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Diesel Soot Oxidation with NO2: Engine Experiments and Simulations Ioannis P. Kandylas, Onoufrios A. Haralampous, and Grigorios C. Koltsakis* Laboratory of Applied Thermodynamics, Aristotle University Thessaloniki, 541 24 Thessaloniki, Greece
The diesel particulate filters (DPFs) technology has impressively advanced especially during the last years, driven by the interest in the reduction of automobile particulate emissions. This paper is concerned with the effect of NO2 as an active oxidation agent in the regeneration process of the soot accumulated in the particulate filter. Experiments at realistic conditions using a diesel engine equipped with a standard oxidation catalyst and a particulate filter are carried out at a wide range of operating conditions. These results are used to validate an already available mathematical model of the NO2-assisted regeneration phenomena in the particulate filter. The combined use of experimental and modeling results provides interesting conclusions regarding the significance and the chemistry of the reaction of soot with NO2. The advantages and drawbacks of such an approach compared to standard laboratory synthetic gas studies are discussed. The agreement between experimental and simulation results in terms of engineering interest (rate of soot accumulation or depletion) is quite satisfactory and indicates that such a type of model could be a promising design tool. Introduction Particulate filtration in the exhaust system of diesel engines is increasingly gaining in importance for both light- and heavy-duty applications. Passenger cars equipped with diesel particulate filters (DPFs) already appeared in the market as a means to achieve the low particulate emission standards in Europe.1 The particulate filter technology is also considered the most promising solution toward attaining the emission standards of heavy-duty vehicles.2-5 Filter regeneration, i.e., the process of soot removal from the filter to avoid excessive backpressure buildup, can be accomplished by thermal soot oxidation by the exhaust gas oxygen. This reaction occurs with noticeable rates at temperatures above 500-550 °C, which are rarely met under typical operating conditions. On the other hand, NO2 is highly reactive with soot.6 NO2 is able to oxidize soot at temperatures as low as 250 °C, which can be encountered in diesel exhaust during normal driving cycles. However, NO2 is present in diesel raw exhaust at very low concentrations (5-15% of total NOx, or less than 50 ppm), which are not sufficient to provide the required reaction rates. The concentration of NO2 in the exhaust gas entering the filter can be increased by placing upstream of the filter an oxidation catalyst, which oxidizes NO to NO2. This is the main idea underlying the continuously regenerating trap (CRT) concept, which is the trade name of a system composed of a selective oxidation catalyst placed directly upstream of the particulate filter.7 At temperatures of 300-350 °C, the oxidation catalyst oxidizes a proportion of the NO in the exhaust stream to form NO2, increasing the NO2 fraction to about 50% of total NOx.8-10 The increased interest in particulate filter regeneration systems and the promising results of NO2-assisted * To whom correspondence should be addressed. Tel: +30-310-996066. Fax: +30-310-996019. E-mail: greg@ antiopi.meng.auth.gr.
systems have motivated a number of recently published research works.11-16 However, these works are rather few, compared to the high commercial interest of such systems. Moreover, these works deal mostly with reaction rate studies at laboratory scale using synthetic soot or synthetic gas. Hardly any published data can be found on the reactivity of NO2 with soot in real engine conditions. Reaction studies can be very helpful toward understanding the mechanisms and inter-relations of operating and design parameters, especially when combined with mathematical modeling of the transient particulate filter operation. Such an approach has been recently presented by the authors in a purely modeling study, using literature data to describe the rate laws.17 The present work aims at exploiting experimental data and mathematical modeling, toward better understanding, and describing the NO2-soot reaction phenomena under real-world diesel engine operating conditions. Experimental Setup: Test Protocol The experiments were carried out on an engine bench, using a diesel engine equipped with an oxidation catalyst and a particulate filter in series. Figure 1 shows schematically the experimental layout. The engine displacement is 1.9 L. It is a directinjection, turbocharged, and intercooled engine with exhaust gas recirculation (EGR). The basic engine specifications are given in Table 1. Further details on the engine can be found in ref 18. The oxidation catalyst is the original part aged at real driving conditions for approximately 20 000 km. Its geometrical data are given in Table 2. This catalyst is mounted at the exhaust pipe 0.70 m downstream of the turbocharger. It has to be mentioned that the oxidation catalyst used in this study is not optimized for NO2 production because the manufacturer’s target was the elimination of CO and HC emissions. The cordierite particulate filter is installed directly downstream of the
10.1021/ie020379t CCC: $22.00 © 2002 American Chemical Society Published on Web 09/20/2002
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Figure 1. Experimental layout: T, temperature thermocouple; P, pressure transducer. Table 1. Diesel Engine Specifications manufacturer engine type cylinders displacement compression ratio injection system type rated power rated torque
Volkswagen direct injection, turbocharged, intercooled four, in line 1896 cm3 19.5:1 Bosch VP 34 66 kW at 4000 rpm 182 Nm at 2300 rpm
Table 2. Geometrical Data of the Oxidation Catalyst catalyst diameter (mm) catalyst length (mm) channel density (cells/in.2) wall thickness (mm)
130 100 400 0.15
Table 3. Geometrical Data and Thermophysical Properties of the Particulate Filter filter material cell density (cells/in.2) wall thickness (mm) diameter (mm) length (mm) plug length (mm) substrate permeability (m2) substrate density (kg/m3)
cordierite 100 0.43 144 152 10 4 × 10-3 1600
oxidation catalyst. The geometrical and thermophysical properties of the filter are given in Table 3. The intake air mass flow rate is continuously measured by a hot wire anemometer placed in the engine intake manifold. Two identical pressure transducers (JUMO type 4 A Ä P-30; measurement range -1 to +3 bar) are placed at the inlet and outlet of the particulate filter to monitor the pressure drop. Temperatures are measured simultaneously at three locations: catalyst inlet, filter inlet, and filter outlet using three thermocouples Ni-Cr-Ni with 0.5 mm thickness. The carbon monoxide concentrations are measured using a nondispersive infrared (NDIR) analyzer (Horiba VIA-510). For carbon dioxide, an NDIR analyzer (Hartmann & Braun Utas 3G) is used. The NO and NOx concentrations are measured by a chemiluminescence (Signal series 4000) analyzer. The NO2 concentration is calculated by the difference between NOx and NO
concentrations. Gas analysis is performed by sampling before and after the particulate filter alternatively using a three-way valve. Universal exhaust gas oxygen (UEGO) sensors are placed upstream of the catalyst and downstream of the filter. These sensors provide the air-to-fuel (A/F) mass ratio, which is used together with the intake air flow to calculate the exhaust mass flow rate. The A/F ratio can be used together with the exhaust gas analysis to calculate the O2 content in the exhaust gas. The signals of the measuring instruments (thermocouples, pressure transducers, sensors, and exhaust analyzers) were recorded in a PC through an A/D converter. The fuel used for these experiments was the Environmental Class 1 low sulfur content fuel (less than 10 ppm wt S). The tests were carried out at selected steady-state engine operating points, defined by constant engine revolutions and torque. The engine-out soot mass emissions rates at all of these operating points were known from previous measurements. Each steady-state operating point was held constant for 9-12 min, before switching to the next point. This time period was sufficient to ensure stabilization of the engine operating conditions and the filter temperature. Experimental Results A typical example of the main recordings during the experiments is presented in Figure 2. Periodically, the engine is operated at a fixed “reference” point (4000 rpm/40 Nm) easily recognized in the figure by the high exhaust flow rate (>0.08 kg/s). The backpressure measured at these conditions can be used for a first assessment of the soot loading in the filter. Moreover, because of the high soot emissions rate at these conditions, this operating point is also used to load the filter with soot when desired. The figure contains the measured filter temperature, the exhaust flow rate, the NOx and NO2 concentrations at filter inlet, and the backpressure. The bottom graph is a computational assessment of the instantaneous soot mass in the filter. This is performed, in principle, by using a model-based procedure involving an “inverse” solution of the pressure drop problem, solving for the soot mass as a function of the exhaust flow rate, temperature, and backpressure. The pressure drop model used for this calculation is presented below. More details on this calculation procedure are given elsewhere.19 After initial operation at the reference point, the engine operates at three successive operating points (700-2500 s) corresponding to conditions of relatively low flow rate, moderate-to-high NOx emissions, and temperatures ranging from 290 to 340 °C. The NO2 content at the filter inlet is around 250 ppm. The backpressure remains almost constant at each one of the three operating points, indicating “equilibrium” conditions. This is also indicated by the estimated evolution of soot mass, as shown in the bottom graph. The three operating points between 2800 and 4400 s are characterized by low flow rate, temperatures between 340 and 380 °C, and quite high NOx emissions. Combined with the favorable temperature for oxidation catalyst activity, the NO2 concentration at the filter inlet reaches values close to 400 ppm. The backpressure shows a very small decreasing trend (barely visible because of the graph scaling). However, the soot mass assessment indicates a net soot consumption of about
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Figure 2. Test protocol: typical recordings during a series of steady-state points operation.
2 g. The soot consumption is also visible by comparing the measured backpressure at the reference point at 2800 and 4400 s. From 4700 to 8200 s, the engine is operated at conditions of high temperature (>400 °C). The flow rate is moderate-to-high, and the NOx emissions are between 700 and 900 ppm. The NO2 concentration at the filter inlet is always around 200 ppm. Looking at the backpressure traces, especially at the reference point as well as the estimated soot mass evolution, it is clear that
these operating points are characterized by net soot accumulation, even though the temperature is high. Finally, between 8500 and 9600 s the two operating points are characterized by low flow rate, high NOx and NO2 emissions (250-360 ppm), and temperatures on the order of 370-390 °C. The backpressure indications and the soot assessment show clearly a significant net soot consumption. Summarizing the findings of this experiment, the NO2 reactivity with soot and the net result on filter soot
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occur at low-flow-rate conditions, high NO2 concentration in the filter, and temperatures between 350 and 400 °C. A thorough understanding of the phenomenon would be possible by describing the related phenomena in a mechanistic mathematical model, validated by experimental data. This is actually the scope of the work described onward. To generate a sufficiently large experimental database, 44 operating points have been tested covering a wide range of combinations of different conditions regarding temperature, flow rate, NO2 concentration, and soot loading. Figure 3 shows the operating points on the speed-load diagram of the engine. More details about the conditions prevailing at each operating point are given in Table 4. The numbering of the operating conditions does not refer to the order in which they have been conducted. The soot loading mentioned in this table was assessed at the beginning of each test point by the inverse soot mass calculation as discussed previously. It was avoided to work at temperatures higher than 450 °C to minimize the contribution of thermal soot oxidation with O2. Table 4 also includes the NO and CO production in the filter, as well as the index of the NO2-soot reaction selectivity R2, defined below.
Figure 3. Operating points on the engine speed-load map.
loading depend on a number of parameters in a nontrivial way. The best regeneration behavior seems to Table 4. Test Matrix
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
filter inlet temp (°C)
exhaust flow rate (kg/s)
NOx/soot ratio
NOx filter inlet (g/h)
NO2/NOx ratio
estimated soot loading (g)
∆(NO) in filter (ppm)
∆(CO) in filter (ppm)
index R2 (eq 3)
165 243 249 250 220 255 253 248 267 249 275 330 275 324 299 296 331 324 330 318 332 328 370 387 334 377 376 375 372 379 377 366 372 397 387 428 406 425 391 424 438 426 424 416
0.0229 0.0222 0.0283 0.0387 0.0258 0.0437 0.0362 0.0387 0.0380 0.0573 0.0480 0.0229 0.0226 0.0340 0.0326 0.0244 0.0477 0.0459 0.0581 0.0645 0.0684 0.0570 0.0348 0.0340 0.0333 0.0548 0.0477 0.0620 0.0738 0.0717 0.0770 0.0778 0.0817 0.0398 0.0323 0.0727 0.0409 0.0853 0.0516 0.0502 0.0541 0.0659 0.0849 0.0781
32.7 21.6 18.9 15.7 14.9 19.2 12.5 9.3 13.8 15.8 9.5 51.8 30.2 20.2 26.2 24.9 16.7 14.2 13.9 14.6 13.1 8.8 29.6 31.0 30.3 16.1 14.0 11.4 10.5 12.8 12.9 12.2 9.3 20.3 25.2 15.2 11.2 12.8 11.2 10.3 11.0 8.8 10.6 7.7
22.9 41.0 47.2 44.1 28.3 53.6 37.6 36.5 49.8 75.6 50.6 82.9 66.4 91.1 65.4 94.5 92.1 85.4 90.3 133.9 144.5 83.3 118.5 108.4 81.9 136.9 104.8 153.6 168.0 166.9 168.3 179.6 158.2 91.3 88.1 197.2 101.2 185.4 111.9 112.9 131.9 149.0 204.1 169.2
0.27 0.13 0.14 0.12 0.16 0.13 0.11 0.10 0.16 0.47 0.17 0.31 0.33 0.19 0.26 0.25 0.20 0.19 0.19 0.26 0.25 0.20 0.29 0.31 0.32 0.28 0.27 0.32 0.37 0.29 0.26 0.31 0.33 0.38 0.27 0.32 0.26 0.33 0.27 0.21 0.21 0.25 0.31 0.31
9.7 17.4 15.2 16.6 9.9 17.2 15.5 16.0 13.2 7.3 11.0 8.7 7.5 17.8 7.5 7.6 18.1 19.4 18.4 11.7 19.0 19.9 8.1 15.0 7.4 2.4 21.6 21.9 22.4 2.8 14.7 12.8 23.2 11.9 7.3 23.0 8.9 22.8 9.2 11.6 9.6 12.3 13.6 13.3
8 12 13 23 22 31 13 16 15 55 26 264 131 76 71 100 80 68 51 85 95 61 307 280 169 172 153 179 180 153 107 128 128 287 255 206 235 167 178 164 176 180 171 186
1 2 2 1 1 1 1 1 2 8 5 42 17 25 18 27 14 13 11 5 13 9 47 45 32 29 30 27 26 25 21 20 19 42 45 36 42 28 27 34 40 33 35 31
1.78 1.71 1.73 1.92 1.91 1.94 1.86 1.88 1.76 1.75 1.68 1.73 1.77 1.50 1.60 1.57 1.70 1.68 1.65 1.89 1.76 1.74 1.73 1.72 1.68 1.71 1.67 1.74 1.75 1.72 1.67 1.73 1.74 1.74 1.70 1.70 1.70 1.71 1.74 1.66 1.63 1.69 1.66 1.71
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Figure 4. Soot consumption rate vs temperature.
As a first step for the analysis and understanding of the experimental results, it is reasonable to assume that the following general soot oxidation reactions prevail under real-world conditions:
C + R1O2 f 2(R1 - 0.5)CO2 + 2(1 - R1)CO
(1)
C + R2NO2 f R2NO + (2 - R2)CO + (R2 - 1)CO2 (2) where R1 and R2 are indexes of the completeness of the reactions,20 characterizing the selectivity toward CO or CO2 production. The direct reaction with O2 is mentioned here only for reasons of completenessbecause it is unlikely to be significant at temperatures below 450 °C, which is the case in all of our measurements. Therefore, any soot consumption will occur from reaction with NO2. By measurement of the exhaust flow rate m ˘ g, the CO and NO production in the filter, it is possible to calculate R2 of reaction (2) as well as the apparent rate of soot consumption by NO2 as below. From the stoichiometry of reaction (2):
∆(NO)/∆(CO) R2 ) 2 1 + ∆(NO)/∆(CO)
(3)
The value of R2 for all measurement points is presented in Table 4. When the low-temperature conditions ( 350 °C and lower rates at T < 350 °C. Exactly the opposite will hold for lower activation energies. Figure 8 presents a comparison of the apparent and the computed gross soot consumption rates due to the C + NO2 reaction for four different sets of kinetic parameters. The apparent rate is inferred by adding the net apparent consumption rate (as described above) with the raw engine soot emissions rate. The ideal fitting line (y ) x) is also given in these graphs for comparison with the respective fitting curves to facilitate judgment of the optimum fit. Additionally, Table 6 presents the linear fitting laws obtained with different parameters set for activation energies ranging from 10 to 80 kJ/mol, together with the respective correlation coefficient. From
these results, it can be concluded that the activation energy of 40 kJ/mol provides an optimum linear fit with a very good correlation coefficient of 0.989. This approach illustrates the potential of combining measurements with modeling toward providing at least a rough indication of the governing kinetics at real exhaust conditions. Concluding Remarks In the presented work, engine experiments together with mathematical modeling have been employed toward understanding and describing the reaction phenomena involving NO2 under realistic conditions. The followed approach has a number of advantages and drawbacks compared to usual laboratory practice. In the case of reaction studies with synthetic gas, it is very difficult to simulate exactly the reaction conditions in regards to the composition of the real diesel exhaust. Moreover, the reactor parameters, including residence time, soot composition, and packing conditions, are rarely representative of the real-world conditions in the particulate filter. Modeling of the reaction kinetics in laboratory conditions is easier and straightforward by plotting Arrhenius curves, but the kinetic parameters cannot be directly used in a complete particulate filter simulation model. In the approach presented in this paper, all of the above difficulties are handled by employing engine experiments and using a mathematical model of the complete DPF operation. This model includes the prediction of the flow, temperature, and pressure distribution along the filter at both steady-state and transient conditions. The unknown parameters remain the kinetic constants to be used in the NO2-induced reaction with soot, which were fitted based on the experimental database of 44 different operating points. The main drawbacks of the procedure followed are related first to the inherent difficulty of achieving perfectly repeatable and steady-state in-engine operation and second to the inability to measure directly the soot depletion rate in the filter. The indirect method proposed here, which is based on the measurement of the exhaust gas composition before and after the filter, is subject to minor inaccuracies when measuring small differences. The experimental and modeling results showed that the role of the NO2 as a regeneration agent can be
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Figure 8. Sensitivity analysis of model results against the reaction kinetic parameters of the NO2 + carbon reaction.
significant at selected operating points when using lowsulfur fuel and a standard oxidation catalyst upstream of the filter. These operating points are characterized by high NO2 emissions upstream of the filter. It is sensed that an optimized oxidation catalyst with an increased reactivity for NO to NO2 conversion would allow much higher potential for NO2-assisted soot regeneration. This will be a subject of further research. In regards to the reaction mechanism of soot oxidation by NO2, an apparent Arrhenius-type reaction rate was found to be satisfactory for all of the conditions tested. The activation energy derived is close to the reported values for this reaction with synthetic gas. Overall, the model predictions in terms of prediction of the soot accumulation or depletion rate in the filter are promising. The transient model is readily applicable to transient conditions, which is especially interesting in order to simulate the filter performance in transient cycles used for emissions measurement of diesel engines.29
Acknowledgment The director (Associate Professor Z. Samaras) and the laboratory personnel (P. Pistikopoulos and A. Tzilvelis) of the Laboratory of Applied Thermodynamics, Aristotle University Thessaloniki, are gratefully acknowledged for their support in setting up and carrying out the experimental work. Notation Variables A ) frequency factor, m/s‚K A/F ) air to fuel mass ratio b ) soot layer width, m C4 ) slip correction factor, 500 ms/(kg‚mol‚T)1/2 Cp ) specific heat capacity, J/kg‚K CRT ) continuously regenerating trap
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Nomenclature
Literature Cited
D ) channel hydraulic diameter, m DPF ) diesel particulate filter E ) apparent activation energy, J/mol EGR ) exhaust gas recirculation h ) heat convection coefficient, W/m2‚K Hcond ) conductive heat flux, W/m2 Hreact ) reaction heat release, W/m2 ∆Ha ) heat of adsorption, J/mol ∆Hk ) enthalpy of reaction, J/mol k ) rate of soot oxidation, m/s k0 ) permeability of the particulate deposit layer, 4.2 × 10-11 m2 kp ) apparent permeability of the particulate deposit layer, m2 ks ) permeability of the ceramic substrate, 1.2 × 10-12 m2 M ) molecular weight, kg/mol m ) mass, kg m ˘ ) mass flow rate, kg/s NDIR ) nondispersive infrared p ) pressure, bar p0 ) reference pressure for soot permeability, 103 250 Pa ∆p ) trap backpressure, bar R ) universal gas constant, J/mol‚K R2 ) correlation coefficient sp ) specific area of the deposit layer, m-1 t ) time, s T ) temperature, K UEGO ) universal exhaust gas oxygen sensors v ) velocity, m/s w ) thickness of the deposit layer, m ws ) channel wall thickness, m x ) distance across the soot layer, m yk ) species concentration (mole fraction) z ) axial distance, m
(1) Salvat, O.; Marez, P.; Belot, G. Passenger Car Serial Application of a Particulate filter System on a Common Rail Direct Injection Diesel Engine; SAE: Warrendale, PA, 2000; Paper 200001-0473. (2) Khair, M.; Lemair, J.; Fischer, S. Achieving Heavy-Duty Diesel NOx/PM Levels Below the EPA 2002 StandardssAn Integrated Solution; SAE: Warrendale, PA, 2000; Paper 2000-010187. (3) Chandler, G. R.; Cooper, B. J.; Harris, J. P.; Thoss, J. E.; Uusima¨ki, A.; Walker, A. P.; Warren, J. P. An Integrated SCR and Continuously Regenerating Trap System to Meet Future NOx and PM Legislation; SAE: Warrendale, PA, 2000; Paper 2000-01-0188. (4) Lu¨ders, H.; Stommel, P.; Geckler, S. Diesel Exhaust TreatmentsNew Approaches to Ultralow Emission Diesel Vehicles; SAE: Warrendale, PA, 1999; Paper 1999-01-0108. (5) Zelenka, P.; Egert, M.; Cartellieri, W. Ways to Meet Future Emission Standards with Diesel Engine Powered Sport Utility Vehicles; SAE: Warrendale, PA, 2000; Paper 2000-01-0181. (6) Cooper, B. J.; Thoss, J. E. Role of NO in Diesel Particulate Emission Control; SAE: Warrendale, PA, 1989; Paper 890404. (7) Cooper, B. J.; Jung, H. J.; Thoss, J. E. Treatment of Diesel Exhaust Gases. U.S. Patent 4,902,487, 1990. (8) Hawker, P.; Myers, N.; Hu¨thwohl, G.; Vogel, H. T.; Bates, B.; Magnusson, L.; Bronnenberg, P. Experience with a New Particulate Trap Technology in Europe; SAE: Warrendale, PA, 1997; Paper 970182. (9) Allanson, R.; Blakeman, P. G.; Cooper, B. J.; Hess, H.; Silcock, P. J.; Walker, A. P. Optimising the Low Temperature Performance and Regeneration Efficiency of the Continuously Regenerating Diesel Particulate Filter (CR-DPF) System; SAE: Warrendale, PA, 2002; Paper 2002-01-0428. (10) Ecopoint, Inc. CRT Filter. DieselNet Technology Guide, http://www.dieselnet.com, Revision 2002. (11) Jacquot, F.; Logie, V.; Brilhac, J. F.; Gilot, P. Kinetics of the oxidation of carbon black by NO2. Influence of the presence of water and oxygen. Carbon 2002, 40, 335-343. (12) Liu, S.; Obuchi, A.; Uchisawa, J.; Nanba, T.; Kushiyama, S. An exploratory study of diesel soot oxidation with NO2 and O2 on supported metal oxide catalysts. Appl. Catal. B 2002, 37 (4), 309-319. (13) Setiabudi, A.; van Setten, B. A. A. L.; Makkee, M.; Moulijn, J. A. The influence of NOx on soot oxidation rate: molten salt versus platinum. Appl. Catal. B 2002, 35 (3), 159-166. (14) Stanmore, B. R.; Brilhac, J. F.; Gilot, P. The oxidation of soot: a review of experiments, mechanisms and models. Carbon 2001, 39, 2247-2268. (15) Ciambelli, P.; Palma, V.; Russo, P.; Vaccaro, S. The role of NO in the regeneration of catalytic ceramic filters for soot removal from exhaust gases. Catal. Today 2000, 60, 43-49. (16) Mul, G.; Zhu, W.; Kapteijn, F.; Moulijn J. A. The effect of NOx and CO on the rate of transition metal oxide catalyzed carbon black oxidation: An exploratory study. Appl. Catal. B 1998, 17, 205-220. (17) Kandylas, I. P.; Koltsakis, G. C. NO2-Assisted Regeneration of Diesel Particulate Filters: A Modeling Study. Ind. Eng. Chem. Res. 2002, 41, 2115-2123. (18) Goergens, G.; Strauss, A.; Willmann, M. Ein neuer Turbodieselmotor mit Direkteinspritzung und 1,9 l Hubraum (A New 1.9-1-Turbocharged Diesel Engine with Direct Injection). Motortech. Z. 1992, 53, 94-103. (19) Haralampous, O. A.; Kandylas, I. P.; Koltsakis, G. C.; Samaras, Z. C. Diesel particulate Filter pressure Drop. Part II: On Board Calculation of Soot Loading. Int. J. Energy Res., submitted for publication. (20) Jacquot, F.; Logie, V.; Brilhac, J. F.; Gilot, P. Kinetics of the oxidation of carbon black by NO2. Influence of the presence of water and oxygen. Carbon 2002, 40, 335-343. (21) Bissett, E.; Shadman, F. Thermal Regeneration of DieselParticulate Monolithic Filters. AIChE J. 1985, 31 (5), 753. (22) Bissett, E. J. Mathematical Model of the Thermal Regeneration of a wall-flow monolith diesel particulate filter. Chem. Eng. Sci. 1984, 39 (7/8), 1233-1244.
Greek Letters R1 ) index of the completeness of thermal soot oxidation (0.9) R2 ) index of the completeness of the NO2-soot reaction (1.7) R ) constant in channel pressure drop correlation β ) Forchheimer pressure drop coefficient, 8 × 109 m-1 λ ) thermal conductivity, W/m‚K µ ) exhaust gas viscosity, kg/ms F ) exhaust gas density, kg/m3 Fp ) particulate layer density, 100 kg/m3 Subscripts 0 ) reference c ) carbon g ) exhaust gas i ) space node index, indication of region (1, inlet; 2, outlet channel) in ) inlet conditions j ) indication of the region (1, deposit; 2, ceramic wall) k ) indication of reaction or gaseous reactants (1, O2; 2, NO2) p ) particulate layer s ) ceramic substrate w ) wall
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Received for review May 21, 2002 Revised manuscript received August 20, 2002 Accepted August 21, 2002 IE020379T
