Development of Reduced Combustion Mechanisms for Premixed

Energy & Fuels 2006, 20, 103-113

103

Development of Reduced Combustion Mechanisms for Premixed Flame Modeling in Steam Cracking Furnaces with Emphasis on NO Emission G. D. Stefanidis, G. J. Heynderickx,* and G. B. Marin Laboratory for Petrochemical Engineering, Ghent UniVersity, Krijgslaan 281 Block S5, Ghent B9000, Belgium ReceiVed July 1, 2005. ReVised Manuscript ReceiVed October 3, 2005

A systematic reduction of the detailed combustion chemistry based on the application of quasi steady state (QSS) approximation for some species leads to several reduced mechanisms (7- to 12-step) for a hydrocarbonhydrogen fuel with a composition representative for industrial steam cracking furnaces. The basis for the construction of all reduced mechanisms is a skeletal mechanism obtained from the detailed GRI-Mech 3.0 and consisting of 223 elementary reaction steps. The performance of reduced chemistry was assessed under different flame regimes and over a wide range of operating conditions. An eight-step mechanism provides satisfactory temperature and major and minor species concentration predictions including NO. Therefore, it is put forward for combustion simulations in steam cracking furnaces.

1. Introduction In most steam cracking furnaces, the necessary heat is supplied by combustion of mixed fuels, containing methane, ethane, propane, and hydrogen, in long-flame burners in the furnace floor and/or in radiation burners in the furnace walls. When the flow, concentration, and temperature profiles in the furnace are to be calculated, the corresponding conservation equations have to be solved. The computational fluid dynamics (CFD) type of software package FLOWSIM was developed at the Laboratory for Petrochemical Engineering to calculate these profiles in the radiation section of steam cracking furnaces.1-3 When long-flame burners are used in these furnaces, the conservation equations for the fuel and flue gas components in the flames have to be integrated. However, the use of detailed combustion mechanisms in CFD calculations is not advisable because of the large number of components and reactions involved. The use of reaction models consisting of one global reaction or a set of quasi global reactions is considered to be an oversimplification of the chemistry involved and does not provide detailed predictions of concentration profiles and combustion heat release in the furnace. Furthermore, these simple combustion models do not allow accurate prediction of NOx formation, an ecologically important issue. To tackle both problems, the use of validated, reduced combustion mechanisms4-6 in CFD software is needed.7 * Corresponding author. Phone: +32-9-264-4516. Fax: +32-9-264-4999. E-mail: [email protected]. (1) Heynderickx, G. J.; Oprins, A. J. M.; Marin, G. B.; Dick, E. AIChE J. 2001, 47, 388-400. (2) Oprins, A. J. M.; Heynderickx, G. J.; Marin, G. B. Ind. Eng. Chem. Res. 2001, 40, 5087-5094. (3) Oprins, A. J. M.; Heynderickx, G. J. Chem. Eng. Sci. 2003, 40, 48834893. (4) Peters, N. In Numerical Simulation of Combustion Phenomena, Proceedings of the Symposium held at INRIA, Sophia-Antipolis, France, May 21-24, 1985; Glowinski, R., Larrouturou, B., Temum, R., Eds.; Lecture Notes in Physics 241; Springer-Verlag: Berlin, 1985; pp 90-109. (5) Bilger, R. W.; Starner, S. H.; Kee, R. J. Combust. Flame 1990, 80, 135-149.

Different techniques have been developed to systematically reduce a detailed mechanism into reduced mechanisms that usually contain between four and 20 steps and whose reaction rates depend on the elementary reaction rates of the detailed mechanism. The first group of techniques can be referred to as mathematical techniques. The computational singular perturbation (CSP) method is described by Lam and Goussis.8 The intrinsic low dimensional manifolds (ILDM) method is described by Maas and Pope,9 and the method of invariant manifolds is described by Ducheˆne and Rouchon.10 These techniques make use of a time scale analysis to reduce stiffness introduced by chemistry. Originally, these methods were developed for spatially homogeneous premixed reactive systems, in the absence of any transport processes, which can be modeled by sets of ordinary differential equations (ODEs). The behavior of those systems can be described by trajectories in the composition space starting from an initial state and relaxing to chemical equilibrium. In more recent works, both ILDM and CSP have dealt with properly diffusive systems.11 The ILDM method uses the tendency of a chemical system to relax to a lower dimensional subspace, the so-called manifold, to simplify the chemistry. The manifold is identified beforehand by means of a local eigenvalue-eigenvector analysis of the Jacobian matrix of the chemical source term. Then, the only variables that are kept track of are the ones that parametrize this manifold. For discrete values of these control variables, (6) Chung, S. H.; Lee, S. R.; Mauss, F.; Peters, N. In Reduced Kinetic Mechanisms for Applications in Combustion Systems; Peters, N., Rogg, B., Eds.; Springer-Verlag: Berlin, 1993; p 308. (7) Montgomery, C. J.; Shino, D. M.; Yang, C.; Brunson, S.; Parkinson, A. R.; Chen, J.-Y.; Goldin, G. M.; Kong, S.-C.; Reitz, R. D. Proceedings of the 2003 NSF Design, Service, and Manufacturing Grantees and Research Conference; Birmingham, AL, Jan 6-9, 2003. (8) Lam, H.; Goussis, D. A. Proc. Combust. Inst. 1988, 22, 931-941. (9) Maas, U.; Pope, S. B. Combust. Flame 1992, 88, 239-264. (10) Ducheˆne, P.; Rouchon, P. Chem. Eng. Sci. 1996, 51, 4661-4672. (11) Valorani, M.; Najm, H. N.; Goussis, D. A. Combust. Flame 2003, 134, 35-53.

10.1021/ef0501952 CCC: $33.50 © 2006 American Chemical Society Published on Web 10/29/2005

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compositions of the manifold are computed and put into a table. That way, a significant reduction in CPU time is gained due to both a reduction in the number of variables and the reduced stiffness of the system. The CSP method also uses a local eigenvalue-eigenvector analysis to reduce the stiffness of the system but does not reduce the dimension of the state space globally so that it is possible to describe the reaction system by means of only a few control variables. Another advantage of the ILDM method is that the ILDM can be computed before the actual flame modeling and stored in a database. In this manner, the computation of the local eigenvectors, which is a computationally intensive task, is not required during the calculations with the reduced chemistry model. That gives the ILDM method a computational advantage over the CSP method.12 On the other hand, the multidimensional tables used to store all the state variables as functions of the reaction progress variables cannot exceed two or three dimensions for reasons of storage and accuracy of interpolation.13 That limits the ILDM method to chemical systems with one or two degrees of freedom. A review of the mathematical reduction techniques is given by Tomlin and coworkers.14 Another systematic approach is based on the application of the quasi steady state (QSS) assumption for some reacting species15,16 and is referred to as the conventional reduction method (CRM) by some authors.9 Optionally, the first step of this method is the construction of a skeletal network by eliminating unimportant reaction steps under a specified flame condition. Rate sensitivity analysis combined with rate of production analysis is used for that purpose. More specifically, the sensitivity coefficients Sk,j (eq 1) as well as the normalized production and consumption rates, rpk,j and rck,j, respectively (eqs 2 and 3), are examined:

Sk,j ) rpk,j )

∂ ln Xk ∂ ln kj

(1)

max(νkj,0)qj NR

(2)

∑j max(νkj,0)qj rck,j )

min(νkj,0)qj NR

(3)

∑j min(νkj,0)qj where Xk is the mole fraction of species k, kj is the forward rate constant of reaction j, νkj is the stoichiometric coefficient of species k in the reaction j, qj is the rate of reaction j, and NR is the total number of reactions. Elementary reaction rates for which the values Sk,j, rpk,j, and rck,j are smaller than a cutoff level are considered to be unimportant and are discarded from the simulation of the overall combustion process. Finally, the (12) Singh, S.; Powers, J. M.; Paolucci, S. J. Chem. Phys. 2002, 117, 1482-1496. (13) Peters, N. Turbulent Combustion; Cambridge University Press: Cambridge, 2000; p 24. (14) Tomlin, A. S.; Turańyi, T.; Pilling, M. J. Mathematical Tools for the Construction, Investigation and Reduction of Combustion Mechanisms. In Low-Temperature Combustion and Autoignition; Pilling, M. J., Hancock, G., Eds.; Elsevier: Amsterdam, 1997; pp 293-437. (15) Peters, N.; Kee, R. J. Combust. Flame 1987, 68, 17-29. (16) Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames: A Topical Volume; Smooke, M. D., Ed.; Lecture Notes in Physics 384; Springer-Verlag: Berlin, 1991; pp 1-28.

criterion that should be satisfied by the remaining skeletal mechanism is:

|

max k

|

Vdk - Vsk Vdk

< , k ) 1,2....,NS + 1

(4)

where Vdk and Vsk are the values for species concentrations and temperature when using the detailed and the skeletal mechanism, respectively. NS is the total number of species, and is a small number specified by the user. The next step is the identification of the QSS species on the basis of their concentration levels and rate of production analysis. For every species that is considered to be in QSS the following equation is satisfied: NR

νkjqj ) 0 ∑ j)1

(5)

with NR, νkj, and qj as defined before. Each one of the equations above (eq 5) can be used to eliminate one elementary reaction rate qj. Eventually, the skeletal mechanism or the detailed mechanism is reduced by as many reactions as there are steadystate species. The strategy is to eliminate the fastest reactions that consume or produce the steady-state species because the slowest ones are rate-determining. The last step involves linear algebra with the set of mass balances resulting in the final form of the reduced mechanism and the corresponding net production rates that are linear combinations of elementary reaction rates (e.g., eq 6).

RR(SS8.4) ) W(11) - W(52) + W(53) + W(98) + W(130) - W(160) - W(161) (6) Equation 6 gives the net production rate for the fourth reaction step RR(SS8.4) in the proposed eight-step reduced combustion mechanism, which is presented in the next section. The net production rate is given as a function of several elementary reaction rates W(i) of the detailed combustion mechanism. Those elementary reaction rates involve major species as well as radical species that are considered to be in QSS. More information about the CRM can be found elsewhere.17,18 Finally, other important automatic reduction methodologies that should be acknowledged are the adaptive chemistry concept,19 the piecewise reusable implementation of solution mapping (PRISM) approach,20 and the directed relation graph (DRG) method.21 Several recently developed mechanisms for methane combustion are available in the literature. Chen17 developed three reduced mechanisms, starting from GRI-Mech 1.2 and 2.122 using the Computer Assisted Reduction Mechanism (CARM) software package17 and the CRM. The available mechanisms (17) Chen, J.-Y. Workshop on Numerical Aspects of Reduction in Chemical Kinetics, CERMICS-ENPC Cite Descartes-Champus sur Marne, France, Sept 2, 1997. http://firebrand.me.berkeley.edu/reduced. (18) Somers, L. M. T. Simulation of flat flames with detailed and reduced chemicalmodels. Ph.D. Thesis, University of Eindhoven, The Netherlands, 1994. (19) Green, W. H.; Barton, P. I.; Bhattacharjee, B.; Matheu, D. M.; Schwer, D. A.; Song, J.; Sumathi, R.; Carstensen, H.-H.; Dean, A. M.; Grenda, J. M. Ind. Eng. Chem. Res. 2001, 40, 5087-5094. (20) Tonse, S. R.; Moriarty, N. W.; Brown, N. J.; Frenklach, M. Isr. J. Chem. 1999, 39, 97-106. (21) Lu, T.; Law, C. K. Proc. Combust. Inst. 2005, 30, 1101-1109. (22) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.; Lissianski, V. V.; Qin, Z. GRI-Mech, version 3.0; 2002. http://www.me.berkeley.edu/gri_mech/.

Reduced Combustion Mechanisms for Flame Modeling Table 1. Fuel Composition species

mass fraction

CH4 C2H6 C3H8 CO CO2 H2

0.893 0.0241 0.0140 0.0060 0.0060 0.0563

contain 9, 10, and 12 steps. Validation was done for several flame types using the reduced mechanisms and GRI-Mech 2.1. Massias et al.23 developed and tested two reduced mechanisms (seven and 10 steps) starting from GRI-Mech 2.11, using the S-STEP software and the CSP method. The laminar premixed flame model was considered to test the reduced mechanisms. Finally, reference is made to the work of Sung et al.24 who developed four so-called augmented reduced mechanisms (ARM) containing 12, 14, 15 and 17 steps. Use was made of CARM for the construction of the mechanisms starting from GRI-Mech 3.0.22 Validation was based on continuous stirred tank reactor (CSTR) calculations and calculations with the freely propagating flame model. Chemistry-radiation interaction was studied in nonpremixed counterflow flames. As opposed to the aforementioned works, where the fuel was 100% methane, the target in this work is the development of a reduced mechanism for a mixed fuel containing primarily methane but also an important amount of hydrogen as well as ethane and propane. Such a technical fuel (usually a recycle stream from the demethanizer) is a typical fuel for industrial steam cracking furnaces. In the work presented here, the CRM that is incorporated in the CARM code will be used to construct several reduced mechanisms for the combustion of a mixed fuel, starting from GRI-Mech 3.0. The ultimate goal is the use of the reduced mechanism in CFD codes modeling turbulent combustion in steam cracking furnaces or other applications for which the fuel composition described above is applicable. Therefore, it is of paramount importance that it includes the least possible number of steps and involves the least possible number of elementary reactions that still allow accurate prediction of temperature and concentration distribution profiles. The reduced mechanisms are validated against the detailed GRIMech 3.0 using three reactor and flame models: CSTR, plug flow reactor (PFR), and one-dimensional freely propagating flame. Special attention is always given to the formation of nitrogen oxides, in view of environmental regulations. All validation simulations have been done with the CHEMKIN 4.0 software package.25 2. Construction of Reduced Mechanisms for a Mixed Hydrocarbon-Hydrogen Fuel Using CARM The construction of the reduced mechanisms is done under CSTR conditions. As the reduced mechanism is to be used for the simulation of combustion in steam cracking furnaces, the fuel composition that is chosen for the CSTR test cases has to be representative for such furnaces (Table 1). Two inlet temperatures (Tinlet) of 300 and 350 K, because typically the fuel entering the radiation section is slightly preheated, and five (23) Massias, A.; Diamantis, D.; Mastorakos, E.; Goussis, D. A. Combust. Theor. Model. 1999, 3, 233-257. (24) Sung, C. J.; Law, C. K.; Chen, J.-Y. Combust. Flame 2001, 125, 906-919. (25) Kee, R. J.; Rupley, F. M.; Meeks, E.; Miller, J. A. Chemkin III: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical and Plasma Kinetics, Technical Report SAND96-8216, Sandia National Laboratories: Albuquerque, NM, 1996.

Energy & Fuels, Vol. 20, No. 1, 2006 105

different residence times (τ) varying from 10-4 to 1 s are used for the construction of the reduced mechanisms. The pressure (P) is 1 atm. The fuel equivalence ratio (φ) is 0.94, corresponding to a slightly lean mixture. The range of conditions considered for the construction of the reduced mechanisms is kept narrow to secure the fidelity of the product performance to that of the detailed mechanism at the most plausibly encountered operating conditions in steam cracking furnaces. Afterward, the reduced mechanisms are assessed using different reactor and flame models and within a much wider operating condition range. Since the eight-step mechanism, which is eventually put up for use, has satisfactory performance throughout the whole condition range, it was considered that there is no need to add to the number of test cases (actually expand the condition range) used for the development of the reduced mechanisms. The first step in the reduction process is the construction of a skeletal mechanism out of the detailed GRI-Mech 3.0. This procedure, which was described in section 1, removes 102 reactions out of the 325 reactions of GRI-Mech 3.0. NH3 has been removed in the reaction elimination process that results in the skeletal mechanism. Keeping in mind that the reduced mechanism is intended for use in CFD calculations, the advantage of constructing a reduced mechanism that is deduced from a skeletal mechanism is that the number of elementary reaction terms that are to be calculated in the species net production rates is significantly reduced. From the skeletal mechanism that retains only 223 reactions, the mechanism reduction proceeds automatically by the CARM software package. The reduction process is based on the choice of a number of species for which the QSS approximation is made. For the selection of the QSS species several methods have been suggested. Chen17 proposes to evaluate the so-called QSS-error :

)

(

|ω˘ pk - ω˘ ck|

)

max(|ω˘ pk|,|ω˘ ck|)

n

Xkm

(7)

where the numerator represents the net production rate of the species k, and Xk is the mole fraction of the k-th species. ω˘ pk and ω˘ ck are the production and consumption rates, respectively, of the species k. In the same article, n ) m ) 1 is proposed. These values are used in the present work, too. In Table 2, the QSS error values obtained with CARM for stoichiometric combustion of pure methane and for combustion of the mixed fuel with the composition given in Table 1 under the conditions described above are compared. To have a better overview of these results, the species for which the QSS error lowers by more than a factor of 3 and the species for which the QSS error rises by more than a factor of 3 when going from stoichiometric pure methane combustion to fuel-lean combustion of the mixed fuel are given in Table 3. Note that the inert argon is not considered in this work. For the former type of species, the largest change is detected for methanol. Methanol is an intermediate formed by the recombination of CH3 and OH radicals:

CH3 + OH T CH3OH

(R1)

This is an important step in the reaction path from CH3 to CH2O that is further converted into HCO, CO, and CO2 successively.26 This change should mainly be attributed to the presence of C2H6 (26) Turns, S. R. An Introduction to Combustion: Concepts and Applications; McGraw-Hill International Editions: Singapore, 2000; p 158.


Stefanidis et al.

Table 2. Maximum QSS Error Values for Stoichiometric Combustion of Pure Methane and Combustion of the Hydrocarbon-Hydrogen Fuel combustion of pure methane

combustion of the hydrocarbon-hydrogen fuel

species

max QSS error

species

max QSS error

C3H7 C3H8 NNH H2CN C2H HCNN NO2 HNO CH2CHO HOCN CN HCCOH C2H5 CH3O NH2 NCO NH CH2(S) H2O2 HCCO HCNO C2H3 N CH C2H6 CH3CHO C CH2OH N2O CH2 HCO CH3OH HNCO HO2 CH2CO C2H2 C2H4 CH2O HCN CH3 O OH NO H H2 CH4 N2 O2 CO H2O CO2

2.81E-15 1.95E-13 2.80E-13 6.20E-13 1.01E-12 2.41E-12 6.70E-12 8.85E-12 1.03E-11 1.09E-11 1.13E-11 2.57E-11 3.57E-11 7.80E-11 9.03E-11 9.99E-11 1.02E-10 1.05E-10 2.74E-10 3.74E-10 5.98E-10 6.10E-10 7.77E-10 9.58E-10 1.55E-09 1.88E-09 2.32E-09 2.33E-09 6.95E-09 8.29E-09 1.00E-08 1.15E-08 1.16E-08 2.37E-08 2.78E-08 3.63E-08 4.77E-08 3.59E-07 3.90E-07 1.05E-06 2.02E-05 3.33E-05 6.88E-05 7.63E-05 4.78E-04 1.24E-03 1.48E-03 1.69E-02 2.19E-02 4.67E-02 7.48E-02

NNH H2CN HCNN HOCN C2H CN HCCOH HNO NH2 NCO NH CH2CHO NO2 CH2(S) HCNO HCCO CH3O N C2H5 C3H7 CH C2H3 CH3OH C H2O2 HNCO CH2OH HCO CH2 N2O CH3CHO C2H2 CH2CO C2H4 HO2 HCN CH2O CH3 C3H8 C2H6 O OH NO H H2 CH4 N2 O2 CO H2O CO2

8.84E-13 1.25E-12 3.34E-12 3.39E-12 3.97E-12 4.75E-12 1.25E-11 1.80E-11 2.16E-11 3.43E-11 3.92E-11 1.19E-10 1.27E-10 1.60E-10 1.62E-10 2.21E-10 2.79E-10 3.67E-10 3.78E-10 5.06E-10 7.58E-10 1.04E-09 1.09E-09 1.37E-09 1.74E-09 3.02E-09 3.07E-09 3.22E-09 3.36E-09 6.53E-09 1.03E-08 1.08E-08 1.50E-08 2.07E-08 2.84E-08 9.75E-08 1.54E-07 4.78E-07 8.80E-07 2.81E-06 3.26E-05 4.00E-05 7.37E-05 9.91E-05 4.14E-04 7.28E-04 2.54E-03 1.27E-02 1.27E-02 3.61E-02 5.34E-02

Table 3. Ranking Lists of Species with the Largest Reduction and the Largest Increase in the Maximum QSS Errors between the Simulations with Pure Methane (Case 1, Left Column) and the Mixed Fuel (Case 2, Right Column) species

max QSS error 2/max QSS error 1

CH3OH NH2 HCN HNCO HCNO C2H2 HOCN HCO

0.10 0.24 0.25 0.26 0.27 0.30 0.31 0.32

NNH CH3O C2H CH3CHO H2O2 C2H5 CH2CHO NO2 C2H6 C3H7 C3H8

3.2 3.6 3.9 5.5 6.3 10.6 11.6 18.9 1.8 × 103 1.8 × 105 4.5 × 106

that are to be developed for combustion of the mixed fuel. Furthermore, it has to be said that the CARM software does not allow selecting ethane and propane, which are feeding species, as QSS species. The rise of these QSS errors is mainly due to a rise in the mole fractions (eq 7). Additionally, it is remarkable that although a significant amount of H2 is present in the mixed fuel the changes in the QSS errors for the H2 related components are limited. It can also be concluded from Table 2 that important radicals such as CH2O, an intermediate product during combustion mainly formed by CH3 reacting with O or OH, have a high QSS error. Also, HCN, an important intermediate in the prompt NO mechanism, has a large QSS error as seen in Table 2. CH2O was already considered as a major component by Sung et al.24 in their 12- to 17-step mechanisms for combustion of pure methane. HCN was considered as a major component by Massias et al.23 and by Sung et al.24 On the basis of these observations, a QSS error of the order of 10-7 is taken as a (first) limit to separate major and QSS species, completely in agreement with the suggestion of Cremer et al.:28

QSS - error )

(

|ω˘ pk - ω˘ ck|

max(|ω˘ pk|,|ω˘ ck|)

)

Xk < 10-7

(8)

which takes place immediately after the production of methyl radicals. Inevitably, as the amount of C2H6 increases in the fuel, reaction R2 acts competitively with reaction R1. Furthermore, it is clear from Table 3 that because ethane and propane are part of the mixed fuel, the importance of those two components during combustion has risen. Therefore, it is advisable to use ethane and propane as major species in the reduced mechanisms

All the species with a QSS error smaller than that of HCN are considered to be QSS species for combustion of the mixed hydrocarbon-hydrogen fuel (see Table 2). This implies that 16 major species are considered, resulting in a 12-step mechanism generated by CARM. Next, HCN, CH2O, and CH3 are considered consecutively as QSS species, further reducing the mechanism to an 11-, 10-, and 9-step reduced mechanism, respectively. Sung et al.24 suggest O as a possible QSS species leading to an eight-step mechanism. Note that ethane and propane are still considered as major species, although they have a QSS error lower than that of O. This has already been discussed above. Finally, H is taken as a QSS species rather than OH. The latter is the key radical for the formation of formaldehyde (CH2O) from CH3 via different pathways at all temperatures. Moreover, OH is an important radical for CO

(27) Westbrook, C. K.; Dryer, F. L. Prog. Energy Combust. Sci. 1984, 10, 1-57.

(28) Cremer, M. A.; Montgomery, C. J.; Wang, D. H.; Heap, M. P.; Chen, J.-Y. Proc. Combust. Inst. 2000, 28, 2427-2434.

in the feed which renders C2- chemistry more important. More specifically, it is known that an important reaction of the C2H6 combustion chemistry is:27

C2H6 + CH3 T C2H5 + CH4

(R2)

Reduced Combustion Mechanisms for Flame Modeling


Table 4. Major Species in the Constructed Global Reduced Mechanisms 12-step/ 11-step/ 10-step/ 9-step/ 8-step/ 7-step/ species 16 species 15 species 14 species 13 species 12 species 11 species HCN CH2O CH3 C3H8 C2H6 O OH NO H H2 CH4 N2 O2 CO H2O CO2

X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X x

X X X X X X X X X X X X X X

X X X X X X X X X X X X X

X X

X X

X X X X X X X X X X

X X X X X X X X X

oxidation, since reaction (R3) is the key step in the overall oxidation scheme of CO.

CO + OH T CO2 + H

Figure 1. Comparison of predicted temperatures for a CSTR containing a mixture of a hydrocarbon-hydrogen fuel and air using the sevenstep and eight-step reduced mechanisms and GRI-Mech 3.0. Fuel composition (wt %): Table 1, φ ) 0.94, Tinlet ) 300 K, P ) 1 atm, τ ) 10-4 to 1 s.

(R3)

A seven-step mechanism is the result of considering H to be in steady state. NO is not removed from the list of the major species. An overview of the major species in the six reduced mechanisms is given in Table 4. The eight-step mechanism, which is finally proposed, is:

H2 + OH T H + H2O

(SS8.1)

H + OH T H2O

(SS8.2)

3OH T H + O2 + H2O

(SS8.3)

4OH + CH4 T 2H + 3H2O + CO

(SS8.4)

2OH + CO T H2O + CO2

(SS8.5)

6OH + C2H6 T 4H + 4H2O + 2CO

(SS8.6)

8OH + C3H8 T 6H + 5H2O + 3CO

(SS8.7)

H + H2O + 2NO T 3OH + N2

(SS8.8)

In this mechanism, the SS8.1-SS8.3 submechanism represents H2 oxidation. Reactions SS8.4-SS8.5 represent the CH4 f CO f CO2 and H2O oxidation path. Reactions SS8.6 and SS8.7 account for the oxidation of higher hydrocarbons (C2H6 and C3H8), which are present in the feed. Finally, reaction SS8.8 accounts for NO formation. The net production rates and the algebraic equations for the QSS species are given in the appendix as a combination of the elementary reaction rates of GRI-Mech 3.0, which can be found on the website.22 3. Validation of Reduced Chemistry 3.1. Introduction. In this section, validation results for the eight-step mechanism with GRI-Mech 3.0 are presented. Validation was done with the CSTR, the one-dimensional freely propagating flame and the PFR models. Selected simulation results with the seven-step mechanism are also presented to show that the QSS assumption for H leads to inaccurate predictions. It is worth mentioning that only steady-state simulations are considered in this work. Time-dependent processes and transient phenomena (e.g., autoignition) as well as relevant parameters such as ignition delay that are important

for other applications (e.g., diesel engines) are not investigated because they are beyond the scope of this work. It is stressed that, in terms of flame modeling in industrial processes, like steam cracking furnaces, the points of interest concern the accurate prediction of temperature distribution that determines the heat fluxes toward the steam cracking reactor and the accurate prediction of NO emission at steady-state conditions. 3.2. Continuous Stirred Tank Reactor Model. The CHEMKIN 4.0 simulation module AURORA is used for the validation calculations comparing the results obtained with the six reduced mechanisms to the results obtained with GRI-Mech 3.0. The CSTR, which corresponds to a perfectly stirred reactor, forms an interesting validation test since radicals are present in higher amounts compared to the other reactor models, and reactants and products coexist. In addition, this reactor model is used as an approximation for modeling the burning fine structures in turbulent reactive flows.29-31 Consequently, good performance of a reduced mechanism under CSTR conditions should be an indication that it gives reliable results for turbulent flames as well. In Figures 1 and 2, the calculated temperature and some species mole fractions in the CSTR are shown for different residence times (10-4 to 1 s). The inlet temperature is 300 K and pressure is 1 atm. The temperature predictions with the eight-step mechanism are adequate (Figure 1). Only a very small deviation is found. The same holds for the CH4, H2, H2O, and CO2 mole fractions (Figure 2a-c) as well as the mole fractions of C3H8 and C2H6 (not shown). The deviation is larger in the case of the seven-step mechanism where H radicals are assumed to be in steady state and is especially pronounced at low residence times. This is linked to the fact that hydrogen oxidation is faster than hydrocarbon oxidation. As a consequence, hydrogen chemistry as well as the presence of H2 in the feed become more important at lower residence times. The QSS assumption for the H radicals at very low residence times leads to an overprediction of their amount in the reactor and an inevitably faster oxidation of CH4 since H is one of the main radicals attacking CH4 to produce methyl radicals. As a result, CH4 concentration is underestimated and temperature is over(29) Gran, I. R.; Magnussen, B. F. Combust. Sci. Technol. 1996, 119, 191-217. (30) Chakraborty, D.; Paul, P. J.; Mukunda, H. S. Combust. Flame 2000, 121, 195-209. (31) Han, X.; Wei, X.; Schnell, U.; Hein, K. R. G. Combust. Flame 2003, 132, 374-386.


Stefanidis et al.

Figure 3. Comparison of (a) predicted temperatures and (b) predicted NO mole fractions for a CSTR containing a mixture of a hydrocarbonhydrogen fuel and air using the eight-step reduced mechanism and GRIMech 3.0. Fuel composition (wt %): Table 1, φ ) 0.8 and φ ) 1.2, Tinlet ) 300 K, P ) 1 atm, τ ) 10-4 to 1 s.

Figure 2. Comparison of some predicted species mole fractions for a CSTR containing a mixture of a hydrocarbon-hydrogen fuel and air using the seven-step and eight-step reduced mechanisms and GRI-Mech 3.0. (a) CH4 and NO. (b) CO and H2. (c) CO2 and H2O. Fuel composition (wt %): Table 1, φ ) 0.94, Tinlet ) 300 K, P ) 1 atm, τ ) 10-4 to 1 s.

estimated. For CO and NO (Figure 2a,b), very good results are obtained with both mechanisms. In Figure 3a,b, temperature and NO predictions with the eight-step mechanism and GRIMech 3.0 are compared for two different equivalence ratios (φ ) 0.8 and φ ) 1.2) and an inlet temperature of 300 K. The performance of the eight-step mechanism is as satisfactory as for an equivalence ratio of φ ) 0.94 (Figures 1 and 2a). In Figure 4a,b, the temperature and NO predictions with the eightstep mechanism are compared against those determined from GRI-Mech 3.0 at elevated inlet temperatures (400 and 500 K). It is observed that the temperature (Figure 4a) is predicted very well with the eight-step mechanism at higher residence times (from τ ) 0.01 s and up), whereas the deviation at lower residence times is somewhat more pronounced than in the case of Tinlet ) 300 K (Figures 1 and 3a). On the other hand, very good agreement with respect to NO predictions is obtained over the entire range of residence times (Figure 4b). Additional calculations with the 10-step mechanism have shown improved accuracy with respect to temperature and CH4 concentration predictions at very low residence times (0.0001 s). However,

such low residence times are not likely to be encountered in steam cracking furnaces under normal firing conditions. 3.3. Freely Propagating Flame Model. Laminar premixed flames are the basis for the development of turbulent flame theories. In many turbulent combustion models, turbulent flames can be considered as a set of laminar flame sheets (the flamelet models). Consequently, physical insight in the structure and the dynamic behavior of those flamelets is important. The most important physical phenomenon is the back diffusion of radicals in the fast-chemistry region that along with the backward heat conduction causes the flame to be self-sustaining. Simulation results obtained with the reduced and detailed mechanisms using the freely propagating flame configuration of the PREMIX module, incorporated in the CHEMKIN 4.0 software, are presented in Figures 5-11. The unburned gas composition is given in Table 1. The pressure is 1 atm. Validation is done at several initial temperatures and equivalence ratios and under adiabatic conditions. In all presented simulations, intense grid refinement has been applied in regions of high gradients and high curvature to ensure that the evolution of all variables is well-captured and the results are gridindependent. The calculated temperature and NO mole fraction profiles with the seven-step, eight-step, and GRI-Mech 3.0 are presented in Figure 5 for Tinlet ) 350 K and φ ) 0.94. The temperature evolution is predicted very well with the eight-step mechanism. The seven-step mechanism underestimates the temperature profile by up to 200 K in the fast-chemistry region of the



Figure 6. The four most important reactions producing NO and the three most important reactions consuming NO according to rate of production analysis for a freely propagating mixture of a hydrocarbonhydrogen fuel and air using GRI-Mech 3.0. Reactions 1 and 2: Zeldovich mechanism; reactions 7 and 3: HNO production-destruction path; reactions 5 and 4: NO2 production-destruction path. Fuel composition (wt %): Table 1, φ ) 0.94, Tinitial ) 350 K, P ) 1 atm.

Figure 4. Comparison of (a) predicted temperatures and (b) predicted NO mole fractions for a CSTR containing a mixture of a hydrocarbonhydrogen fuel and air using the eight-step reduced mechanism and GRIMech 3.0. Fuel composition (wt %): Table 1, φ ) 0.94, Tinlet ) 400 K and Tinlet ) 500 K, P ) 1 atm, τ ) 10-4 to 1 s.

Figure 5. Comparison of predicted temperature and NO mole fraction profiles for a freely propagating mixture of a hydrocarbon-hydrogen fuel and air using the seven-step and eight-step reduced mechanisms and GRI-Mech 3.0. Fuel composition (wt %): Table 1, φ ) 0.94, Tinitial ) 350 K, P ) 1 atm.

reaction zone and overestimates it in the slow-chemistry region of the reaction zone. The eight-step mechanism also predicts very well the NO mole fraction profile, whereas a significant discrepancy is obtained when using the seven-step mechanism. To investigate this issue, rate of production analysis is performed with GRI-Mech 3.0, and selected results are presented in Figure 6. Figure 6 shows the rate evolution in space of the four most important reactions that produce NO and of the three most

Figure 7. Comparison of some predicted species mole fraction profiles for a freely propagating mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. (a) CH4, CO2, and CO. (b) H2 and H2O. Fuel composition (wt %): Table 1, φ ) 0.94, Tinitial ) 350 K, P ) 1 atm.

important reactions that consume NO, without counting forward and backward reactions individually. As expected, the two highest positive peaks (reactions 1 and 2) represent two reactions of the thermal mechanism of Zeldovich. Reactions 7 and 3 show that the second most important chemical path for the formation of NO is the nitrosyl hydride (HNO) production-destruction path. Furthermore, reactions 5 and 4 show that the nitrous oxide (NO2) production-destruction path is the third most important path via which NO is formed. Both chemical paths have already


Stefanidis et al.

Figure 8. Comparison of predicted temperature and NO mole fraction profiles for a freely propagating mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. (a) φ ) 0.8. (b) φ ) 1.2. Fuel composition (wt %): Table 1, Tinitial ) 350 K, P ) 1 atm.

been considered as important among others in lean premixed air-methane combustion,32 but they appear to be dominant over the range of conditions considered in this work. Finally, it turns out that an important amount of NO is consumed through reaction with methylene (reaction 6). Taking into account the importance of the H radicals in the reactions in Figure 6, it turns out that the big discrepancy for the NO concentration when going from the eight-step to the seven-step mechanism can be attributed to the QSS approximation for H in the latter mechanism (see Table 4), resulting in a poor prediction of its concentration. The concentration profiles for CH4, CO2, and CO are presented in Figure 7a under the same initial conditions (Tinitial ) 350 K and φ ) 0.94). Again, satisfactory agreement between the eight-step mechanism and GRI-Mech 3.0 is observed. The same applies to the H2 and H2O profiles (Figure 7b). Figure 8a,b displays the temperature and NO profiles for φ ) 0.8 and φ ) 1.2, respectively, while Tinitial ) 350 K. The temperature evolution predicted with the eight-step mechanism follows faithfully that determined from GRI-Mech 3.0 while the NO evolution is predicted accurately enough in both cases. The same (32) Sańchez, A. L.; Le´pinette, A.; Bollig, M.; Linań, A.; La´zaro, B. Combust. Flame 2000, 123, 195-209.

Figure 9. Comparison of final (peak) temperatures and final (peak) NO mole fractions with fuel equivalence ratio variations for a freely propagating mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. Fuel composition (wt %): Table 1, φ ) 0.6-1.4, Tinitial ) 350 K, P ) 1 atm.

high accuracy is obtained for a wide range of equivalence ratios as shown in Figure 9. Figure 9 displays the final (xf + ∞) temperature and the final NO mole fraction with φ ) 0.6-1.4. In the simulations presented thus far with the freely propagating


Figure 10. Comparison of final (peak) NO mole fractions with initial temperature variations for a freely propagating mixture of a hydrocarbonhydrogen fuel and air using the eight-step reduced mechanism and GRIMech 3.0. Fuel composition (wt %): Table 1, φ ) 0.94, Tinlet ) 300600 K, P ) 1 atm.


Figure 12. Comparison of predicted NO mole fraction profiles at different temperatures for an isothermal plug flow mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. Fuel composition (wt %): Table 1, φ ) 1.0, T ) 1600-2200 K, Pinlet ) 1 atm.

Figure 11. Comparison of predicted laminar burning velocities with fuel equivalence ratio variations for a freely propagating mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. Fuel composition (wt %): Table 1, φ ) 0.6-1.4, Tinitial ) 350 K, P ) 1 atm.

flame model, the initial temperature is 350 K. In Figure 10, the final NO predictions with the eight-step mechanism and GRIMech 3.0 are compared for elevated inlet temperatures over the range 300-600 K. It is shown that the performance of the eightstep mechanism does not deteriorate with increasing initial temperature. The same holds for temperature and other variables (results not shown here). The satisfactory performance of the eight-step mechanism within a wide range of equivalence ratios and initial temperatures is remarkable considering the narrow range of conditions under which it was developed. That success should be attributed to the proper selection of steady-state species, which turns out to be valid over the range of conditions for which validation is performed. Finally, the ability of the reduced mechanism to reproduce the laminar burning velocity is assessed in Figure 11. The most important deviation between the predicted laminar burning velocities is found in the region around the stoichiometric point. However, the maximum error does not exceed 10% (9.4% at φ ) 1.1). Better agreement is obtained in the fuel-lean and fuelrich regions. The predicted flame speed values in this work are somewhat higher than those for hydrocarbons (0.4-0.6 m/s) due to the presence of H2 in the feed. The laminar flame propagation speed of H2 is more than 1 m/s.

Figure 13. Comparison of some predicted outlet species mole fractions at different temperatures for an isothermal plug flow mixture of a hydrocarbon-hydrogen fuel and air using the eight-step reduced mechanism and GRI-Mech 3.0. (a) CO2 and CO. (b) H and OH. Fuel composition (wt %): Table 1, φ ) 1.0, T ) 1600-2200 K, Pinlet ) 1 atm.

3.4. Plug Flow Reactor Model. Although the use of the PFR model in the literature to validate reduced reaction mechanisms is limited, this reactor model remains a useful validation test since it is characterized by a different residence time span as compared to the CSTR model. It also serves at testing the reduced mechanism in the limit of poor macromixing conditions. For that reason, the PLUG application of CHEMKIN 4.0 is used


Stefanidis et al.

in this work for further validation. Simulations are performed under isothermal conditions at four different temperatures (1600, 1800, 2000, and 2200 K). Use of a temperature lower than 1600 K will produce a negligible amount of NO under plug flow conditions, whereas temperatures higher than 2200 K are not encountered in steam cracking furnaces. In all simulations, a very fine grid corresponding to mesh spacing of 0.002 cm has been applied. Some selected calculated concentration profiles for Pinlet ) 1 atm and φ ) 1.0 are shown in Figures 12 and 13. Figure 12 displays the evolution of NO in space. A small overprediction is obtained with the eight-step mechanism at all temperatures, while the outlet concentration predictions are very close to those obtained with GRI-Mech 3.0. Figure 13a,b shows that the eight-step mechanism is able to accurately predict the outlet concentration of products (CO2), intermediate species (CO), as well as radicals (OH, H) at various temperatures. Similar results have been obtained for other equivalence ratios (not presented). It can be concluded that the performance of the eight-step mechanism under PFR conditions is satisfactory especially considering that axial mixing is neglected whereas the mechanism has been developed under perfect mixing conditions. 4. Conclusions The CARM software was used to construct six reduced combustion mechanisms (from seven to 12 steps) for flame modeling in steam cracking furnaces with a fuel-air mixture composition representative for such furnaces. The mechanisms were tested with a CSTR, a PFR, and a laminar premixed flame model over a wide range of operating conditions. Satisfactory results with respect to temperature predictions as well as major and pollutant species evolution are obtained with an eight-step mechanism that is deduced from a skeletal one, constructed out of GRI-Mech 3.0. Therefore, the proposed eight-step mechanism is expected to lead to a significant gain in CPU time in CFD calculations through significant reduction in the number of reaction terms that need to be computed as well as reduction in the degree of stiffness characterizing the differential equation system of species mass balances. Acknowledgment. We acknowledge the Fund for Scientific Research-Flanders (FWO-N) for financial support through project No. G.0070.03.

Appendix: Net Production Rates and QSS Equations for the Eight-Step Mechanism Numbers within parentheses refer to those of GRI-Mech Net Production Rates.

3.0.22

RR(SS8.1) ) W(3) - W(45) - W(47) - W(49) W(51) - W(53) - W(55) - W(58) - W(60) - W(65) W(68) - W(69) - W(73) - W(75) - W(78) - W(80) + W(83) + W(84) + W(126) + W(146) + W(172) W(174) + W(190) + W(192) + W(193) + W(198) + W(199) + W(201) - W(202) - W(208) - W(209) W(214) + W(217) + W(221) + W(222) + W(224) + W(227) + W(228) + W(229) - W(239) - W(240) W(244) - W(246) - W(247) - W(249) - W(250) W(251) - W(252) - W(254) - W(255) - W(274) W(275) + W(280) - W(284) - W(288) - W(293) W(299) - W(300) - W(309) - W(314)

RR(SS8.2) ) W(6) + W(16) + W(24) + W(26) W(30) + W(33) + W(35) + W(36) + W(43) + W(49) + W(52) + W(55) + W(60) + W(61) + W(62) + W(65) + W(66) + W(67) + W(73) + W(76) + W(85) - W(99) + W(100) + W(111) - W(119) + W(131) + W(132) + W(133) + W(140) + W(145) + W(153) - W(155) W(159) + W(160) + W(168) + W(169) + W(170) W(185) + W(187) - W(204) - W(205) + W(212) W(224) - W(227) - W(229) + W(240) + W(246) + W(247) + W(249) + W(250) + W(251) + W(252) + W(254) + W(255) + W(257) + W(261) - W(262) W(268) - W(269) + W(274) + W(280) + W(283) + W(286) - W(290) - W(305) + W(309) - W(311) + W(313) + W(314) + W(315) - W(322) RR(SS8.3) ) W(20) - W(22) - W(38) - W(46) W(49) + W(85) + W(90) + W(106) - W(109) W(119) + W(124) - W(125) - W(135) - W(144) W(145) - W(155) + W(172) - W(176) -W(179) W(186) - W(220) + W(239) - W(241) + W(244) + W(245) + W(257) + W(260) + W(261) - W(290) W(291) - W(294) RR(SS8.4) ) W(11) - W(52) + W(53) + W(98) + W(130) - W(160) - W(161) RR(SS8.5) ) W(14) + W(30) + W(99) - W(132) W(153) + W(229) + W(262) + W(268) - W(280) W(283) + W(290) + W(305) RR(SS8.6) ) W(27) - W(76) + W(78) + W(113) W(158) RR(SS8.7) ) -W(312) + W(313) + W(314) + W(315) W(320) RR(SS8.8) ) W(178) - W(182) + W(198) + W(199) W(208) + W(228) + W(229) - W(239) - W(240) QSS Equations. Setting all W(*X) ) 0 results in the set of algebraic equations for the QSS species:

W(*NNH) ) -W(204) - W(205) - W(206) - W(207) W(208) - W(209) - W(210) W(*H2CN) ) W(237) + W(275) W(*C2H) ) -W(20) + W(22) - W(106) + W(109) + W(123) - W(171) - W(172) W(*HCNN) ) W(241) - W(257) - W(259) - W(260) W(261) W(*HOCN) ) W(234) - W(273) W(*HCCOH) ) -W(82) + W(108) W(*CN) ) -W(217) - W(218) - W(219) - W(220) W(221) + W(233) + W(239) + W(244) W(*HNO) ) W(192) + W(197) + W(201) + W(212) W(213) - W(214) - W(215) + W(280) W(*CH2CHO) ) W(285) + W(294) + W(299) + W(304) - W(305) - W(308) - W(309) - W(311) W(*NH2) ) -W(201) - W(202) - W(203) + W(265) + W(268)


W(*NCO) ) W(218) + W(220) - W(222) - W(223) W(224) - W(227) - W(228) - W(229) + W(231) + W(247) + W(267) W(*NH) ) -W(190) - W(191) - W(192) - W(193) W(197) - W(198) - W(199) + W(202) + W(203) + W(208) + W(223) + W(232) + W(262) + W(269) W(280) W(*C3H7) ) W(313) + W(314) + W(315) + W(318) W(319) - W(320) - W(321) - W(322) W(*C2H5) ) -W(26) + W(27) + W(74) - W(76) + W(78) + W(113) + W(159) - W(286) - W(312) + W(319) + W(321) + W(322) W(*HCCO) ) W(21) - W(28) - W(79) + W(80) + W(106) + W(114) + W(131) - W(176) - W(274) W(*NO2) ) W(186) + W(187) - W(189) W(*CH2(S)) ) -W(51) + W(62) + W(67) + W(79) + W(97) - W(142) - W(144) - W(145) - W(146) W(147) - W(148) - W(152) - W(153) - W(252) W(254) - W(293) W(*HCNO) ) W(251) + W(254) - W(270) - W(271) + W(274) W(*CH3O) ) W(19) + W(57) - W(65) - W(66) W(67) + W(69) + W(105) + W(119) + W(155) W(170) W(*CH3CHO) ) W(286) - W(297) - W(299) W(300) - W(301) W(*C2H3) ) -W(24) + W(71) - W(73) + W(75) W(111) + W(112) + W(129) - W(294) W(*N) ) -W(178) - W(179) - W(180) + W(191) + W(193) + W(217) + W(227) + W(239) + W(240) + W(245) + W(248) - W(275) - W(283) W(*CH) ) -W(6) + W(20) - W(49) + W(51) W(91) + W(93) - W(125) - W(126) - W(127) W(129) - W(130) - W(131) - W(132) - W(133) W(240) - W(241) - W(246) - W(247) - W(248) W(*H2O2) ) -W(47) + W(85) - W(89) W(*CH3OH) ) -W(18) - W(19) - W(68) - W(69) + W(95) - W(104) - W(105) + W(147) W(*C) ) W(49) - W(90) - W(122) - W(123) W(124) - W(239) - W(244) - W(245) W(*HCO) ) W(7) - W(14) + W(15) + W(25) W(55) + W(58) + W(91) - W(100) + W(101) + W(125) + W(132) - W(160) + W(161) - W(166) W(167) - W(168) + W(171) + W(248) + W(259) + W(260) + W(308) + W(311) W(*CH2OH) ) -W(16) + W(18) + W(56) - W(60) W(61) - W(62) + W(68) + W(104) - W(169) + W(311) + W(322)


W(*CH2) ) -W(7) + W(23) + W(30) - W(92) W(93) + W(96) - W(123) + W(126) - W(135) W(138) - W(140) + W(142) + W(148) + W(152) W(249) - W(250) - W(251) + W(261) - W(290) W(291) + W(305) W(*HNCO) ) W(235) + W(249) + W(252) - W(262) W(265) - W(267) - W(268) - W(269) + W(270) + W(273) W(*N2O) ) -W(182) - W(183) - W(185) + W(199) + W(228) W(*CH2CO) ) W(24) - W(30) - W(80) - W(81) + W(82) + W(107) - W(114) + W(133) + W(140) W(304) + W(309) W(*C2H2) ) -W(21) - W(22) - W(23) - W(71) + W(73) - W(107) - W(108) - W(109) + W(111) + W(124) + W(172) + W(174) W(*C2H4) ) -W(25) - W(74) - W(75) - W(112) + W(130) + W(138) - W(174) - W(285) - W(318) W(*HO2) ) -W(4) + W(33) + W(35) + W(36) W(45) - W(46) + W(47) - W(87) + W(89) - W(119) + W(168) + W(169) + W(170) - W(186) + W(206) W(287) W(*O) ) -W(3) - W(4) - W(6) - W(7) - W(10) W(11) - W(14) - W(15) - W(16) - W(18) - W(19) W(20) - W(21) - W(22) - W(23) - W(24) - W(25) W(26) - W(27) - W(28) - W(30) + W(38) + W(86) + W(122) + W(125) + W(155) + W(178) + W(179) W(182) + W(185) - W(187) - W(190) - W(201) W(207) - W(208) - W(213) - W(217) + W(220) W(222) - W(231) - W(232) - W(233) + W(244) + W(246) - W(257) + W(259) - W(262) - W(284) W(285) - W(286) + W(291) + W(294) - W(297) W(305) - W(313) - W(319) W(*CH3) ) -W(10) + W(11) + W(25) + W(26) W(52) + W(53) + W(61) + W(66) + W(81) - W(95) W(96) - W(97) + W(98) - W(119) - W(124) W(129) - W(138) + W(146) - W(155) - 2*W(158) 2*W(159) - W(160) - W(161) - W(255) - W(275) W(284) - W(288) + W(297) + W(300) + W(301) + W(308) - W(312) - W(318) + W(321) W(*CH2O) ) W(10) - W(15) + W(16) + W(26) W(56) - W(57) - W(58) + W(60) + W(65) + W(83) + W(92) - W(101) + W(127) - W(133) + W(153) W(161) + W(169) + W(170) + W(288) + W(291) + W(293) + W(319) W(*HCN) ) W(219) + W(221) - W(231) - W(232) W(233) - W(234) - W(235) - W(237) + W(240) + W(246) + W(250) + W(255) + W(271) EF0501952

Development of Reduced Combustion Mechanisms for Premixed

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