Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Kočí, Petr; Kubı́ček, Milan; Marek, M.

doi:10.1021/ie034137k

Cited by 71 publications

(9 citation statements)

References 19 publications

(31 reference statements)

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“…The importance of the dissociation of adsorbed NO, and the formation of N 2 O by the reaction between adsorbed NO and adsorbed N, is indicated. Kočí et al 12 developed a detailed microkinetic model based on the results of Harmsen et al 11. In their mechanism, NO first reduces to N 2 O, which acts as an intermediate in further reduction to N 2 .…”

Section: The No–co Reaction On Ptmentioning

confidence: 99%

Microkinetic model for NO–CO reaction: Model reduction

Ravikeerthi

Thyagarajan

Kaisare

et al. 2012

Int J of Chemical Kinetics

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The objective of this work is to elucidate controlling mechanisms in NO x reduction, develop reduced-order reaction models, and analyze the reactor performance using the reduced-order reaction model for the NO-CO reaction. We start with the microkinetic model on platinum, which describes the mechanism of catalytic reduction of NO by CO. The formation of the main product N 2 and the competitive formation of the side product N 2 O are accounted for in the microkinetic model. Sensitivity and reaction path analysis have been carried out to determine the rate-limiting steps as well as the most abundant reactive intermediates in the system. Owing to the differences between system performance at high and low temperatures, the model has been analyzed in detail in these temperature regimes. Two closed-form expressions, corresponding to the two global reactions involved, have been derived. The characteristic features of the microkinetic model such as the sharp increase in NO conversion and the selectivity to N 2 O are captured well by the reduced model. The reduced-order model has been extended to the rhodium catalyst as well.

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Section: The No–co Reaction On Ptmentioning

confidence: 99%

Microkinetic model for NO–CO reaction: Model reduction

Ravikeerthi

Thyagarajan

Kaisare

et al. 2012

Int J of Chemical Kinetics

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“…12,[43][44][45][46][47] This begs the question as to whether ADM is applicable to such problems. The increase in the number of differential equations is primarily reflected in A (i,n) (y B(t)).…”

Section: Articlementioning

confidence: 99%

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Younker

2011

Ind. Eng. Chem. Res.

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Chemists are frequently interested in rate equations, which are first-order differential equations. Numerical integration of these equations allows the researcher to accurately predict the concentrations of chemical species at any time given the initial conditions. Explicit Runge-Kutta (RK) integration is widely used for solving the rate equations. In this article, Adomian decomposition methods (ADM) are used to obtain the solutions of chemical rate equations. The Adomian method outlined here outperforms high-order RK routines in the arenas of accuracy and truncation error. Additionally, four modifications are introduced that place the Adomian integration on par with RK in terms of speed (a primary reason for which Adomian decomposition methods are currently underemployed). The inclusion of up to the fifth term in the Adomian expansion gives a truncation error of order O(h 10 ). The method as presented yields solutions which are step-size independent in the nonstiff regime. The problem of rapid polynomial divergence is addressed through discretizing the time axis. Performance of the ADM method against an implicit algorithm is also given. ' INTRODUCTIONThe construction of a chemical mechanism is one of the first steps a chemist takes following the discovery of a novel reaction. Many tools are employed in order to determine the sequence of intermediates and the rates at which they change. The results of these studies can be succinctly expressed as coupled differential equations, the solutions of which yield the concentrations of the experimentally observed reactants at all times of interest. To uncover the desired rate constants, chemists and biochemists frequently analyze reactions under limiting conditions. These pseudo-first-order, steady-state, 1 and quasi-steady-state kinetics 2 simplify the differential equations through elimination of one or more degrees of freedom. When these conditions cannot be met, kinetic inversion or global analysis is employed to determine the rates. 3-14 These nonlinear regression techniques require solutions of the coupled chemical rate equations. Symbolic integration of the equations can be difficult and is, in most cases, impossible. 5-7 Thus, numerical integration is necessary. One popular numerical integration method was originally proposed in 1895 by Runge and later expanded by Kutta. 15,16 Fourth-order (RK4) and fourth-/fifth-order adaptive step size (RKF45) RungeKutta routines are frequently used to approximate ordinary differential equations as initial-value problems (IVP), 17,18 of which the rate equations are prime examples. 3,8,11 An alternative approach for solving differential equations was proposed by Adomian in the 1980s. His solution involves decomposing the nonlinear terms in the differential equation(s) into a series of polynomials. 19,20 The integration of this infinite series of polynomials, under known initial or boundary conditions, is called the Adomian Decomposition Method (ADM). 21 Truncation of the series yields an analytic approximation to the solution. Th...

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“…The wall of the individual channel is coated with a porous, catalytically active layer (i.e., washcoat) of uniform thickness and it is also assumed that the washcoat is sufficiently thin (typically 50 μm or less) so that its curvature is unimportant and diffusion resistance within the washcoat can be neglected. 23 The governing model equations derived under these assumptions are given below:…”

Section: ' Mathematical Modelmentioning

confidence: 99%

Electrically Heated Catalysts for Hybrid Applications: Mathematical Modeling and Analysis

Ramanathan

Bissett

2011

Ind. Eng. Chem. Res.

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In view of the significant cold-start hydrocarbon emission reduction potential of the electrically heated converter (EHC) technology for conventional stoichiometric gasoline engines, there is considerable interest in better understanding of the thermal and emission performance characteristics and optimizing the design/operating aspects of an EHC system as applied to plugin hybrid electric vehicles (PHEVs) and extended-range electric vehicles (EREVs). The application of the EHC technology to these hybrid vehicles is unique in that catalyst cooling to below reaction temperatures can occur during extended periods of electric vehicle driving (with engine off) or during intermittent engine stops/starts, and the EHC can be heated prior to engine start (preheating) for enhanced emission reduction. In this study, the design aspects and heating strategies of an EHC system have been analyzed using a transient monolith converter model which accounts for the resistive heating of an inert metalÀsubstrate monolith placed ahead of a conventional three-way catalytic converter. The results of model calculations presented here quantify the effects of various heating strategies on the emission performance of hybrid vehicles during the first 250 s of the Federal Test Procedure (FTP) drive cycle. It is also shown that there exists an optimum electric heater volume for cases with either preheating only or a combination of pre-and postheating. For the latter case, the emission performance can be further improved by adding a smaller electric heater (downstream of the existing heater) which is capable of heating the gas rapidly and efficiently during postheating. ' INTRODUCTIONAs part of the continuing drive toward near-zero vehicle emissions, another round of stricter exhaust emission regulations is expected to be in place by the middle of this decade, including the fleet-average SULEV (super ultra-low emission vehicle) emission requirement in California starting in 2014. The SULEV standards are very stringent particularly with respect to allowed tailpipe hydrocarbon (HC) emission levels, mandating a 9-fold reduction from the current Tier 2 Bin 5 HC standard. Since a large fraction (typically >80% for late model gasoline vehicles) of the total exhaust emissions of HC and CO occurs during the first few minutes after an engine cold start, it is crucial to further shorten the time required for an exhaust catalyst to reach its operating temperature in order to meet the stringent future emission control requirements. Strategies for reducing cold-start emissions include electrically heated catalysts, 1À10 fuel-burner heated catalysts, 11,12 hydrocarbon adsorbers, 13À17 exhaust gas ignitors, 18 and energy storage devices. 19,20 Electrically heated converter (EHC) technology is designed to heat the incoming exhaust gas via resistive heating of a metal-substrate monolith catalyst (mounted ahead of a conventional ceramic-substrate catalytic converter) using electrical power drawn from a vehicle battery or alternator. This technology has been exte...

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Modeling of Three-Way-Catalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat

Cited by 71 publications

References 19 publications

Microkinetic model for NO–CO reaction: Model reduction

Microkinetic model for NO–CO reaction: Model reduction

Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

Electrically Heated Catalysts for Hybrid Applications: Mathematical Modeling and Analysis

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