A low-dimensional model for describing the oxygen storage capacity and transient behavior of a three-way catalytic converter

Published on May 7, 2012in Chemical Engineering Science3.871
· DOI :10.1016/J.CES.2011.12.001
Pankaj Kumar5
Estimated H-index: 5
(UH: University of Houston),
Imad Hassan Makki7
Estimated H-index: 7
(Ford Motor Company)
+ 3 AuthorsVemuri Balakotaiah53
Estimated H-index: 53
(UH: University of Houston)
Sources
Abstract
Abstract We propose a low-dimensional model of the three-way catalytic converter (TWC) that would be appropriate for real-time fueling control and TWC diagnostics in automotive applications. The model reduction is achieved by approximating the transverse gradients using multiple concentration modes and the concepts of internal and external mass transfer coefficients, spatial averaging over the axial length and simplified chemistry by lumping the oxidants and the reductants. The reduced order model consists of seven ordinary differential equations and captures the essential features of a TWC providing estimates of the oxidant and reductant emissions, fractional oxidation state (FOS) and total oxygen storage capacity (TOSC). The model performance is tested and validated using data on actual vehicle emissions resulting in good agreement for both green and aged catalysts including cold-start performance. We also propose a simple catalyst aging model that can be used to update the oxygen storage capacity in real time so as to capture the change in the kinetic parameters with aging. Catalyst aging is accounted via the update of a single scalar parameter in the model. The computational efficiency and the ability of the model to predict FOS and TOSC make it a novel tool for real-time fueling control to minimize emissions and diagnostics of catalyst aging.
📖 Papers frequently viewed together
27 Citations
112 Citations
30 Citations
References34
Newest
#1Saurabh Y. Joshi (UH: University of Houston)H-Index: 14
#2Yongjie Ren (UH: University of Houston)H-Index: 6
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 4 authors...
Abstract Recently developed criteria [S.Y. Joshi, M.P. Harold, V. Balakotaiah, Chemical Engineering Science 65 (2010) 1729–1747] are used to characterize the various controlling regimes (kinetic, pore diffusion and mass transfer controlled) during H2 oxidation on Pt/Al2O3 monolithic catalyst. The hydrogen conversion was measured over a wide range of temperatures and space velocities. Experiments at typical space velocities (104–105 h−1) revealed that complete conversion can be achieved at ambien...
29 CitationsSource
#1Saurabh Y. Joshi (UH: University of Houston)H-Index: 14
#2Michael P. Harold (UH: University of Houston)H-Index: 52
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
Abstract We utilize the recently developed concept of internal or intraphase mass transfer coefficient to simplify the problem of diffusion and reaction in more than one spatial dimension for a washcoated monolith of arbitrary shape. We determine the dependence of the dimensionless internal mass transfer coefficient ( Sh i ) on washcoat and channel geometric shapes, reaction kinetics, catalyst loading and activity profile. It is also reasoned that the concept of intraphase transfer coefficient i...
64 CitationsSource
#1Roman Möller (ETH Zurich)H-Index: 1
#2Martin Votsmeier (Umicore)H-Index: 26
Last. Jürgen Gieshoff (Umicore)H-Index: 19
view all 5 authors...
Abstract Existing reaction mechanisms for three-way catalysts ignore the oxidation of Ce 2 O 3 by H 2 O or CO 2 and therefore treat oxygen storage on ceria as a kinetically controlled non-equilibrium process. Such mechanisms do not correctly reproduce a number of practically important phenomena. Based on transient concentration step experiments, this paper demonstrates that the oxidation of reduced ceria by H 2 O or CO 2 plays an important role for the understanding of the oxygen storage dynamic...
51 CitationsSource
#1Divesh Bhatia (UH: University of Houston)H-Index: 8
#2Robert D. Clayton (Caterpillar Inc.)H-Index: 7
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 4 authors...
Abstract A global kinetic model for NOx storage and reduction for the case of anaerobic regeneration with hydrogen is developed, based on parallel experimental studies [R.D. Clayton, M.P. Harold, V. Balakotaiah, Appl. Catal., B 84 (2008) 616; R.D. Clayton, M.P. Harold, V. Balakotaiah, C.Z. Wan, Appl. Catal., B 90 (2009) 662.]. The existence of two different types of BaO storage sites on the catalyst is proposed, which differ in their storage as well as regeneration activity. The two-site model e...
39 CitationsSource
#1Saurabh Y. Joshi (UH: University of Houston)H-Index: 14
#2Michael P. Harold (UH: University of Houston)H-Index: 52
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
We present accurate low-dimensional models for real time simulation, control, and optimization of monolithic catalytic converters used in automobile exhaust treatment. These are derived directly by averaging the governing equations and using the concepts of internal and external mass transfer coefficients. They are expressed in terms of three concentration and two temperature modes and include washcoat diffusional effects without using the concept of the effectiveness factor. The models reduce t...
46 CitationsSource
#1Divesh Bhatia (UH: University of Houston)H-Index: 8
#2Michael P. Harold (UH: University of Houston)H-Index: 52
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
Abstract Existing micro and global reaction kinetic models are not able to capture some of the key experimentally observed light-off trends of the CO – H 2 – O 2 system in a monolithic reactor. We modify the literature microkinetic mechanisms to correctly predict the H 2 light-off at room temperature in the absence of CO, selectivity towards CO oxidation before the simultaneous light-off of CO and H 2 , the enhancement effect of H 2 , and the inhibiting effect of CO on light-off in a CO – H 2 – ...
33 CitationsSource
A heterogeneous one-dimensional model is used to simulate a three way catalytic converter (TWC). The mathematical model consists of mass and energy balance equations in the gas and solid phases and accounts for 15 heterogeneous chemical reactions. Langmuir−Hinshelwood type kinetics is used to represent most of the reaction rates. In this work, the kinetic parameters of the various reactions occurring in a TWC are estimated using vehicle data based on a genetic-algorithm-based optimization. The m...
30 CitationsSource
Abstract We present a general solution of the diffusion–reaction problem for linear kinetics and an expression for the effectiveness factor ( η ) in terms of the shape normalized Thiele modulus ( Φ ) for a catalyst particle of arbitrary shape and with an arbitrary activity profile. We also show that the Sherwood number ( Sh Ω ) or the dimensionless mass transfer coefficient between the interior of a particle or region (denoted by Ω ) and its boundary ( ∂ Ω ) is related to the effectiveness facto...
38 CitationsSource
#1G. S. KonstantasH-Index: 2
#1G KonstantasH-Index: 1
Last. A M StamatelosH-Index: 1
view all 2 authors...
AbstractThe need to deliver ultra-low emitting vehicles at a reasonable cost is driving the automotive industry to invest significant manpower in computer aided design and optimization of exhaust treatment systems. The significant fluctuations in the stock exchange market values of the precious metals employed in the manufacture of automotive catalytic converters has increased interest in the possibility of assisting precious metal loading optimization by means of mathematical modelling. Current...
13 CitationsSource
#1Pankaj KumarH-Index: 5
#2Ankur GuptaH-Index: 5
Last. Bhaskar D. KulkarniH-Index: 52
view all 4 authors...
It is well known that Dynamic Time Warping (DTW) is superior to Euclidean distance as a similarity measure in time series analyses. Use of DTW with the recently introduced warping window constraints and lower bounding measures has significantly increased the accuracy of time series classification while reducing the computational expense required. The warping window technique learns arbitrary constraints on the warping path while performing time series alignment. This work utilizes genetic algori...
4 CitationsSource
Cited By35
Newest
#1Bhaskar Sarkar (UH: University of Houston)H-Index: 1
#2Ram R. Ratnakar (Royal Dutch Shell)H-Index: 11
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
Abstract We use the Lyapunov-Schmidt (L-S) reduction technique of bifurcation theory to develop reduced order models for monolith reactors with catalytic reactions in the washcoat layer and homogeneous reactions in the flow channel, and with thermal effects. The L-S technique eliminates the two transverse coordinates and converts the detailed models expressed in terms of three spatial coordinates and time to multi-mode models in axial coordinate and time. The reduced order models are expressed i...
3 CitationsSource
#1Zhiyu Zhou (UH: University of Houston)H-Index: 2
#2Michael P. Harold (UH: University of Houston)H-Index: 52
Last. Dan Luss (UH: University of Houston)H-Index: 49
view all 3 authors...
A combined experimental and modeling study of dynamic oxygen storage capacity (DOSC) of ceria-zirconia (CZO) and Al2O3-supported Mn0.5Fe2.5O4 (MFO) spinel using CO and H2 as reductants is conducted...
Source
#1Marcelo Real (Polytechnic University of Valencia)H-Index: 2
#2Raffael Hedinger (ETH Zurich)H-Index: 3
Last. Christopher H. Onder (ETH Zurich)H-Index: 25
view all 4 authors...
This article introduces a physical model of a three-way catalytic converter oriented to engine cold-start conditions. Computational cost is an important factor, particularly when the modelling is oriented to the development of engine control strategies. That is why a one-dimensional one-channel real-time capable model is proposed. The present model accounts for two phases, gas and solid, respectively, considering not only the heat transfer by convection between both, but also the water vapour co...
4 CitationsSource
#1Pengfei Feng (Hunan University)H-Index: 1
#1Pengfei Feng (Hunan University)H-Index: 1
Last. JaeEkSonH-Index: 1
view all 4 authors...
An SCR catalyst is used as an example to investigate the effects of the washcoat diffusion limitation on the performance of monolith reactors. One-dimensional model and three-dimensional CFD model with and without washcoat diffusion limitation were established. The washcoat diffusion was modeled by using an effective diffusivity in the washcoat region (CFD modeling) and the internal mass transfer coefficient between the interface and the interior of the washcoat (One-dimensional modeling). The r...
5 CitationsSource
#1Mingjie Tu (UH: University of Houston)H-Index: 1
#2Ram R. Ratnakar (Royal Dutch Shell)H-Index: 11
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
Abstract We present a novel and accurate reduced order model with local property dependent internal and external mass transfer coefficients for real time simulations of monolith reactors. We compare the accuracy of the present approach with other reduced order models in the literature and with exact (numerical) solution of the detailed washcoat diffusion model. We illustrate the application of the reduced order models with three examples: a four reaction model of a three-way catalytic converter ...
6 CitationsSource
#1Carlos Guardiola (Polytechnic University of Valencia)H-Index: 24
#2Héctor Climent (Polytechnic University of Valencia)H-Index: 18
Last. Marcelo Real (Polytechnic University of Valencia)H-Index: 2
view all 4 authors...
The purpose of this paper is to introduce a grey-box model of three-way catalytic converter, which is capable of estimating the oxygen storage level to aid the fuel-to-air ratio control in spark ig...
Source
#1Klemens SchürholzH-Index: 2
#2Daniel BrücknerH-Index: 2
Last. Dirk Abel (RWTH Aachen University)H-Index: 17
view all 3 authors...
In this paper recurrent neural networks are used for modelling of the exhaust gas aftertreatment system of a spark-ignition engine including a three-way catalytic converter and oxygen sensors. Different network architectures are compared based on their achieved mean squared error. We find that physically inspired architectures surpass naive architectures built without knowledge of the physical system. The best resulting model is evaluated by giving the quantiles of the absolute error.
3 CitationsSource
#1Ram R. Ratnakar (Royal Dutch Shell)H-Index: 11
#2Rama Krishna Dadi (UH: University of Houston)H-Index: 5
Last. Vemuri Balakotaiah (UH: University of Houston)H-Index: 53
view all 3 authors...
Abstract We develop and use a multi-scale averaging technique based on the Lyapunov-Schmidt (L-S) reduction method to obtain reduced order models for monolith reactors with multiple washcoat layers. These models are expressed in terms of phase-averaged concentration modes and inter as well as intra-phase (dispersion) fluxes. The various fluxes are determined by the local equations that are linear in the concentration modes and fluxes. It is shown that the structure of the multi-phase averaged mo...
5 CitationsSource
#1José M. Desantes (Polytechnic University of Valencia)H-Index: 26
#2Carlos Guardiola (Polytechnic University of Valencia)H-Index: 24
Last. Marcelo Real (Polytechnic University of Valencia)H-Index: 2
view all 4 authors...
Abstract This paper presents and experimentally evaluates different model-based O2 depletion strategies for the TWC during a tip-in after a fuel cut-off. The objective is to find an optimal depletion strategy in the sense of minimum fuel consumption while keeping NOx emissions during the transient below certain limit. To do that, in the present paper, a control oriented model of the TWC is combined with a Direct Method to solve the corresponding Optimal Control Problem. The analysis of the obtai...
3 CitationsSource
#1Jian GongH-Index: 3
#2Di WangH-Index: 14
Last. Aleksey YezeretsH-Index: 35
view all 6 authors...
Abstract The aging impact on oxygen storage capacity (OSC) of three-way catalyst was investigated through experiments and modeling. OSC measurements were conducted on two commercial TWCs (one fresh and one aged) over the temperature window of 100–600 °C. The amount of OSC decreased by 44% at 400 °C and the kinetic restrictions of OSC reductions extended towards higher temperatures after standard bench cycle (SBC) aging at 955 °C for 57 h. The relationship between OSC and temperature was modified...
16 CitationsSource