Optimal Reduction of the C1–C3 Combustion Mechanism for the

Article pubs.acs.org/IECR

Optimal Reduction of the C1−C3 Combustion Mechanism for the Simulation of Flaring Helen H. Lou,*,† Daniel Chen,† Christopher B. Martin,‡ Xianchang Li,§ Kuyen Li,† Hitesh Vaid,† Kanwar Devesh Singh,† and Preeti Gangadharan† †

Dan F. Smith Department of Chemical Engineering, ‡Department of Chemistry and Biochemistry, and Department of Mechanical Engineering, Lamar University, Beaumont, Texas 77710, United States

§

ABSTRACT: Flaring is a combustion process designed to relieve pressures and safely dispose of vent gases from chemical and petrochemical plants. An industrial flaring activity typically involves various combustible waste gases and a large number of reactions and species. Because most of the detailed kinetic mechanisms for the speciation study of flaring events are too complicated to use in the computational fluid dynamics simulation of industrial-scale flares, several techniques for reduction of the detailed combustion mechanisms have been developed. In this paper, a new rigorous skeleton mechanism (RSM) based reduction technique, namely, the LU 2.0 algorithm, is proposed. It falls under the category of identification of redundancy. Other techniques in this category try to remove redundant species and reactions based on criteria such as sensitivity and quasi-steadystate analyses. These are highly dependent on the preanalysis of the mechanism and require species concentration sets for the conditions of interest. This algorithm tries to find out the skeleton mechanism with the lowest possible error. It works by rigorously testing all of the possible combinations of species sets. This RSM-based optimized mechanism was validated successfully against experimental data for various key performance indicators (laminar flame speeds, burner-stabilized flame, adiabatic flame temperature, and ignition delay) for methane, ethylene, and propylene flames. The efficacy of this algorithm was demonstrated by its improved predictability.

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INTRODUCTION Flares are used to dispose of unwanted vent gases, by burning them in an open flame, generally at elevated heights.1 According to the U.S. Environmental Protection Agency, the destructive combustion efficiency of the flares should be greater than 98%.2 During the combustion of flares, besides CO2, H2O vapor, and CO, many other intermediate products are generated, in addition to the unburned hydrocarbons.2 The combustion efficiency depends on the amount of stoichiometric air supplied for combustion, fuel−air mixing, wind speed, fuel exit velocity, temperature of the flare, and heat value of the gas.3,4 Recent studies have shown that the combustion efficiency of the industrial flares is underdetermined and uncertain.5−8 The unburned hydrocarbons include volatile organic compounds (VOCs) such as formaldehyde and highly reactive VOCs (HRVOC). 1,3-Butadiene and all isomers of butene, propylene, and ethylene have been designated as HRVOCs in Texas. Industrial point sources in the Houston−Galveston area are possible sources of HRVOCs that result in the formation of ozone.9 It is desirable to identify speciated emissions and the combustion efficiency using field measurements.10 However, because of problems such as the minimum detection limit and accuracy of the system setup, the development of a practical and reliable system for the routine detection of VOCs through field measurement is still under study. Field measurements are also difficult and costly, which contributes to the current lack of field deployment. Therefore, a reliable and practical alternative, such as a computational model for flare speciation, is greatly needed. Computational methods employed to predict the amount of underestimated VOCs, like formaldehyde, require solution of the governing chemical transport equations with detailed © 2012 American Chemical Society

kinetic mechanisms. Detailed chemical kinetic mechanisms for some of the fuels are available,11−14 but they contain hundreds of species and up to thousands of reactions. Hence, solving equations of hundreds of species with such complicated mechanisms coupled with continuity, momentum, energy, radiation, and gravity equations in a computational fluid dynamics (CFD) grid becomes computationally expensive and, in most cases, infeasible. To alleviate this computational difficulty, several techniques for the reduction of mechanisms have been proposed. These techniques can be broadly classified into three categories:15 (1) Tabulation methods, where the reactive propensity and corresponding system status are stored in the form of tabulated entries. Typical tabulation methods include in situ adaptive tabulation (ISAT)16 and intrinsic low-dimensional manifolds (ILDM).17 (2) Identification of redundancy: species and reactions that can be removed from the mechanism without inducing significant errors are considered as redundant. Kuo and Wei18 proposed a lumping approach, which lumps concentrations of chemical species into a reduced species set. Other approaches that aim at identifying redundant species and reactions include sensitivity analysis proposed by Turanyi19 and Rabitz et al.,20 optimization-based approaches proposed by Androulakis,21 Bhattacharjee et al.,22 and Petzold and Zhu,23 the relation graph method method proposed by Lu and Law,24 a dynamic adaptive Special Issue: Industrial Flares Received: Revised: Accepted: Published: 12697

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Figure 1. Diagrammatic view of the CHEMKIN PSR reactor.

Figure 2. Algorithm for the RSM.

approach developed by Liang et al.,25 and a flux graph-based reduction approach proposed by Androulakis et al.26 (3) Timescale decoupling methods that decouple species and reactions with different time scales. Good examples are the quasisteady-state approximation (QSSA),27 augmented reduced mechanism (ARM) generation,28 computational singular perturbation (CSP),29,30 and nonlinear perturbation methods.31,32 This paper proposes a rigorous skeleton mechanism (RSM) generation technique, which falls under the second category,

identification of redundancy. Other techniques in this category try to remove redundant species and reactions based on criteria such as sensitivity and quasi-steady-state analyses. These are highly dependent on preanalysis of the mechanism and require species concentration sets for the conditions of interest. The proposed technique tries to determine the skeleton mechanism with the lowest possible error. It works by rigorously testing all of the possible combinations of species sets for the skeleton mechanism. The main advantage of this methodology is that 12698

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the algorithm is straightforward and simple because it does not involve any mathematical derivatives or assumptions like the other models mentioned in this section. The search will not be trapped at the local optimum, and it will not be affected by the discontinuity of the equation. However, because this algorithm is based on an exhaustive search, it does not have an advantage regarding the computational speed. This method can be combined with techniques like the formation of global reactions33,34 and others mentioned above, for further optimization of the reduced mechanism. The challenge in forming global reactions is to find a set of suitable global reactions that is capable of reproducing the detailed mechanism to a high degree. The rate coefficients appearing in these reactions have to be optimized in order to deliver the best possible fit against corresponding detailed data. In the proposed method, starting with a detailed 93-species mechanism, the reduced 50-species mechanism is generated onthe-fly from the combination sets using an in-house code. The idea of on-the-fly reduction is to generate a reduced mechanism for each time step.35,36 These reduced mechanisms are sent to a kinetic solver along with associated files. On the basis of the error of the generated reduced mechanisms, they are automatically ranked for pick.

mechanism gives more satisfactory results for the combustion of ethylene than the USC mechanism alone. To form a base case for comparison with the RSM-based optimized mechanism, the algorithm presented by Lou et al.39 (hereinafter referred to as the LU 1.0 algorithm, and the resulting reduced mechanism is referred to as the LU 1.0 mechanism) was selected.40 This algorithm is based on the process of screening out those species not critical to the accuracy of the reduced mechanism. The algorithm basically consists of three major steps: time-based sensitivity analysis, examination of species in the reaction pathway, and progress variable analysis. These steps are interlinked through an iterative process. The solution file was obtained by solving the mechanism in a perfectly stirred reactor (PSR) model of CHEMKIN, a zerodimensional kinetic solver, a schematic of which is depicted in Figure 1. Table 1 shows the input conditions for the CHEMKIN PSR reactor.39

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GENERATION OF THE OPTIMIZED MECHANISM Optimization of the reduced mechanism is performed by rigorously testing all of the possible combinations of the species sets to form a skeleton mechanism with the lowest cumulative error possible. For example, to form the skeleton mechanism consisting of 50 species from a total of 93 species, 6.29544 × 1026 possible species combinations exist. However, among the 50 species to be selected, some of the species are of special interest to the system. Hence, species involved in fuel or the flare gas were ruled out from being sent to the combination generator. Also, some of the species that were of special interest in the flaring study, such as formaldehyde and NOx, were also not sent to the combination generator. Table 2 shows those species always kept in

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DETAILED COMBUSTION MECHANISM Several detailed reaction mechanisms, i.e., the GRI 3.037 and USC38 mechanisms, for the combustion of hydrocarbons are available. These mechanisms have been validated under different conditions and used for predicting different results. So, the authors of this work chose the GRI 3.0 and USC mechanisms as the starting point for the CFD simulation of flaring based on the conditions specified in Table 1 and the range of validation conditions Table 1. Input Conditions for the CHEMKIN PSR Reactor inlet fuel and oxidizer temperature (K) equivalence ratio of fuel to oxidizer reactor temperature (K)

Table 2. Important Species Considered in Simulations

500 1.0 1800

of these mechanisms. The GRI-Mech 3.0 performs well for an extensive range of combustion conditions for methane, which has been validated, as shown on their Web site. The USC mechanism, consisting of 75 species, is a comprehensive kinetic model for representing ethylene and acetylene combustion. It has been evaluated for predicting the combustion properties of both C2 and C3 fuels. However, because of some of their limitations, as described below, none of them were used independently in this work. 1 The GRI 3.0 mechanism (with 53 species) was developed and optimized for the combustion of methane but not ethylene. A few aspects of natural gas combustion chemistry are not described by GRI-Mech 3.0; these include soot formation and the chemistry involved in the selective noncatalytic reduction of NO. The latter may be important in natural gas reburning at lower temperatures. 2 The USC mechanism (containing 75 species) was optimized for ethylene combustion reactions, but the absence of NOx species in the mechanism was not desirable. To overcome this problem, both reaction mechanisms were combined so as to yield a mechanism that could satisfy all of the above-mentioned criteria. Inclusion of the NOx species contained in the GRI

species

comment

CH4, C2H4, and C3H6 CO2, H2O, and N2 O2 CH2O, HNO, NO2, and NO

main fuel components complete combustion products oxidizer pollutants of interest

the reduced species set because of the modelers’ interest due to the importance of these species in atmospheric chemistry and the impact on emission inventories. This amounts to a total of 11 species to be kept out of the combination generator or, in other words, to be kept by default in the reduced mechanism. Hence, there is a reduction in the number of combinations to be tested. In the RSM procedure, the optimization process is divided into two steps: generation of validation data from the detailed mechanism and optimized skeleton mechanism generation. This can be seen in Figure 2, which also illustrates the overall logic flow of the RSM-based optimization algorithm, namely, LU 2.0. The first step in this algorithm is the random generation of sets of up to 50 species (including those default species, which are of particular concern to the modelers) to be tested. After the combinations are generated, they are sent to the mechanism processing block (MPB) using a loop. It should be noted that the search can be expanded to reach a skeletal mechanism with an even lower number of species than 50, but additional time for an exhaustive search will have to be incorporated. The results presented in this paper were produced 12699

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using a well-optimized multithreaded algorithm over a period of 1 month running continuously in a high-performance workstation consisting of 24 CPUs and 48 GB RAM. In the MPB, the first step is to generate the reduced mechanism on-the-fly35 for further processing. This was established using the MECHMOD, version 3.4.1,41 library. MECHMOD requires the usage of either the CHEMKIN-II or CHEMKIN-III package. In this study, the CHEMKIN-III package was used for generation of chem.asc, a binary linking file produced by the CHEMKIN preprocessor and an input required by MECHMOD. Along with the chem.asc file, MECHMOD also required a control file containing the list of species to be eliminated. This control file was generated using the inverse of the combination set. Once the reduced mechanism was produced on-the-fly, it was sent to the CHEMKIN PSR reactor, a zero-dimensional kinetic solver.42 A snapshot of this solution process is shown in Figure 3.

Table 3. Overall Cumulative Error for Different Skeleton Mechanisms reduced mechanism set set set set set set set set set set set set

1 2 3 4 5 6 7 8 9 10 11 12

overall cumulative error

rank

0.000068 0.000652 0.001114 0.001741 0.002135 0.003577 0.004714 0.006836 0.009491 0.009665 0.01355 0.015408

1 2 3 4 5 6 7 8 9 10 11 12

eq 2. Then every species set is ranked based on its cumulative error. δi , j =

[X i , j] − [X i] [X i]

(1)

where [Xi] = concentration of species i in the detailed mechanism, [Xi,j] = concentration of species i in the reduced mechanism j, and δi,j = error in concentration of species i in the reduced mechanism j. n

Δj =

∑ δi , j i=1

(2)

where n = number of species in the reduced mechanism and Δj = cumulative error of the reduced mechanism. The final selected species set is listed in Table 5. This reduced mechanism with the lowest percentage error (set 1) is termed the LU 2.0 mechanism.

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RESULTS AND DISCUSSION Validation of the new RSM-based optimized mechanism, namely, the LU 2.0 mechanism, was carried out by comparison against experimental data from the literature and a reduced mechanism generated by the same group,37 namely, LU 1.0, considering the same factors (laminar flame speed, adiabatic flame temperature, and ignition delay). It is observed that the LU 2.0 mechanism shows better agreement with the experimental results for all of the factors. Also, when compared in terms of the average error, the LU 2.0 mechanism performs better than LU 1.0, as shown in Table 6. Laminar Flame Speed. The experimental results from Vagelopoulos and Egolfopoulos43 and Davis and Law44 were considered to validate the mechanism for methane and propylene laminar flame speeds, respectively. Figures 4 and 5 show a comparison between the CHEMKIN simulations, optimized mechanism, and experimental results of laminar flame speeds of methane and propylene air mixtures at different equivalence ratios, respectively. The maximum laminar flame speed of 41− 47 cm/s is achieved for an equivalence ratio in the range of 1.0−1.1 for the optimized mechanism, which is very close to the experimental data. Adiabatic Flame Temperature. To validate the mechanism for methane and ethylene adiabatic flame temperatures, the experimental results from Law et al.45 were considered. Adiabatic flame temperature comparisons of the LU 2.0 and LU 1.0 mechanisms and experimental results, for methane and

Figure 3. Snapshot of the RSM process.

Along with the reduced mechanism, other files, such as the thermodynamic data file and the input condition file, are also required as input to the PSR reactor. Once the solution is generated, it is processed automatically for mechanism ranking.

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DEMONSTRATION OF THE RSM FRAMEWORK As per the algorithm, the RSM framework for the original 93species mechanism was demonstrated. To generate the skeleton mechanism with minimal error, 4.7626 × 1025 possible species combinational sets were generated and subsequently tested. The mechanism set was ranked based on the procedure described below. Table 3 shows the various sets of skeleton mechanisms generated with their overall cumulative error and corresponding mechanism rank. Also, Table 4 shows the concentration values of some important species for the detailed mechanism versus skeleton mechanisms. The resulting reduced species set is shown in Table 5.

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MECHANISM RANKING The relative error for each species is calculated via eq 1. The cumulative error shown in Table 2 is calculated based on 12700

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Table 4. Concentration (moles) of Some Important Species for the Detailed Mechanism versus Reduced Mechanisms (in Order of Increasing Cumulative Error) species

detailed mechanism

set 1

set 2

set 3

set 4

set 5

set 6

set 7

set 8

set 9

O2 CO2 CH2O H2CC C3H6

0.050602 0.031461 0.000149 0.000026 0.000124

0.050633 0.031479 0.00015 2.65 × 10−5 0.000125

0.050669 0.031434 0.000144 2.65 × 10−5 0.000125

0.05076 0.031385 0.000163 2.6 × 10−5 0.000126

0.050872 0.031437 0.000148 0.000028 0.000126

0.050476 0.031517 0.000148 0.000030 0.000152

0.050922 0.031477 0.000165 0.000028 0.000135

0.051358 0.031530 0.000186 0.000027 0.000126

0.051721 0.031438 0.000208 0.000027 0.000128

0.052014 0.031483 0.000211 0.000027 0.000127

Table 5. Resulting Skeletal Mechanism Species Set H2, H, O, O2, OH, H2O, HO2, H2O2, C, CH, CH2, CH2*, CH3, CH4, CO, CO2, HCO, CH2O, CH2OH, C2H2, H2CC, C2H3, C2H4, C2H6, HCCO, CH2CO, HCCOH, CH2CHO, CH3CHO, CH3CO, C3H2, C3H3, CH3CCH2, C3H6, n-C3H7, i-C3H7, C3H8, n-C4H3, i-C4H3, C4H4, NH, NH2, NH3, NNH, NO, NO2, N2O, HNO, NCO, N2 H2, H, O, O2, OH, H2O, HO2, H2O2, CH, CH2, CH2*, CH3, CH4, CO, CO2, HCO, CH2O, CH2OH, CH3O, C2H2, H2CC, C2H3, C2H4, C2H6, HCCO, CH2CO, HCCOH, CH2CHO, CH3CHO, CH3CO, C3H2, C3H3, CH3CCH2, C3H6, n-C3H7, i-C3H7, C3H8, n-C4H3, i-C4H3, C4H4, NH, NH2, NH3, NNH, NO, NO2, N2O, HNO, NCO, N2 H2, H, O, O2, OH, H2O, HO2, H2O2, CH, CH2, CH3, CH4, CO, CO2, HCO, CH2O, CH2OH, CH3OC2H, C2H2, H2CC, C2H3, C2H4, C2H5, HCCO, CH2CO, HCCOH, CH2CHO, CH3CHO, CH3CO, C3H2, C3H3, CH3CCH2, C3H6, n-C3H7, i-C3H7, C3H8, n-C4H3, i-C4H3, C4H4, NH, NH2, NH3, NNH, NO, NO2, N2O, HNO, NCO, N2 H2, H, O, O2, OH, H2O, HO2, H2O2, CH, CH2*, CH3,CH4, CO, CO2, HCO, CH2O, CH2OH, CH3O, CH3OH, C2H, C2H2, C2H3, C2H4, C2H5, C2H6, HCCO, CH2CO, HCCOH, C2O, CH2CHO, CH3CHO, CH3CO, C3H2, C3H3, CH3CCH2, C3H6, n-C3H7, i-C3H7, C3H8, n-C4H3, C4H4, NH, NH2, NH3, NNH, NO, NO2, N2O, HNO, N2

set 1 (LU 2.0) set 2 set 3 set 4

Table 6. % Error of Both Mechanisms for Different Indicators LU 1.0 vs experimental indicators laminar flame speed adiabatic flame temperature ignition delay

methane propylene methane ethylene methane ethylene propylene

LU 2.0 vs experimental

average % error

maximum % error

standard deviation (%)

average % error

maximum % error

standard deviation (%)

7.725 12.860 2.487 1.138 15.140 420.50 29.934

29.882 22.864 4.792 1.863 39.369 1852 40.256

9.640 6.471 1.110 0.433 12.566 800.70 5.162

3.989 3.318 4.764 1.078 14.457 12.393 8.179

15.789 9.682 6.548 2.362 42.857 29.747 18.182

4.598 3.299 1.682 0.770 14.109 10.051 6.269

Figure 4. Laminar flame speed versus equivalence ratio for a methane−air mixture.

Qin et al.48 were considered, respectively. Figures 8−10 show a comparison of the LU 2.0 and LU 1.0 mechanisms and experimental results of ignition delays for methane, ethylene, and propylene flames at different inlet temperatures, respectively. The LU 2.0 mechanism fits better to the experimental data compared to the LU 1.0 mechanism for methane, ethylene, and propylene flames. This is shown quantitatively in Table 6.

ethylene flames at different equivalence ratios, are shown in Figures 6 and 7, respectively. Both mechanisms show a reasonably good fit to the experimental results, as shown by the indicators in Table 6. Ignition Delay. Ignition delay validation was conducted for methane, ethylene, and propylene flames. The experimental results from Serry and Bowman,46 Brown and Thomas,47 and 12701

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Figure 5. Laminar flame speed versus equivalence ratio for a propylene−air mixture.

Figure 6. Adiabatic flame temperature versus equivalence ratio for a methane−air mixture.

Figure 7. Adiabatic flame temperature versus equivalence ratio for an ethylene−air mixture.

From the complete results table (Table 6), it is apparent that the LU 2.0 mechanism outperforms LU 1.0 in terms of the average relative error for all of the indicators. For the adiabatic flame temperature, the average percentage error for the LU 2.0 mechanism for methane (4.764%) is higher than that of LU 1.0 (2.487%). For ethylene, the average percentage error of the LU 2.0 mechanism (1.078%) is lower than that of LU 1.0 (1.138%), but the maximum percentage error and standard

deviation are higher. For the ignition delay of methane, the average percentage error of LU 2.0 (14.457%) is lower than that of LU 1.0 (15.14%), but the maximum percentage error and the standard deviation are higher than those of LU 1.0. The LU 2.0 mechanism yields good results for simulating the laminar flame speed of methane (average percentage error 3.989%, maximum percentage error 15.789%, and standard deviation 4.598%) and propylene (average percentage error 12702

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Figure 8. Ignition delay versus temperature for a methane−air mixture.

Figure 9. Ignition delay versus temperature for an ethylene−air mixture.

Figure 10. Ignition delay versus temperature for a propylene−air mixture.

technique is that it is an exhaustive search approach and is straightforward. No assumptions or mathematical derivatives are needed. The LU 2.0 mechanism was validated successfully against the experimental data for various key performance indicators (laminar flame speeds, burner stabilized flame, adiabatic flame temperature, and ignition delay tests) for methane, ethylene, and propylene flames and compared alongside the LU 1.0 reduced mechanism. The LU 2.0 mechanism shows an

3.318%, maximum percentage error 9.682%, and standard deviation 3.299%).

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CONCLUSION

In this work, a new RSM generation technique is proposed for the formation of a skeleton mechanism with minimal error. The method is very general and fully automated and can be readily applied to any reaction mechanism. The main advantage of this 12703

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(8) Areas, D. C. A Computational Fluid Dynamics Simulation Model for Flare Analysis nnd Control. Doctoral Thesis, University of Texas, Austin, TX, 2006. (9) Murphy, C. F.; Allen, D. Event Emissions in the Houston Galveston Area (HGA); University of Texas: Austin, TX, Jan 14, 2008. (10) Peters, N.; Kee, R. J. The Computation of Stretched Laminar Methane−Air Diffusion Flames Using a Reduced Four-Step Mechanism. Combust. Flame 1987, 68, 17. (11) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. A comprehensive modeling study of n-heptane oxidation. Combust. Flame 1998, 114 (1−2), 14 9−177. (12) Faravelli, T.; Bua, L.; Frassoldati, A.; Antifora, A.; Tognotti, L.; Ranzi, E. A new procedure for predicting NOx emissions from furnaces. Comput. Chem. Eng. 2001, 25 (4−6), 613−618. (13) Granata, S.; Faravelli, T.; Ranzi, E.; Olten, N.; Senkan, S. Kinetic modeling of counterflow diffusion flames of butadiene. Combust. Flame 2002, 131 (3), 273−284. (14) Lindstedt, R. P.; Meyer, M. P. A dimensionally reduced reaction mechanism for methanol oxidation. Proc. Combust. Inst. 2003, 29, 1395−1402. (15) Kaiyuan, H.; Androulakis, I. P.; Ierapetritou, M. G. On-the-fly reduction of kinetic mechanisms using element flux analysis. Chem. Eng. Sci. 2010, 65, 1173−1184. (16) Pope, S. B. Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theory Modell. 1997, 1 (1), 41−63. (17) Mass, U.; Pope, S. B. Simplifying chemical kinetics: intrinsic low dimensional manifold in composition space. Combust. Flame 1992, 88, 239−264. (18) Kuo, J.; Wei, J. A lumping analysis in monomolecular reaction systems. Analysis of exactly lumpable systems. Ind. Eng. Chem. Fundam. 1969, 8 (1), 114−123. (19) Turanyi, T. Reduction of large reaction mechanisms. New J. Chem. 1990, 14, 795−803. (20) Rabitz, H.; Kramer, M.; Dacol, D. Sensitivity analysis in chemical kinetics. Annu. Rev. Phys. Chem. 1983, 34, 419−461. (21) Androulakis, I. P. Kinetic mechanism reduction based on an integer programming approach. AIChE J. 2003, 46 (2), 361−371. (22) Bhattacharjee, B.; Schwer, D. A.; Barton, P. I.; Green, W. H. Optimally-reduced kinetic models: reaction elimination in large-scale kinetic mechanisms. Combust. Flame 2003, 135 (3), 191−208. (23) Petzold, L.; Zhu, W. J. Model reduction for chemical kinetics: an optimization approach. AIChE J. 1999, 45 (4), 869−886. (24) Lu, T. F.; Law, C. K. A directed relation graph method for mechanism reduction. Proc. Combust. Inst. 2005, 30 (1), 1333−1341. (25) Liang, L.; Stevens, J. G.; Farrell, J. T. A dynamic adaptive chemistry scheme for reactive flow computations. 32nd International Symposium on Combustion in Production Progress, Montreal, Canada, Aug 3−8, 2008. (26) Androulakis, I. P.; Grenda, J. M.; Bozzelli, J. W. Time-integrated pointers enabling the analysis of detailed reaction mechanisms. AIChE J. 2004, 11, 2956−2970. (27) Peters, N. Systematic reduction of flame kineticsprinciples and details. 11th International Colloquium on Dynamics of Explosions and Reactive Systems, Warsaw, Poland, 1988. (28) Chen, J. Y. A general procedure for constructing reduced reaction mechanisms with given independent reactions. Combust. Sci. Technol. 1988, 57, 89−94. (29) Lam, S. H.; Goussis, D. A. The CSP method for simplifying kinetics. Int. J. Chem. Kinet. 1994, 26 (4), 461−4 86. (30) Lu, T. F.; Ju, Y. G.; Law, C. K. Complex CSP for chemistry reduction and analysis. Combust. Flame 2001, 126 (1−2), 1445−1455. (31) Kaper, H. G.; Kaper, T. J. Asymptotic analysis of two reduction methods for systems of chemical reactions. Physica D 2002, 165 (1−2), 66−93. (32) Tomlin, A. S.; Li, G. Y.; Rabitz, H.; Toth, J. A general analysis of approximate nonlinear lumping in chemical kinetics. J. Chem. Phys. 1994, 101 (2), 1188−1201.

improvement in the predictability compared to the LU 1.0 mechanism. Future work would include validation of the mechanism against measured data from full-scale flares. Another possible direction for improvement is to combine this technique with other techniques, such as forming global reactions to optimize the reduced mechanism even further.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 409-880-8207. Fax: 409-880-2197. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from Texas Air Research Center (Grant 079LUB0096A), AQRP (Project 10-022), and Texas Commission on Environmental Quality (SEP Agreement 2009-009).

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NOMENCLATURE

Abbreviations

CFD VOCs HRVOCs GRI RSM USC PSR MPB

computational fluid dynamics volatile organic compounds highly reactive organic compounds Gas Research Institute rigorous skeleton mechanism University of Southern California perfectly stirred reactor mechanism processing block

Symbols

δi,j Δj

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error in the concentration of species i in the reduced mechanism j cumulative error of the reduced mechanism

REFERENCES

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dx.doi.org/10.1021/ie2027684 | Ind. Eng. Chem. Res. 2012, 51, 12697−12705