SAE TECHNICAL
PAPER SERIES
2000-01-1953
Comparison of Chemical Kinetic Mechanisms in
Simulating the Emission Characteristics
of Catalytic Converters
Tariq Shamim, Huixian Shen and Subrata Sengupta
The University of Michigan - Dearborn
Reprinted From: Advanced Emissions Aftertreatment for Gasoline Applications
(SP–1544)
and
International Spring Fuels & Lubricants
Meeting & Exposition
Paris, France
June 19-22, 2000
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A.
Tel: (724) 776-4841 Fax: (724) 776-5760
The appearance of this ISSN code at the bottom of this page indicates SAE’s consent that copies of the
paper may be made for personal or internal use of specific clients. This consent is given on the condition,
however, that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center, Inc.
Operations Center, 222 Rosewood Drive, Danvers, MA 01923 for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying such as
copying for general distribution, for advertising or promotional purposes, for creating new collective works,
or for resale.
SAE routinely stocks printed papers for a period of three years following date of publication. Direct your
orders to SAE Customer Sales and Satisfaction Department.
Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department.
To request permission to reprint a technical paper or permission to use copyrighted SAE publications in
other works, contact the SAE Publications Group.
All SAE papers, standards, and selected
books are abstracted and indexed in the
Global Mobility Database
No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written
permission of the publisher.
ISSN 0148-7191
Copyright © 2000 CEC and SAE International.
Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely
responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in
SAE Transactions. For permission to publish this paper in full or in part, contact the SAE Publications Group.
Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300
word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE.
Printed in USA
2000-01-1953
Comparison of Chemical Kinetic Mechanisms in Simulating
the Emission Characteristics of Catalytic Converters
Tariq Shamim, Huixian Shen and Subrata Sengupta
The University of Michigan - Dearborn
Copyright © 2000 CEC and SAE International.
an important role in such design modification efforts. In
addition to proper and accurate flow, heat and mass
transfer models, the accuracy of numerical simulations
depend on the accurate description of chemical kinetic
mechanisms.
ABSTRACT
Engine exhaust systems need to undergo continuous
modifications to meet increasingly stricter regulations. In
the past, much of the design and engineering process to
optimize various components of engine and emission
systems has involved prototype testing. The complexity
of modern systems and the resulting flow dynamics, and
thermal and chemical mechanisms have increased the
difficulty in assessing and optimizing system operation.
Due to overall complexity and increased costs associated
with these factors, modeling continues to be pursued as a
method of obtaining valuable information supporting the
design and development process associated with the
exhaust emission system optimization.
Several chemical reaction mechanisms are available in
literature. Oh and Cavendish [1] used a three step
reaction mechanism.
Their model only considered
oxidation processes of CO, HC, and H2. They assumed
that HC oxidation is represented by the reaction of
propylene (“fast-oxidizing HC”) and neglected other HC
as insignificant influence on the converter thermal
performance. Siemend et al. [2] used similar oxidation
kinetic rates in their study of comparison between model
simulations and experiments. In addition to oxidation,
their reaction mechanism also includes the NO reduction.
The rate expression for NO reduction by CO was taken
from Subramanian and Verma [3,4]. In both models, all
unburned hydrocarbons are represented by CHy (y is the
ratio of hydrogen to carbon in the fuel). The heat of
formation of CHy was assumed to be one-third of C3H6.
Due to its simplicity and good accuracy, the 4-step
mechanism is widely used in simulating the catalyst
performance. However, this mechanism ignores the
variation in the reaction rates of several HC species by
lumping them into one category. It also ignores the effect
of water gas shift and steam reforming effects, which
become especially important under sever transient
driving conditions.
Insufficient kinetic mechanisms and the lack of adequate
kinetics data are major sources of inaccuracies in
catalytic converters modeling. This paper presents a
numerical study that investigates the performance of
different chemical mechanisms in simulating the
emission conversion characteristics of catalytic
converters during both steady state and transient
conditions. The model considers the coupling effect of
heat and mass transfer with the catalyst reactions as
exhaust gases flow through the catalyst. The heat
transfer model includes the heat loss due to conduction
and convection. The effect of radiation is assumed to be
negligible and is not considered. The resulting governing
equations based on the conservation of mass,
momentum and energy are solved by a tridiagonal matrix
algorithm (TDMA) with a successive line under relaxation
method. The performance of different chemical kinetic
schemes is reviewed by comparing the results of
numerical model with the experimental measurements.
An improvement in the reaction mechanisms may be
made by lumping several HC species into more than one
category. Koltsakis et al. [5] used a six-step chemical
mechanism to describe the chemical reactions occurring
on the surface of the automotive catalyst. Their model
assumed the HC to be lumped into two categories: fast
burning and slow burning. In addition to the oxidation
and reduction processes, they also considered the steam
reforming reaction. This reaction was attributed to high
HC conversion efficiencies in fresh catalysts during
operation in rich exhaust. Similar to most of the previous
studies, their kinetic expressions were of the form
proposed by Votz et al. [6]. They employed a tunable
factor to match their NO reduction rate with the
INTRODUCTION
Catalytic converters have been employed in vehicles for
decades and have been proven to be very successful in
reducing the exhaust emissions. However, with the
worldwide trend of stringent emission regulations, their
designs need to undergo continuous modifications.
Mathematical modeling and numerical simulations play
1
The gas phase species equation:
experimental measurements. A more detailed kinetic
mechanism was proposed by Otto and LeGray (7), which
was later modified to include an elaborate NOx
mechanism and the formation of ammonia and its effect
on NO oxidation under fuel-rich conditions.
A
methodology for updating steady-state kinetic data for
this 13-step reaction mechanism was presented by
Montreuil et al [8]. These kinetic rate expressions are to
date the most detailed. In this mechanism, all the
unburnt hydrocarbons are lumped into three categories:
fast burning, slow burning, and inert. The mechanism
has been found to simulate the performance of catalytic
converters fairly well under both steady state and
transient conditions [9]. However, the use of these
detailed kinetic rate expressions require the knowledge of
97 constants, which requires detailed experimentation for
different type of catalysts.
(ε
∂C gj
∂t
+ vg
∂C gj
∂z
) = − km j G a (C gj − C sj )
(3)
where the superscript j varies from 1 to 7 representing,
respectively, following gas species: CO, NO, NH3, O2,
C3H6, H2 and C3H8.
The surface species equation:
∂C sj
N
= km j Ga (C gj − C sj ) − Ga R j (Ts , C 1s ,⋅ ⋅ ⋅ ⋅ ⋅⋅, C c species )
∂t
(4)
(1 − ε )
where superscript j varies from 1 to 7 representing the
surface species in the same order as the gas phase
species equation.
Even though all of the chemical reaction models
mentioned above are applied to catalyst simulations,
there exist differences in catalyst performance
predictions because of variations in the chemical
mechanisms. However, it is difficult to isolate the effect of
chemical mechanism by simply comparing the above
studies. As the differences in catalyst performance
prediction may also be attributed to the differences in
these studies related to test conditions, heat and mass
transfer modeling, catalyst conditions, etc. The present
study was motivated by recognizing the need for a
systematic evaluation of the existing chemical reaction
schemes under similar and realistic conditions. The
study compares the performance of various mechanisms
in simulating the catalyst operation during both steady
and transient conditions. The model predictions were
compared with experimental measurements.
The
transient conditions were simulated by considering the
catalyst operation during the US Federal Test Procedure
(FTP). In addition to the comparison, the study also
identifies the salient feature of each mechanism. It is
anticipated that this sensitivity study will lead to efforts in
modifying or devising a better chemical catalyst
mechanism.
CHEMICAL REACTION MECHANISMS – As described
in the Introduction, the present study considers several
different chemical reaction mechanisms existing in
literature. A brief description of these mechanisms is
listed below:
MATHEMATICAL FORMULATION
where
3-Step Chemical Reaction Mechanism – This reaction
mechanism, listed below, was proposed by Seh Oh and
co-workers [1,10]
1
O 2 → CO2
2
CO +
C3 H 6 +
H2 +
9
O2 → 3CO2 + 3H 2 O
2
1
O2 → H 2O
2
QR = -2.832*105 (J/mol)
QR = -1.928*106 (J/mol)
QR = -2.42*105 (J/mol)
The expressions for reaction rates are as following:
R1 = k1C CO C O2 / G
R 2 = k 2 C C3 H 6 C O2 / G
R3 = k1C H 2 C O2 / G
GOVERNING EQUATIONS – The governing equations,
as listed below, were developed by considering the
conservation of mass, energy and chemical species.
k1 = 6.699 × 109 exp(−12556 / TS )
mol / cm 2 ⋅ s
k 2 = 1.392 ×1011 exp(−14556 / TS )
mol / cm 2 ⋅ s
The gas phase energy equation:
2
G = T S (1 + K 1 C CO + K 2 C C 3 H 6 ) 2 (1 + K 3 C CO
C C2 3 H 6 )
∂T g
ρ g C Pg (ε
∂t
+ vg
∂T g
∂z
) = − h g G a (T g − T s )
0 .7
(1 + K 4 C NO
)
(1)
The surface energy equation:
(1−ε)ρsCPs
+ Ga
∂Ts
∂T
= (1−ε)λs 2s + hgGa (Tg −Ts ) − h∞Sext(Ts −T∞)
∂t
∂z
2
nreaction
∑R (T ,C ,⋅⋅⋅⋅⋅⋅,C
j
s
j=1
1
s
nspecies
) ⋅ ∆H j
s
(2)
2
K1 = 65.5EXP (961 / TS )
dimensionless
K 2 = 2.08 × 10 3 EXP (361 / TS )
dimensionless
K 3 = 3.98 EXP (11611 / T S )
dimensionless
K 4 = 4.79 × 10 5 EXP ( −3733 / TS )
dimensionless
α
⋅ H 2O
2
α
CH α + M 2 ⋅ O 2 → CO + ⋅ H 2 O
2
4-Step Chemical Reaction Mechanism – A widely used
reaction scheme considers the above three reactions
with the NO reduction by CO. The resulting 4-step
mechanism has been shown to simulate the catalyst
reactions with a reasonable accuracy [2]. The NO
reduction used in this mechanism is as follows:
CO + NO = CO 2 +
1
N2
2
CH α + M 1 ⋅ O2 → CO2 +
H2 +
QR = -3.73*105 (J/mol)
R4 =
TS−0.17 (T + k 5CCO ) 2
mole / cm 2 ⋅ s
k 5 = 1.2028 × 10 5 EXP (653 .5 / T S )
H 2 + NO → H 2 O +
K
1
N2
2
1
N2
2
2.5 H 2 + NO → NH 3 + H 2 O
Modified 4-Step Chemical Reaction Mechanism – This
reaction mechanism is essentially similar to the 4-step
mechanism described previously. The only difference is
the modification in the rate expression of NO reduction.
Based on the comparison with the experimental
measurement, the authors modified the exponent of CO
concentration in the rate expression R4 from 1.4 to 1.9.
The modified reaction rate of NO reduction is as
following:
CH α + M 1 ⋅ O 2 → CO 2 +
α
⋅ H 2O
2
α
1
1
1
CHα + NO →
CO +
H 2O + N 2
2M 2
2M 2
4M 2
2
CH α + M 3 ⋅ NO → CO 2 +
M
α
⋅ H20 + 3 ⋅ N2
2
2
2.5
(3 − α )
2.5
CHα + NO +
H 2O → NH3 +
CO
2M 2
4M 2
2M 2
1.9 0.3 0.13
k 4 CCO
CO2 C NO
TS−0.17 (T + k 5CCO ) 2
(HCS)
(HCF)
(HCF)
(HCF)
(5)
where α = Hydrogen-to-Carbon ratio, and
M 1 = [1 +
5-Step Chemical Reaction Mechanism – This mechanism
was obtained by adding the steam reforming reaction in
the above modified 4-step reaction scheme. The steam
reforming reaction and its rate expression used, as
shown below, are similar to those used by Koltsakis et al.
[5].
C 3 H 6 + 3H 2 O = 3CO + 6 H 2
1
N2
2
2.5CO + NO + 1.5H 2 O → NH 3 + 2.5CO 2 +
k 4 = 3.067 × 10 8 EXP ( −8771 / T S )
R4 =
3
1
O 2 → 1.5H 2 O + N 2
4
2
CO + NO → CO2 +
1.4 0.3 0.13
k 4 CCO
CO2 C NO
(HCF)
1
O2 → H 2O
2
NH 3 +
And the reaction rate expressions for the above reactions
is:
(HCF)
1 α
α
α
] M 2 = [ + ] M 3 = [2 + ]
4 ;
2 4 ;
2
HCF = Fast burning HC; HCS = Slow burning HC.
The corresponding reaction rate expressions are listed
elsewhere [9].
For different catalyst formulations, the coefficients in the
reaction rate expressions are different. They also vary
with the aging of catalytic converters. The present study
uses a palladium-based catalyst. The coefficients in the
reaction rate expressions were taken from Montreuil et al.
[8] wherein they were appropriately adjusted using
experimental flow reactor measurements.
QR = 3.7346*105 (J/mol)
And the reaction rate expression:
R 5 = k 5 C C 3 H 6 C H 2O / G
k 5 = 1 .7 × 10 12 EXP (12629 / T S )
OXYGEN STORAGE MECHANISM – The conversion
efficiency of a three-way catalytic converter can be
improved by storing the extra oxygen under fuel lean
conditions and releasing it under rich conditions [11,12].
The released oxygen may participate in the reactions
with the reducing agents, thereby increasing the
conversion of CO and HC in a rich exhaust-gas
environment [13-15]. Such an oxygen storage capacity
(OSC) is developed in the modern catalyst by coating its
substrate with a wash-coat material containing ceria.
13-Step Chemical Reaction Mechanism – This mechanism
consists of 13 independent forward pathways for
oxidation of CO, H2, C3H6, C3H8, and NH3 with O2 and
NO as oxidizing agents, and their corresponding rich and
lean kinetic rate expressions. This chemical reaction
scheme and kinetic data were originally presented by
Otto and LeGray [7] and later presented with the modified
kinetic data by Montreuil et al. [8]. The reaction scheme
is shown as follows:
1
CO + O2 → CO2
2
3
The oxygen storage and release mechanism used in this
study was modeled by a 9-step site reaction mechanism.
This mechanism was developed by designating two kinds
of sites that can be oxidized and reduced through a 9
step site reaction mechanism [14]. The reduced metal
site on the surface is defined as <S> and the oxidized site
is defined as <OS>. This 9 step reaction mechanism is
listed as following:
implicit difference scheme in the spatial direction. Since
more chemical reactions take place near the inlet,
smaller grid spacing was used near the inlet and larger
spacing near the exit. A standard tridiagonal matrix
algorithm (TDMA) with an iterative successive line under
relaxation method was used to solve the finite difference
equations. Details of the solution procedure are
described elsewhere [9].
1
< S > + O2 →< OS >
2
RESULTS AND DISCUSSION
Site Oxidation
< OS > + CO →< S > + CO 2
The performance of different chemical mechanisms was
assessed by comparing the numerical predictions with
the experimental measurements under both steady and
transient conditions. The converters used for both steady
state and transient performance assessment were
palladium-based catalysts. For the steady state case,
the catalyst has a length of 3.81 cm, cross-sectional area
of 5.0671x10-4 m2, cell density of 620,000 cell/m2, and
wall thickness of 1.88x10-4 m. And the feed gas
composition was 1% CO, 0 ppm CH4, 1000 ppm C3H6,
500 ppm C3H8, and 1000 ppm NO. The feed gas
temperature was 371 °C, and space velocity of 50,000
hr-1. For the transient case, the catalyst used has a
length of 8.001 cm, cross-sectional area of 8.69254x10-3
m2, cell density of 620,000 cell/m2, and wall thickness of
1.905x10-4 m.
Site reduction by CO
H 2 O + CO → H 2 + CO 2
Water-Gas shift
< OS > + H 2 →< S > + H 2 O
CH α + H 2 O → CO + (1 +
Site reduction by H2
α
) ⋅ H2
2
Steam reforming
3
1
3
CH α + < OS >→< S > + C + CO + ( α ) H 2
2
2
4
Reduction by HC
C + O 2 → CO 2
Coke Burn-off
< S > + NO →< OS > +
< OS > +
1
N2
2
NO Storage
2
2
3
NH 3 →< S > + NO + H 2 O
5
5
5
STEADY STATE PERFORMANCE – The steady state
performance of the reaction mechanisms was assessed
by comparing the model results with the experimental
measurements of Montreuil et al. [8]. For this case, all
transient terms in the governing equations were set to be
zero. Figure 1 shows the comparison of the converter
pollutant conversion efficiencies as predicted by different
chemical mechanisms. Here, the conversion efficiencies
are plotted as a function of redox ratio, which is defined
as:
NH3 Site reduction
where α is hydrogen-to-carbon ratio of the hydrocarbon.
Each reaction has two rate expressions, one being the
fast site rate expression and another the slow site rate
expression. The total sites are conserved for both fast
site and slow site. Therefore,
S total , f =< S > f + < OS > f
S total , s =< S > s + < OS > s
(7)
Redox Ratio =
The rates of the transient reactions are of the form
(OXSW ) ⋅ CTR − E / RTs ⋅
Rtransient =
( X si ) EX ( i )
1
N specie
1+
∑k
n
⋅ X sn
n =1
(9)
Figure 1a shows the results of the 3-step mechanism.
The results depict a good agreement between the model
predictions of CO and HC conversion and the
experimental measurements. The agreement is
particularly excellent in the range of low redox ratio.
However, when the redox ratio increases, i.e., in rich
mixture zone, the discrepancies between the model
predictions and measurements increase. For a wide
range of redox ratio greater than unity, the model
underpredicts the CO conversion. The HC conversion is
also initially slightly underpredicted. However, beyond
redox ratio of 2.5, the model overpredicts HC conversion
efficiency. The overall prediction of HC conversion is
better than that of CO.
The NO conversion, as
mentioned earlier, is not included in this mechanism.
The elimination of NO reaction may have some influence
on the model prediction of CO and HC.
N specie
∏
α
)[ HC ]
4
[ NO ] + 2 ⋅ [ O 2 ]
[ CO ] + [ H 2 ] + 6 ⋅ ( 1 +
(8)
where
OXSW =1, if Redox ratio <1
OXSW =0, if Redox ratio >1
The corresponding coefficients for calculating the
transient reaction rates are based on experimental data.
SOLUTION PROCEDURE – The governing equations
were discretized by using a non-uniform grid and
employing the control volume approach with the central
4
redox ratio of 1.1 and 2.5. Beyond this value, the
conversion is underpredicted by the mechanism. The
model prediction of HC conversion is similar to the 3-step
mechanism,
and
has
good
agreement
with
measurements. The HC conversion efficiency is slightly
overpredicted for redox ratio greater than unity.
Figure 1a. Comparison of 3-step model results with
experimental measurements under steady
state condition
Figure 1b shows the results of the 4-step mechanism,
which was obtained by adding the NO reduction reaction
in the previous 3-step mechanism. For redox ratios
greater than unity, the results show an excellent match
between the model NO prediction and the experimental
measurement. However, the NO prediction for redox
ratio less than unity is very inaccurate. The addition of
NO reaction also significantly influences the CO and HC
conversion rates. It increases the conversion rates of
both HC and CO. The results show large differences
between the model predictions and the measurements.
These discrepancies are due to inaccuracies in the
model of NO reduction reaction.
Figure 1c. Comparison of modified 4-step model results
with experimental measurements under
steady state condition
Figure 1d shows the results of the 5-step mechanism.
This chemical scheme, as mentioned earlier, was
obtained by adding a steam reforming reaction to the
modified 4-step mechanism.
The reaction rate
expression for the steam reforming was obtained from
literature [15]. The rate expressions for other reactions
were similar to that of the modified 4-step. The results
show that the model prediction of NO emission remains
excellent and is not much influenced by steam reforming
reaction. The major influence of steam reforming is
found to be on HC emission. As expected, the results
show an improvement in HC conversion efficiency due to
steam reforming reaction. With the overprediction of HC
conversion, the agreement between the model prediction
and measurement is reduced. The prediction of CO
conversion, however, is improved especially for the redox
ratios between 1.1 and 2.5.
Figure 1b. Comparison of 4-step model results with
experimental measurements under steady
state condition
Figure 1c shows the results of the modified 4-step
mechanism. Except for a slight modification in the
reaction rate of NO, this mechanism including the
reaction rates and other kinetic data is essentially similar
to the previously discussed 4-step mechanism. The
modification in the NO rate expression, as mentioned
earlier, is made by changing the exponent of CO
concentration from 1.4 to 1.9. The figure depicts a much
better agreement between the model and the
measurements. The prediction of NO conversion is
particularly excellent over a wide range of redox ratio.
The prediction of CO conversion also shows
improvement.
It matches very well with the
measurements in the vicinity of redox ratio of unity. The
CO conversion is slightly overpredicted between the
Figure 1d. Comparison of 5-step model results with
experimental measurements under steady
state condition
The results of the model with the 13-step chemical
mechanism are shown in Figure 1e. The figure depicts
that the model predictions, particularly at low redox
ratios, are in good agreement with the measurements.
5
results of the 13-step mechanism may indicate a
transient phenomenon that is not captured well by both
the 4-step chemistry and the measurements that were
limited by 1 Hz.
The measurements with higher
resolution are needed to clarify this point.
NO prediction is excellent over a wide range of redox
ratios. The predictions of CO and HC, however, are not
as good as those of 3 or 4 step mechanisms. For redox
ratios greater than unity, the model significantly
underpredicts the CO conversion and overpredicts the
HC conversion. One reason for such a disagreement is
the inaccuracy in chemical kinetic data, which are
obtained by comparing with the actual measurements
during engine operation. Since the engine operating
conditions are in the close vicinity of redox ratio of unity,
the constants and the rate expressions are tuned to
better simulate the converter performance under these
conditions. Hence the model can be used with a good
accuracy to simulate the converter performance under
normal engine operating conditions.
However, a
modification of its rate expressions will be required if the
mechanism is employed to simulate the converter
subjected to highly fuel rich conditions.
Figure 2a. Comparison of transient output HC emissions
with experimental measurements
Figure 1e. Comparison of 13-step model results with
experimental measurements under steady
state condition
Figure 2b. Comparison of accumulated HC with
experimental measurements
TRANSIENT PERFORMANCE – The steady state
performance results clearly show that the modified 4-step
mechanism is better than the 3-step mechanism. The
modified mechanism also simulates the NO conversion in
addition to embodying all the other features of the 3-step
mechanism. Hence, the assessment of the transient
performance of different mechanisms was limited to the
modified 4-step and the 13-step mechanisms. The
transient conditions were simulated by considering the
converter performance during the US Federal Test
Procedure (FTP).
Figure 2b depicts the accumulated HC emission during
the first 100 seconds of the FTP. The 4-step chemistry
predicts less HC emission than the 13-step mechanism,
and its predictions are closer to the experimental
measurements.
Both
mechanisms,
however,
underestimate the catalyst HC conversion performance.
A major reason for this discrepancy is that the
simulations do not take into account the effect of oxygen
storage capacity, which significantly improves the
converter performance during the rich operating
conditions. The effect of this mechanism is discussed in
the later section. The converter HC conversion efficiency
during the whole FTP cycle is measured to be 95.88%,
compared to 80.37% and 85.14% predicted respectively
by the 4-step and the 13-step mechanisms.
Figure 2a shows the comparison of instantaneous HC
emissions as determined by measurements and
predictions by using the modified 4-step and the 13-step
reaction schemes. The figure depicts a reasonable
overall agreement between both model predictions and
the measurements. Both of the mechanisms capture the
major trends of HC emissions. The relatively large
production of HC at the initial stage of cycle corresponds
to the cold start conditions. This cold start behavior is
also well simulated by both mechanisms. However, the
model predictions have more spikes than those shown in
measurements. Compared to the 13-step mechanism,
the 4-step mechanism shows better agreement with the
measurements. The more number of spikes in the
Figure 3 shows the instantaneous and accumulated CO
emissions. The results show that the instantaneous CO
emission is well predicted by both the mechanisms.
These models capture the initial high CO production
corresponding to cold start conditions, and simulate fairly
well the various CO peaks during the FTP cycle. Similar
to the HC emission prediction, the CO predictions of the
13-step mechanism have more spikes. The accumulated
emission results depict a good agreement between the
6
Figure 3a. comparison of transient output CO emissions
with experimental measurements
Figure 4a. Comparison of transient output NO emissions
with experimental measurements
Figure 3b. Comparison of accumulated CO with
experimental measurements
Figure 4b. Comparison of accumulated NO with
experimental measurements
measurements and the predictions of the 4-step
mechanism. Contrary to the case of HC conversion
performance, the models overestimate the converter CO
performance. The converter CO conversion efficiency
during the whole FTP cycle is measured to be 91.53%,
compared to 86.51% and 85.40% predicted respectively
by the 4-step and the 13-step mechanisms.
developed mainly by coating the catalyst substrate with a
washcoat material containing ceria, allows oxygen
storage under lean operating conditions and its release
under rich conditions. The released oxygen improves the
conversion of CO and HC during the rich cycle. During
normal driving operation, the OSC plays an important
role in improving the converter efficiency since there are
continuous oscillations of rich and lean conditions due to
rapid fluctuations in air-fuel ratio about stoichiometric
conditions.
The instantaneous and accumulated NO emissions are
shown in Figure 4. The trend of instantaneous NO
emission is fairly well predicted by both the 4-step and
13-step mechanisms. However, the 4-step mechanism
shows
larger
spikes
than
those
determined
experimentally. Compared to the 4-step, the 13-step
mechanism predictions are generally in closer agreement
with the measurements. The accumulated NO emission
results reveal that the 13-step overpredicts and the 4step underpredicts the converter performance. The
converter NO conversion efficiency during the whole FTP
cycle is measured to be 92.03%, compared to 86.49%
and 95.09% predicted respectively by the 4-step and the
13-step mechanisms.
The 4-step and the 13-step mechanisms were compared
by adding the OSC. The reaction scheme used for the
OSC, as mentioned earlier, was a 9-step mechanism.
Figures 5-7 show the accumulated HC, CO, and NO
conversions. The results show that the model predictions
of both mechanisms are improved by considering the
OSC. The prediction of HC conversion especially shows
significant improvement.
The 13-step mechanism
predictions are in excellent agreement with the
measurements. The prediction of the 4-step mechanism
is also improved, however, not as much as in the case of
the 13-step mechanism. The HC conversion efficiency
during the whole FTP cycle is 88.15% for the 4-step and
94.84% for the 13-step, compared to 95.88% as
determined by measurements.
EFFECT OF OXYGEN STORAGE CAPACITY – Most of
the modern 3-way catalytic converters have oxygen
storage capacity (OSC). This capacity, which is
7
step mechanism is better than that of the 4-step
mechanism. The prediction of NO conversion efficiency
is not much influenced by the OSC for the 13-step
mechanism, and it decreases significantly for the 4-step
mechanism.
Figure 5.
Comparison of accumulated HC with
experimental measurements
Figure 7.
Comparison of accumulated NO with
experimental measurements
CONCLUSIONS
Figure 6.
A numerical study was carried out to investigate the
performance of different chemical reaction mechanisms
under both steady state and transient conditions. The
results led to the following conclusions:
Comparison of accumulated CO with
experimental measurements
• The converter steady state performance can be
simulated by several different chemical reaction
mechanisms. The kinetic expressions of most of
these mechanisms are generally tuned to yield
optimum
model
performance
near
the
stoichiometeric conditions. The 3-step mechanism,
proposed by Seh Oh, which considers only the
oxidation of CO, C3H6, and H2, gives satisfactory
results of CO and HC conversion.
The NO
conversion performance can be obtained by adding
the reaction of NO reduction by CO. The resulting 4step mechanism is widely used in simulating the
converter performance. A slight modification in the
NO reduction rate expression is found to give the
best results compared to measurements.
Figure 6 shows that the addition of the OSC does not
appreciably influence the CO conversion prediction of the
13-step reactions during the first 100 seconds of the FTP.
The results of the 4-step mechanism with the OSC show
an improvement of the CO conversion performance.
However, since the mechanism with no OSC already
overpredicts the CO conversion (see Figure 3), addition
of the OSC makes the disparity between the model
results and the experimental measurements larger. For
the total FTP cycle, the OSC improves the CO conversion
efficiency, which is underpredicted without OSC by both
mechanisms. The CO conversion efficiency is 87.33%
for the 4-step and 88.69% for the 13-step, as compared
to 91.53% determined by measurements.
• The steam reforming reaction is found to mainly
influence the HC emission by increasing its oxidation
rate. It also affects CO oxidation but does not have
much influence on NO reduction.
Similar to the case of CO emissions, there is not much
influence of the OSC on the NO conversion prediction of
the 13-step mechanism at both the beginning of the FTP
(Fig.7) and during the whole FTP cycle (the total NO
conversion efficiency changing to 95.93%, comparing
with 95.09% of no OSC case). With the addition of the
OSC, the 4-step mechanism predicts an increase in the
NO and underpredicts the NO conversion performance
(the total NO conversion efficiency decreasing to 75.38%
from 86.49%). Compared to the 4-step, the 13-step
mechanism is in closer agreement with the experimental
measurements.
• The transient performance of reaction mechanisms
studied is acceptable. The model predictions with
13-step mechanism have the best agreement with
experimental measurements during the whole FTP
test. The consideration of the oxygen storage
mechanism improves the model predictions of HC
and CO conversions for both 13-step and 4-step
mechanisms. However, on the NO conversion
predictions, it has almost no effect for 13-step
mechanism and adverse effect for 4-step
mechanism. In addition, the oxygen storage capacity
has major influence on HC conversion.
In summary, the results show that OSC improves the
predictions of total conversion efficiencies of HC and CO
during the whole FTP test, and the improvement of 13-
8
12. Taylor, K. C., "Automobile Catalytic Converters",
Springer-Verlag, Berlin, Heidelberg, 1984.
13. Herz, R. K., " Dynamic Behavior of Automotive
Catalysts. 1. Catalyst Oxidation and Reduction." Ind.
Engng Chem. Prod. Res. Dev.20, pp. 451-457, 1981.
14. Li, P., Adamczyk, A. A., and Pakko, J. D., "Thermal
Management of Automotive Emission Systems:
Reducing the Environmental Impact," The Japan-U.
S. Seminar on Thermal Engineering for Global
Environment Protection (A-3), 1994.
15. Koltsakis, G. C. and Stamatelos, A. M., “Catalytic
Automotive Exhaust Aftertreatment,” Progress in
Energy and Combustion Science, v 23 n 1, 1997, pp.
1-39.
ACKNOWLEDGMENTS
The financial support from the Ford Scientific Research
Laboratory, Oak Ridge National Laboratory and the
Center for Engineering Education and Practice (CEEP) of
the University of Michigan-Dearborn is greatly
appreciated..
REFERENCES
1. Oh, S.H. and Cavendish, J.C., "Transients of
Monolithic Catalytic Converters: Response to a Step
Change in Freestream Temperature as related to
Controlling Automobile Emissions," Ind. Eng. Chem.
Prod. Res.Dev., 21, p. 29, 1982.
2. S. Siemund, P. Leclerc, D. J. Schweich, M. Prigent
and F. Castagna, "Three-way Monolithic Converters:
Simulations
versus
Experiments,"
Chemical
Engineering Science, Vol. 51, N0. 15, pp. 3709-3720,
1996.
3. Subramanian, B. and Varma, A., "Reactions of CO,
NO, O2, and H2O on Three-way and Pt/AL2O3
Catalyst," Frontiers in Chemical Engineering
Proceedings of the International Chemical
Engineering Conference, Vol.1, pp. 231-240. 1984.
4. Subramanian, B. and Varma, A., "Reaction Kinetics
on a Commercial Three-way Catalyst: the CO-NOO2-H2O System," Ind. Engng Chem., Prod. Res.
Dec. 24, pp. 512-516, 1985.
5. Koltsakis, G. C., Konstantinidis, P. A. and Stamatelos,
A. M., "Development and Application Range of
Mathematical
Models
for
3-way
Catalytic
Converters," Applied Catalysis B: Environmental, Vol,
12, No. 2-3, pp. 161-191, 1997.
6. Voltz, S. E., Morgan, C. R., Liederman, D. and
Jacob, S. M., “Kinetic Study of Carbon Monoxide and
Propylene Oxidation on Platinum Catalysts,” Ind.
Engng Chem. Prod. Res. Dev. 12, p. 294, 1973.
7. Otto, N. C. and LeGray W. J., “Mathematical Models
for Catalytic Converter Performance,” SAE paper No.
800841, 1980.
8. Montreuil, C. N., Williams, S. C., and Adamczyk, A.
A., “Modeling Current Generation Catalytic
Converters: Laboratory Experiments and Kinetic
Parameter Optimization – Steady State Kinetics,”
SAE paper No. 920096, 1992.
9. Shen, H., Shamim, T., Sengupta, S., Son, S. and
Adamczyk, A., "Performance Simulations of Catalytic
Converters during the Federal Test Procedure,"
Proceedings of the 33rd National Heat Transfer
Conference, August 15-17, 1999, Albuquerque, New
Mexico.
10. Chen, D. K., Oh, S. H., Bisselt, E. J. and Van Ostrom,
D. L., "A Three-dimensional Model for the Analysis of
Transient Thermal and Conversion Characteristics of
Monolithic Catalytic Converters," SAE paper 880282,
1988.
11. Gandhi, H. S., Delosh, R. G., Piken, A. G. and
Shelef, M., “Laboratory Evaluation of Three-way
Catalysts,” SAE Transactions, Sec.2, Vol.85, 1976, p.
201.
NOMENCLATURE
Cg j
= gas phase concentration, moles/M3
Csj
= surface concentration, moles/M3
Cpg
= specific heat of gas, J/kg*K
Cps
= specific heat of substrate, J/kg*K
EA, E = activation energy, Pa-m3/g-mole
9
Ga
= geometric surface to volume ratio, M2/M3
∆Hj
= heat of reaction j, J/mole
hg
= heat transfer coefficient between flow and
substrate, J/M2*s*K
h∞
= heat transfer coefficient between substrate and
atmosphere, J/M2*s*K
kmj
= mass transfer coefficient for species j, M/s
QR
= reaction heat, J/mol
Rj
= reaction rate of jth reaction, mole/M3*s
Sext
= external surface to volume area ratio, M2/M3
t
= time, s
T∞
= ambient temperature, K
Tg
= gas temperature, K
Ts
= substrate temperature, K
Vg
= gas flow velocity, m/s
Xsi
= mole fraction of species i in substrate
z
= axial coordinate, m
α
= hydrogen-to-carbon ratio in the fuel
ε
= void volume fraction
λs
= thermal conductivity of substrate, J/M*s*K
ρg
= gas density, kg/M3
ρs
= substrate density, kg/M3