Energy Fuels 2010, 24, 2883–2890 Published on Web 04/15/2010
: DOI:10.1021/ef100028e
A Simplified Model for Volatile-N Oxidation Stine Hansen and Peter Glarborg* Department of Chemical Engineering Technical University of Denmark, 2800 Lyngby, Denmark Received January 8, 2010. Revised Manuscript Received April 1, 2010
In solid fuel flames, NOx is largely formed from the oxidation of volatile nitrogen compounds such as HCN and NH3. To be able to model the nitrogen chemistry in these flames, it is necessary to have an adequate model for volatile-N oxidation. Simple global models for oxidation of HCN and NH3 from the literature should be used cautiously, since their predictive capabilities are limited, particularly under reducing conditions. Models for HCN/NH3/NO conversion based on the systematic reduction of a detailed chemical kinetic model offer high accuracy but rely on input estimates of combustion intermediates, including free radicals. In the present work, simple, semiempirical expressions are presented for estimation of H, O, and OH radicals. Correlations are derived for volatile compositions representative of solid fuels ranging from bituminous coal to biomass, for temperatures of 1200-2000 K, and excess air ratios in the range 0.6 e λ e 2.0. The radical estimation tool is combined with the analytically reduced N-scheme of Pedersen et al. [Combust. Sci. Technol. 1998, 131, 193-223], and the combined model is tested against reference calculations with a comprehensive mechanism. For excess air ratios of λ g 0.8 and temperatures of 1400 K and above, the prediction of NO formation from both HCN and NH3 is very good for volatile compositions representing all tested fuels. For lower values of λ, the predictions are good for biomass and lignite, while they become less accurate for the sub-bituminous and bituminous coals, especially at lower temperatures. The semiempirical correlations for estimating radical concentrations may also be useful in combination with models for other trace species, such as sulfur oxides, organic species, etc.
affect the nitrogen chemistry selectivity. Even though comprehensive mechanisms for oxidation of HCN5 and NH36,7 are available in the literature, it is often chosen in CFD modeling to use a simplified scheme to reduce the computational load. Several simplified approaches for modeling nitrogen chemistry in combustion have been reported. Typically, they involve either the empirical fitting of a set of global reaction parameters to experimental data or the analytical reduction of comprehensive models through sensitivity analysis and equilibrium considerations. Global schemes developed to predict volatile-N oxidation in combustion include those of De Soete,8 Mitchell and Tarbell,9 and Brink et al.10 The De Soete scheme is the default volatileNO mechanism in FLUENT11 for NH3 or HCN as the intermediate N compound. The De Soete scheme for HCN was later modified by Chen et al.12 to improve the predicted selectivity toward NO under fuel-lean conditions. Pedersen et al.,13 Norstr€ om et al.,14 and recently Andersen et al.2 compared selected global schemes with reference calculations with detailed reaction mechanisms under ideal reactor conditions (perfectly stirred or plug-flow reactor) over a range of conditions. In all of
1. Introduction Computational fluid dynamics (CFD) models are becoming an important industrial tool for analysis and troubleshooting in practical combustion systems.1,2 An important area for CFD is predictions related to pollutant formation, in particular nitrogen oxides (NOx). Most solid fuels contain significant amounts of nitrogen, which will be released during devolatilization and char burnout. For coal and higher ranked fuels, the fuel-bound nitrogen is primarily released as HCN during devolatilization, while for biomass, volatile N may evolve as NH3.3 During the oxidation of volatile matter, HCN and NH3 are converted mainly to NO or to N2, with the selectivity depending on reaction conditions.3,4 Although significant efforts have been aimed at modeling and understanding NO formation and destruction, it remains a challenge to quantitatively predict NO emissions from large combustion systems. Turbulent combustion involves the complexities of turbulence/chemistry interactions, and local fluctuations in temperature and oxygen concentration may *To whom correspondence should be addressed. Fax: þ45 45882258. E-mail:
[email protected]. (1) Andersen, J.; Jensen, P. A.; Meyer, K. E.; Hvid, S. L.; Glarborg, P. Energy Fuels 2009, 23, 5773–5782. (2) Andersen, J.; Jensen, P. A.; Hvid, S. L.; Glarborg, P. Energy Fuels 2009, 23, 5783–5791. (3) Glarborg, P.; Jensen, A. D.; Johnsson, J. E. Prog. Energy Combust. Sci. 2003, 29, 89–113. (4) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287–338. (5) Dagaut, P.; Glarborg, P.; Alzueta, M. U. Prog. Energy Combust. Sci. 2008, 34, 1–46. (6) Skreiberg, Ø.; Kilpinen, P.; Glarborg, P. Combust. Flame 2004, 136, 501–536. r 2010 American Chemical Society
(7) Tian, Z.; Li, Y.; Zhang, L.; Glarborg, P.; Qi, F. Combust. Flame 2009, 156, 1413–1426. (8) De Soete, G. G. Proc. Combust. Inst. 1975, 15, 1093–1102. (9) Mitchell, J. W.; Tarbell, J. M. AIChE J. 1982, 28, 302–311. (10) Brink, A.; Kilpinen, P.; Hupa, M. Energy Fuels 2001, 15, 1094– 1099. (11) Fluent 6.3 Users Guide; Fluent Inc.: Lebanon, NH, 2005. (12) Chen, W.; Smoot, L. D.; Fletcher, T. H.; Boardman, R. D. Energy Fuels 1996, 10, 1036–1045. (13) Pedersen, L. S.; Glarborg, P.; Dam-Johansen, K. Combust. Sci. Technol. 1998, 131, 193–223. (14) Norstr€ om, T.; Kilpinen, P.; Brink, A.; Vakkilainen, E.; Hupa, M. Energy Fuels 2000, 14, 947–952.
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: DOI:10.1021/ef100028e
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the reduction reaction. Contrary to the reference calculations, the De Soete scheme predicts negligible NO formation under stoichiometric or reducing conditions. For fuel-lean conditions, some formation of NO is predicted, but the yield is greatly underestimated. The mechanism by Chen et al. yields improved estimates under fuel-lean conditions but is not recommended for use under stoichiometric or reducing conditions. Contrary to the global schemes, the reduced mechanism by Pedersen et al. provides a good description of volatile-N oxidation (both HCN and NH3) at all the examined conditions. Even though the analytically reduced schemes are superior to the global models in terms of accuracy, their use has so far been limited since they are computationally more demanding and rely on input estimates of combustion intermediates. In particular, these schemes require estimates of free radical concentrations, values which in the past have been available only from modeling with either comprehensive mechanisms or with analytically reduced fuel oxidation schemes. Global schemes like the two-step hydrocarbon oxidation mechanism by Westbrook and Dryer18 or the four-step mechanism of Jones and Lindstedt19 offer estimates of the fuel oxidation rate and concentrations of intermediates like CO, but not radical concentrations. The objective of the present work is to develop a simple approach for estimating radical concentrations, combine it with the analytically reduced N-scheme of Pedersen et al.,13 and test the combined model against reference calculations with a comprehensive mechanism. The radical estimation tool, which is developed for volatile compositions typical of solid fuels ranging from bituminous coal to biomass, may also be useful in combination with models for other trace species (sulfur oxides, organic species, etc.).
Figure 1. Predictions of NO formation during combustion of the gaseous volatiles of a bituminous coal in the air. The N volatiles are represented as 1000 ppm HCN. The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The analytically reduced volatile-N oxidation model by Pedersen et al. (LSP).13 Dash-dotted lines: The global volatile N oxidation model by De Soete.8 Dotted lines: The global volatile N oxidation model by Chen et al.12
these studies, it was concluded that the global schemes did not compare well with the reference calculations, especially under fuel-rich conditions, and that they should be used with care outside their region of validation. The poor performance under reducing conditions is a significant concern when using the modeling tools to improve primary measures for NOx control, such as low-NOx burners. More elaborate schemes for nitrogen chemistry, based on analytical reduction of a detailed mechanism, have been proposed; e.g.,13,15 Figure 1 compares modeling predictions with the global schemes of De Soete8 and Chen et al.,12 the analytically reduced scheme by Pedersen et al.13 (denoted LSP), and the recent detailed chemical kinetic model by Mendiara and Glarborg16,17 (denoted DCKM). The calculations show the NO formation during combustion of the gaseous volatiles of a bituminous coal in the air at selected excess air ratios (λ) and temperatures under isothermal conditions. The N volatiles are represented as 1000 ppm HCN. In order to exclude differences in the selected mechanisms caused by anything other than the nitrogen chemistry descriptions, other species concentrations (O2, H2, radicals, etc.) are drawn from the detailed mechanism. The calculations shown in Figure 1, along with similar comparisons made for CH4/NH3 mixtures,2 confirm earlier findings in the literature that the De Soete scheme, as well as other global models, has considerable shortcomings, particularly under reducing conditions. The main problem with the De Soete model is that NO is only formed when sufficient oxygen is present to make the oxidation reaction faster than
2. Numerical Procedure The simplified model is developed for the volatiles of four selected fuels, ranging from bituminous coal to biomass. For each fuel, a volatile composition is estimated, as described below. Reference chemical kinetic calculations are then conducted with a full reaction mechanism for the oxidation of these volatile compositions as a function of the temperature and stoichiometry. The full mechanism is adopted from the work of Mendiara and Glarborg.16,17 Subsets of the mechanism have been validated against a range of experimental data for oxidation of HCN5 and NH3.6,7,16 On the basis of the reference calculations, semiempirical equations are set up to describe formation and consumption of the O/H radical pool. The radical model is finally combined with the analytically reduced scheme for reactive nitrogen conversion reported by Pedersen et al.13 and tested by comparison with reference calculations with the full mechanism. 2.1. Fuel Characteristics. It is desired to examine the radical concentrations for four solid fuels, three coals and a biomass. The three coals selected are Montana lignite, Dietz sub-bituminous coal, and Pittsburgh #8 bituminous coal, while the biomass is poplar wood. The dry-ash-free compositions of the fuels are listed in Table 1. For the biomass, we have adopted the volatile composition reported by Vilas et al.24 For the coals, it is assumed that all O and H are released with the volatiles. The distribution of
(15) Glarborg, P.; Lilleheie, N.; Byggstøyl, S.; Magnussen, B.; Kilpinen, P.; Hupa, M. Proc. Combust. Inst. 1992, 24, 889–898. (16) Mendiara, T.; Glarborg, P. Combust. Flame 2009, 156, 1937– 1949. (17) Mendiara, T.; Glarborg, P. Energy Fuels 2009, 23, 3565–3572.
(18) Westbrook, C. K.; Dryer, F. L. Combust. Sci. Technol. 1981, 27, 31–44. (19) Jones, W. P.; Lindstedt, R. P. Combust. Flame 1988, 73, 233–249.
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chemical reactions are assumed to Gran and Magnussen, occur in the fine structures of the computational cells. The EDC model evaluates the volume of each cell, where mixing on a molecular scale is occurring, and treats this part of the cell as an ideal reactor. Originally, the concept involved a perfectly stirred reactor (PSR/CSTR), but the EDC implemention in CFD codes such as FLUENT often employs an integration in time (i.e., a plug-flow reactor calculation) to minimize convergence problems. In the present work, the calculation is conducted assuming plug-flow. 2.2.1. Estimation of the H Concentration. In combustion there is an initial radical build-up (the induction period), followed by radical consumption as the fuel is depleted. We found it difficult to describe the entire development of the H atom concentration with only one correlation based on major species concentrations. Hence, separate descriptions of the radical concentration during the induction period and the major fuel oxidation period were developed. H Atom Build-Up. Pedersen et al.13 proposed an expression for formation of H2O and H from the reaction between H2 and O2. In the present work, it was found that a correlation based on a similar functional relationship between H, H2O, and H2 could provide a satisfactory estimate of the H concentration during radical build-up. This correlation is shown as eq 1. ½H2 O - ½H2 Oin ð1Þ ½H ¼ Q1 3 ½H2
Table 1. Elemental Compositions of Fuels Given as wt % of Dry-Ash-Free (daf) Coal/Biomass fuel no.:a
1
2
3
4
C H O N S
71.2 3.8 21.8 1.1 1.3
75.6 5.2 17.9 0.9 0.4
81.4 4.6 9.5 1.6 2.3
50.4 5.9 43.3 0.3 0
a (1) Montana lignite.20 (2) Dietz sub-bituminous coal.22 (3) Pittsburgh #8 bituminous coal.23 (4) Biomass; poplar wood.24
Table 2. Volatile Compositions of Fuels composition (vol %) a
fuel no.:
1
2
3
4
H2O CO CO2 H2 CH4 C2H4 sootb
16.5 12.3 5.0 46.7 3.4 1.1 14.9
12.5 8.5 3.2 39.1 4.6 1.6 30.5
5.0 6.9 1.2 37.5 6.9 2.9 39.7
1.7 38.2 9.1 41.4 9.6
a
0
b
Explanations to keys in Table 1 Not included in simulations.
volatile compounds from the coals was determined on the basis of results from Suuberg et al.,20 Neoh and Gannon,23 and Niksa and co-workers.21,22 The results are listed in Table 2. As indicated, soot is not included in the simulations conducted in this work. When entering the volatile composition into the simulations, the remaining components are normalized to yield 100%. 2.2. Radical Concentrations. Pedersen et al.13 determined correlations for the OH and O concentrations during combustion of CO/H2 mixtures. It was found that these concentrations could be determined from the concentration of H, along with the concentrations of the major species H2, O2, and H2O, three species that are also part of the HCN oxidation mechanism of Pedersen et al. It is thus desired to obtain a description of the concentration of H from the major species concentrations, temperature, and stoichiometry. Our approach is to develop a semiempirical correlation that applies for the following conditions: • Oxidation of volatiles from the four solid fuels selected above • The temperature range 1200-2000 K • Excess air ratios in the range 0.6 e λ e 2.0 • Oxygen concentrations in the oxidizer stream in the range 1-21 vol % • Integration in time as used by FLUENT to describe chemistry in the fine structures when applying the eddy dissipation concept
This relation is expected to be valid for combustion of coal and biomass volatiles, where H2 is released in significant quantities with the volatiles. During the H atom build-up, the concentration of water simultaneously increases and the H2 concentration is decreased. The inlet water vapor concentration is included in the correlation to account for the fact that no H atoms are present prior to radical build-up. The empirical constant Q1 is a function of various combustion parameters. In order to obtain a correlation for this constant, a series of simulations was performed for the conditions listed above. The simulations were conducted in the software CHEMKIN,27 which offers a concentration vs time profile for all species involved in the combustion. For each simulation, the constant Q1 was determined at the time where the H radical concentration peaked. The variation in Q1 with the temperature, inlet oxygen concentration (prior to mixing with the fuel), and stoichiometry was examined. Different functional forms of describing Q1 have been tested. As a result, it was found that Q1 can be calculated according to eq 2: qffiffiffiffiffiffiffiffiffiffiffiffi ð2Þ Q1 ¼ ðRðTÞ 3 λβðTÞ Þ ½O2 in R and β can be described by second-order polynomials as a function of the temperature. The constants for the polynomials are listed in Table 3, based on concentrations in moles per cubic meter and temperatures in Kelvin. H Atom Consumption. The semiempirical correlation for H radical consumption developed in this work is based on a
The eddy dissipation concept (EDC) is a popular turbulence chemistry interaction model for CFD analysis of combustion applications. In the EDC model, developed by (20) Suuberg, E. M.; Peters, W. A.; Howard, J. B. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 37–46. (21) Chen, J. C.; Castagnoli, C.; Niksa, S. Energy Fuels 1992, 6, 264–271. (22) Niksa, S.; Cho, S. Energy Fuels 1996, 10, 463–473. (23) Neoh, K. G.; Gannon, R. E. Fuel 1984, 63, 1347–1352. (24) Vilas, E.; Skifter, U.; Jensen, A. D.; L opez, C.; Maier, J.; Glarborg, P. Energy Fuels 2004, 18, 1442–1450. (25) Gran, I.; Magnussen, B. F. Combust. Sci. Technol. 1996, 119, 171–190. (26) Gran, I.; Magnussen, B. F. Combust. Sci. Technol. 1996, 119, 191–217.
(27) Kee, R. J.; Rupley, F. M.; Miller, J. A.; Coltrin, M. E.; Grcar, J. F.; Meeks, E.; Moffat, H. K.; Lutz, A. E.; Dixon-Lewis, G.; Smooke, M. D.; Warnatz, J.; Evans, G. H.; Larson, R. S.; Mitchell, R. E.; Petzold, L. R.; Reynolds, W. C.; Caracotsios, M.; Stewart, W. E.; Glarborg, P.; Wang, C.; Adigun, O.; Houf, W. G.; Chou, C. P.; Miller, S. F.; Ho, P.; Young, D. J. CHEMKIN Release 4.0; Reaction Design, Inc.: San Diego, CA, 2004.
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: DOI:10.1021/ef100028e
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Table 3. Values for Calculation of Q1a
Table 4. Values for Calculation of Q2a
R = ART2 þ BRT þ CR
γ = AγT2 þ BγT þ Cγ
AR
BR -8
-7.96 10 -7.19 10-8 -4.36 10-8 -1.48 10-8
fuel no.
CR -4
3.03 10 2.87 10-4 1.89 10-4 8.28 10-5
-1
-2.15 10 -2.26 10-1 -1.58 10-1 -6.62 10-2
1 2 3 4
Aγ
Bγ -5
-3.84 10 -4.41 10-5 -6.38 10-5 -1.22 10-4
β = AβT2 þ BβT þ Cβ
Cγ -1
1.30 10 1.51 10-1 2.19 10-1 4.25 10-1
-1.02 10-2 -1.19 10-2 -1.75 10-2 -3.44 10-2
η = AηT2 þ BηT þ Cη
fuel no.
Aβ
Bβ
Cβ
fuel no.
Aη
Bη
Cη
1 2 3 4
2.83 10-6 3.81 10-6 3.96 10-6 4.33 10-6
-1.03 10-2 -1.39 10-2 -1.46 10-2 -1.54 10-2
7.73 11.0 11.5 11.7
1 2 3 4
8.68 10-6 1.52 10-5 3.30 10-5 5.04 10-5
-3.17 10-2 -5.49 10-2 -1.16 10-1 -1.88 10-1
3.43 10-1 5.48 10-1 1.08 10-2 1.82 10-2
a The values are based on concentrations in units of mol/m3 and temperatures in Kelvin.
a The values are based on concentrations in units of mol/m3 and temperatures in Kelvin.
three-step combustion mechanism proposed by Pedersen et al.,13 CO þ H2 O h CO2 þ H2 ðR1Þ H þ H þ M h H2 þ M
ðR2Þ
3H2 þ O2 h 2H þ 2H2 O
ðR3Þ
By assuming that the reactions are irreversible and that [H] is in a quasi-steady state, the H concentration in the CO/H2/O2 system can be determined from the following relationship: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kR3 ½H2 3 ½O2 ð3Þ ½H ¼ kR2 ½M
Figure 2. Predictions of H formation and decay during combustion of the gaseous volatiles of a bituminous coal in the air (T = 1800 K, λ = 1). The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dash-dotted lines: The semiempirical correlation for H atom build-up. Dashed lines: The semiempirical correlation for H atom consumption.
Here, ki are reaction rate constants, which in the work of Pedersen et al.13 were calculated as a function of numerous kinetic parameters and species concentrations. Under the conditions of interest in the present work, the presence of hydrocarbons in considerable quantities may affect [H], and eq 3 is no longer accurate. To simplify the calculation and obtain a better estimate of [H], the ki parameters are replaced by a single parameter Q2, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½H2 3 ½O2 ð4Þ ½H ¼ Q2 ½M
for reaction times outside their designated period. A satisfactory prediction of the H concentration at any time is found as the minor of the two: ½H ¼ minf½Hbuild-up , ½Hconsumption g
Figure 3 compares predictions of the simple model with reference calculations for the oxidation of volatiles for each of the selected solid fuels at two selected stoichiometries (λ = 0.8 and 1.5) and a temperature of 1800 K. It is seen that the estimates obtained with the semiempirical correlation are satisfactory for all four types of fuel volatiles. The minor underestimation of the peak concentrations is considered to be acceptable. The correlations for the H atom concentration were developed for the conditions listed in section 2.2. However, for very fuel-rich conditions (λ e 0.6) and temperatures below 1400 K, the functional expressions for Q1 and Q2 were less accurate, and predictions in this range are associated with a larger uncertainty. 2.2.2. Estimation of the OH and O Concentrations. The OH and O concentrations are linked to the H concentration and can be determined through partial equilibrium and steady state considerations. Hence, these can be calculated once the H concentration is determined. The concentration of OH is linked to the concentration of H through reaction R4:13
Here, the total gas concentration [M] is calculated at the given temperature and pressure from the ideal gas equation. For simplicity, the enhanced collision efficiency of species like H2O is not accounted for. The method for determining Q2 was similar to that employed in the determination of Q1. Hence, the value of Q2 was for each simulation determined at the peak of the H radical concentration. The resulting correlation for Q2 is given in eq 5: Q2 ¼
γðTÞ 3 λ þ ηðTÞ ½O2 in
ð6Þ
ð5Þ
γ and η are functions of temperature, as given in Table 4. Overall Estimation of H Concentration. Figure 2 compares the reference H concentration profile for oxidation of bituminous coal volatiles with the descriptions from the two empirical correlations, i.e., for [H] during radical build-up and consumption, respectively. It is seen that each correlation provides a good description of the H profile within the validated time range, but they both highly overestimate [H]
OH þ H2 h H2 O þ H
ðR4Þ
Reaction R4 is generally found to be close to partial equilibrium. The OH concentration can thus be determined 2886
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Hansen and Glarborg Table 5. Kinetic Parameters for Reactions R5-R8.13 reaction rate constant, k = A 3 Tβ 3 exp(-E/(RT)) reaction R5 R6 R7 R8
β
A [m, mol, s] 2.0 10-8 5.0 10-2 4.3 10-3 4.7 10-6
-0.40 2.67 2.70 -1.00
E/R [K] 0 3165 -1250 0
equilibrium constant, K = A 3 Tβ 3 exp(-E/(RT)) reaction R5 R6 R7 R8
β
A -3
2.575 10 1.391 1.024 10-2 5.760 10-3
0.4059 0.05876 0.2713 -0.9823
-E/R [K] 8644 874 8927 51630
Figure 3. Predictions of H formation and decay during combustion of the gaseous volatiles of selected solid fuels in the air at reducing and oxidizing conditions (T = 1800 K). The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The semiempirical correlation for [H] (with major species input data from DCKM).
from eq 7, where K is the equilibrium constant. ½OH ¼
½H½H2 O KR4 ½H2
ð7Þ
KR4 ¼ ð1:424 10 - 2 ÞT 0:3301 expð8052=TÞ The concentration of O is influenced by the following four reactions:13 O þ OH h H þ O2 ðR5Þ O þ H2 h OH þ H
ðR6Þ
OH þ OH h H2 O þ O
ðR7Þ
H þ O þ M h OH þ M
ðR8Þ
Figure 4. Predictions of OH and O formation and decay during combustion of the gaseous volatiles of selected solid fuels in the air under reducing and oxidizing conditions (T = 1800 K). The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The semiempirical correlations for [OH] and [O] (with major species input data from DCKM).
By employing partial equilibrium assumptions, the O concentration can be determined by eq 8.
described satisfactorily, and the partial equilibrium and steady state assumptions for the two radicals are thus valid under the investigated conditions.
DO ¼ kR5 ½OH þ kR6 ½H2 þ ðkR7 =KR7 Þ½H2 O þ kR8 ½H½M
3. Results and Discussion
NO ¼ ðkR5 =KR5 Þ½H½O2 þ ðkR6 =KR6 Þ½OH½H
The semiempirical equations developed to describe the formation and consumption of the O/H radical pool are combined with the analytically reduced scheme for reactive nitrogen conversion reported by Pedersen et al.13 to yield a model for volatile nitrogen oxidation in solid fuel combustion. In the following, predictions obtained with this model are compared to reference calculations with the full mechanism.16,17 The figure legends below are defined as follows: DCKM: Detailed chemical kinetic model16,17 LSP: Volatile-N oxidation by Pedersen et al.;13 radicals and major species from DCKM
2
þ kR7 ½OH þ ðkR8 =KR8 Þ½OH½M ½O ¼
NO DO
ð8Þ
ki are forward reaction rate constants, and Ki are equilibrium constants. These are listed in Table 5. Comparison of the estimates for OH and O with reference calculations is seen in Figure 4. Though slightly less accurate than the predictions for H, the OH and O concentrations are 2887
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Figure 6. Predictions of NO formation during combustion of the gaseous volatiles of selected solid fuels in the air at λ = 0.5 and two selected temperatures. The N volatiles are represented as 1000 ppm HCN. The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The analytically reduced volatile-N oxidation model by Pedersen et al. (LSP).13 Dash-dotted lines: The semiempirical radical estimation tool combined with the reduced N scheme of Pedersen et al. (LSP).13 Both simplified models use major species input data from DCKM.
Figure 5. Predictions of NO formation during combustion of the gaseous volatiles of selected solid fuels in the air at λ = 0.8 and two selected temperatures. The N volatiles are represented as 1000 ppm HCN. The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The analytically reduced volatile-N oxidation model by Pedersen et al. (LSP).13 Dash-dotted lines: The semiempirical radical estimation tool combined with the reduced N-scheme of Pedersen et al. (LSP).13 Both simplified models use major species input data from DCKM.
of NO for biomass and lignite have a similar accuracy. However, for bituminous and sub-bituminous coals, with a higher ratio of hydrocarbons to hydrogen in the volatiles, the simplified model clearly overestimates the NO formation compared to the reference calculations. The estimates of the radical pool are based on H2/O2 reactions, and a high fraction of hydrocarbons cause the predictions of the O/H radical pool to become less accurate. The error in the O/H radical pool estimates is mainly associated with the prediction of [H]; the correlations for [O] and [OH] as a function of [H] are generally valid. Even more important, the hydrocarbons may act to reduce NO in reburn type reactions, a chemistry not considered in the present work. It has been found that the lowest values of λ, where the model has a reasonable accuracy at 1400 K, is approximately 0.6 for the sub-bituminous coal and 0.7 for the bituminous coal. The LSP mechanism in combination with the semiempirical radical scheme has also been tested for combustion cases with NH3 as volatile N. The results for λ = 0.8 and λ = 0.5 are seen in Figures 7 and 8, respectively. The results are similar to those observed for HCN. At λ = 0.8, the prediction of NO formation from NH3 is very good for both temperatures and all four fuels. The predictions are also satisfactory at λ = 0.5 for biomass and lignite, while they are less accurate for the subbituminous and bituminous coals, especially at the low temperature. For the bituminous coal, a considerable discrepancy is observed even at 1800 K. As discussed above, the discrepancy may partly be attibuted to reburn type reactions that are more prominent for the fuels with high hydrocarbon levels in the volatiles. It is found that, for λ g 0.6, the descriptions are
LSPþempirical: Volatile-N oxidation according to Pedersen; H, OH, and O calculated from the semiempirical model (eqs 1-8); major species (H2, O2, and H2O) from DCKM The DCKM calculations are conducted for a plug-flow reactor, using the volatile composition for the selected fuel, together with the desired reaction conditions (T, P, stoichiometry). The calculations shown are all conducted at reducing conditions (with reference to the gas-phase volatiles). At higher values of λ, full conversion of volatile-N to NO was obtained (Figure 1), making comparisons less instructive. In the simulations shown below, the volatile-N concentration (HCN or NH3) is set to 1000 ppm, which is considered to be a reasonable level for coal combustion. The simulations were conducted for volatile-N concentrations as low as 200 ppm with accuracies similar to that obtained at 1000 ppm. The predicted NO formation from HCN oxidation during combustion of the volatiles of each of the four fuels at λ = 0.8 is seen in Figure 5. It is seen that the final level of NO is well described (i.e., within (30%) for all fuels at both 1400 and 1800 K. The NO concentration is generally slightly underestimated, most pronounced at 1400 K. Part of the underestimation can be attributed to the LSP NO mechanism, but the difference is enhanced by inaccuracies in the description of radical concentrations. Figure 6 shows simulations with λ = 0.5 for the four selected fuels. Even at these strongly reducing conditions, the modeling predictions at the high temperature of 1800 K (right figures) are satisfactory for all four fuels employed. For the lower temperature of 1400 K (left figures), the predictions 2888
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: DOI:10.1021/ef100028e
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Figure 7. Predictions of NO formation during combustion of the gaseous volatiles of selected solid fuels in the air at λ = 0.8 and two selected temperatures. The N volatiles are represented as 1000 ppm NH3. The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The analytically reduced volatile-N oxidation model by Pedersen et al. (LSP).13 Dash-dotted lines: The semiempirical radical estimation tool combined with the reduced N scheme of Pedersen et al. (LSP).13 Both simplified models use major species input data from DCKM.
Figure 8. Predictions of NO formation during combustion of the gaseous volatiles of selected solid fuels in the air at λ = 0.5 and two selected temperatures. The N volatiles are represented as 1000 ppm NH3. The calculations are conducted under isothermal conditions assuming plug-flow. Solid lines: The detailed chemical kinetic model (DCKM).16,17 Dashed lines: The analytically reduced volatile-N oxidation model by Pedersen et al. (LSP).13 Dash-dotted lines: The semiempirical radical estimation tool combined with the reduced N scheme of Pedersen et al. (LSP).13 Both simplified models use major species input data from DCKM.
deactivate the nitrogen chemistry when calculating the main scalars, and then activate it upon convergence. 3.1.1. The Main Combustion Calculation. The main calculation establishes the flow-field, the temperature field, and the major species concentrations. The main issue for the present purpose is the choice of models for pyrolysis and volatile oxidation. Depending on the complexity of the volatile oxidation model, the major species may comprise just a single volatile component, together with final products CO2 and H2O, or a more complete set of fuel components, intermediates, and products. The use of a simple one or twostep volatile oxidation model is compatible with the NOx model, as described below. However, while this approach will save computational ressources, it could also be expected to yield less accurate modeling predictions compared to using a more advanced pyrolysis/volatile oxidation model. If a more complex model is chosen for pyrolysis and volatile oxidation, it is important that it be compatible with the NOx model in terms of composition of the volatiles. This issue is discussed in detail below. 3.1.2. The Postprocessing. The calculations of the nitrogen chemistry can be conducted in a postprocessing step. The main calculation provides information on flow-field, temperature field, and major species concentrations. However, the time-dependent concentration profiles of O2, H2, and H2O for each cell, required for the NOx model, are not available from the main calculation. For this reason, the postprocessing calculations must combine a volatile oxidation model with the O/H radical scheme and the N-oxidation model.
good at 1800 K for all four fuels, while at 1400 K, satisfactory predictions are obtained for λ g 0.7. 3.1. Practical Application. It is most efficient in terms of computational efforts to conduct the calculations on the nitrogen chemistry as postprocessing. This approach implies that the nitrogen chemistry does not affect the overall flow pattern and temperature. Even though trace species including NO have been reported to affect emissions and combustion rates,29 the assumption is justifiable since only a small fraction of the overall gas flow is involved in the active nitrogen chemistry. The solution procedure is then to solve initially the main scalars, i.e., velocity, temperature, and concentration of major species, and then model NO as a postprocessing task. Andersen et al.2 recently reported results obtained with this approach for turbulent combustion of CH4/NH3 mixtures. Turbulent fluctuations were accounted for by applying probability density functions for temperature and O2 concentration.11 The analytically reduced scheme for reactive nitrogen conversion reported by Pedersen et al.13 was tested in a postprocessing mode, using a detailed mechanism to describe the combustion. The present approach is less computationally demanding. To facilitate the practical implementation of the NOx model, i.e., the O/H radical model and the Pedersen N scheme, we discuss the implications for the main calculation and the postprocessing. An alternative to postprocessing could be to (28) Andersen, J.; Rasmussen, C. L.; Giselsson, T.; Glarborg, P. Energy Fuels 2009, 23, 1379–1389. (29) Glarborg, P. Proc. Combust. Inst. 2007, 31, 77–98.
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: DOI:10.1021/ef100028e
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The fitting parameters in the functional form chosen for the radical scheme are fuel-specific, as is typical for semiempirical approaches. The volatile composition entering the postprocessing calculation should be consistent with the data for one of the fuels listed in Table 2. The data in the table are categorized according to fuel rank (bituminous coal, subbituminous coal, lignite, biomass) and cover most solid fuels of importance. The correlations for the four fuels developed in this work may be applicable to other fuels within the same rank, as minor variations in volatile composition will only have a small impact on modeling predictions. If the pyrolysis model used in the main calculation provides only a simplified volatile composition, the split between the chosen fuel components (hydrocarbons, H2, and CO) needed for the postprocessing computations must be estimated algebraically. The volatile model must describe the oxidation of the fuel elements, i.e., hydrocarbons, hydrogen, and carbon monoxide. The estimated concentrations of O2, H2, and H2O for each time step are then used as input to both the O/H radical scheme (eqs 1, 4, 7, and 8) and the N-oxidation model. The choice of volatile oxidation model will affect the computational effort as well as the expected accuracy.28 The model could be a collection of global reactions, i.e., a single oxidation reaction for each fuel component in the volatiles. Rate constants for global oxidation steps are available for a range of fuel components18,30,31 and may be readily available in the chosen CFD software. For a more accurate prediction, the Jones and Lindstedt global four-step combustion mechanism19 can be implemented. Four-step mechanisms are offered for several hydrocarbon fuels and involve also steps for the oxidation of H2 and CO.
4. Conclusion Simple global models for the oxidation of HCN and NH3 from the literature should be used cautiously, since their predictive capabilities are limited, particularly under reducing conditions. Models for HCN/NH3/NO conversion based on systematic reduction of a detailed chemical kinetic model offer high accuracy but rely on input estimates of combustion intermediates, including free radicals. In the present work, simple, semiempirical expressions are presented for the estimation of H, O, and OH radicals. Correlations were derived for volatile compositions representative of solid fuels ranging from bituminous coal to biomass, for temperatures of 1200-2000 K, and excess air ratios in the range 0.6 e λ e 2.0. The radical estimation tool is combined with the analytically reduced N scheme of Pedersen et al.,13 and the combined model is tested against reference calculations with a comprehensive mechanism. For excess air ratios of λ g 0.8 and temperatures of 1400 K and above, the prediction of NO formation from both HCN and NH3 is very good for volatile compositions representing all tested fuels. For lower values of λ, the predictions are good for biomass and lignite, while they are less accurate for the subbituminous and bituminous coals, especially at lower temperatures. The semiempirical correlations for estimating radical concentrations may also be useful in combination with models for other trace species (sulfur oxides, organic species, etc.). Acknowledgment. The work was funded by Vattenfall Research and Development AB and DONG Energy Power A/S, with Karin Eriksson and Maja Bøg Toftegaard, respectively, as project managers. The authors would like to thank Søren Lovmand Hvid for helpful discussions. Supporting Information Available: To facilitate implementation of the model, Matlab scripts for the NOx model are included. The scripts are available as a PDF file and as an ASCII file (latex). This material is available free of charge via the Internet at http://pubs.acs.org.
(30) Hautman, D. J.; Dryer, F. L.; Schug, K. P.; Glassman, I. Combust. Sci. Technol. 1981, 25, 219–235. (31) Babushok, V. I.; Dakdancha, A. N. Combust. Explos. Shock Waves 1993, 29, 464–489.
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