Oxygen Storage Modeling in Three-Way Catalytic ... - ACS Publications

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Ind. Eng. Chem. Res. 2002, 41, 1152-1165

Oxygen Storage Modeling in Three-Way Catalytic Converters Dimitrios N. Tsinoglou and Grigorios C. Koltsakis* Laboratory of Applied Thermodynamics, Aristotle University at Thessaloniki, 540 06 Thessaloniki, Greece

James C. Peyton Jones Electrical & Computer Engineering, Villanova University, Villanova, Pennsylvania 19085

Mathematical modeling of three-way catalytic converter (3WCC) operation is increasingly employed in automotive catalyst and converter systems optimization. Oxygen storage is known to strongly affect catalytic converter operation under real world transient operating conditions. This paper presents a modeling approach embodying a comprehensive oxygen storage and release submodel into an existing 3WCC quasi-steady model. The dynamic model developed according to this approach is validated against previously published experimental data. The model sensitivity to each of the oxygen storage parameters is examined. The results of this investigation encourage further application of mathematical modeling in areas such as air-to-fuel (A/F) ratio control strategy optimization, which lie beyond the scope of traditional kinetic 3WCC models. 1. Introduction The three-way catalytic converter (3WCC) is an indispensable device for the reduction of CO, HC, and NOx emissions of gasoline engines. For steady-state operating conditions, the optimum operating point is stoichiometric, and engine management systems are intended to keep the engine operating as close to stoichiometry as possible. However, under real world driving conditions, the catalytic converter operates at highly transient conditions. The temperature, flow rate, and composition of the exhaust gas flowing through the converter honeycomb monolith change significantly according to the driving mode, with a typical time scale of several seconds. At the same time, the closed-loop control of the fuel management system induces transients of the feed gas composition, with a typical time scale of less than a second. The oxygen sensor is used as a feedback control signal for the fuel injection system in order to supply the engine cylinders with a stoichiometric fuel-air mixture. Under real world driving conditions, the air-to-fuel (A/F) ratio actually oscillates around the stoichiometric value because of the system’s response lag.1 Moreover, fuel cutoff phases or engine misfire causes much more extreme deviations from stoichiometric operation. The behavior of the 3WCC under such dynamic conditions is, therefore, of high practical interest. Since the early 1980s, it has been recognized that three-way catalyst efficiency is significantly affected when the composition of the feed gas is perturbed with different amplitudes and frequencies,2-6 and even more recent publications are in agreement with this observation.7,8 This behavior is mainly attributed to the ability of some washcoat components to be periodically oxidized and reduced depending on the exhaust gas redox environ* To whom correspondence should be addressed. Tel: +30-31-996066. Fax: +30-31-996019. E-mail: greg@ antiopi.meng.auth.gr.

ment. The most important of these components is cerium, which is added in the washcoat as a stabilizer and an oxygen storage component. The role of cerium has been reviewed by Fisher et al.9 The advent of stricter U.S. and European emission standards has increased the need for reliable 3WCC models supporting the design of demanding exhaust after-treatment systems. A number of mathematical models working in this direction have already been presented in the literature and employed in optimization procedures.10-12 The most recent models include submodels to describe oxygen storage phenomena. Meanwhile, simplified “storagebased” models for on-board use have been developed, assuming that catalyst behavior is dominated by the dynamics of oxygen storage.13 In this work, the potential for modeling catalyst dynamic operation using a “quasi-steady” model, equipped with a comprehensive oxygen storage and release submodel, is investigated. A series of simple published experimental tests are employed to support the validity of the approach and to tune the basic kinetic parameters involved. Having established the mathematical model, the effect of the use of the oxygen storage submodel is highlighted by modifying some of its tunable kinetic constants. Finally, the influence of the mean value of the A/F modulation on the tailpipe emissions is investigated, in a first attempt to apply 3WCC modeling to optimize the A/F control strategy. 2. Transient 3WCC Model 2.1. Model Description. As mentioned in the Introduction, a previously developed 3WCC mathematical model will be extended and equipped with an oxygen storage and release submodel. A detailed description of the basic model can be found in a previous authors’

10.1021/ie010576c CCC: $22.00 © 2002 American Chemical Society Published on Web 01/30/2002

Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 1153

work.14 The basic features of the quasi-steady mathematical model can be summarized as follows: (i) The convective heat and mass transfer from the exhaust gas to the catalytic surface is computed. A “film approach” is adopted by employing mean bulk values for the gas phase and solid-gas interface values for the solid-phase species concentrations. (ii) The heterogeneous chemical reactions taking place on the catalytic surface are taken into account based on Langmuir-Hinshelwood (L-H) based rate expressions. Surface adsorption/desorption and pore diffusion phenomena are “lumped” in the kinetic rate expressions. (iii) The two-dimensional transient temperature field in the cylindrical converter is computed by taking into account the heat conduction in the substrate, the surrounding insulation, and the heat losses to the surroundings via convection and radiation. Detailed formulations of the energy and mass balance equations, as well as the solution procedure followed, are described in detail elsewhere.14 As with all quasisteady models, the computation of the species concentrations is based on the equation of the diffusion and the reaction rates for each species. The reaction rates are nonlinear functions of the local temperature and composition at the gas-solid interface. The reactions and kinetic expressions used in the present model are listed in the Appendix. The rates of reaction and mass transfer to the catalytic surface are always in quasi-steady state, implying that there are no species accumulation phenomena on the solid catalytic surface. This assumption is realistic for steady-state operation but not necessarily for operation under highly transient temperature and composition conditions. To account for the effects of transient adsorption-desorption and heterogeneous reaction phenomena, the kinetic model should include the detailed computation of the time-dependent surface coverage of each species on the active sites. Such models have been presented by a number of researchers15,16 for the case of a one-dimensional isothermal reactor using simple gas mixtures (with up to three reacting species). These models are aimed at studying the effects of the oscillatory equivalence ratio on the catalyst performance. However, the number of kinetic parameters needed for such a task are numerous and very difficult to estimate. In our model, the quasi-steady approach is retained, while highly transient effects, which are probably the most dominant for practical application cases are taken into account through the use of an oxygen storage and release submodel. This aims to retain an acceptable degree of model simplicity, and thus flexibility, while at the same time profiting from the available experience regarding L-H kinetic rate expressions for three-way catalysts. 2.2. Oxygen Storage Submodel. The washcoat component that seems to play the most important role in dynamic oxidation-reduction phenomena is cerium. Cerium is normally present in high quantities in the washcoat (order of 30% by weight, i.e., 1000 g/ft3 or 35.31 kg/m3) and has multiple functions: stabilization of the washcoat layer, improvement of thermal resistance, enhancement of precious metal catalytic activity, and operation as an oxygen storage component. The function of cerium as an oxygen storage component is based on its ability to form both 3- and 4-valent

oxides.17 Under net oxidizing conditions, the following cerium oxide reaction is the most representative for the realization of oxygen storage:

Ce2O3 + 1/2O2 f 2CeO2

(1)

This reaction represents the storage of an oxygen atom by increasing the oxidation state of Ce2O3. Apart from the direct oxidation of Ce2O3 by O2, previous studies18,19 have shown that NO may also oxidize Ce2O3. This is described by reaction (2) and has been included in the oxygen storage submodel. On the other hand, CeO2 may

Ce2O3 + NO f 2CeO2 + 1/2N2

(2)

function as an oxidizing agent of the exhaust gas species under net reducing conditions according to the following reactions:

CO + 2CeO2 f Ce2O3 + CO2

(3)

H2 + 2CeO2 f Ce2O3 + H2O

(4)

(

C x Hy + 2 x +

y CeO2 f 2

)

(x + 2y)Ce O 2

3

y + xCO + H2O (5) 2

Each of the above reactions denotes the release of an oxygen atom, which is made available to react with a reducing species of the exhaust gas (CO or HC). We define the auxiliary number ψ as

ψ)

2 × mol of CeO2 2 × mol of CeO2 + mol of Ce2O3

(6)

which can be considered as the fractional extent of oxidation of the oxygen storage component. The value of ι is changing continuously during transient converter operation and is affected by the relative reaction rates of reactions (1)-(5). The rates of reactions (1) and (2) (oxidation reactions) are expected to be proportional to the available active sites of “reduced-state” cerium oxides, which is expressed by the factor Ψcap(1 - ψ). The rate should also be dependent on the prevailing oxygen concentration at the gas-solid interface. A linear dependence on O2 concentration is considered a realistic assumption. The oxidation reaction rates are thus

Rox,O2 ) kox,O2(T) cs,O2Ψcap(1 - ψ)

(7)

Rox,NO ) kox,NO(T) cs,NOΨcap(1 - ψ)

(8)

Rox ) Rox,O2 + Rox,NO

(9)

where kox is a characteristic rate constant, which exhibits an Arrhenius-type dependence on temperature:

kox,O2 ) Aox,O2e-Eox/RT

(10)

kox,NO ) Aox,NOe-Eox/RT

(11)

Analogous considerations are made for the reduction reaction rates. Here, the rates are expected to be directly proportional to Ψcapψ and should exhibit a dependence

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Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002

on the local CO, H2, and HC concentrations, respectively:

Rred,CO ) kred,CO(T) cCOΨcapψ

(12)

Rred,H2 ) kred,H2(T) cH2Ψcapψ

(13)

Rred,HC ) kred,HC(T) cHCΨcapψ

(14)

Rred ) Rred,CO + Rred,H2 + Rred,HC

(15)

kred,CO ) Ared,COe-Ered/RT

(16)

kred,H2 ) kred,CO

(17)

kred,HC ) Ared,HCe-Ered/RT

(18)

with

The variation of the oxidation extent ψ should be computed at each location by the following differential equation:

1 dψ ) (R - Rred) dt Ψcap ox

(19)

which is solved numerically by the implicit Euler method for each node, along the catalyst channels. 3. Experimental Facility To validate the model, previously published8 experimental findings were used. A Rover K series, 1.8 L, 4 cylinder, multipoint injection petroleum engine was used to provide the exhaust gases. The engine was connected to a dynamometer and controlled through its management system. The latter was modified so that a regular sequence of step changes to the engine fueling, between two set levels, could be induced, thus providing corresponding steps in the A/F. The exhaust gases passed through a 3WCC (60 g/ft3 or 2.12 kg/m3 loading, 8:1 Pd/Rh composition, aged to 80 h, 850 °C lean spike), positioned to simulate underfloor operation in a vehicle. Exhaust gas component concentrations (CO, CO2, and NO) were recorded before and after the converter by using fast-response gas analyzers of 30 ms rise or better. The HC components, before and after the converter, were measured using a flame ionization detector with a rise time of 1 ms. A/F measurements were also taken, upstream and downstream of the converter, using UEGO sensors. Temperature before the catalyst was measured using a K-type thermocouple mounted 1 in. before the front surface of the brick. The inner temperature was measured at the middle of the catalytic converter by a thermocouple inserted from the rear of the brick. Start-up procedures were followed to allow the engine and the converter to reach thermal equilibrium. Measurements were taken after allowing at least 60 s to precondition the catalyst, thus enabling it to reach an equilibrium state. For the results reported here, the engine operating condition were set at 4000 rpm speed and 50 kPa inlet manifold pressure. 4. Results and Discussion 4.1. Model Validation. In this section, we examine the ability of the dynamic model to simulate transient

phenomena related to oxygen storage during step feed gas composition changes. For this purpose, previously published experimental findings are compared with model predictions. To tune the tunable parameters of the mathematical model, we begin by using kinetic constants of similar catalysts from our database. Then, a try-and-error approach is followed to fine tune some of these constants for the specific catalyst formulation: the experimental tests are simulated, using different values for the reaction kinetics constants, until good agreement between experimental and simulation results is achieved. Simulations were performed on an IBMPC compatible machine, equipped with a Pentium III processor operating at 500 MHz. The computational grid consisted of 15 axial and 5 radial nodes for the monolith, and a time step of 0.1 s was used. Simulation time was approximately 280 s for a test case of 240 s duration. Figure 1 displays the experimental and calculated results of a rich-to-lean step change with a long (120 s) cycling period. Precatalyst concentrations are indicated as “pre”, measured postcatalyst concentrations are indicated as “post exp.”, and calculated postcatalyst concentrations are indicated as “post-calc”. “Stored O2” represents the oxygen stored on the catalyst as a fraction of the total oxygen storage capacity (OSC). The temperatures referred to as “inlet” and “mid exp.” are measured at converter inlet and at the middle of the converter, respectively, while the temperature indicated as “mid calc.” is calculated at the middle of the converter. λ is defined as the ratio of the A/F versus the stoichiometric A/F of the mixture. Figure 2 presents the respective results for a step change experiment across stoichiometric with a shorter cycling period (2 s) and lean preconditioning, while in Figure 3, rich preconditioning is performed. The legend key is similar to the one in Figure 1. The predicted amount of oxygen stored on the catalyst is also plotted as a fraction of the maximum OSC. The model returns realistic results very close to the experimental values for the entire range of simulated experiments. The difference between inlet and outlet λ values in the rich region of Figure 1 is not expected and is most probably attributed to rear UEGO sensor distortion, possibly by hydrogen. Moreover, shortly after the rich-to-lean transition, the rear UEGO sensor returns a slightly rich signal, which is neither commensurate with the near-zero concentrations of reducing species recorded on other data channels nor predicted by the model. This indicates that the actual λ value is about 0.8-1% higher than the UEGO sensor signal in this region. It is also noticeable that the analyzers show a slow rise in outlet HC and NO concentrations during the rich phase, which is not predicted by the model. The reason behind this is not clear because both the catalyst temperature and the inlet concentrations are almost constant in this area. Although similar phenomena have been previously recorded and attributed to sulfur poisoning,20 this point still requires further investigation. NO conversion is slightly overpredicted after the rich-to-lean transition. This is due to the simplified oxygen storage scheme, which overpredicts the NO reaction with Ce2O3 in that region. The simulation results for the test with the short cycling period and lean preconditioning (Figure 2) are also in close agreement with the experimental data. The rise in CO and HC emissions recorded in the experiment and predicted by the simulation is caused by the


Figure 1. Step changes across stoichiometric (120 s cycling period).

reduction in the amount of stored oxygen inside the catalyst, as is seen on the first plot. The gradual “emptying” of oxygen stored on the catalyst occurs because the mean value of the A/F oscillation is slightly shifted toward the rich side. The simulation is also successful in the case where the preconditioning is rich (Figure 3). There is a small difference between steady-state measured and predicted CO emissions, although the predicted values are in agreement with the respective steady-state-rich phase of Figure 1. It is worth mentioning that the influence of the pretreatment is another transient phenomenon, which

lasts until the mean stored oxygen level reaches a constant value. In the experiment with the lean pretreatment, this occurs approximately 30 s after the oscillation begins. After that point, the catalytic converter operation in both experiments is identical. The above results indicate that it is possible to simulate successfully catalytic converter operation under dynamic conditions using a “traditional” quasi-static reaction kinetics scheme with an embedded oxygen storage and release submodel. 4.2. Sensitivity Analysis. The role of oxygen storage in the above simulations is investigated below. In this

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Figure 2. Step changes across stoichiometric with lean pretreatment (2 s cycling period).

paragraph the model sensitivity in the oxygen storage parameters is examined. 4.2.1. Role of Catalyst OSC. The effect of different OSC values is of high practical interest not only for reasons of catalytic converter composition optimization but also because catalyst OSC reduces as a result of

thermal aging.21 The experiments described above are simulated with three different values of OSC: the “reference” value, used in the model validation, an increased OSC value by 50%, and a reduced OSC value by 50%. The simulation results for each of these cases are indicated on the plots as “post-100% OSC”, “post-


Figure 3. Step changes across stoichiometric with rich pretreatment (2 s cycling period).

50% OSC”, and “post-150% OSC”, respectively. For the experiment with the long cycling period, the results are plotted in Figure 4. The plots show that, for a rich-tolean or a lean-to-rich transition, higher values of OSC increase the time period after the transition, during

which the conditions inside the catalyst approach stoichiometric. As a result, after a lean-to-rich transition, CO and HC conversion remains high for a longer time because of CO and HC oxidation by CeO2. Similarly, after a rich-to-lean transition, the NO efficiency remains

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Figure 4. Effect of catalyst OSC on catalyst operation during step changes across stoichiometric (120 s cycling period).

high for a longer period of time because of NO reduction by Ce2O3. Another interesting remark is that the temperature peak observed after the rich-to-lean transition is significantly sharper for higher values of OSC. The reason is that the Ce2O3 oxidation reaction (eq 1) is exothermal. Increasing the OSC increases the amount of Ce2O3 to be oxidized, thus increasing the heat generated after a rich-to-lean transition. The effect of different OSC values on the results obtained from the faster cycling experiments is perhaps of more practical interest because these are more representative of real world operating conditions. Figure 5 illustrates the effect of three different OSC values, as above, in the experiment with 2 s cycling period and lean preconditioning. It can be seen that, as the OSC

decreases, the amount of stored oxygen depletes more rapidly. As a consequence, the peaks in CO and HC during the rich phases of the oscillation develop sooner, thus resulting in higher overall CO and HC emissions. Similar simulation experiments were conducted for the case where the preconditioning is rich (as in Figure 3), but the value of OSC did not seem to affect the results, which are therefore not shown; there is no stored oxygen at the beginning of the A/F oscillation and, because the mean value of the oscillation is slightly rich, the mean level of stored oxygen does not increase, irrespective of the total OSC. 4.2.2. Role of Ce2O3 Oxidation by NO. As previously mentioned, the reaction usually considered responsible for Ce2O3 oxidation is the direct oxidation by


Figure 5. Effect of catalyst OSC on catalyst operation during step changes across stoichiometric with lean pretreatment (2 s cycling period).

O2. However, NO may also oxidize Ce2O3, thus providing a mechanism for NO reduction under lean conditions, which can be particularly important under real world

driving conditions. To assess the effect of NO reduction by Ce2O3, the step change experiments have been simulated without taking into account this reaction. The

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Figure 6. Effect of Ce2O3 oxidation by NO on NO conversion for the slow and fast A/F oscillation experiments.

NO conversion plots for each of the experiments are presented in Figure 6, in comparison with the reference results presented in the model validation section. In all three plots, it can be seen that NO reaction with Ce2O3 has a very small effect under steady-state conditions. However, under dynamic conditions the importance increases. The experiment with the long cycling period shows that the increased NO conversion following a rich-to-lean transition is attributable to NO reaction with Ce2O3. This reaction is favored by the strongly reduced state of the ceria after the prolonged period of rich operation. The relative contribution of NO reaction with Ce2O3 seems to be of even greater importance for faster A/F

oscillations. Although at steady-state lean operating conditions there is no NO conversion, the conversion during the lean phase of the fast A/F oscillation appears to be total. NO reduction by Ce2O3 enables total NO conversion during the lean phase of the oscillation. Ignoring this reaction causes NO conversion during the lean phase of the oscillation to be practically zero. The results presented in this section prove that oxygen storage and release phenomena play an important role under dynamic catalyst operating conditions; their correct prediction is, therefore, essential in order to simulate the operation of a 3WCC. 4.3. Parametric Study: Effect of the Oscillation Mean Value. To assess the effect of the mean value of


Figure 7. Simulation of A/F step changes with lean pretreatment and different values of oscillation mean value.

the A/F oscillation in the catalytic converter operation, simulations with three different mean values have been

performed: one at stoichiometric, one slightly lean (λ ) 1.01), and one slightly rich (λ ) 0.99). The cycling

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Figure 8. Simulation of A/F step changes with rich pretreatment and different values of oscillation mean value.

period was 2 s, as in the experiments previously presented, and a 6% ((3%) oscillation amplitude was

used. The value of λ was modified by adjusting the oxygen content of the exhaust gas, assuming that the


concentrations of the other species are the same as those in the experimental tests. Figure 7 shows the results of such an oscillation with lean pretreatment, while in Figure 8 a rich pretreatment is assumed. The tailpipe concentration curves referring to the stoichiometric, slightly lean, and slightly rich mean values are indicated as “post-1”, “post-1.01”, and “post-0.99”, respectively. The results show that HC conversion is almost unaffected by the oscillation mean value, regardless of the pretreatment. NO conversion deteriorates when the mean value is lean because there are less reducing species available for NO reduction. The deterioration is especially bad in the case of a lean pretreatment, which results in a high amount of stored oxygen. CO conversion, on the other hand, is worse when the mean value is rich shifted because there are less oxidizing species available; this effect is less severe when the pretreatment is lean because oxidized cerium is then able to compensate for the lack of oxidizing species by releasing the oxygen it stores. Based on the above observations, the optimum target value for the λ ratio appears to be stoichiometric. In real world driving conditions, a slightly rich shift could be applied without severe deterioration in the catalyst performance, and this would favor NOx conversion. At the same time, the possible fuel cuts encountered during gear shifting or decelerations would increase the stored oxygen level, thus compensating for the lack of oxidizing species under close-loop λ control operation. According to the same rationale, a lean shift would result in a constantly reduced NO conversion, which would not be acceptable, taking into account the tailpipe emission targets. 5. Conclusions The quasi-steady models presented in the past are not able sufficiently to simulate 3WCC operation under highly transient conditions. In this work, a quasi-steady model, equipped with a comprehensive oxygen storage and release submodel, is presented. The assumed oxygen storage scheme takes into account ceria oxidation by O2 and NO and ceria reduction by CO, HC, and H2. The model was successfully validated against a series of experimental tests, thereby demonstrating that the proposed model structure can capture a wide range of the dynamic phenomena encountered in a 3WCC under real world driving conditions. The validated model was then used as a simulation engine in order to investigate the sensitivity of 3WCC operation to a variety of reactions and input variables. When the mechanism by which ceria is oxidized by NO was disabled, for example, it was demonstrated that this reaction does indeed make a significant contribution to the dynamic response of the catalyst, particularly on rich-to-lean transitions. The optimum mean value of the λ oscillation was shown to lie at stoichiometry, though slightly rich conditions interspersed with short lean phases to reoxidize ceria, such as fuel cuts, are also likely to be very favorable. These results indicate that mathematical modeling is a promising tool for λ control system optimization. Appendix Reactions considered in the mathematical model are as follows:

1. CO + 1/2O2 f CO2 2. H2 + 1/2O2 f H2O

( 4y)O f xCO + 2yH O (fast HC) y y 4. C H + (x + )O f xCO + H O (slow HC) 4 2 y 5. C H + xH Of xCO + (x + )H (fast HC) 2 y 6. C H + xH O f xCO + (x + )H (slow HC) 2 3. CxHy + x + x

y

x

y

2

x

y

2

2

2

2

2

2

2

2

2

7. CO + NO f CO2 + 1/2N2 8. CO + 2NO f CO2 + N2O 9. CO + N2O f CO2 + N2 10. H2 + NO f H2O + 1/2N2 11. CO + H2O f CO2 + H2 The rate expressions employed in the above reactions are the following: reaction

rate expression

(1) CO/O2

R1 ) (2) H2/O2

R2 ) (3) CxHy/O2 (fast)

R3 )

A1e-E1/RTcCOcO2 G2(Ts,cs) A2e-E2/RTcH2cO2 G2(Ts,cs) A3e-E3/RTcCxHycO2 G1(Ts,cs)

(4) CxHy/O2 (slow)

R4 ) (5) CxHy/H2O (fast)

R5 ) (6) CxHy/H2O (slow)

A4e-E4/RTcCxHycO2 G1(Ts,cs) G3(Ts,cs) A5e-E5/RTcCxHycH2O Eq5 G1(Ts,cs)

A6e-E6/RTcCxHycH2O Eq6 R6 ) G1(Ts,cs)

(7) CO/NO

R7 ) (8) CO/2NO

R8 ) (9) CO/N2O

R9 )

A7e-E7/RTcCOcNO G6(Ts,cs) A8e-E8/RTcCOcNO G6(Ts,cs) A9e-E9/RTcCOcN2O

(10) H2/NO

R10 ) (11) CO/H2O

R11 )

G4(Ts,cs) A10e-E10/RTcH2cNO G6(Ts,cs) A11e-E11/RTcCOcH2O Eq11 G2(Ts,cs)

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The reaction rate constants are the following: reaction

E [J/mol]

A [mol‚K/(m3‚s)]

(1) CO/O2 (2) H2/O2 (3) CxHy/O2 (fast HC) (4) CxHy/O2 (slow HC) (5) CxHy/H2O (fast HC) (6) CxHy/H2O (slow HC) (7) CO/NO (8) CO/2NO (9) CO/N2O (10) H2/NO (11) CO/H2O

100 000 100 000 100 000 120 000 75 000 65 000 80 000 80 000 120 000 85 000 50 000

1 × 1020 4 × 1020 2 × 1019 1 × 1021 2 × 1013 1 × 1013 4 × 1015 8 × 1015 7 × 1016 5 × 1015 1 × 1014

with the following expressions accounting for the inhibition terms:

G1 ) Ts(1 + K1cCO + K2cHC1)2(1 + K3cCO2cHC12) × (1 + K4cNO0.7) G2 ) Ts(1 + K5cCO + K6cHC)2(1 + K7cCO2cHC2) × (1 + K8cNO0.7) G3 ) (1 + K9cO2)

1.5

G4 ) 1 + K10cCO G6 ) Ts(1 + K11cCO + K12cHC)2(1 + K13cCO2cHC2) × (1 + K14cNO0.7) where

cHC1 ) 0.25cHC,slow + cHC,fast cHC ) cHC,slow + cHC,fast with

Ki ) Aie-Ei/RT where Ai and Ei take the values shown below: Ki K1 K2 K3 K4 K5 K6 K7

Ai [mol‚K/(m3‚s)] Ei [J/mol] -7990 -3000 -96534 31036 -7990 -3000 -96534

65.5 6.43 × 103 3.98 4.79 × 105 400 2.57 × 104 3.98

Ki K8 K9 K10 K11 K12 K13 K14

Ai [mol‚K/(m3‚s)] Ei [J/mol] 4.79 × 105 90000 1500 400 200 3.98 2·105

31036 0 -65 -7990 -3000 -96534 31036

To account for the chemical equilibrium of the watergas and the steam reforming reaction, an additional factor is considered in the respective reaction rate expressions:

Eq5,6 ) 1 -

cs,CO2xcs,H2x+0.5y cCxHycH2OxKp(T)

Eq11 ) 1 -

cs,CO2cs,H2 cCOcH2OKp(T)

Nomenclature Variables/Acronyms 3WCC ) three-way catalytic converter

A ) preexponential factor, mol‚K/m3‚s A/F ) air-to-fuel ratio c ) species concentration, mole fraction E ) activation energy, J/mol G ) inhibition factor, K HC ) hydrocarbon kox ) oxidation rate constant, mol/m3‚s kred ) reduction rate constant, mol/m3‚s K ) adsorption equilibrium constant Kp ) chemical equilibrium constant OSC ) oxygen storage capacity R ) reaction rate or gas constant, mol/m3‚s or J/mol‚K t ) time, s T ) temperature, K UEGO ) universal exhaust gas oxygen sensor x ) carbon atoms in the hydrocarbon molecule y ) hydrogen atoms in the hydrocarbon molecule Greek Letters ψ ) oxidation fraction Ψcap ) oxygen storage capacity, mol/m3

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Received for review July 5, 2001 Revised manuscript received October 30, 2001 Accepted November 21, 2001 IE010576C

Oxygen Storage Modeling in Three-Way Catalytic ... - ACS Publications

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