Role of the Chemical Kinetics on Modeling NOx Emissions in Diesel

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Energy & Fuels 2008, 22, 262–272

Role of the Chemical Kinetics on Modeling NOx Emissions in Diesel Engines J. J. Hernández,* J. Pérez-Collado, and J. Sanz-Argent UniVersidad de Castilla-La Mancha. Departamento de Mecánica Aplicada e Ingeniería de Proyectos, and E.T.S. Ingenieros Industriales. AVenida Camilo José Cela s/n. 13071 Ciudad Real, Spain ReceiVed July 27, 2007. ReVised Manuscript ReceiVed September 29, 2007

New diesel engine strategies (involving high injection pressure and multiple injections) have been proposed in recent years aiming to reduce pollutant emissions (mainly NOx and particulate matter). These strategies have led to very fast combustion processes as a consequence of the improvement on the fuel atomization, evaporation, and air entrainment phenomena. Although NOx emissions models for diesel engines usually assume equilibrium and/or the steady state hypothesis together with the consideration of very simplified kinetic reaction mechanisms (such as the Lavoie method based on the extended Zeldovich reaction mechanism), modern diesel engine combustion models require more complex chemical kinetic approaches due mainly to the lack of time to reach the equilibrium state. These kinetic considerations are even more important for simulating new diesel combustion concepts (such as homogeneous charge compression ignition (HCCI) and low temperature combustion (LTC)), which are well-known to be kinetically controlled. In such a frame, this work shows, through a reaction mechanism which considers 83 reactions and 38 chemical compounds, the role of the kinetics on the local NO formation/destruction paths under typical diesel engine conditions. The analysis has been carried out for different combustion and dilution rates, showing that equilibrium assumptions overestimate the engine NO emissions. Reactions controlling NO formation during both the combustion and dilution processes have been identified through a sensitivity analysis carried out by using the chemical package CHEMKIN 4.0. This analysis suggests a coupling between the fuel oxidation process and the thermal NO mechanism, which is not considered in most of the diesel engine NOx models. Finally, the differences in modeled engine NO emissions caused by the uncertainties derived from the different kinetic rate values used in the literature are also presented, showing a significant need for more reliable experimental kinetic data obtained under engine pressure and temperature conditions.

1. Introduction In the last years, the presence of diesel engine vehicles in the European car fleet has reached all-time levels due mainly to their higher efficiency (which implies lower CO2 emissions) when compared to petrol-fueled vehicles. However, the vehicle industry faces stringent legislative restrictions on pollutant emissions (Euro IV1 and future Euro V), nitrogen oxides (NOx, mainly NO) and particulate matter (PM) being the main regulated diesel emissions. This fact has promoted the development of emission reduction techniques that affect not only the combustion process (high injection pressure, exhaust gas recirculation (EGR), homogeneous charge compression ignition (HCCI), etc.) but also the pollutant emissions once they have been formed, thus acting in the exhaust system (DeNOx catalysers, particulate matter traps, etc.). In order to contribute to the design and optimization of current and future diesel engines and to minimize the number of very expensive and hardworking experimental tests, combustion models for pollutant prediction provide a better understanding of the very complex physical and chemical phenomena involved in diesel combustion, thus allowing the establishment of cause-effect relationships between the engine operating conditions (load, speed, injection rate, etc.) and the pollutant emissions level. * Corresponding author. Phone: 34 926 295300 ext 3880. Fax: 34 926295361. E-mail: [email protected]. (1) Directive 98/69/EC of the European Parliament and of the Council of 13 October 1998. Official J. Eur. Communities 1998, L350, 1–56.

Owing to the very complex and unknown chemical kinetic mechanisms regarding the oxidation of a diesel fuel (mainly due to its content on a great variety of medium-large molecular weight hydrocarbons whose oxidation paths are not well-known yet) and to the computational difficulties (too high solving time) regarding the consideration of kinetic schemes in engine fluiddynamic codes, very simplified reaction mechanisms together with chemical equilibrium and/or steady state assumptions have been widely used for estimating pollutant emissions, the Lavoie method based on the extended Zeldovich mechanism2 being the method typically used for engine purposes.3–9 However, new direct injection (DI) diesel engine strategies (involving high injection pressure, multiple injections, and high turbocharger (2) Lavoie, G. A.; Heywood, J. B.; Keck, J. C. Combust. Sci. Technol. 1970, 1, 313–326. (3) Pipho, M. J.; Kittelson, D. B.; Zarling, D. D. NO2 formation in a diesel engine. SAE Paper 910231, Society of Automotive Engineers: Warrendale, PA, 1991. (4) Arcoumanis, C.; Jou, C. S. Proc. Inst. Mech. Eng. 1992, C448/039, 97–105. (5) Rakopoulos, C. D.; Hountalas, D. T. Development and validation of a 3-D multizone combustion model for the prediction of DI diesel engines performance and pollutant emmissions. SAE Paper 981021, Society of Automotive Engineers: Warrendale, PA, 1998. (6) Bazari, Z. A DI diesel combustion and emmission predictive capability for use in cycle simulation. SAE Paper 920462, Society of Automotive Engineers: Warrendale, PA, 1992. (7) Egnell, R. A simple approach to studying the relation between fuel rate, heat release rate and NO formation in diesel engines. SAE Paper 199901-3548, Society of Automotive Engineers: Warrendale, PA, 1999. (8) Gao, Z.; Schreiber, W. Int. J. Energy Res. 2001, 2, 177–188.

10.1021/ef700448w CCC: $40.75  2008 American Chemical Society Published on Web 11/15/2007

Modeling NOx Emissions in Diesel Engines

Energy & Fuels, Vol. 22, No. 1, 2008 263

Table 1. Forward Kinetic Constants for the Considered Reactions kf reaction

A

m

Ea

ref

7470 3160 1828 0 -900 0

31 31 32 33 33 33

H + O2 S OH + O H2 + O S OH + H H2 + OH S H + H2O OH + OH S O + H2O O + O + M S O2 + M H + H + M S H2 + M

Dissociation/Recombination of Radicals (H/O/OH) 9.76E+10 0 5.12E+01 2.67 1.17E+06 1.3 6.00E+05 1.3 1.89E+07 0 1.00E+12 -1

7. H + OH + M S H2O + M

M: H2 ) 0/H2O ) 0/CO2 ) 0 1.60E+16 -2

0

33

8. H + O2 + M S HO2 + M

M: H2O ) 5 3.61E+11

0

33

0 0

33 3

1.3 0 0 0

-385 11548 20645 1515

34 33 33 33

Thermal NO Formation/Destruction 3.30E+09 0.3 6.43E+06 1 4.10E+10 0

0 3145 0

33 23 23

0 0 0 0

25980 14199 14199 7600

33 33 33 34

NO2 Formation/Destruction 2.11E+09 0 1.00E+10 0 3.47E+11 0

-240 300 740

33 34 34

1. 2. 3. 4. 5. 6.

9. HO2 + H S H2 + O2 10. O + H + M S OH + M

-0.72

M: H2O ) 18.6/CO2 ) 4.2/H2 ) 2.9/CO ) 2.1/ N2 ) 1.3 1.25E+10 0 6.20E+10 -0.6 M: H2O ) 5

11. 12. 13. 14.

CO CO CO CO

+ + + +

OH S CO2 + H HO2 S CO2 + OH O2 S CO2 + O O + M S CO2 + M

15. N + NO S N2 + O 16. N + O2 S NO + O 17. N + OH S NO + H 18. 19. 20. 21.

N2O N 2O N 2O N2O

+ + + +

M S N2 + O + M O S NO + NO O S N 2 + O2 H S N2 + OH

22. NO + HO2 S NO2 + OH 23. NO2 + O S NO + O2 24. NO2 + H S NO + OH

CO Formation/Destruction 1.51E+04 5.80E+10 1.60E+10 6.20E+08

N2O Formation/Destruction 1.62E+11 1.00E+11 1.00E+11 7.59E+10

25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

HCN + O f NCO + H HCN + O f NH + CO CN + H2 S HCN + H HCN + OH S CN + H2O CN + OH f NCO + H CN + O2 f NCO + O NCO + H f CO + NH NCO + NO f N2 + CO2 NCO + O f NO + CO NCO + NO S N2O + CO

Cyano compounds reactions 1.38E+01 2.64 3.45E+00 2.64 2.95E+02 2.45 1.45E+10 0 6.02E+10 0 7.23E+09 0 5.00E+10 0 1.39E+15 -1.73 2.00E+10 0 1.00E+10 0

2508 2508 1124 5509 0 -210 0 380 0 -196

33 33 33 33 31 31 33 31 33 33

35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

NH3 + OH S NH2 + H2O NH3 + H S NH2 + H2 NH2 + H S NH + H2 NH2 + OH S NH + H2O NH2 + NO S N2 + H2O NH + H S N + H2 NH + O f NO + H NH + OH S N + H2O NH + O f N + OH NH + NO S N2O + H NH + NO S N2 + OH NH + O2 f NO + OH

NHx Reactions 2.04E+03 6.36E+02 6.92E+10 4.00E+03 6.20E+12 1.02E+10 9.20E+10 5.00E+08 7.00E+08 2.40E+12 2.20E+10 7.60E+07

2.04 2.39 0 2 -1.3 0 0 0.5 0.5 -0.8 -0.23 0

285 5111 1838 503 0 0 0 1007 0 0 0 771

33 33 33 33 33 31 11 34 11 33 11 33

47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57.

S2 + O S SO + S S + O2 S SO + O S + OH S SO + H SO + O + M S SO2 + M SO + OH S SO2 + H SO + O2 S SO2 + O SO2 + O + M S SO3 + M SO3 + O S SO2 + O2 COS + O S SO + CO HS + H S S + H2 HS + O S S + OH

Sulfur Compound Reactions 6.31E+08 0.5 6.31E+08 0.5 7.20E+10 0 1.20E+16 -1.84 1.00E+11 0 1.81E+08 0 1.00E+11 0 2.80E+11 0 6.60E+09 0 5.16E+11 0 6.31E+08 0.5

0 0 323 0 0 2820 0 6040 0 1057 4030

35 35 36 36 37 35 37 35 37 36 35

264 Energy & Fuels, Vol. 22, No. 1, 2008

Hernández et al. Table 1. Continued kf

reaction

A

m

Ea

ref

0 0 0 0 0 0

323 1660 859 452 0 0

36 35 36 35 37 37

0 3 2.1 0 0 0 0 1.18 1.62 0 0 0 0 0 0 1.88 -0.78 0 0 0

43303 4045 1236 22864 906 0 7930 -225 1090 0 15504 0 12629 2985 7487 91 1579 -126 21148 201

38 31 29 29 29 32 29 11 27 31 39 29 27 31 31 11 11 33 11 11

58. 59. 60. 61. 62. 63.

HS + O S SO + H H2S + O S HS + OH H2S + H S HS + H2 H2S + OH S HS + H2O SO + NH S HS + NO N + SO S NO + S

3.56E+11 4.34E+09 1.20E+10 1.40E+10 1.00E+10 5.10E+08

64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83.

CH4 + M S CH3 + H + M CH4 + H S CH3 + H2 CH4 + OH S CH3 + H2O H2O2 + M S OH + OH + M H2O2 + OH S H2O + HO2 HCO + H S CO + H2 HCO + M S CO + H + M CH2O + OH S HCO + H2O CH2O + H S HCO + H2 CH3 + O S CH2O + H CH3 + O2 S CH3O + O CH3O + H S CH2O + H2 CH3O + M S CH2O + H + M C2H4 + OH S C2H3 + H2O C2H4 + H S C2H3 + H2 C2H4 + O S CH2HCO + H C2H3 + O2 S CH2HCO + O C2H3 + O2 S CH2O + HCO CH2HCO S CH3 + CO HCO + O2 S CO + HO2

C1 and C2 Oxidation 1.00E+14 1.32E+01 1.60E+03 1.30E+14 1.00E+10 1.00E+11 1.59E+11 3.40E+06 1.26E+05 8.43E+10 4.30E+10 2.00E+10 1.00E+11 2.00E+10 5.40E+11 4.70E+03 2.50E+12 4.00E+09 1.00E+13 7.60E+09

levels) have led to a very fast combustion process (which takes place mostly on the diesel jet contour) due to the improvement of the atomization, evaporation, and air entrainment phenomena. Thus, despite of the high local burnt temperature inside the combustion chamber, more complex kinetic reaction mechanisms are required to obtain more reliable results due to several reasons: the lack of time to reach the equilibrium state (mainly for the radical species controlling the combustion process, such as H, OH, and HO2), the kinetically controlled autoignition of some part of the fuel when pilot and/or postinjections are used (as occurs in HCCI engines, where the H2O2 plays also an important role),10 the current observed destruction of NO through reaction with unburnt hydrocarbons (reburning) derived from the use of high EGR rates (as occurs in low temperature combustion (LTC) processes),11–14 and the use of NOx control techniques based on kinetic aspects (such as selective noncatalytic reduction (SNCR), which involves the addition of urea (CO(NH2)2) or ammonia (NH3) to the combustion products at the end of the engine expansion stroke15,16). Besides the need of more complex kinetic approaches, the time evolution of the local equivalence fuel/air ratio ((F/A)r, defined with respect to the stoichiometric one) during the engine (9) Miller, R.; Davis, G.; Lavoie, G.; Newman, C.; Gardner, T. A superextended eldovich mechanism for NOx modelling and engine calibrations. SAE Paper 980781, Society of Automotive Engineers: Warrendale, PA, 1998. (10) Hernandez, J. J.; Sanz-Argent, J.; Benajes, J.; Molina, S. Fuel, published online June 11, http://dx.doi.org/10.1016/j.fuel.2007.05.019. (11) Glarborg, P.; Alzueta, M. U.; Dam-Johansen, K.; Miller, J. A. Combust. Flame 1998, 115, 1–27. (12) Chen, W.; Smoot, L. D.; Fletcher, T. H.; Boardman, R. D. Energy Fuels 1996, 10, 1036–1045. (13) Chen, W.; Smoot, L. D.; Hill, S. C.; Fletcher, T. H. Energy Fuels 1996, 10, 1046–1052. (14) Xu, M.; Fan, Y.; Yuan, J.; Sheng, C.; Yao, H. Int. J. Energy Res. 1999, 23, 157–168. (15) Nam, C. M.; Gibbs, B. M. Proc. Combust. Inst. 2000, 28, 1203– 1209. (16) Miyamoto, N.; Ogawa, H.; Wang, J.; Shudo, T.; Yamazaki, K. Int. J. Vehicle Design 1995, 16, 71–79.

cycle is one of the lesser known processes when modeling diesel combustion, which affects significantly the instantaneous composition of the combustion products and the burnt temperature through the kinetic calculations. Although the local (F/A)r value in the flame has been reported to be very close to the stoichiometric one or slightly rich in diffusion flames,7,17,18 the decreasing rate of this parameter from the injection time until the stoichiometric conditions are reached (at which the complete combustion is believed to occur) is an important factor that affects pollutant emission modeling. After combustion, burnt products are diluted with the excess of air typical of diesel conditions until a complete mixture is achieved, the rate of such a dilution-cooling process being the other uncertainty. The experimental measurements obtained by Dec19 have shown the interaction between the mentioned air mixing rate and the chemical mechanisms that control the pollutant formation. In this work, a chemical kinetic scheme which considers 83 reactions and 38 chemical compounds has been used to analyze the effect of the diesel combustion and dilution rates on the local formation and destruction of NO. The first process studied is the combustion-heating of a fuel package from its initial rich premixed combustion, that takes place at equivalence fuel/air ratios around 4 (according to the diesel combustion conceptual model proposed by Dec19), to its complete combustion at the stoichiometric conditions reached in the jet periphery. The second phenomenon analyzed is the dilution-cooling of the burnt products with the excess of air. Results obtained have allowed the identification of the role of kinetic approaches for modeling diesel NOx emissions when compared to equilibrium assumptions, mainly during the combustion (heating) process. In order to analyze the main reactions controlling the NO formation (17) Glassman, I., Ed. Combustion; Academic Press, Inc.: New York, 1987. (18) Kamimoto, T.; Kobayashi, H. Prog. Energy Combust. Sci. 1991, 17, 163–189. (19) Dec, J. E. Conceptual model of DI diesel combustion based on laser-sheet imaging. SAE Paper 970873, Society of Automotive Engineers: Warrendale, PA, 1997.


during the mentioned combustion-dilution processes, a sensitivity analysis has been carried out by using the kinetic package CHEMKIN 4.0.20 Finally, and due to the significant differences among the kinetic rate values (kf) typically used in the literature, the sensitivity of modeled NO results to the kf value has been analyzed, showing the importance of a proper selection of kf to obtain reliable results and encouraging further and deeper research on the experimental determination of kinetic parameters under engine thermodynamic conditions (high pressure and temperature). The latter study has been carried out by comparing experimental diesel NO emissions with those coming from a complete diesel combustion model, described in ref 21, under several engine conditions (injection pressure and injection timing) and using different kf values for the most sensitive reaction controlling the NO production. 2. Kinetic Reaction Mechanism A generic fuel molecule composed of carbon, hydrogen, oxygen, nitrogen. and sulfur atoms, CnHmOpNkSs, has been used in this work. This molecule permits the extension the range of application not only to conventional diesel fuel but also to fuels in which the oxygen content may not be negligible, such as many biofuels with interesting current and future perspectives. Although NO is the compound on which the present work has been focused, the selection of 38 chemical species in the kinetic scheme was based on two criteria: either they have a significant pollutant effect or they are relevant as precursors of other pollutant species. The following species were selected: N2, O2, CO2, H2O, CO, H2, NO, OH, N, H, O, Ar, N2O, NO2, HO2, H2O2, NH3, NH2, NH, CN, HCN, NCO, CH4, CH3, CH3O, CH2O, CHO, C2H4, C2H3, CH2HCO, S, S2, SO, SO2, SO3, HS, H2S, and COS. The former twelve species are relevant in lean or slightly rich combustion processes of nonsulfured hydrocarbons at high temperature.22,23 The nitrous oxide, N2O, is important for three reasons. First, it constitutes an important intermediate compound in the NO formation path at temperatures below 1500-1600 K.24–26 Second, N2O is produced in significant amounts in locally lean, low temperature regions,27 as it happens in the combustion chamber of a diesel engine operating with high EGR rates. Finally, N2O has higher GWP (global warming potential) than NO. Nitrogen dioxide, NO2, is formed when NO molecules coming from high temperature regions are transported through the mixing process toward low temperature ones where there are significant concentrations of HO2.27 NO2 emissions in diesel engines can reach between 10 and 30% of the total NOx emissions,4,22 and it has higher toxicity than NO as well as higher potential than NO to produce photochemical smog.3 The radical HO2 is not only the main oxidant agent in the conversion from NO to NO2 but constitutes also, together with (20) Kee, R. J. et al. CHEMKIN Collection, release 3.7.1; Reaction Design, Inc.: San Diego, CA, 2003. (21) Hernandez, J. J.; Lapuerta, M.; Perez-Collado, J. Combust. Theory Model. 2006, 10, 639–657. (22) Olikara, C.; Borman, G. L. A computer program for calculating properties of equilibrium combustion products with some applications to I.C. engines. SAE Paper 750468, Society of Automotive Engineers: Warrendale, PA, 1975. (23) Heywood, J. B., Ed. Internal combustion engines fundamentals; McGraw-Hill: New York, 1988. (24) Bowman, C. T. Prog. Energy Combust. Sci. 1975, 1, 33–45. (25) Kramlich, J. C.; Linak, W. P. Prog. Energy Combust. Sci. 1994, 20, 149–202. (26) Tomeczek, J.; Gradon, B. Combust. Sci. Technol. 1997, 125, 159– 180. (27) Turns, S. R., Ed. An introduction to combustion. Concepts and applications; McGraw-Hill: New York, 1996.


radical OH, an important path in the oxidation of any hydrocarbon.23,24,27 H2O2 is involved in some important reactions of recombination and dissociation of the OH and HO2 radicals27 and, as mentioned above, plays an important role during the autoignition of large hydrocarbons (being the most significant species during the low temperature oxidation of these hydrocarbons, causing the so-called “cool flames”). The consideration of species of the types NHx and cyano (CN, HCN, and NCO) is justified because they present significant concentrations at very rich mixture ratios (equivalence fuel/air ratios above 2.5), which might exist locally in the diesel combustion chamber and because they become important intermediate compounds in other NO formation mechanisms such as the prompt and the N-fuel ones.24,27,28 The species CHx and CHxO are important in the decomposition mechanisms of methane,29 which should be considered in locally rich zones under moderate temperature, and they could play a significant role during the NO destruction through the reburning process (the latter causing a decrease in the NO concentration due to reactions with unburnt hydrocarbons derived from the use of high EGR rates). Besides, three other intermediate hydrocarbon compounds have been considered (C2H4, C2H3, and CH2HCO) because their concentrations are also important at low temperatures and rich conditions, these conditions being usually during the premixed rich partial oxidation of the fuel prior to its complete combustion process (as described in the following section). In addition, they could be converted into cyano compounds, which are important in the formation of prompt NO as mentioned above, and their consideration in the kinetic scheme improves the modeling of CO and unburnt hydrocarbons. Finally, although the sulfur content of automotive fuels is not significant (it will be limited to 10 ppm in the year 2009), a set of sulfur compounds has been taken into account in order to extend the model application to the future analysis of particulate matter (PM) formation processes, in which sulfates can play an important roles through the scrubbing effect.30 The kinetic scheme (Table 1) is composed of 83 reactions and uses the fourth-order Rosenbrock method to solve the stiff set of 38 differential equations leading to the calculation of the instantaneous composition of the different species. This method permits a flexible control of the integration step, as well as a selective scaling of errors for each chemical compound. The forward kinetic constants, kf (kmol m3 s), were modeled through Arrhenius type equations (eq 1). The kf data shown in Table 1 were selected among the wide stock of values reported in the literature, trying to find a maximum coherence between different references and certain similitude between the reported temperature and pressure ranges and those used in this work. Anyway, a study to analyze the sensitivity of the model to the kf value is presented at the end of the paper in order to identify the importance of a proper selection of kf when modeling engine NOx emissions.

( )

kf ) AT m exp

-Ea T

(1)

The values for the pre-exponential factor, A, exponent m, and activation energy, Ea, for each reaction, and the reference used, are also listed in Table 1. The backward kinetic constants were (28) Caretto, L. S. Prog. Energy Combust. Sci. 1976, 1, 47–71. (29) Kaplan, C. R.; Patnaik, G.; Kailasanath, K. Combust. Sci. Technol. 1998, 131, 39–65. (30) Duran, A.; Monteagudo, J. M.; Armas, O.; Hernandez, J. J. Fuel 2006, 85, 923–928.


Hernández et al.

obtained from the forward ones and the equilibrium constants referred to concentrations (kmol/m3). In the table, the sign “S” indicates reversible reactions, while “f” indicates single direction reactions. All the considered species were used as thirdbody, M, with efficiency equal to unity, except when efficiency values are indicated below the corresponding reaction. 3. Role of Kinetics on Modeled Engine NO Emissions 3.1. Combustion (Heating) Process. It is usual in pollutant modeling to assume the hypothesis of an instantaneous and adiabatic combustion process when the fuel/air mixture has reached stoichiometric or slightly rich conditions, while considering chemical equilibrium for estimating the composition of the burnt products.3,4 However, despite the high local temperature inside the diesel combustion chamber, the residence time of the gas at this temperature is not high enough for reaching the equilibrium state, and thus, the product compositions are being controlled by the kinetics. As mentioned before, this fact is even more evident in modern direct injection (DI) diesel engines, for which new strategies for reducing pollutant emissions have led to very fast combustion processes. To verify the mentioned statement, a kinetic study has been carried out in order to prove the need of considering the kinetics of the process prior to the complete combustion, by which the fuel mixes with air until the mixture reaches stoichiometric conditions. As diesel combustion is a very heterogeneous process controlled by local composition and thermodynamic conditions, in which fuel is injected in a sequential way (as indicated by the injection system), the study shown in the current section is based on the evolution of a single fuel package (which is identified as the fuel injected in a given period of time). The total engine NO emissions would be calculated as the sum of the local NO emissions corresponding to each fuel package. Anyway, the conclusions obtained about the need for kinetic approaches for a fuel package can be extrapolated to the rest of the injected fuel, the total error derived from equilibrium assumptions being the integrated effect of the single packages errors. A fuel molecule C14.7H28.8O0.096N0.012S0.0017, describing the diesel fuel currently supplied in Spanish petrol stations, has been used in this work. Figure 1 shows the development of a diesel jet from its injection to its complete combustion, as proposed by Dec.19 The progressive leaning of the fuel/air mixture is also illustrated in this figure by means of a schematic equivalence fuel/air ratio ((F/A)r) evolution, starting from the package injection ((F/A)r ) ∞), passing through a rich premixed combustion ((F/A)r ) 4) and finally reaching stoichiometric conditions ((F/A)r ) 1), around which complete combustion is supposed to occur. The local temperature evolution, corresponding to the adiabatic flame temperature at each (F/A)r value considered, is also shown in Figure 1. A constant reactants temperature of 900 K and a constant pressure equal to 80 bar have been used, these values being typical at the end of the compression stroke in turbocharged diesel engines. A generic path of a fuel package has been represented with a dashed line, as an example, for illustrating its correspondence with the (F/A)r and temperature evolution. The kinetic study has been carried out for different combustion (heating) rates: tcomb ) 0.5, 1, 3, 5, 10, and 15 ms, where tcomb represents the time required for a fuel package to reach the stoichiometric conditions starting from the premixed rich combustion ((F/A)r ) 4). This heating process, combined with air mixing, aims to simulate the heat release period of a fuel package from its chemical decomposition to its complete combustion. In order to avoid the consideration of the unknown and very complex oxidation mechanism of the diesel fuel, the

Figure 1. Local (F/A)r and temperature evolutions of a diesel fuel package during the combustion process.

composition of the first point of the evolution ((F/A)r ) 4) has been calculated assuming an instantaneous rich premixed combustion19 at which chemical equilibrium is reached. This composition, in which methane is the main component, is in agreement with that obtained by other authors using diesel fuel surrogate kinetic mechanisms to simulate the premixed combustion process previous to the main diffusion combustion phase.40,41 From (F/A)r ) 4 to the end of the process, the instantaneous composition (as a function of temperature and the increasing amount of mixed air) is calculated through the kinetic scheme shown in Table 1, by solving at each point the set of 38 differential equations leading to the compounds concentration calculation. The instantaneous NO concentration is shown in (31) Baulch, D. L. Combust. Flame 1994, 98, 59–79. (32) Zanforlin, S.; Reitz, R. D.; Gentili, R. Studying the roles of kinetics and turbulence in the simulation of Diesel combustion by means of an extended characteristic-time-model. SAE Paper 1999-01-1177, Society of Automotive Engineers: Warrendale, PA, 1999. (33) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287–338. (34) Salimian, S.; Hanson, R. K. Combust. Sci. Technol. 1980, 23, 225– 230. (35) Wendt, J. O.; Wootan, E. C.; Corley, T. L. Combust. Flame 1983, 49, 261–274. (36) Zachariah, M. R.; Smith, O. I. Combust. Flame 1987, 69, 125– 139. (37) Pfefferler, L. D.; Churchill, S. W. Ind. Eng. Chem. Res. 1989, 28, 1004–1010. (38) Kennedy, I. M.; Yam, C.; Rapp, D. C.; Santoro, R. J. Combust. Flame 1996, 107, 368–382. (39) Hunter, S. C. Trans. ASME 1982, 104, 44–51. (40) Flynn, P. F.; Durrett, R. P.; Hunter, H. L.; zur Loye, A. O.; Akinyemi, O. C.; Dec, J. E.; Westbrook, C. K. Diesel combustion: an integrated view combining laser diagnostics, chemical kinetics, and empirical validation. SAE Paper 1999-01-0509, Society of Automotive Engineers: Warrendale, PA, 1999. (41) Kitamura, T.; Ito, T.; Senda, J.; Fujimoto, H. Extraction of the suppression effects of oxygenated fuels on soot formation using a detailed chemical kinetic model. J. Soc. AutomotiVe Eng. 2001, 22, 139–145. (42) Flynn, P. F.; Hunter, G. L.; Durret, R. P.; Farrell, L. A.; Akinyemi, W. C. Minimum engine flame temperature impacts on Diesel and sparkignition engine NOx production. SAE Paper 2000-01-1177, Society of Automotive Engineers: Warrendale, PA, 2000. (43) Zeldovich, Y. Acta Phys. USSR 1946, 21, 577–628.


Figure 2. NO concentration evolution (ppm) for different tcomb values.

Figure 3. Local (F/A)r ratio and temperature evolutions of a diesel fuel package during the combustion-dilution process.

Figure 2 for the different tcomb values, together with the concentration resulting from assuming chemical equilibrium when complete combustion is reached (nonlinked black circles). As it can be observed in Figure 2, the slower the process (i.e., the more time required by the mixture for reaching stoichiometric conditions), the higher the NO concentration. This can be explained by the increase in the residence time of the gas at high temperature, which causes a higher NO formation due mainly to the thermal mechanism contribution (reactions R15 to R17 in Table 1). Nevertheless, only for tcomb values above 10 ms is the equilibrium state reached. Considering that the residence time of the burnt gas in the diesel flame is believed to remain between 1 and 5 ms,42 Figure 2 emphasizes the importance of the chemical kinetics to simulate the combustion products composition during the diesel combustion process. (44) Kusaka, J.; Daisho, Y.; Ikeda, A.; Saito, H. Proc. CIMAC Congress 1998, 5, 1283–1299. (45) Pedersen, L. S.; Glarborg, P.; Dam-Johansen, K. Combust. Sci. Technol. 1998, 131, 193–223. (46) Zabetta, E. C.; Kilpinen, P.; Hupa, M.; Stahl, K.; Leppälahti, J.; Cannon, M.; Nieminen, J. Energy Fuels 2000, 14, 751–761. (47) Meunier, Ph.; Costa, M.; Carvalho, M. G. Fuel 1998, 77, 1705– 1714.


3.2. Combined Combustion (Heating) and Dilution (Cooling) Processes. Although the previous paragraph shows the effect of the combustion time on the instantaneous NO values, the NO formation is believed to take place mostly in the postcombustion gas rather than inside the flame.43 This evidence has motivated the kinetic study presented in this paragraph, with the aim of analyzing the NO behavior not only during the combustion process but also through the subsequent dilution (cooling) phenomena of the burnt products with the excess of air typical of diesel engines. In this study, different combustion (tcomb ) 0.5, 1.5, 3, and 5 ms) and dilution times (tdil ) 1, 3, 5, and 10 ms) have been used, where tdil represents the time required by the burnt products derived from the complete and stoichiometric combustion (((F/A)r ) 1) to reach the global equivalence fuel/ air ratio in the combustion chamber (which has been supposed to be close to 0.4, typical of diesel engines operating at medium load conditions). Figure 3 shows the (F/A)r and temperature evolution, which are similar to those typically suffered by a fuel package from its rich premixed combustion ((F/A)r ) 4) until its complete dilution ((F/A)r ) (F/A)r,global). Figures 4 and 5 show the kinetic NO concentration evolutions for the different tdil values, together with the equilibrium concentration at each (F/A)r value (dashed line) and that derived from the consideration of chemical equilibrium composition when the complete combustion is reached ((F/A)r ) 1). The variation of the composition along the dilution process (from ((F/A)r ) 1 to (F/A)r ) (F/A)r,global ) 0.4) corresponding to the latter evolution has also been determined through the reaction mechanism presented in Table 1, and this evolution has been identified by eq((F/A)r ) 1) + kinetics. As it can be observed, NO is a kinetically controlled compound, as its concentration is far from the equilibrium composition (dashed line) for the whole process. For slow dilution processes (tdil > 5 ms), the combustion (heating) rate has a small influence on the final NO concentration, this value being very similar to that obtained starting from the chemical equilibrium composition at stoichiometric conditions. This result suggests that equilibrium assumptions for the complete combustion could be reliable enough to predict NO emissions under diesel engine conditions, thus avoiding the consideration of reaction mechanisms in engine models to simulate the fuel decomposition until such complete combustion. However, for fast dilution processes (tdil < 5 ms), such as those taking place in modern diesel engines, significant differences between those concentrations are observed, these differences are also increasing as the combustion process become faster. Thus, equilibrium assumptions overestimate both the NO concentration after the complete combustion (Figure (48) Nightingale, D. R. A fundamental investigation into the problem of NO formation in Diesel engines. SAE Paper 750848, Society of Automotive Engineers: Warrendale, PA, 1975. (49) Way, R. J. Proc. Inst. Mech. Eng. 1977, 190, 687–697. (50) Tinaut, F. V.; Melgar, A.; Horrillo, A. J. Utilization of a quasidimensional model for predicting pollutant emissions in SI engines. SAE Paper 1999-01-0223, Society of Automotive Engineers: Warrendale, PA, 1999. (51) Yu, R. C.; Shaded, S. M. Effect of injection timing and exhaust gas recirculation on emissions from a D.I. diesel engine. SAE Paper 811234, Society of Automotive Engineers: Warrendale, PA, 1981. (52) Clutter, J. K.; Mikolaitis, D. W.; Shyy, W. Proc. Combust. Inst. 2000, 28, 663–669. (53) Easley, W. L.; Mellor, A. M. NO decomposition in diesel engines. SAE Paper 1999-01-3546, Society of Automotive Engineers: Warrendale, PA, 1999. (54) Konnov, A. A.; De Ruyck, J. Proc. Detail. Stud. Comb. Phen. Semin. (EUROTHERM) 1998, 1. (55) Edelman, R. B.; Harsha, P. T. Prog. Energ. Comb. Sci. 1978, 4, 1–62.


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Figure 4. NO concentration evolution (ppm) for tdil ) 1 (left) and 3 ms (right) and different tcomb values.

Figure 5. NO concentration evolution (ppm) for tdil ) 5 (left) and 10 ms (right) and different tcomb values.

Figure 6. Sensitivity coefficients Cj for tcomb ) 1.5 (left) and 3 ms (right).

2) and the NO concentration at the end of the combustion-heating process (Figures 4 and 5), although the dilution with the excess of air compensates the differences between equilibrium assumptions and kinetic approaches (higher differences between both methodologies have been obtained at (F/A)r ) 1). Figures 4 and 5 also show that the maximum NO concentrations obtained with both kinetic and equilibrium approaches get closer when the total time of the process increases due to the greater NO formation, while the differences in the final NO

concentrations become more significant due to the freezing of the thermal NO reactions, which dominate the dilution process as shown in the following section. 4. Reaction Mechanism Sensitivity Analysis A sensitivity analysis has been performed with the CHEMKIN code20 in order to identify the main reaction paths (among those shown in Table 1) involved in the NO formation/destruction



Figure 7. Sensitivity coefficients Cj for tdil ) 2.5 (left) and 5 ms (right). Table 2. Engine Operating Conditions point

pinj (bar)

injection timing (deg before TDC)

A B C D

300 300 1100 1100

0 10 0 10

mechanisms under diesel engine conditions. This analysis has been carried out for both the combustion (heating) and the dilution (cooling) processes of a fuel package, widely described in the previous section. The parameter used for estimating the sensitivity of the reaction j on the NO formation is the sensitivity coefficient (Cj), defined as follows: Cj )

Aj ∂[NO] ∂ln[NO] ) ∂ln Aj [NO] ∂Aj

(2)

where Aj is the pre-exponential factor of the Arrhenius equation for reaction j. A large sensitivity coefficient indicates a strong influence of the reaction on the NO formation (if Cj is positive, that reaction promotes the NO production, while a negative value indicates that the reaction inhibits the NO formation). Figure 6 shows the most important reactions affecting the NO formation during the combustion process for two different combustion rates (tcomb ) 1.5 and 3 ms). As mentioned before, CHx species (mainly methane) have been considered as representative of the hydrocarbons derived from the premixed rich partial oxidation of the fuel ((F/A)r ) 4). Thus, reactions involving these latter products could be representative of the fuel decomposition paths. As it can be observed in Figure 6, the reactions that promote significantly NO formation during the combustion process are reactions R.1 (H + O2 S OH + O), R.73 (CH3 + O S CH2O + H), and R.74 (CH3 + O2 S CH3O + O); the former corresponding to a branching reaction. All these reactions accelerate the fuel decomposition, the first one through the increase in the very reactive OH and O radicals which react preferably with the fuel. Due to the faster fuel extinction (which acts as a radicals sink), a larger availability of H and OH radicals for reacting with N and N2 through the thermal mechanism, mainly through the reaction R.15 (N + NO S N2 + O), favors NO formation (since there is no unburnt hydrocarbons in the high temperature range, in which reaction R.15 plays an important role). Reaction R.66 (CH4 + OH S CH3 + H2O), although it reduces the OH concentration, is a key path in the oxidation process of any fuel (H-abstraction reaction), thus also improving the fuel decomposition. On the contrary, the reactions leading to NO destruction during the combustion process are R.11 (CO + OH S CO2 + H) and R.4 (OH + OH S O +

H2O). Reaction R.11 destroys the very reactive OH radical while reaction R.4 is a termination reaction (causing a lower number of radicals). Thus, they slow down the fuel oxidation process and inhibit the thermal NO formation at high temperatures due to the lack of radicals which react with the unburnt hydrocarbons rather than with the air nitrogen. Reaction R.8 (H + O2 + M S HO2 + M) is also a termination reaction, thus acting as reaction R.4. Figure 6 shows that the combustion time does not have a significant effect on the sensitivity analysis, since similar Cj values have been obtained for 1.5 and 3 ms. CN compounds (reaction R.30) seem to be more important on the NO formation paths for larger combustion processes, in which the prompt NO mechanism could be significant (higher residence time of hydrocarbons in the flame). As also observed in Figure 6, Cj peaks are obtained for temperatures around 1800 K. This temperature is high enough to produce a significant increase in the very reactive radical concentrations (H, OH, and O) through dissociation paths involving more stable compounds (such as HO2 and H2O), thus promoting all the reactions shown in Figure 6. Figure 7 shows the most important reactions affecting NO formation during the dilution (cooling) process for two different dilution rates (tdil ) 2.5 and 5 ms). As observed in that figure, only the extended Zeldovich mechanism reactions (R.15, R.16, and R.17) and one of the reactions including N2O (R.19) affect the NO formation/destruction processes during the dilution process. In addition, the Cj values are smaller than those obtained for the combustion process and they are mostly positive for the whole temperature range, thus contributing to an increase in the NO concentration. The results obtained in this section show that not only should the thermal NO mechanism considered for estimating diesel engine NO emissions but other phenomena involving the radical recombination and dissociation reactions and the fuel decomposition paths should also be taken into account, since they are very significant mainly during the fuel oxidation process at low temperatures. These results suggest a coupling between the combustion process (fuel decomposition) and the NO formation mechanisms, which is not considered in most of the engine combustion models. 5. Sensitivity of Modeled NO Emissions to kf Values The main objectives of this paragraph are to show the influence of the reaction rate parameter (A, m, and Ea) values on the modeled NO emissions ([NO]final) under diesel engine conditions and to emphasize the importance of a proper selection


Hernández et al.

Figure 8. Evolution of kf for reaction R.15.



of these values among those typically used in the literature. In order to avoid an excessive number of calculations, only the most important reactions affecting the NO formation during the dilution process (reactions R.15, R.16, R.17, and R.19) have been analyzed, since those reactions control the NO formation in the postcombustion gas through the widely used thermal NO mechanism. The study has been carried out by comparing experimental engine NO emissions (obtained in a 0.5 l singlecylinder DI diesel engine) with those coming from a complete combustion engine model described in ref 21, in which the experimental setup was also presented. The engine operating conditions (Table 2) were selected among those with a

significant effect on the rate of the combustion process, such as the injection pressure (pinj) and the injection timing (defined with respect to top dead center (TDC)). The engine load and speed were kept constant at (F/A)r,global ) 0.43 and 2250 rpm, respectively. The reference values for kf were those shown in Table 1. For each of the above-mentioned reactions, different modeled NO emission results were obtained by changing the A, m, and Ea parameters of the corresponding reaction, keeping the rest of kf as the reference data. Figures 8-11 show the kf evolution as a function of temperature and the kinetic parameters values for the selected reactions as used by different authors. The



Figure 11. Evolution of kf for reaction R.19 (values derived from ref 26 are represented in the right axis).

Figure 12. NO emission obtained using different correlations for reaction R.15: horizontal line, experimental NO; bars, modelled NO.



literature review has been carried out trying to select the rate constants obtained under thermodynamic conditions (pressure and temperature) similar to those tipically involved during the engine combustion process. Due to the significant differences between the kf data regarding the reaction R.19, two y-axes have

been used, the values shown in ref 26 (dashed line) being the only ones represented in the right side. Figures 12-15 show the experimental and modeled NO emissions for the different engine conditions (points A, B, C, and D). The theoretical NO results correspond to the different


Hernández et al.


correlations shown previously. As it can be observed, there are very significant differences in the theoretical NO results when using different kinetic rate parameters, especially for reactions R.15 and R.19, for which dispersions up to 68% and 20% have been obtained, respectively. As shown in Figures 12 and 15, the kf correlation appearing in the work carried out by Lavoie et al.,2 which is one of the classical references widely used for NO estimation in internal combustion engines, significantly underestimates the NO emission when compared with other kf values, mainly for high injection pressures (typical in current diesel engines). Thus, more reliable experimental data regarding the kinetic rate constants of the main reactions affecting the NO formation and destruction mechanisms under engine conditions are necessary; this issue requires further and deeper research efforts. 6. Conclusions A kinetic reaction mechanism, which considers 38 species and 83 chemical reactions, describing the chemical paths leading to the NOx formation/destruction in high injection pressure diesel combustion has been used in this work in order to analyze the role of kinetic approaches for reliably estimating NOx emissions when compared with equilibrium or steady state assumptions, such as the widely used Lavoie method based on the extended Zeldovich mechanism. The study has been carried out both during the combustion (heating) process of a fuel package (from the fuel package injection to its complete combustion at stoichiometric conditions) and during the subsequent dilution (cooling) of the burnt products with the excess of air typical of diesel engines. The results obtained show that, despite the high local temperature inside the combustion chamber, the residence time of the burnt gas in the flame is not high enough to reach the equilibrium state after the stoichiometric combustion process. Although the dilution (which is responsible for the thermal NO formed in the postcombustion gas) lightly compensates the effect of the combustion time on the NO concentration, this process is too fast in current diesel engines so as to assume equilibrium. A reaction mechanism sensitivity analysis has been carried out in order to identify the main chemical paths causing the NO formation. The results obtained prove that the extended Zeldovich mechanism reactions and one of these describing the intermediate N2O route (N2O + O S NO + NO) are the most

important reactions during the dilution process. However, reactions involving radical dissociation and recombination (such as H + O2 S OH + O, OH + OH S O + H2O, and H + O2 + M S HO2 + M) and the fuel partial oxidation (such as CH3 + O S CH2O + H, CH3 + O2 S CH3O + O, CH4 + OH S CH3 + H2O, and CO + OH S CO2 + H) should be considered during the combustion process due to the coupling between the radical availability (which are mainly responsible for the thermal NO formation) and the fuel decomposition (since radicals react with unburnt or partially burnt hydrocarbons rather than with other nitrogen compounds). This coupling is not considered in most of the engine combustion models including NO formation submodels. Due both to the role of the kinetics on diesel engine NOx modeling and to the uncertainties derived from the rate constant (kf) values usually found in literature, the analysis shown in section 5 proves the need for more reliable kinetic parameters data, mainly for reactions R.15 (N + NO S N2 + O, involved in the thermal NO mechanism) and R.19 (N2O + O S NO + NO). This fact, besides increasing interest in kinetic calculations to simulate new and innovative engine combustion processes (such as HCCI combustion and the use of multiple fuel injections), suggests that further and deeper research on the experimental determination of kf values under engine thermodynamic conditions (high pressure and temperature) is needed. Acknowledgment. The authors wish to acknowledge the Spanish Ministry of Education and Science for the financial support (Project COMEC, ref TRA2004-06739-C04-02).

Nomenclature A ) pre-exponential factor in the Arrhenius equation (m3 kmol s) Cj ) sensitivity coefficient Ea ) activation energy in the Arrhenius equation (K) (F/A)r ) local equivalence fuel/air ratio (F/A)r,global ) engine equivalence fuel/air ratio kf ) kinetic rate constant (m3 kmol s) m ) temperature exponent in the Arrhenius equation pinj ) injection pressure (bar) T ) temperature (K) tcomb ) combustion time (ms) tdil ) dilution time (ms) EF700448W

Role of the Chemical Kinetics on Modeling NOx Emissions in Diesel

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