Kinetic Parameter Estimation of a Diesel Oxidation Catalyst under

Mar 13, 2008 - A realistic numerical model of a commercial diesel oxidation catalyst (DOC) was developed under an actual vehicle operating condition. ...
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Ind. Eng. Chem. Res. 2008, 47, 2528-2537

Kinetic Parameter Estimation of a Diesel Oxidation Catalyst under Actual Vehicle Operating Conditions Tae Joong Wang,*,† Seung Wook Baek‡ Propulsion and Combustion Laboratory, School of Mechanical, Aerospace and Systems Engineering, Korea AdVanced Institute of Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea (Republic of)

Je-Hyung Lee§ AdVanced Technology and Analysis Team, AdVanced Technology Center, Hyundai-Kia Motors, 772-1 Jangduk-dong, Hwaseong-si, Gyeonggi-do 445-706, Korea (Republic of)

A realistic numerical model of a commercial diesel oxidation catalyst (DOC) was developed under an actual vehicle operating condition. To provide the material data as well as to examine the performance characteristics, conversion experiments through the DOC were performed with a 2.0 liter EGR-mounted diesel engine on a dynamometer test bench. Then, on the basis of the currently developed in-house computational code, kinetic parameters of the model reactions were calibrated through a numerical fit to the experimental data. To cover a wide range of operating temperatures, the experiments and modeling were conducted under low engine speeds (i.e., 1000 and 1500 rpm). Main objectives of this study are to develop not only a numerical model based on real-world experiments but also a methodology of how to construct it. Details of the procedure are described step-by-step in this article. Also, on the basis of the experimental results currently observed, it is proposed that additional models considering the NO2 reaction to produce NO are further required than the generally adopted DOC models to capture the negative efficiency behavior in NO oxidation at low temperatures. Because the present DOC model does not take these reactions into account, its prediction performance with experimental results at 1000 rpm is poor for NO and NO2 emissions at low temperatures but is fairly good for CO and HC emissions. On the other hand, the prediction performance at 1500 rpm is good for all of the species as well as over all of the operating temperature ranges. 1. Introduction Since a first introduction of DOC in the 1970s, its technology has been well established for an automotive application.1 Mainly through an employment of highly active noble metal-based (e.g., platinum, rhodium) catalysts, the current DOC brings about satisfactory reductions in gaseous CO and HC emissions from diesel engines, including HC-derived emissions, such as aldehyde, polynuclear aromatic hydrocarbon (PAH), and the soluble organic fraction (SOF) of particulates. The state-of-the-art technologies of commercial automobile DOC achieve over 90% removal of CO and more than 70∼80% reduction of total HC over a wide range of operations. Recently, along with the gradually strengthened emission standards, a combined use of various diesel aftertreatment systems has become indispensable to the worldwide carmakers. Usually located upstream of integrated converter systems, a DOC exerts considerable effects on the performances of downstream diesel particulate filter (DPF) and selective catalytic reduction (SCR). In particular, a low-temperature performance of the DOCs equipped in light-duty vehicles (i.e., passenger cars and light commercial vehicles) is an important issue in an urban driving environment including cold-start and idling operation, which would be one of the major sources of air pollution. * To whom correspondence should be addressed. Tel.: +82-42-8693754. Fax: +82-42-869-3710. E-mail: [email protected]. † Ph. D. Candidate, Korea Advanced Institute of Science and Technology (KAIST). ‡ Professor, Korea Advanced Institute of Science and Technology (KAIST). § Principal Research Engineer, Advanced Technology and Analysis Team, Advanced Technology Center, Hyundai-Kia Motors.

Mathematical modeling has been widely employed for several decades to support the analysis and design of automotive catalytic converters. Among the literature, several articles relative to DOC modeling can be summarized as follows; Kandylas et al.2 presented a mathematical model of a catalytic converter for diesel application, whereas Pontikakis et al.3 produced a model validated versus experimental data in driving cycles including cold-start effects. Koltsakis et al.4 and Kandylas and Koltsakis5 performed a modeling study of DOC with DPF at downstream. Triana et al.6 conducted a modeling work of DOC based on an engine-dynamometer test result. On modeling automobile catalytic converters, the reaction kinetics is definitely one of the most important factors to determine its reliability. However, the kinetics of catalytic reaction has a case-by-case nature because it is affected by a number of chemico-physical factors. When we deal with a commercial catalyst, this problem-dependent feature becomes more severe. Thus, strictly speaking, there exist some limitations in re-using the reaction kinetics taken from other sources so that the calibration of kinetic parameters is required for an accurate modeling on a certain commercial system. In the current study, kinetic parameters for the selected catalytic reactions are tuned through a numerical fit to engine-dynamometer test results so that a quite realistic model is established. Moreover, through this article, a methodology of how the tuning procedure proceeds is given in detail. As a result of this work, a new data set of activation energy and pre-exponential factor is finally obtained for each species with the currently employed Arrhenius type of reaction kinetics. Accurate NO and NO2 predictions through DOC gather interest regarding its upstream application wth DPF or SCR. In

10.1021/ie071306i CCC: $40.75 © 2008 American Chemical Society Published on Web 03/13/2008

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this study, it is suggested that additional models considering a NO2 reaction to produce NO are further required to capture the negative efficiency behavior in NO oxidation observed at temperatures below around 200 °C. Without employing these reaction models, predictions for NO and NO2 emissions at low temperatures exhibit poor performances. This is argued in the current study through the comparison of simulations with experiments. The present DOC model formulates the catalytic surface area as an independent variable in the volumetric reaction-rate term. For this, the active metal surface area is measured through chemisorption experiments. Therefore, the current study establishes a foundation toward the model that renders it possible to predict converter performances with different catalyst loading amounts. However, this makes sense under the assumption that the surface reaction rate varies not so much, even though the catalyst area is changed. Thus, the feasibility of this assumption must be checked beforehand. To cover a wide range of operating temperatures, the present experiments were conducted at low engine-speed conditions. Here, the 1000 and 1500 rpm results were used simultaneously in the model development to produce one set of a preexponential factor and an activation energy for each species. Note that, because all of the experimental data were measured using a real diesel engine with EGR, they exhibited more complex characteristics in comparison with those created from laboratory-scale experiments. Therefore, we confirmed their reliabilities through some repeated experiments.

the experiments was a 2.0 liter, 4-cylinder in-line with a rated power of 126 hp at 4000 rpm. This engine is operated with an exhaust gas recirculation (EGR), high-pressure common rail direct injection, and turbocharged/aftercooled system. The present commercial DOC is a flow-through type and formed into a honeycomb structure. Also, it is composed of dual monoliths with a small gap between them. Its specifications are summarized in Table 1. Note that, because the current DOC is Table 1. Specifications of a Commercial DOC shape of cross-section material of substrate diameter × length cell density substrate wall thickness catalyst

round cordierite 110 mm × 94.7 mm 400 cpsi 6.5 m in Pt/Al2O3

not a used one, the aging status of the catalyst is expected to be almost fresh. The diesel engine was connected to a 160 kW EC dynamometer controlled with a PUMA 5.3 control system. A test-cell computer controls the engine speed and load, while recording all of the test data. A schematic diagram on the test-cell setup is illustrated in Figure 1. The test cell has a full emissions bench

2. Experimental Section 2.1. Measurement of Catalyst Surface Area. The active metal surface area is a crucial factor for modeling catalytic converters. Therefore, in this work, it was experimentally determined. The catalyst loaded on the present commercial DOC is a Pt/Al2O3 system so that a specific platinum surface area can be deduced from a CO adsorption isotherm with the use of following eq 1.7

SPt )

Vads 100 1 N n a 22 414 A m m,Pt wt

(1)

Chemisorption experiments were performed with an ASAP 2010 (Micromeritics Ins. Corp.) instrument. A 2.0 g sample was prepared by pounding and grinding up the entire monolith after uncovering the canning and insulating materials. In eq 1, CO: Pt chemisorption stoichiometry was set to 0.7,7-8 whereas the surface area occupied by a single platinum atom was taken as 8.07 Å2.7-8 Avogadro’s number used was 6.022 × 1023 mol-1. Also, platinum loading of the sample was 0.163% by weight. As a result of the experiments, the chemisorbed CO volume was measured to be 0.007611 ((0.000465) cm3/g, and eq 1 leads to a specific platinum surface area of 7.08675 m2/g platinum. In addition, platinum dispersion is calculated to be 2.845%. A platinum surface area per unit reactor volume can be obtained simply by using

ac ) SPtwPt

(2)

Here, the loaded mass of platinum per unit reactor volume was measured to be 0.7 g/liter. 2.2. Engine, DOC, and Test Cell Instrumentation. Enginedynamometer experiments were performed with a commercial DOC mounted on the exhaust lines. The diesel engine used in

Figure 1. Schematic diagram of the experimental setup.

with a HORIBA MEXA-9100DEGR analyzer. In this facility, a nondispersive infrared detector is used for the CO instrument, whereas the heating flame ionization detection method is used for the HC analyzer and a paramagnetic detector is used for the O2 instrument. In addition, to separately measure the concentrations of NO and NO2, we utilized the EUROTRON GREENLINE 9000 analyzer, which uses temperature-compensated electrochemical sensors and has a 1 ppm resolution for NO and NO2. For verifying the accuracy of the NO and NO2 measurements, total NOx was also monitored with the HORIBA analyzer, which uses the chemiluminescence principle. The diesel fuel used in the current experiment is an ultralow sulfur diesel, which has 13 wt ppm sulfur and no oxygen contents. Also, the cetane number is 55.7, and the density is 0.82 g/cm3 at 15 °C. 2.3. Testing and Sampling Strategies. To measure the experimental data, an engine load was raised under a fixedspeed condition of 1000 and 1500 rpm. All measurements were taken after both the engine and DOC reached their steady states. Especially, to obtain the conversion data at temperatures as low as possible, sampling was initiated from the lowest limit of each engine operation. The present study develops a 1D DOC model without considering heat exchanges between the exhaust gas and the monolith substrate. For developing a reliable DOC model, it is necessary to measure the temperatures of active metal sites

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Figure 2. Space velocities of the exhaust gases emitted from a 2.0 liter EGR-mounted diesel engine for 1000 and 1500 rpm.

Figure 3. Conversion of CO versus catalyst temperature for 1000 and 1500 rpm.

where the catalytic reaction takes place. To do that, we drilled into the substrate to insert a K-type thermocouple. This thermocouple was radially positioned along the center line of monolith cross-section, while axially at the middle of upstream DOC. To verify if it is exactly placed at the intended location inside the thin substrate, we monitored simultaneous variations of both gas and catalyst temperatures and confirmed their reasonable separate tendencies. There exist spatial differences in substrate temperatures due to various heat-transfer effects. However, we roughly assume the substrate temperature measured at the center of monolith cross-section as a representative one for the entire catalyst, which may introduce some errors in the model. Actually, measurements of substrate temperature distributions inside the DOC support this assumption (i.e., uniform catalyst temperatures). Here, internal substrate temperatures were measured at nine points; three axial points along three radial lines (i.e., center-line, midline, and near boundary). Over all of the operating ranges for a 1000 rpm condition, we observed the following deviations compared to the center temperature: (1) along the center-line: -2.2 ∼ +1.6%, (2) along the mid-line: -5.0 ∼ -0.7%, (3) along near boundary: -25.7 ∼ -17.0%. Surely, the model accuracy can be improved if a multidimensional model is adopted with the heat-transfer modeling. Moreover, both inlet and outlet gas temperatures were also measured at the front (about 110 mm ahead) and rear (about 80 mm behind) of the monolith, which showed the following deviations compared to the center temperature: (1) gas inlet: +2.1 ∼ +11.5%, (2) gas outlet: +4.1 ∼ +9.2%. 2.4. Experimental Results. Because the current experiments are performed with actual vehicle systems, the measured data inevitably show some scattering. Thus, their reliabilities are confirmed through repeated experiments. Although the same results were not obtained from these experiments, they showed a satisfactory similarity each other. Therefore, the experimental data presented in this section are used as representative materials for modeling as well as for examining the DOC behaviors. Figure 2 illustrates variations of space velocity against catalyst temperatures measured under two different engine-speed conditions. The space velocity is observed to increase with catalyst temperature. As an engine load is increased at a fixed engine speed, a larger amount of fuel and air is supplied into the engine cylinder. Consequently, a vigorous combustion occurs, thereby

releasing more heat, which leads to a simultaneous increase in space velocity and temperature. Note that the presented space velocity was calculated based on both DOC volume and volumetric flow rate of exhaust gas. Here, the volume flow rate was obtained from the fuel and air-flow measurements. The airflow meter works according to the principle of the hot-film anemometer, whereas the fuel flow rate is measured based on the weight loss. Figure 3 displays a conversion result of CO. When discussing catalytic reactions, the term light-off is commonly used as the minimum temperature necessary to initiate the reaction. For a more precise quantitative definition, the light-off temperature is the temperature at which a conversion reaches 50%.9 On the basis of that definition, the 1000 rpm result reveals that CO light-off begins at about 160 °C. However, for 1500 rpm, it is impossible to identify where the light-off begins because the catalytic reaction of CO is sufficiently activated even at the measurable lowest temperature. Both 1000 and 1500 rpm results shown in Figure 3 reveal that, within the range of the space velocities currently measured, a complete removal of CO takes place at temperatures above about 190 °C regardless of the space velocity. Hence, the mass-transfer limitation phenomenon, which represents a slight decrease in conversion rate at higher temperatures due to a simultaneous increase in space velocity, was not observed for CO even at the highest power in 1000 and 1500 rpm. Figure 4 exhibits a conversion result of total HC. From the 1000 rpm result, almost no reduction in HC emission is observed at temperatures below about 130 °C. A noticeable decrease in HC occurs at a catalyst temperature of 140 °C, whereas its lightoff begins at about 190 °C. Compared to the 100% consumption of CO over a wide range of temperatures, the DOC displays a weaker performance capability in reducing HC, which is mainly due to the slowly oxidized hydrocarbon species. The maximum conversion rate of HC is lower than 80% in this experiment. Also, Figure 4 reveals that the rate of HC conversion at 1500 rpm is lower than that at 1000 rpm. This is because a higher engine speed leads to a higher space velocity to obtain the same temperature. Variations of the conversion rate in Figure 4 indicate that the mass-transfer limitation takes place for HC species at both engine-speed conditions. Figures 5 and 6 depict conversion results of NO and NO2, respectively. Figure 7 illustrates variations of the measured NO2/ NOx ratio with equilibrium values for NO + NO2 + O2 mixture.

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Figure 4. Conversion of HC versus catalyst temperature for 1000 and 1500 rpm.

Figure 5. Conversion of NO versus catalyst temperature for 1000 and 1500 rpm (Negative conversion data below 193 °C for 1000 rpm are not presented).

Here, the equilibrium NO2/NOx compositions are calculated for 7% and 17% of O2 mole fractions because these two values are respectively the lowest and highest O2 concentrations measured in the present 1000 rpm experiment. They are obtained using the Gibbs free energy formulation for the equilibrium constant and compared to the data from the JANAF Thermochemical Table10 for their verifications. In Figures 5 and 6, each concentration of NO and NO2 measured at the inlet and outlet of DOC for 1000 rpm crosses over at temperatures near 200 °C. Note that each turning point for NO and NO2 does not exactly coincide because the total NOx concentration changes through DOC. At temperatures below 200 °C, so-called negative efficiency behavior in NO oxidation is observed. This is probably related to NO2 reaction with CO or hydrocarbons producing NO.4 Figure 5 displays that the NO conversion reaches almost 65% at 1000 rpm and 55% at 1500 rpm. Each NO conversion, after reaching a maximum value, decreases with further catalyst temperature increases. It is well-known that this drop in NO conversion is mainly due to the thermodynamic limitation effect.5,11-12 In fact, mass transfer

Figure 6. Conversion of NO2 versus catalyst temperature for 1000 and 1500 rpm (Only positive conversion data below 193 °C for 1000 rpm are presented).

Figure 7. NO2/NOx ratio at DOC inlet and outlet for 1000 rpm with their equilibrium compositions at 7% and 17% of O2 mole fractions under a NO + NO2 + O2 mixture condition.

may limit the efficiency to a certain level but it is not really possible to reduce the efficiency at higher temperatures. In Figure 7, the data points at temperatures below 200 °C move in the opposite direction to a thermodynamic equilibrium for the NO + NO2 + O2 mixture through DOC. Thus, the decrease in NO2 at low temperatures is obviously not attributed to NO2 self-dissociation but is able to be explained by the NO2 reaction with CO or by hydrocarbons producing NO as mentioned above. Figure 8 gives conversion results of total NOx. The present experiments exhibit a slight decrease in NOx concentration through DOC. As can be seen from Figure 8, its conversion rate reaches at most approximately 15% at 1000 rpm and 11% at 1500 rpm. It seems that this total NOx reduction is ascribed to a SCR reaction over a platinum-based catalyst by hydrocarbons present in the exhaust gas stream13-15 or its conversion into nitrogen-containing species other than NO and NO2.16 However, because the level of NOx conversion is not so high, the current model assumes the total NOx to be conserved through DOC.

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introduced during the calibration process can be reduced with a hydrocarbon species having a relatively small carbon number. There are modeling studies4-5,19 employing NO2 self-dissociation reaction (i.e., the reverse of reaction 5) for a thermodynamic consideration at high temperatures (over around 350 °C). However, the current model performs theoretical fits to the experimental results accounting only for NO oxidation without adopting NO2 self-dissociation. 3.2. Kinetics. In this study, all of the catalytic reactions are assumed to follow the well-known Langmuir-Hinshelwood mechanism. Rate-law expressions are referred to the form, which was originally suggested by Voltz et al.18 and modified by Oh and Cavendish.20 Adopted forms of the rates of CO and HC oxidations are as follows.

RCO ) Figure 8. Conversion of total NOx versus catalyst temperature for 1000 and 1500 rpm.

RC3H6 )

k1Xs,COXs,O2 G(Xs,i,Ts) k2Xs,C3H6Xs,O2 G(Xs,i,Ts)

(6)

(7)

3. Modeling Apart from reducing CO and HC emissions, achieving a higher NO2/NOx ratio is also recognized as an important role of DOC when it is combined with DPF or SCR downstream. Thus, monitoring NO and NO2 variations through DOC has become a matter of concern. Therefore, the current model accounts for NO oxidation as well as CO and HC oxidation reactions. In the present modeling, because any model reaction describing NO or NO2 consumption into N2 is not employed, total NOx must be conserved through DOC. Note that total NOx is assumed to be composed only of two components (i.e., NO and NO2) here. However, the current measurement reveals that total NOx is not actually conserved. Thus, the experimental results need some adjustments for their use as material data. These modifications are made by changing the exit concentrations of NO and NO2 (in proportion to their original values) such that total NOx is conserved through DOC. In the end, these modified experimental data are used for tuning the kinetic parameters. 3.1. Model Reactions. To describe catalytic reactions occurring in DOC, three basic reactions for CO, HC, and NO over a Pt/Al2O3 are considered as follows.

For NO oxidation, its kinetic expression must work over a wide temperature range encompassing both kinetic and thermodynamic considerations.12 This is because, at higher temperatures where chemical equilibrium favors NO2 self-dissociation, the rate of NO oxidation should be zero.4-5 Therefore, in the current model, the rate-law expression for NO oxidation accounts for the thermodynamic equilibrium limitation as follows.4-5,12,19

RNO )

(

k3Xs,NOXs,O2 G(Xs,i,Ts)

1-

)

K′ K′ < Kp Kp

(8)

In eq 8, the parameter K′ indicates how the current mixture deviates from equilibrium (denoted by Kp) and is defined as19

K′ )

XNO2 XNOXO21/2

(9)

1 CO + O2 f CO2 2

(3)

Accurate prediction of O2 concentration along DOC is also important because it is involved in the rate expressions of other species. The reaction rate for O2 is obtained by assuming all of the reactions to be occurred in stoichiometric conditions as follows.

9 C3H6 + O2 f 3CO2 + 3H2O 2

(4)

1 9 1 RO2 ) RCO + RC3H6 + RNO 2 2 2

1 NO + O2 f NO2 2

(5)

Kuo et al.17 showed that hydrocarbons in real engine exhaust could be divided kinetically into two groups of compounds. Propylene is representative of the easily oxidized hydrocarbons, which constitute about 80% of the total hydrocarbons found in a typical exhaust gas. Methane and other saturated hydrocarbons that are resistant to oxidation usually make up the remaining 20%.18 There exist modeling works2-5 employing several hydrocarbon species to represent diesel exhaust. However, for the simplicity in the calibration process with engine-dynamometer test data, the current model considers only the propylene as a representative HC as in refs 6 and 18. This is not only because easily oxidized hydrocarbons constitute the majority of real exhaust gas but also because numerical errors

(10)

The inhibition factor appearing in eqs 6 to 8 is given by

G(Xs,i,Ts) ) Ts(1 + K1Xs,CO + K2Xs,C3H6)2(1 + K3Xs,CO2Xs,C3H62)(1 + K4Xs,NO0.7) (11) In eq 11, adsorption equilibrium constants are described as an Arrhenius form of

(

Ki ) Kio exp -

)

Ea,i , i ) 1∼4 R uT s

(12)

where the adsorption pre-exponential factor and adsorption heat are referred to the values that have been extensively adopted in the studies of modeling automobile catalytic converters21-26 after a pioneering work by Voltz et al.18 These are summarized in

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Therefore, time accumulation terms on the left-hand side in eqs 14 and 15 are all neglected. Mass-transfer coefficients between phases are determined by

Table 2. Parameters for Determining Adsorption Equilibrium Constants adsorption pre-exponential factor, dimensionless K1o K2o K3o K4o

adsorption heat/Ru, K

65.5 2.08 × 103 3.98 4.79 × 105

Ea,1/Ru Ea,2/Ru Ea,3/Ru Ea,4/Ru

-961 -361 -11 611 3733

Table 3. Initial Values of Kinetic Parameters Used for the Calibrations pre-exponential factor, mol‚K/(m2‚s) o

k1 k2o k3o

activation temperature, K

1× 4 × 1020 4.5 × 1014 1017

E1/Ru E2/Ru E3/Ru

9622 12 028 8420

Table 2. Specific reaction-rate constants are also represented by the following Arrhenius form.

(

ki ) kio exp -

)

Ei , i ) 1∼3 RuTs

(13)

Because there are numerous factors influencing the catalytic reactions under an actual diesel exhaust environment, the prescribed kinetic expressions and referred parameter values may not be sufficient to model the current commercial DOC. Nevertheless, we do not explicitly give any additional consideration more than those presented above, except for modifications to kinetic parameter values. Through iterative calculations, new kinetic parameters such as the pre-exponential factor and activation energy, which can yield the best fits to experimental data, are sought and presented in this study. Initial parameter values for the present calibrations are taken from Kandylas and Koltsakis5 and are listed in Table 3. 3.3. Mass Balances. Solid-phase mass balances for all of the species can be written in a single form as

(1 - )

a cR i ∂Xs,i ,i) ) km,iasf(Xg,i - Xs,i) ∂t Ctot CO, HC, NO, NO2, O2 (14)

As described on the second term of the right-hand side in eq 14, the present model formulates the volumetric reaction-rate term as consisting of both catalytic surface area and surface reaction rate. Hence, catalytic surface area is considered as an independent variable. Therefore, the current study establishes a foundation toward the model that renders it possible to predict DOC performances with different catalyst loading amounts. Surely, these predictions make sense under the assumption that the surface reaction rate (Ri) varies not so much even though the catalyst area is changed. Further works are needed to confirm the feasibility of this assumption. Unlike the solid-phase equations, the reaction-rate term does not appear in gas-phase mass balances because gas-phase species do not participate directly in catalytic reactions. Gas-phase mass balances for all of the species can also be formulated in a single form as



∂Xg,i ∂Xg,i ) -uD - km,iasf(Xg,i - Xs,i), i ) ∂t ∂x CO, HC, NO, NO2, O2 (15)

In the present model, a quasi-steady-state assumption is employed for all of the gas- and solid-phase mass balances.

km,i )

Sh∞Di , i ) CO, HC, NO, NO2, O2 Dh

(16)

where the asymptotic Sherwood number is set to 2.89, which is an analytic solution for the fully developed laminar flow with constant wall temperature, as in other works of simulating automobile catalytic converters.27-28 Also, the binary diffusion coefficients are estimated using the method proposed by Wilke and Lee,29 whereas the hydraulic diameter of a single channel is calculated from the geometrical information of the honeycomb monolith. 3.4. Numerical Method. By virtue of the quasi-steady approximation, the gas-phase governing equations are expressed as a nonlinear ordinary differential form, and the solid-phase equations become a simple algebraic form. To get their 1D solutions, the computational domain is divided into 400 grid points. And then, all of the governing equations for gas and solid phases are discretized on each node. Finally, the linearized governing equations are solved using numerical techniques by developing a source code written in FORTRAN 90. In this study, because the two-phase governing equations are coupled with each other, an iterative method is implemented for their simultaneous solutions. As a convergence criterion, the iterative calculation is continued until the error defined in eq 17 reaches as small as 10-6. IMAX

δ ) n

∑

x)1

(|

X(x)g,in - X(x)g,in-1 X(x)g,in

| | +

X(x)s,in - X(x)s,in-1

)

|

,i) X(x)s,in CO, HC, NO, NO2, O2 (17)

where IMAX indicates total number of nodal points, that is, 400. The superscript n means the current iteration step, whereas n - 1 is the previous step. The present study employs an under-relaxation technique to prevent solutions from diverging. The under-relaxation factor of 0.2 is adopted for HC and NO, whereas smaller factors from 0.1 to 0.01 are used for CO. This is because the reaction rate of CO is much higher (approximately 2 orders of magnitude at the DOC inlet over a wide range of operations) than that of other species. However, a smaller under-relaxation generally leads to a longer computational time. Therefore, for efficient calculations, a higher value of the CO under-relaxation factor is used at low temperatures, whereas a lower value is used at high temperatures. Because the current Arrhenius form of reaction kinetics is an exponential function of temperature, numerical errors can be easily augmented and transferred to downstream of the computational domain. It is not sufficient to employ the firstorder upwind scheme or the second-order central difference scheme,30 as is widely accepted in CFD applications. In this study, the fifth-order Runge-Kutta method31 is adopted to increase the accuracy of numerical solutions. 4. Kinetic Parameter Estimation For each species, an iterative calculation is continued while updating the pre-exponential factor until a deviation of the calculated exit concentration from the measured one becomes as small as 0.1 ppm. This is done for the entire operating conditions, and then the fitted pre-exponential factors are

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Figure 9. Arrhenius plot with a linear-fit curve for tuning CO kinetic parameters. Curve information: slope ) -3039.39, intercept ) 34.8016.

obtained as a function of the solid temperature. Least-square regression for Arrhenius plot yields

ln(kio,f) ) C1 -

C2 Ts

(18)

Inserting eq 18 into eq 13 leads to a new reaction-rate constant as

(

kinew ) exp(C1) exp -

)

Ea,i/Ru + C2 Ts

(19)

Equation 19 then gives a new pre-exponential factor and activation energy as follows.

kio,new ) exp(C1)

(20)

Ea,inew/Ru ) Ea,i/Ru + C2

(21)

The above arguments are applied for tuning the kinetic parameters of all of the species. Particularly, during iteration processes, a successive determination of a new kinetic parameter for species leads to a more accurate estimation result compared to a simultaneous one. This is due to the coupling of the kinetics of each species through balance equations as well as the inhibition factor. In this study, after many preliminary calculations, an efficient procedure is found for the best calibration result. Also, in this study, the calibrations are performed simultaneously using the experimental data obtained at both engine speeds (i.e., 1000 and 1500 rpm). All of the details are given below. 4.1. CO. Because the experimental result for CO emission exhibits a 100% conversion over a wide range of operations, the kinetics of CO seems to be the most weakly affected by other species. Thus, CO is selected as the first calibration species. In Figure 9, an Arrhenius plot is presented with a linearfit curve to the newly obtained pre-exponential factors for CO oxidation. Here, only the 1000 rpm data are adopted for the calibration, whereas the 1500 rpm results are excluded because a complete CO conversion is already achieved even at its minimum temperature (226 °C). Exact magnitude of reaction rate cannot be estimated from the data with a zero exit concentration. Reaction rates larger than a certain threshold value, which corresponds to a complete CO consumption exactly

Figure 10. Arrhenius plot with a linear-fit curve for tuning HC kinetic parameters. Curve information: slope ) 6112.32, intercept ) 18.2354.

at DOC exit, also yield zero CO emission so that these data are not useful for estimating its kinetic parameters. Even among the 1000 rpm results, a small number of data are used in the calibration. The data above 193 °C are not employed because of their complete CO conversion. Moreover, the data below 136 °C (i.e., five points represented by the hollow symbol in Figure 9) are also excluded because CO consumptions at this low-temperature region are probably attributed to reaction pathways other than reaction 3. Therefore, to get more accurate CO predictions at lower temperatures, additional CO consumption models are required in addition to the currently adopted CO oxidation with O2. Note that the exclusion of lowtemperature data will introduce some prediction errors in the corresponding temperature zone. Light-off data that do not correspond to either ∼0 or 100% conversion are used for the calibration. However, because the light-off band for CO oxidation is narrow, it is difficult to get a sufficient number of light-off data from the current types of engine-dynamometer tests. Thus, to complement this lack of data, two sets of experimental results are utilized. The data points present in Figure 9 are composed of two repeated test results at 1000 rpm. 4.2. HC. Second, the calibration for HC is carried out with employing the newly determined CO kinetics. Through many preliminary simulations over a wide range of operations, it is observed that the kinetic constants of HC show relatively less sensitivity to those of NO compared to the opposite case. This can be also expected from inspecting the terms of the inhibition factor shown in eq 11. Thus, the tuning of HC is performed prior to NO. Figure 10 displays an Arrhenius plot with a linear-fit curve to the new pre-exponential factors for HC oxidation. Here, both the 1000 and 1500 rpm data are simultaneously used for the calibration to produce one set of pre-exponential factor and activation energy. However, similar to the case of CO, lowtemperature data at 104 and 113 °C (i.e., two points represented by the hollow symbol) are excluded from the calibration because these HC consumptions may be ascribed to reaction pathways other than reaction 4. Therefore, some prediction errors are expected at this temperature zone. 4.3. NO. With an employment of the newly determined CO and HC kinetics, the calibration for NO is finally performed using both the 1000 and 1500 rpm data simultaneously. Figure

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Figure 11. Arrhenius plot with a linear-fit curve for tuning NO kinetic parameters. Curve information: slope ) 3686.87, intercept ) 15.6000.

Figure 12. Comparison of the calculated and measured exit concentrations for 1000 rpm.

Table 4. Kinetic Parameters Currently Obtained through the Best Fits of Numerical Simulations to Experimental Data for a Commercial DOC with a 2.0 Liter EGR-Mounted Diesel Engine species CO HC NO

pre-exponential factor, mol‚K/(m2‚s) 1.30060 × 8.30871 × 107 5.95654 × 106

1015

activation temperature, K 12661.39 5915.68 4733.13

11 shows an Arrhenius plot with a linear-fit curve to the newly obtained pre-exponential factors for NO oxidation. Among the experimental results shown in Figure 5, negative conversion data obtained at temperatures below 193 °C are not used for the calibration. As mentioned previously, these negative efficiencies in NO oxidation are probably attributed to the generation of NO by NO2 reaction with CO or hydrocarbons. However, because the current model does not account for other reactions of NO2 to produce NO than reaction 5, prediction errors are expected in the corresponding temperature region. Moreover, even among the positive conversion data, the data below 233 °C (i.e., three points represented by the hollow symbol) are also excluded from the calibration because they are also affected to a certain extent by the reactions causing negative efficiencies. 5. New Kinetic Parameters and Its Validation New pre-exponential factors and activation temperatures determined through the current calibrations for CO, HC, and NO are summarized in Table 4. On the basis of the obtained kinetic parameters, predicted exit concentrations of all of the species are compared to experimental results for 1000 and 1500 rpm, respectively. Figure 12 shows the validation results at 1000 rpm. As observed from the figure, there are quite good agreements in both CO and HC emissions. However, as expected, poor predictions are given for both NO and NO2 emissions, particularly at low temperatures. On the other hand, predictions at 1500 rpm exhibit excellent agreements for all of the species as well as over all of the operating ranges as shown in Figure 13. Figures 14 and 15 provide exemplary simulation results, which show the variations of gas- and solid-phase concentration and reaction rates for each species along the axial length inside the DOC. Operating conditions and inlet concentrations are taken from the second measurement data for 1500 rpm. As depicted

Figure 13. Comparison of the calculated and measured exit concentrations for 1500 rpm.

in Figure 14, a complete consumption of CO is achieved earlier in the DOC, whereas other species gradually vary along the axial position. This is due to the fact that the CO reaction rate is larger than those of HC and NO by 2 orders of magnitude at the DOC inlet zone as shown in Figure 15. Some interesting phenomena are observed here; even though solid-phase concentrations of HC and NO decrease monotonically along the axial position, their reaction rates slightly increase near the inlet zone. This is because, as can be seen from Figure 16, the inhibition factor decreases more rapidly there. Note that a decrease in the inhibition factor along the axial position is ascribed to the reduction of the species affecting it (eq 11). 6. Conclusions For a commercial DOC, a set of conversion experiments were performed with a light-duty EGR-mounted diesel engine on a dynamometer test bench. Also, on the basis of the currently developed in-house computer code, we numerically tuned kinetic parameters for the model reactions by finding the best fits to the experimental data. As a consequence, a realistic 1D model of the DOC was established. It is expected that the present numerical procedures can be applied to other modeling works

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Figure 14. Comparisons of gas- and solid-phase species along DOC at a steady-state condition for 1500 rpm. Operating conditions: catalyst temperature ) 261 °C, space velocity ) 56 000 h-1, inlet CO ) 351 ppm, inlet HC ) 166 ppm, inlet NO ) 109 ppm, inlet NO2 ) 42 ppm, inlet O2 ) 8.5%.

Figure 16. Inhibition factors along DOC at a steady-state condition for 1500 rpm.

3. The present DOC model formulates the volumetric reaction-rate term as consisting of both catalytic surface area and surface reaction rate. Hence, catalytic surface area is considered as an independent variable. Therefore, the current study establishes a foundation toward the model that renders it possible to predict DOC performances with different catalyst loading amounts. However, this makes sense under the assumption that the surface reaction rate varies not so much even though the catalyst area is changed. Thus, the feasibility of this assumption must be checked beforehand, thereby remaining further works. Nomenclature

Figure 15. Reaction rates along DOC at a steady-state condition for 1500 rpm.

of commercial diesel aftertreatment systems. A summary of main results is as follows. 1. The present commercial DOC displays an excellent removal performance for CO over a wide range of operating conditions. Within the range of space velocities currently measured, a complete consumption of CO takes place at temperatures above approximately 190 °C, regardless of the space velocity. However, the DOC presents a relatively weaker performance capability in removing HC. Its conversion rate does not exceed 80% over the whole operating range. 2. Experimental observations at temperatures below around 200 °C reveal that additional models considering the NO2 reaction to produce NO are further required for capturing the negative efficiency behavior in NO oxidation at this lowtemperature zone. Because the present DOC model does not take these reactions into account, its prediction performance with experimental results at 1000 rpm is poor for NO and NO2 emissions at low temperatures but is fairly good for CO and HC emissions. On the other hand, the prediction performance at 1500 rpm is good for all of the species as well as over all of the operating temperature ranges.

ac ) platinum surface area per unit reactor volume, [m2Pt /m3] am,Pt ) surface area of a single platinum atom, [Å2] asf ) gas/solid interfacial area per unit reactor volume, [m2/ m3] C ) constant in Arrhenius plot Ctot ) total molar concentration of exhaust gas, [mol/m3] D ) binary diffusion coefficient, [m2/s] Dh ) hydraulic diameter of a single channel, [m] E ) activation energy, [J/mol] Ea ) adsorption heat, [J/mol] G ) inhibition factor, [K] k ) reaction-rate constant, [mol‚K/m2/s] km ) mass-transfer coefficient between gas and solid phases, [m/s] ko ) pre-exponential factor, [mol‚K/m2/s] K ) adsorption equilibrium constant Kp ) equilibrium constant Ko ) adsorption pre-exponential factor m ) sample mass, [kg] n ) CO:Pt chemisorption stoichiometry, iteration index NA ) Avogadro’s number, [mol-1] Ri ) reaction rate of species i, [mol/m2/s] Ru ) universal gas constant, [J/mol/K] SPt ) specific Pt surface area, [m2/gPt] Sh∞ ) asymptotic Sherwood number t ) time, [s] T ) temperature, [K] uD ) superficial velocity, [m/s] Vads ) chemisorbed CO volume per unit sample mass, [cm3/g] wPt ) loaded mass of platinum per unit reactor volume, [g/liter]

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wt ) mass fraction of platinum loaded on sample, [%] x ) axial position, [m] Xi ) mole fraction of species i Greek Symbols δ ) iterative error  ) porosity Subscripts g ) gas phase s ) solid phase Superscripts f ) fitted value Acknowledgment This work is part of the project “Development of Partial Zero Emission Technology for Future Vehicle” funded by the Ministry of Commerce, Industry and Energy, and we are very grateful for its financial support. Special thanks are also indebted to Prof. S. K. Ihm and Mr. J. I. Park of Environmental Catalysis Laboratory in Korea Advanced Institute of Science and Technology, who provided a great help and excellent advice on measuring the platinum surface area. Finally, we would like to give many thanks to Dr. J. H. Kang and Dr. Y. T. Kim for their assistance in the engine-dynamometer test. Literature Cited (1) http://www.DieselNet.com; Diesel Oxidation Catalyst in: DieselNet Technology Guide, 1999. (2) Kandylas, I. P.; Koltsakis, G. C.; Stamatelos, A. M. Mathematical Modelling of Precious Metals Catalytic Converters for Diesel NOx Reduction. Proc. Inst. Mech. Eng. Part D 1999, 213, 279-292. (3) Pontikakis, G. N.; Koltsakis, G. C.; Stamatelos, A. M.; Noirot, R.; Agliany, Y.; Colas, H.; Versaevel, P.; Bourgeois, C. Experimental and Modeling Study on Zeolite Catalysts for Diesel Engines. Top. Catal. 2001, 16/17 (1-4), 329-335. (4) Koltsakis, G. C.; Haralampous, O. A.; Dardiotis, C. K.; Samaras, Z. C.; Vogt, C. D.; Ohara, E.; Watanabe, Y.; Mizutani, T. Performance of Catalyzed Particulate Filters without Upstream Oxidation Catalyst; SAE Paper 2005-01-0952; SAE International: Warrendale, PA, 2005. (5) Kandylas, I. P.; Koltsakis, G. C. NO2-Assisted Regeneration of Diesel Particulate Filters: A Modeling Study. Ind. Eng. Chem. Res. 2002, 41, 2115-2123. (6) Triana, A. P.; Johnson, J. H.; Yang, S. L.; Baumgard, K. J. An Experimental and Numerical Study of the Performance Characteristics of the Diesel Oxidation Catalyst in a Continuously Regenerating Particulate Filter; SAE Paper 2003-01-3176; SAE International: Warrendale, PA, 2003. (7) Bergeret, G.; Gallezot, P. Particle Size and Dispersion Measurements in: Handbook of Heterogeneous Catalysis, Vol. 2; Wiley-VCH: Weinheim, Germany, 1997. (8) Crocoll, M.; Kureti, S.; Weisweiler, W. Mean Field Modeling of NO Oxidation over Pt/Al2O3 Catalyst under Oxygen-Rich Conditions. J. Catal. 2005, 229, 480-489. (9) http://www.DieselNet.com; Emission Control Catalysts in: DieselNet Technology Guide, 2000. (10) Stull, D. R.; Prophet, H. JANAF Thermochemical Tables, Second Edition; Nat. Stand. Ref. Data Sys., Nat. Bur. Stand.: U.S., 1971.

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ReceiVed for reView September 28, 2007 ReVised manuscript receiVed December 17, 2007 Accepted January 28, 2008 IE071306I