic. Table 2 also shows the influence of amplitude and frequency on the light-off time. The light-off characteristics are presented in figure 4. Conversions for the oscillating feeds have been calculated by averaging the inlet and outlet concentrations over one period of oscillations. Amplitude of around 0.02 proves to be optimal for the reaction ignition, but smaller amplitude of 0.01 is better to be applied after the conversion starts. Frequency is, interestingly, not a crucial factor because the ethylene light-off time does not differ greatly with changing frequencies. Low frequencies are less beneficial for the conversion. Note that with the amplitude of 0.05 conversions of CO and NO have difficulties to reach 100% because ceria with its oxygen storage capabilities does not have large enough capacity to buffer the oscillations.

Feed oscillations can improve the conversion generally only at lower temperatures by lowering the light-off temperature of a certain exhaust component. After reactions have been ignited the main dynamic effect is imposed by oxygen storage capability of ceria, and the control system should control the amount of stored oxygen on the ceria surface to maximize the conversion under dynamic operating conditions (Balenovic et al. , 2001).

The beneficial effect of the oscillating feed on the ethylene conversion can be explained by figure 5. Noble metal surface coverage at 4.4 cm from the reactor inlet and ethylene outlet concentration, in

4. CONCLUSIONS A mathematical model of a three-way catalytic converter based on elementary step kinetics was 317

Table 2. Light-off times [sJ under oscillating and steady (stoichiometric) inlet as a function of the amount of acetylene in the feed. 30%

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Hoebink , J .H.B.J., J .M.A . Harmsen , M . Balenovic, A.C .P.M . Backx and J.C. Schouten (2000). Automotive exhaust gas conver~ sion: from elementary step kinetics to prediction of emission dynamics. preprints CAPoC5 1 , 225-236. Impens, R . (1987). Automotive Traffic : Risks for the Environment . Stud. Surf. Se. Cata!. 30, 11-30. Koltsakis, e.c., P . A. Konstantinidis and A.M. Stamatelos (1997) . Development and application range of mathematical models for 3-way catalytic converters. App . eatal. B: Environmental 12 , 161 - 191. Kubo, S ., M . Yamamoto, Y . Kizaki, S . Yamazaki, T. Tanaka and K. Nakanishi (1993). Speciated Hydrocarbon Emissions of SI Engine During Cold Start and Warm-up. SAE Paper No . 932706. Mabilon, G., D . Durand and Ph . Courty (1995) . Inhibition of PostCombustion Catalysts by Alkynes : A Clue for Understanding their Behavior under Real Exhaust Conditions. Stud. Surf· Cata!. 96, 775-788 . NAG (1991). Fortran Library Manual, mar'k 15. Oxford. Nibbelke, R .H., A.J.L . Nievergeld. J.RB.J. Hoebink and G .B . Marin (1998) . Development of a Transient Kinetic Model for the CO Oxidation by 02 over a Pt/Rh/Ce02/..,.-AI203 threeway Catalyst. Appl. Catal. B: Environmental 19, 245-259 . Nievergeld , A.J.L., v. E .R. Selow, J.H.B.J. Hoebink and G .B . Marin (1997). Simulation of a catalytic converter of automotive exhaust gas under dynamic conditions . Stud. Surf. Sc . Catal. 109, 449-458. Oh , S.H. and J .C. Cavcndish (1982). Transient Modeling of 3-Way Catalytic Converters: Response to Step Changes in Feedstream Temperature as Related to Controlling Automobile Emissions. [nd . En9 . Chem. Prod . Res . Dev. 21 , 29-37. Oh, S.H., G.B. Fisher, J.E. Carpenter and D.W . Goodman (1986). Comparative Kinetic Studies of CO-02 and CO-NO Reactions over Single Crystal and Supported Rhodium Catalysts. J. Catal. 100, 360-376. Silverston, P.L . (1995). Automotive exhaust catalysis under periodic operation. Catalysis Today 25, 175-195 . Tagliaferri, S ., R. Koppel and A. Baiker (1999). Behavior of NonPromoted and Ceria-Promoted Pt/Rh and Pd/Rh Three-Way Catalysts under Steady State and Dynamic Operation of Hybrid Vehicles. Ind . Eng. Chem . Res. 38, 108-117. Tay1or, K .C. and R .M . Sinkevitch (1983) . Behavior of Automobile Exhaust Catalysis with Cycled Feedstreams . lnd. Eng. Chem. Prod. Res. Dev. 22, 45-51.

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Fig. 5. Effects leading to the ethylene conversion improvement with oscillating feed. Above outlet concentrations with stoichiometric and oscillating (A=O.02 ,f=O.67Hz) feed. Middle - surface coverage at 4.4 cm with stoichiometric feed. Below - surface coverage at the same position with oscillating feed . Note the horizontal scale. developed to analyze dynamic converter behavior and possible ways to improve the conversion at low temperatures . Light-off characteristics with steady and oscillating feeds have been analyzed, together with the corresponding effects on the noble metal surface. Feed oscillations can help to overcome some types of inhibiting processes and improve the light-off of certain components (here ethylene). The control system has to recognize in which conditions these oscillations are beneficial and apply them with proper amplitude and frequency when these conditions are satisfied.

Appendix A. KINETIC REACTION MECHANISM Elementary steps used for the converter simulation (* is an active site in noble metal, s an oxygen storage site on ceria):

4

5 6 7

5. REFERENCES

8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 25

Balenovic, M., A .C.P.M. Backx and J.H .B.J Hoebink (2001 ). On a Model-based Control of a Three-way Catalytic Converter. SAE Paper No. 2001-01-0937. BaLenovic, M., A.J .L . Nievergeld , J.H .B .J. Hoebink and A .C.P.M Backx (1999). Modeling of an Automotive Exhaust Gas Converter at Low Temperatures Aiming at Control Application .

SAE Paper No. 1999-01-3623. Evans , J.M., G.P. Ansell, C.M. Brown, J.P. Cox, D.S. Lafyati5 and P .J. Millington (1999) . Computer Simulation of the FTP Performance of 3-Way Catalysts . SAE Paper No . 1999-013472. Harmsen , J .M .A. , J .H . B .J . Hoehink and J.C. Schouten (1999 ) . Acetylene and carbon monoxide oxidation over a commercial exhaust gas catalyst : transient kineti.c experiments and mod~ elling. Chem. Eng. Sc. submitted. Harmsen , J.M.A. , J.H.B.J. Hoebink and J.C . Schouten (2000 ). 'ITansient kinetic modelling of the ethylene and carbon monoxide oxidation over a c o mmercial automotive exhaust gas catalyst. lnd . Eng. Chem . Res . 39 , 599-609.

318

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