Development and Validation of a Reduced Mechanism for Urea-based

Jun 18, 2009 - This paper reports a reduced mechanism used in urea-based SNCR process for NOx control that is developed from the detailed mechanism ...
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Energy & Fuels 2009, 23, 3605–3611

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Development and Validation of a Reduced Mechanism for Urea-based SNCR Process based on QSS Graph Yu Lv,* Zhihua Wang,* Junhu Zhou, and Kefa Cen State Key Laboratory of Clean Energy Utilization, Institute for Thermal Power Engineering, Zhejiang UniVersity, Hangzhou, 310027, Zhejiang, China ReceiVed February 25, 2009. ReVised Manuscript ReceiVed May 25, 2009

This paper reports a reduced mechanism used in urea-based SNCR process for NOx control that is developed from the detailed mechanism originally proposed by Rota et al. (Chem. Eng. Sci. 2002, 57, 27-38) consisting of 173 elemental reactions and 31 chemical species. Sensitivity analysis and rate-of-production analysis are first conducted to exclude redundant elemental reactions and species, forming a skeletal mechanism. After that, quasi-steady-state species are identified and a 12-step 16-species reduced mechanism is established. The balance equations for quasi-steady-state species are innovatively solved by means of QSS graph method presented by Lu and Law (J. Phys. Chem. A 2006, 110, 13202-13208) with the avoidance of efficiency compromise stemming from algebraic iterations. The predictions of the reduced mechanism show satisfactory agreement with those of the detailed one over a wide range of operating conditions, including various temperatures, molar ratio of CO(NH2)2/NO and O2 and CO concentrations. The performances of QSS graph method and traditional QSSA by iteration are compared in plug-flow computations. The deviation in accuracy is only in order of 0.01%, while QSS graph creates nearly 40% speed-up significantly superior to QSSA by iteration.

1. Introduction As green industry and power production draws more attention of the public, to control nitrogen oxides, known as NOx, a serious threat to environment, is put on the agenda. Many techniques have been developed to handle NOx emissions produced in various combustion processes. Because of low operation cost and no influence on initial combustion, selective noncatalytic reduction (SNCR) has been recognized as one of the most efficient and economic techniques for NOx control.1-3 In SNCR, some kind of reducing agent, generally able to decompose to NHi radicals, is injected into the postcombustion zone at a suitable temperature, and then rapidly mixed with flue gas to reduce NOx with no addition of catalysts. Many types of reagent have been reported to be employed in SNCR processes. Albeit ammonia frequently appears in experimental studies,4-8 since 85-95% NOx reduction has been found, * To whom correspondence should be addressed. Phone: 86-57187952443-8027. Fax: +86-571-87953162. E-mail: [email protected] (Z.W.); [email protected] (Y.L.). (1) Jodal, M.; Lauridson, T. L.; Dam-Johansem, K. EnViron. Prog. 1992, 11, 296–301. (2) Lee, S. M.; Park, K. N.; Kim, B. H. Combust. Flame 2005, 141, 200–203. (3) Hou, X.; Zhang, H.; Pilawska, M.; Lu, J.; Yue, G. Fuel 2008, 87, 3271–3277. (4) Lyon R. K.; Benn D. Proceedings of the 7th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1979; pp 601-610. (5) Duo W.; Dam-Johansem K.; Østergaard K. Proceedings of the 23rd Symposium (International) on Combustion; The Combustion Institute: Pittsburgh. PA, 1990; pp 297-303. (6) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287–338. (7) Miller, J. A.; Glarborg, P. Springer Ser. Chem. Phys. 1996, 61, 318– 333. (8) Zhang, Y.; Cai, N.; Yang, J.; Xu, B. Chemosphere 2008, 73, 650– 656.

more industrial practices9-11 are apt to use urea as the reagent because of its convenience to transportation and storage. To better guide practical operations of SNCR equipments, great effort is made to discover the chemical kinetics behind. The kinetics of the ammonia-based SNCR process has been found and fully included in GRI 3.0.12 However, because of the complex interaction between isocyanic acid, one of the urea-decomposed products, and NOx, the kinetics of ureabased SNCR process was not completely understood until one constructed and strictly tested by Rota et al.,13 which includes 173 elemental reactions and 31 species. Nevertheless, when it comes to doing CFD modeling of urea-based SNCR processes, such a large number of elemental reactions and chemical species in the detailed mechanism, combined with the governing equations of fluid mechanics, makes the relevant simulations in industrial scale yet not accomplished based on the available computational resources. One smart way to deal with this problem is to acquire a reduced mechanism in which the superfluous information involved in detailed kinetics is removed and the representative features of the urea-based SNCR process is retained without losing much accuracy. (9) Lee, J. B.; Kim, S. D. J. Chem. Eng. Jpn. 1996, 29, 620–626. (10) Kim, H. S.; Shin, M. S.; Jang, D. S.; Ohm, T. I. Appl. Therm. Eng. 2004, 24, 2117–2129. (11) Javed, M. T.; Nimmo, W.; Gibbs, B. M. Chemosphere 2008, 70, 1059–1067. (12) 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.; Lissianski, V., Jr.; Qin, Z. GRI-Mech, version 3.0 2002, http://www.me.kerkeley.edu/gri_mech/. (13) Rota, R.; Antos, D.; Zanoelo, E´. F.; Morbidelli, M. Chem. Eng. Sci. 2002, 57, 27–38. (14) Tomlin, A. S.; Turanyi, T.; Pilling, M. J. ComprehensiVe Chemical Kinetics; Elsevier: Amsterdam, 1997; pp 293-437.

10.1021/ef900165k CCC: $40.75  2009 American Chemical Society Published on Web 06/18/2009

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Table 1. Operating Conditions Considered in the Reduction temperature, T (K) 950-1450

initial concentrations

2 × molar ratio of CO(NH2)2/NO, NSR

pressure, P (atm)

residence time, tr (s)

NO (ppm)

H2O (%)

O2 (%)

N2 (%)

1-2

1

0-200/T

300

1.5

4

balance

To simplify a detailed kinetics, skeletal reduction techniques, such as sensitivity analysis,14 principal component analysis,15 computational singular perturbation,16 and directed related graph (DRG),17-19 are usually first used to form a skeletal mechanism, followed by time-scale based analysis to identify and eliminate many radicals with short time scales that still included in this skeletal mechanism. Quasi steady state approximation (QSSA)20,21 is one typical way to do this timescale analysis which is simply to apply and have been extensively exploited in the aspect of kinetics reduction in the past few decades. Many cases of doing mechanism reduction adopted this procedure, such as Sung et al.’s22 and Mendiara et al.’s23 development for methane oxidation, Mallampalli et al.’s24 and Giral et al.’s25 work for the reburning process, and Xu et al. ’s26,27 reduction for the advanced reburning process. Notwithstanding, one primary limitation of using QSSA is that large quantities of algebraic iterations are required to solve a aggregate of coupled nonlinear equations of QSS species concentrations. Consequently, the net efficiencies of incorporating these reduced mechanisms into CFD simulations are usually undermined. In response to such a problem, a method based on graph theory, namely QSS Graph developed by Lu et al.,28 comes up and is expected to efficiently obtain analytic solutions of the equations in QSSA.

Three goals of this paper are to (1) develop a reduced and representative mechanism for urea-based SNCR process from the detailed one reported by Rota et al.,13 (2) validate this reduced mechanism versus the detailed one, over a wide range of practical operations and considering the effects of oxygen and carbon monoxide concentrations, and (3) demonstrate the efficiency and applicability of QSS Graph method through the comparison of the performances with those obtained by applying traditional QSSA. 2. Skeletal Mechanism. To excessively demand the accuracy, full mechanisms generally include some redundant chemical species and unimportant reactions. The first step to obtain a reduced kinetics following the aforementioned procedures is to identify and eliminate them, establishing a skeletal mechanism. Sensitivity analysis is a good tool to do this work. Because of the objective that the developed reduced mechanism should not only accurately predict NO dynamics but also give a reasonable result for byproduct during this process, such as CO and N2O, we select CO(NH2)2, NH3, CO2, HNCO, NO, CO, and N2O as reference species for sensitivity analysis. CO(NH2)2 is the primary reagent, while NH3 and HNCO are the secondary reagent decomposed from CO(NH2)2. When they react with NO, N2O

Figure 1. Comparison between the results of the detailed and skeletal mechanisms for a temperature of 1450 K, various residence times, and NSR ) 2.

Figure 2. Comparison between the results of the detailed and skeletal mechanisms for a temperature of 1250 K, various residence times, and NSR ) 2.

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Table 2. 12-Step Reduced Mechanism for Urea-Based SNCR Process reaction number

reaction number

reaction

R1 R2 R3 R4

2H ) H2 OH + CO ) CO2 + H OH + O ) H + O2 OH + H ) H2O

R7 R8 R9 R10

R5

O2 + N2 ) 2NO

R11

R6

N2 + CO2 ) CO + N2O

R12

reaction OH + NH3 ) NH2 + H2O NO + NH2 ) H2O + N2 NO2 + NH2 ) 2NO + 2H NO + OH + HNCO ) CO2 + N2 + H2O O + O2 + HNCO ) NO + OH + CO2 CO(NH2)2 ) HNCO + NH3

and N2 are formed, and N2O is more sensitive compared to the balance species N2. Additionally, HNCO owns another chemical path to form CO sequentially oxidized to CO2. The operating conditions used in the present work are listed in Table 1. At a given condition, when there is a modification in reaction rate constant, the responses of main species concentrations are quantified as the sensitivity coefficient λi,j in the following way: λj,i )

∂Cj ∂Ai

(1)

where Cj is the concentration of the jth species and Ai is the pre-exponential constant of the ith elemental reaction. Sensitivity coefficients are calculated by running SENKIN module in CHENKIN III, and finally normalized as j,i ) λ(t)j,i ×

Ai C(t)max j

Table 3. Global Reaction Rates of the Reduced Mechanisma WR1 ) -w3 + w17 + w34 WR2 ) w1 + w22 + w27 + w39 + w51 - w57 - w58 + w61 - w62 - w67 w71 + w72 - 2 × w74 WR3 ) w2 + w10 + w16 + w17 + w19 - w22 + w23 + w24 + w30 - w31 w39 - w47 - w51 + w67 - w72 + w74 WR4 ) w3 + w5 + w6 - w10 - 2 × w14 + 2 × w15 - 2 × w16 - 3 × w17 - 2 × w19 - w20 + 2 × w22 - w24 - w25 - 2 × w29 - w30 + 2 × w31 + 2 × w32 + w35 + w36 + w37 + w38 + 2w39 + w41 + w42 + w44 + 3 × w47 + w48 + w50 + 2w51 + w53 + w54 + w56 - w57 w65 + w71 + 2 × w72 + w73 - w74 WR5 ) w4 - w8 + w10 + w12 + w14 - 2 × w15 + w16 + 2 × w17 + w18 + 2 × w19 - 2 × w22 + w24 + w25 - w27 - w28 + w29 + w30 2 × w31 - 2 × w32 - w35 - 2 × w39 - w41 - 2 × w47 - 2 × w51 + w57 - w61 + w65 + w67 + w68 - 2 × w72 + 2 × w74 WR6 ) w22 + w27 + w39 + w51 - w57 - w58 + w61 + w69 + w72 WR7 ) w8 + w9 - w13 - w18 - w38 - w44 - w54 - w66 - w76 WR8 ) w10 + w11 + w12 + w14 - w15 + w16 + 2 × w17 + w18 + 2 × w19 + w20 + w21 + w29 + w30 - w31 - w32 - 2 × w47 - w51 + w60 w62 - w71 - w72 - w76 WR9 ) -w8 - w9 + w10 + w11 + w12 + w13 + w14 - w15 + w16 + 2 × w17 + 2 × w18 + 2 × w19 + w20 + w21 + w22 + w38 + w44 - 2 × w47 - w51 + w54 + w59 + w60 - w62 + w66 WR10 ) w4 - w8 - w11 - w15 + w16 + w17 + w19 - w22 + w24 + w25 w31 - w32 - w35 - w39 - w41 - w47 - w51 - w56 + w57 + w62 + w64 + w65 + w66 - w72 - w73 + w74 + w76 WR11 ) -w4 + w8 + w11 + w15 - w16 - w17 - w19 + w22 - w24 w25 + w31 + w32 + w35 + w39 + w41 + w47 + w51 + w56 - w57 + w63 + w72 - w74 WR12 ) w75 + w76 a Numbers in expressions refers to the reaction number in the skeletal mechanism given in Table A1. Units are mol, s, cm, and K.

(2)

j,i presents the relative influence of the ith elemental reaction on the jth species at the time t domain. If this value is small enough, the corresponding reaction supplies negligible contribution and can be directly removed. In the present work, a threshold value 0.001 is chosen to distinguish these negligible reactions from the important ones. If the normalized sensitivity coefficients for all the previously mentioned reference species are less than the threshold value, the corresponding elemental reactions are discarded. As a complement, rate-of-production analysis is also done and the contributions of the each remaining reaction to the net production rates of the reference species are calculated. Considering the large difference in the value of the production rates for different species with various concentrations, here an indirect standard for selection dependent on rate-ofproduction analysis is set to be that the concentration deviations of reference species from the detailed kinetics result are not more than 5% over tested conditions. Following this procedure, a skeletal mechanism is finally established including 76 elemental reactions and 25 species as shown in Table A1 in the Appendix. (15) Vajada, S.; Valko, P.; Turanyi, T. Int. J. Chem. Kinet. 1985, 17, 55–81. (16) Massias, A.; Diamantis, D.; Mastorakos, E. Combust. Flame 1999, 117, 685–708. (17) Lu, T. F.; Law, C. K. Proc. Combust. Inst. 2005, 30, 1333–1341. (18) Lu, T. F.; Law, C. K. Combust. Flame 2005, 144, 24–36. (19) Lu, T. F.; Law, C. K. Combust. Flame 2006, 146, 472–483. (20) Peters, N.; Kee, R. J. Combust. Flame 1987, 57, 89–94. (21) Lovas, T.; Nilsson, D.; Mauss, F. Proc. Combust. Inst. 2000, 28, 1809–1815. (22) Sung, C. J.; Law, C. K.; Chen, J. Y. Proc. Combust. Inst. 1998, 27, 295–304.

Figure 3. QSS graph to show the simplified dependence among QSS species. Species in arrow end is dependent on species in arrowhead in the process of concentration evaluation, while species is independent with no species to point to.

The validation of the skeletal mechanism is run in a plugflow reactor with various operating conditions according to Table 1. The predicted concentrations of the reference species versus residence time by using the skeletal mechanism are compared with the results acquired from the detailed one. Comparisons at two typical conditions are shown in Figures 1 and 2, where there is an excellent agreement except for a little overprediction of N2O concentration in the interval of 10-20 ms at 1450 K. Moreover, one thing worthy to mention is that the chemical conversion loop from NH2 to N2O indirectly through N2H4 f N2H3 f N2H2 existing in the mechanism has obvious effect on the variation of N2O concentrations as presented in Figure 2. Therefore, N2H4 and N2H3 radicals are still retained in the skeletal mechanism. From the comparisons, it is credible that the accuracy of Rota et al.’s13 mechanism for prediction is well preserved in the skeletal one which is ready to be further reduced. 3. Reduced Mechanism. Although 25 species are included in the skeletal mechanism, several species own very low

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Figure 4. Comparison between the results of the detailed and reduced mechanisms for a temperature of 1250 K, various residence times, and NSR ) 2.

Figure 5. Comparison between the results of the detailed and reduced mechanisms for various temperatures, a residence time of 200/T, and NSR ) 1.

concentrations during the whole reaction process since their consumption rates are very fast and rapidly exhaust all of them as they are formed. Then quasi-steady-state assumption can be employed on this type of chemical species, which is that the net variation rates of them are negligible. Consequently, the differential equations to solve the concentrations of these steadystate species are decoupled from the original equation set and degenerate to general algebraic equations. This set of equations called QSS equation can be independently resolved, which further simplify the obtained skeletal mechanism. Therefore, it is of the great importance to correctly identify QSS species. Here an effective and practical approach proposed by Giral25 is used. If the symbolic value |ωPk - ωCk | max{|ωPk |, |ωCk |}

(3)

where ωPk and ωCk are the production rate and consumption rate, respectively, of the kth chemical species If the symbolic value is generally below or on the order of 10-2 at the time domain, the kth species is considered as QSS species. Every 50 K, the selections are conducted to ensure the determination adaptable for various operating conditions. The species that satisfy the above criteria are HO2, NH, NNH, N2H2, N2H3, N2H4, H2NO, NCO, HNO, OH, O, H, and NH2. However, OH, O, and H

belong to very reactive radicals that control the radical pool in the reaction process, meanwhile larger amounts of these radicals may exist in the flue gas at such a high temperature; therefore OH, O, and H are still included in the reduced global mechanism. On the other hand, NH2 plays essential role in the competitive reactions NH2 + O2 ) H2NO + O and NH2 + NO ) N2 + H2O that directly decide the direction the whole chemical system advanced to. So NH2 remains as well to ensure the accuracy of the reduced mechanism. After 9 QSS species are chosen, the same number of elemental reactions can be eliminated from the skeletal mechanism. Each reaction involving one QSS species should be the fastest one in which the corresponding QSS species is consumed. Several approaches29 have been presented to select appropriate reactions. Here, we directly use the results obtained in doing sensitivity analysis: (HO2, w7), (NH, w26), (NNH, w55), (N2H2, w49), (N2H3, w46), (N2H4, w45), (H2NO, w40), (NCO, w70), and (23) Mendiara, T.; Alzueta, M. U.; Millera, A.; Bilbao, R. Energy Fuels 2004, 18, 619–627. (24) Mallampalli, H. P.; Fletcher, T. H.; Chen, J. Y. J. Eng. Gas Turbines Power Trans. ASME 1998, 120, 703–712. (25) Giral, I.; Alzueta, M. U. Fuel 2002, 81, 2263–2275. (26) Xu, H.; Smoot, L. D.; Hill, S. C. Energy Fuels 1998, 12, 1278– 1289. (27) Xu, H.; Smoot, L. D.; Hill, S. C. Energy Fuels 1999, 13, 411–420. (28) Lu, T. F.; Law, C. K. J. Phys. Chem. A 2006, 110, 13202–13208. (29) Peters, N. Lect. Notes Phys. 1991, 384, 48–67.

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Figure 6. Comparison between the results of the detailed and reduced mechanisms for various temperatures, a residence time of 200/T, NSR ) 2, and various initial O2 concentrations.

Figure 8. Accuracy comparison between QSS graph and QSSA by iteration in 1000 random plug-flow cases. The distributions of errors are shown for NO (a), HNCO (b), NH3 (c), and N2O (d).

Figure 7. Comparison between the results of the detailed and reduced mechanisms for various temperatures, a residence time of 200/T, NSR ) 2, and various initial CO concentrations.

(HNO, w33), where wi refers to the ith reaction in the skeletal mechanism shown in Table A1. Then according to the procedure proposed by Chen,30 a set of independent reactions in which QSS species are all excluded is chosen from the left reactions to represent the global stoichiometry of the chemical system, finally leading to a 12-step reduced mechanism as shown in Table 2. Each step in the reduced mechanism owns a global reaction rate expressed in terms of the elemental reaction rates in the skeletal mechanism, as given in Table 3. One problem still left is how to solve the set of QSS equations. Normally algebraic iteration is used because these equations in the set are coupled with each other. However, it consumes extra computational time and even worse may diverge by chance, finally impairing the efficiency and reliability of using reduced mechanisms. In the present work, QSS graph recently presented by Lu28 is adopted to solve QSS equations without iteration. The expression of the net production rate of one QSS species can be deduced as follows: QSSnum Nj

wP,net i

)

∑ ∑w

P ij,k

j)1,j*i k)1

+

∑w

P i,other

(4)

P is the rate of the kth reaction including the jth QSS where wij,k P species in the net production rate of the ith QSS species; wi,other is the reaction rate without any other QSS species except the

Figure 9. Efficiency comparison between QSS graph and QSSA by iteration in 1000 random plug-flow cases.

ith one; Nj is the total number of the reactions including the jth QSS species in the net production rate of the ith QSS species; QSSnum is the total number of QSS species. In such a manner, the contribution of the jth QSS species to the production rate of the ith one can be quantified by Nj

ζij )

∑w

P ij,k k)1 wP,net i

(5)

If the maximum ζij at the time domain is adequately small, the terms involving the jth QSS species in the above expression contribute negligibly to the net production rate of the ith one and can be truncated. Here a critical value 0.08 is chosen and if the maximum ζij at the time domain is less than this value, the dependent relationship of the ith QSS species on the jth one is neglected. In accordance with this strategy, the QSS graph used to show the dependence among QSS species is largely simplified as shown in Figure 3. Although there are two strongly connected components in the graph, only 19 computer operations are needed to resolve

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each one. If the strongly connected component is viewed as one node entity, there are five nodes in the graph. According to the dependence, the concentrations of QSS species can be computed in the following sequence: {1, 5} f {2} f {3, 4}, with no necessity to iteration. The actual performance of this algorithm will be revealed later. 4. Validation of the Reduced Kinetics. The validity of the reduced mechanism developed is verified by the comparison of the simulation results with those obtained from the detailed mechanism in the conditions with various temperatures and stoichiometries. As shown in Figures 4and 5, the tendencies of the concentration variations for different species follow the results performed by the original detailed mechanism very well, although the deviations of NO and NH3 concentrations tend to be a little larger at the range of 1000-1200 K, and the curve of the N2O concentration budges toward lower temperature region. The relative errors for the reference species with comparatively large concentrations are nearly all bellow 10%, while the relative error for N2O is greater at the temperature range up to 1350 K. The deviations may result from the selection of the elemental reaction in the skeletal mechanism or the application of the quasi-steady-state approximation. However, it is quite normal for a compromise to exist between the simplicity and comprehensiveness. Because in the industrial equipment for urea-based SNCR process flue gas usually composes of variable gas components in which O2 and CO have been reported having obvious effect on urea-based SNCR process by several researchers,9,13,31 our reduced mechanism is expected to adapt to the flue gas surroundings with variable O2 and CO concentrations. Therefore, the adaptability of the reduced mechanism developed is also proven in Figure 6 and 7. It is obviously shown that as O2 concentration in initial flue gas increases the NOx reduction rises at lower temperatures but present a reverse tendency at higher temperature, which well coincides with the prediction from the detailed mechanism and the previous studies. The effect of the presence of carbon monoxide on urea-based SNCR process is found in Figure 7, where the optimal temperature reveals a small shift to lower temperature of the operating window. This shift is also predicted by our reduced mechanism, although the extent is a little smaller than the result predicted by the detailed one. Generally speaking, adaptability of our reduced mechanism to variable gas surroundings is preserved and the accuracy is controlled acceptable. 5. Algorithm Performance. Accuracy and efficiency are two aspects of the most importance to evaluate an algorithm. So in the present work these two aspects of using QSS graph (QSSG) algorithm are both evaluated through the comparisons of the prediction errors for NO, NH3, HNCO, and N2O, four main participants in urea-based SNCR process and case running time, with the corresponding ones obtained based on traditional QSS approximation (QSSA) in which QSS equations are solved by algebraic iterations. One thousand cases with various operating parameters are run in plug-flow configuration and, for each case temperature and NSR, are randomly produced within the corresponding range in Table 1, but the residence time is fixed at 200 ms, which makes the efficiency evaluation convenient. In QSSA, the maximum times for iteration is set to be 300 in solving the group of QSS equations and the tolerance of QSS species concentrations between neighbor iterations is chosen to be 10-3. For each case, the largest relative errors of NO, NH3, HNCO, and N2O concentrations at the time domain are recorded, and the total running time is written down as well. Finally the

LV et al.

distributions of the recorded relative errors for NO, NH3, HNCO, and N2O are individually summarized in Figure 8(a-d). As shown in the figures, the difference between the results based on QSSG and QSSA is negligible, and the accuracy only owns a discrepancy in order of 0.01%. The predicted error for N2O is comparatively larger, which may be the result of its relatively small amount in the chemical system. Moreover, the actual running times by using the detailed kinetics, the skeletal one, the reduced one with QSSA and the reduced one with QSSG are averaged and listed in Figure 9. QSSG provides the largest speed-up up to approximately 40% while the advantage of QSSA is not reflected in such simple calculations and it even consumes more time than the skeletal one. It is evident that compared with 5% speed-up created by QSSA the advantage of QSSG, in term of computational efficiency, is overwhelming. 6. Conclusions A reduced mechanism for urea-based SNCR process has been developed from a detailed one. The former one consists of only 12 elemental steps and 16 chemical species that allows a more efficient computation for the practical prediction and optimization combined with complex fluid dynamics. The fluid parameters of all species involved can be found in CHEMKIN package and ready to be used in CFD simulation. The applicability of our reduced mechanism is strictly verified over a wide range of operating conditions, by comparison with the results obtained from the detailed one. The concentration errors for important species are nearly all below 10% except that of N2O at high temperature region. Quasi-steady-state assumption is imposed on the following radicals: HO2, NH, NNH, N2H2, N2H3, N2H4, H2NO, NCO, and HNO. Instead of algebraic iteration, the QSS graph is used to solve QSS equations and its performance is compared with that of traditional algebraic iteration. In plug-flow computations approximately 40% speed-up is reached by employing QSS graph, much greater than that of algebraic iteration. Moreover, the accuracy is well preserved. It should be noted that less species involved means less equation that need be advanced when dealing with CFD, however, the remained 16 species are all of great important to duplicate the essential characteristics of the original chemical system. If any one is omitted, the predicted results could be unwarranted. In addition since the reported reduced mechanism22-27 that usually includes 10-18 species has been extensively used, the computational expense of using our mechanism is comparatively acceptable. In future work, our reduced mechanism could be incorporated into CFD code to predict practical urea-based SNCR process. Some popular CFD codes, for example FLUENT, have already provided powerful user defined interface that makes our reduced mechanism applicable. Acknowledgment. The authors would like to express their grateful acknowledgment to National Natural Science Foundation of China (50806066) and National Science Foundation for Distinguish Young Scholar (50525620) for their financial support.

Appendix (30) Chen, J. Y. Combust. Sci. Technol. 1988, 57, 89–94. (31) Bilbao, R.; Oliva, M.; Iban˜ez, J. C.; Zapater, A.; Millera, A.; Alzueta, M. U. The use of urea as selective non-catalytic reduction agent to reduce NOx emissions. Proceedings of the ICCS’97, Essen, Germany; 1997;pp 1863-1866.

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Table A1. Skeletal Mechanism from Rota et al.’s13 Detailed One for Urea-Based SNCR Process species considered CO(NH2)2 HO2 N2O

NO CO NCO

NH3 CO2 H2O

reactiona 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

CO + OH ) CO2 + H O + OH ) H + O2 OH + H2 ) H2O + H OH + OH ) H2O + O H + O2 + M ) HO2 + Mb H + O2 + N2 ) HO2 + N2 HO2 + OH ) H2O + O2 NH3 + O ) NH2 + OH NH3 + OH ) NH2 + H2O NH2 + O ) HNO + H NH2 + O ) NH + OH NH2 + OH ) NH + H2O NH2 + HO2 ) NH3 + O2 NH2 + HO2 ) H2NO + OH H2NO + O ) NH2 + O2 NH2 + NH ) N2H2 + H NH2 + NH2 ) N2H2 + H2 NH2 + NH2 ) NH3+NH 2NH2 + M ) N2H4 + Mb low-pressure limit NH2 + NO ) NNH + OH NH2 + NO ) N2 + H2O NH2 + NO2 ) N2O + H2O NH + O ) NO + H NH + OH ) HNO + H NH + O2 ) HNO + O NH + O2 ) NO + OH NH + NO ) N2O + H NH + NO ) N2 + OH NO + HO2 ) NO2 + OH NO + O + M ) NO2 + M NO2 + H ) NO + OH NO2 + O ) NO + O2 HNO + M ) H + NO + Mb HNO + H ) NO + H2 HNO + O ) NO + OH HNO + OH ) NO + H2O HNO + O2 ) NO + HO2 HNO + NH2 ) NO + NH3

NH2 NNH O2

NH N2H2 H

A

β

Ea

1.50 × 107 2.00 × 1014 2.10 × 108 4.30 × 103 2.10 × 1018 6.70 × 1019 2.90 × 1013 9.40 × 106 2.00 × 106 6.60 × 1014 6.80 × 1012 4.00 × 106 1.00 × 1013 2.50 × 1013 2.50 × 1014 5.00 × 1013 8.50 × 1011 5.00 × 1013 1.50 × 1013 1.00 × 1018 8.92 × 1012 1.26 × 1016 3.20 × 1018 9.20 × 1013 2.00 × 1013 4.60 × 105 1.30 × 106 2.90 × 1014 2.20 × 1013 2.10 × 1012 7.50 × 1019 8.40 × 1013 3.90 × 1012 1.50 × 1016 4.40 × 1011 1.00 × 1013 3.60 × 1013 1.00 × 1013 2.00 × 1013

1.30 -0.40 1.52 2.70 -1.00 -1.42 0.00 1.94 2.04 -0.50 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.35 -1.25 -2.20 0.00 0.00 2.00 1.50 -0.40 -0.23 0.00 -1.41 0.00 0.00 0.00 0.72 0.00 0.00 0.00 0.00

-765 0 3450 -2486 0 0 -497 6460 566 0 0 1000 0 0 0 0 0 10000 0 0 0 0 0 0 0 0 100 0 0 -480 0 0 -238 48680 650 0 0 25000 1000

HNCO N2H3 O

HNO N2H4 OH

reactiona 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76.

HNO + HNO ) N2O + H2O H2NO + M ) HNO + H + M H2NO + O ) HNO + OH H2NO + OH ) HNO + H2O H2NO + NO ) HNO + HNO H2NO + NH2 ) HNO + NH3 N2H4 + OH ) N2H3 + H2O N2H3 + M ) N2H2 + H + M N2H3 + H ) NH2 + NH2 N2H3 + OH ) N2H2 + H2O N2H2 + M ) NNH + H + Mb N2H2 + OH ) NNH + H2O N2H2 + NO ) N2O + NH2 NNH ) N2 + H NNH + OH ) N2 + H2O NNH + NH2 ) N2 + NH3 NNH + NO ) N2 + HNO NNH + O ) NH + NO N2O + M ) N2 + O + Mb N2O + H ) N2 + OH NH2 + NO2 ) H2NO + NO NH2 + NO ) N2 + H2O NH + NO ) N2O + H HNCO + H ) NH2 + CO HNCO + O ) NH + CO2 HNCO + OH ) H2O + NCO HNCO + O2 ) HNO + CO2 HNCO + NH2 ) NH3 + NCO NCO + O ) NO + CO NCO + O2 ) NO + CO2 NCO + NO ) N2O + CO NCO + NO ) N2 + CO2 NCO + NO2 ) NO + NO + CO NCO + NO2 ) N2O + CO2 NCO + HNO ) HNCO + NO NCO + NCO ) CO + CO + N2 CO(NH2)2 f NH3 + HNCO CO(NH2)2 + H2O f 2NH3 + CO2

N2 NO2 H2NO

H2

A

β

Ea

4.00 × 1012 5.00 × 1016 3.00 × 107 2.00 × 107 2.00 × 107 3.00 × 1012 4.00 × 1013 3.50 × 1016 1.60 × 1012 1.00 × 1013 5.00 × 1016 1.00 × 1013 3.00 × 1012 1.00 × 1014 5.00 × 1013 5.00 × 1013 5.00 × 1013 5.00 × 1013 4.00 × 1014 4.40 × 1014 1.50 × 1019 -8.92 × 1012 -2.20 × 1013 2.25 × 107 9.60 × 107 6.40 × 105 1.00 × 1012 5.00 × 1012 4.70 × 1013 2.00 × 1012 6.20 × 1017 7.80 × 1017 1.30 × 1013 5.40 × 1012 1.80 × 1013 1.80 × 1013 1.27 × 104 6.13 × 1010

0.00 0.00 2.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.20 -0.35 -0.23 1.70 1.41 2.00 0.00 0.00 0.00 0.00 -1.73 -1.73 0.00 0.00 0.00 0.00 0.00 0.00

5000 50000 2000 1000 13000 1000 0 46000 0 1000 50000 1000 0 0 0 0 0 0 56100 19254 0 0 0 3800 8520 2560 35000 6200 0 20000 763 763 0 0 0 0 15540 20980

a The rate constants are in the form of k ) ATβe-Ea/RT; A units of mol cm s K; E units of cal/mol. b Enhanced third-body efficiencies: (5) N /0.0, H /1.5, a 2 2 H2O/10.0; (19) N2/2.5, H2O/5.0, NH3/10.0; (33) N2/2.0, H2/2.0, O2/2.0, H2O/10.0; (49) N2/2.0, H2/2.0, O2/2.0, H2O/15.0; (57) N2/1.5, O2/1.5, H2O/10.0.

Nomenclature T ) temperature P ) pressure R ) reaction number C ) species concentration λ ) sensitivity coefficient  ) normalized sensitivity coefficient A ) pre-exponential constant β ) temperature coefficient Ea ) activation energy

ωP ) species total production rate ωC ) species total consumption rate w ) elemental reaction rate in detailed and skeletal mechanism W ) global reaction rate in reduced mechanism ζ ) quantitative contribution of one QSS species to the production rate of another NSR ) molar ratio of reagent to NO QSS ) quasi-steady-state EF900165K