Mathematical Modeling of Nitric Oxide Destruction by Reburning

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Energy & Fuels 2006, 20, 1434-1443

Mathematical Modeling of Nitric Oxide Destruction by Reburning Sheng Su,*,† Jun Xiang,† Xuexin Sun,† Zhongxiao Zhang,‡ Chuguang Zheng,† and Minghou Xu† State Key Laboratory of Coal Combustion, Huazhong UniVersity of Science and Technology, Wuhan 430074, People’s Republic of China, and UniVersity of Shanghai for Science and Technology, Shanghai 200093, People’s Republic of China ReceiVed January 19, 2006. ReVised Manuscript ReceiVed March 21, 2006

A nitric oxide model incorporated into a comprehensive coal combustion model is presented for predicting NO reduction in a 93 kW laboratory-scale single-burner furnace with gaseous fuel reburning. This NO model, including the reburning NO submodel based on “partial equilibrium” approach, requires the solution of only two transport equations to model the behavior of NO reduction in the reburning process. A number of experiments have been performed in the same furnace, and the experimental data obtained from the optimized reburn configuration was used to validate the model. Effects of the critical kinetic parameters on predicted NO concentrations were investigated in this study, and the reburning NO submodel was further evaluated by including more reactions of NO reduction and by comparing with the global reburning model. Profile comparisons show that the predicted temperature and oxygen concentration are overall in good agreement with the measurements, and the general trend of predicted NO concentration is very similar to that measured. The results of this study show that the present reburning NO submodel is capable to predict quantitatively the NO reduction levels and depicts quite well the observed behavior of NO annihilation in the reburning process. It is expected that this computationally economic model represents a useful technique to simulate the gaseous fuel reburning process in practical combustors. The model presented in this study also provides a basis for further studies.

1. Introduction Nitrogen oxides (NOx) have been recognized as acid rain precursors that impose a significant threat to the environment. Coal combustion is a major anthropogenic source of NOx. Given the unceasing rise in energy demand and abundance of coal resources, the continuing use of coal in power generation is inevitable. Because of the low thermal efficiency of coal-fired boilers and prevalence of low-rank coal, China has to bear the burden of environmental problems caused by NOx. Recently, China has specified more rigorous limits for the emissions of NOx. As a result of the need to reduce NOx emissions, various NOx reduction strategies have been investigated.1 Among the most recent developments for reducing NOx emissions, reburning technology is considered to be one of the most promising and cost-effective NOx reduction strategies for coal combustion systems, capable of providing 50-70% NOx reduction.2-4 It is economical to use coal or biomass as a reburn fuel but with much more unburned carbon loss than for gaseous fuels.5,6 The * Corresponding author. Telephone: 86-27-87545526. Fax: 86-2787545526. E-mail: [email protected]. † Huazhong University of Science and Technology. ‡ University of Shanghai for Science and Technology. (1) Bowman, C. T. Control of combustion-generated nitrogen oxide emissions: Technology driven by regulation. 24th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1993; pp 859-878. (2) Smoot, L. D.; Hill, S. C.; Xu, H. NOx control through reburning. Prog. Energy Combust. Sci. 1998, 24, 385-408. (3) Pratapas, J.; Bluestein, J. Natural gas reburn: Cost-effective NOx control. Power Eng. 1994, 98, 47-50. (4) Tree, D. R.; Clark, A. W. Advanced reburning measurements of temperature and species in a pulverized coal flame. Fuel 2000, 79, 16871695.

usual gaseous reburn fuels are hydrocarbons such as methane and natural gas.7 Reburning technology is high efficiency on the reduction of NOx emissions, but it is not fully understood theoretically. In the past several years, reburning technology has been largely studied. Many investigators have worked on laboratory-scale measurements, kinetic mechanisms studies, and numerical simulations for the reburning process.8-11 The numerical simulation offers many advantages in analyzing and optimizing the reburning process. However, because of the complex chemistry of NOx in reburning reactions, a large number of transport equations need to be solved in the computation for predicting NOx reduction by reburning. Consequently, the computer limitation restricts the application of numerical simulation for the design and analysis of reburning technology (5) Adams, B. R.; Harding, N. S. Reburning using biomass for NOx control. Fuel Process. Technol. 1998, 54, 249-263. (6) Liu, H.; Hampartsoumian, E.; Bernard, M. G. Evaluation of the optimal fuel characteristics for efficient NO reduction by coal reburning. Fuel 1997, 76, 985-993. (7) Bilbao, R.; Millera, A.; Alzueta, M. U.; Prada, L. Evaluation of the use of different hydrocarbon fuels for gas reburning. Fuel 1997, 76, 14011407. (8) Minghou, X.; Yaoguo, F.; Jianwei, Y. Modelling and mechanism of NOx emissions under fuel staging during combustion. Combust. Sci. Technol. 1998, 133, 377-394. (9) Jamal, B. M.; Wendt, O. L. J. Air staging and reburning mechanisms for NOx abatement in a laboratory coal combustor. Fuel 1995, 73, 10201026. (10) Glarborg, P.; Alzueta, M. U.; Dam-Johansen, K.; Miller, J. A. Kinetic modeling of hydrocarbon/nitric oxide interactions in a flow reactor. Combust. Flame 1998, 115, 1-27. (11) Dagaut, P.; Lecomte, F.; Chevailler, S.; Cathonnet, M. Experimental and detailed kinetic modeling of nitric oxide reduction by a natural gas blend in simulated reburning conditions. Combust. Sci. Technol. 1998, 139, 329-336.

10.1021/ef060026x CCC: $33.50 © 2006 American Chemical Society Published on Web 04/25/2006

Modeling of Nitric Oxide Destruction by Reburning

Energy & Fuels, Vol. 20, No. 4, 2006 1435 Table 1. Test Hole Distribution on Furnace Wall test hole no. 1 2 3 4 5 6 7 8 9 10 11 distance from 0.1 0.35 0.6 0.95 1.3 1.65 2 2.35 2.8 3.3 3.8 burner exit (m) Table 2. Characteristics of Coal (As Received) Proximate Analysis (wt %) moisture ash volatiles fixed carbon Qnet‚p (kJ/kg)

1.48 26.30 12.56 59.66 24715

Ultimate Analysis (wt %)

Figure 1. Schematic of experimental system.

in practical combustors. A compact nitric oxide (NO) submodel, which simulates the vital chemical pathways in reburning reactions, is required. In recent years, the various researchers studying reburning mechanisms found that the reburning reactions can be expressed as the following generalized reaction:2

∑CHi + NO f HCN + products

(R0)

Some of the reburning process predictions with comprehensive combustion codes, making use of reduced kinetic schemes or global rate constants for reaction R0, were reported.12-15 However, the modeling results show that the predictions are still inaccurate.2 It is found that those possible reactions of nitrogen oxides or other key intermediates with hydrocarbons or reburn fuel compounds are important for reburning reactions. Also, the approach to calculate the concentration of important radicals in reburning reactions is critical for predicting NOx reduction by reburning.14 For the design and analysis of largescale reburning technique applications, significant further study for simplifying models and improving predictions for the reburning process is required. In this study, a number of experiments have been performed in a laboratory-scale single-burner furnace with gaseous fuel reburning, and the optimized reburn configuration has been obtained with maximum NOx reduction. A compact NO submodel, including reburning mechanisms, was incorporated into a comprehensive coal combustion model for predicting the optimized reburning process. The modeling results were evaluated and analyzed with experimental values. 2. Experimental Procedure 2.1. Experimental System and Conditions. Figure 1 represents a schematic of the experimental system. Its system comprises furnace, fuel supply, and blower. The 93 kW singleburner furnace (see Figure 1a) is 0.5 m in height, 0.35 m in width, and 4 m in length. From the top to the bottom, the burner is arranged in the order of upper secondary air (USA), middle (12) Chen, W.; Smoot, L. D.; Hill, S. C.; Fletcher, T. H. Global rate expression for nitric oxide reburning. Part 2. Energy Fuels 1996, 10, 10461052. (13) Kandamby, N.; Lazopoulos, G.; Lockwood, F. C.; Perera, A.; Vigevano, L. Mathematical modelling of NOx emission reduction by the use of reburn technology in utility boilers. In ASME International Joint Power Generation Conference and Exhibition; Houston, TX, 1996. (14) Dimitriou, D. J.; Kandamby, N.; Lockwood, F. C. A mathematical modeling technique for gaseous and solid fuel reburning in pulverized coal combustors. Fuel 2003, 82, 2107-2114. (15) Xu, H.; Smoot, L. D.; Hill, S. C. Computational model for NOx reduction by advanced reburning. Energy Fuels 1999, 13, 411-420.

C H O N S

61.89 1.792 6.503 0.978 1.059

Particle Size wt % under 200 µm wt % under 150 µm wt % under 100 µm average size (µm)

100 80 15 134

Table 3. Base and Reburning Cases Operating Conditions Primary Stream (Base Case Operating Conditions) mass flow rate of coal (kg/h) 13 mass flow of primary air (kg/h) 33.56 primary air temperature (K) 473 mass flow of secondary air (kg/h) 78.44 secondary air temperature (K) 573 primary zone SRa 1.15 Reburn Stream CH4 (% total thermal input) 10 volume flow rate of CH4 (m3/h) 1.37 CH4 temperature (K) 300 reburn zone SRa 0.98

15 2.17 300 0.90

20 3.08 300 0.83

Burnout Stream mass flow of burnout air (kg/h) 19.36 burnout air temperature (K) 300 final zone SRa 1.15

30.75 300 1.15

43.56 300 1.15

a

SR ) stoichiometric ratio.

secondary air (MSA), primary air (PA), and lower secondary air (LSA), as shown in Figure 1b. All the secondary air ports have the same cross section of 20 mm × 20 mm, and the primary air port has a diameter of 40 mm. A detailed description of this facility can be found in ref 16. As shown in Figure 1a, eleven test holes are positioned horizontally on one side of the furnace wall for measuring the temperature and species concentrations in the furnace. The distances between the burner exit plane and each test hole are summarized in Table 1. The temperature in the furnace is measured by bare-wire Pt/13%Rh-Pt thermocouple. A watercooled sampling probe is used to extract gaseous combustion products for analyzing O2 and NO. A typical low-volatile Chinese coal serves as the primary fuel. Methane is used as the reburn fuel. The proximate and ultimate analyses, as well as the particle-size distributions of coal, are given in Table 2. For the reburning experiments, the reburn fuel and burnout air are introduced in the furnace from the test holes. The methane is injected horizontally in the furnace from a 12 mm diameter tube. The burnout air is supplied by a centrifugal blower, which maintains 300 K without preheating. The burnout air injector tube, of 40 mm diameter, is also placed horizontally. (16) Jun, X.; Xuexin, S.; Song, H.; Dunxi, Y. An experimental research on boiler combustion performance. Fuel Process. Technol. 2000, 68, 139151.

1436 Energy & Fuels, Vol. 20, No. 4, 2006

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Table 4. NO Reduction under Different Experimental Conditions reburn fuel injection position test hole no.

burnout air injection position test hole no.

2 3 4 5 3 4 5 3

8 8 8 8 7 7 7 6

NO reduction for volume flow rate of reburn fuel CH4 ) 1.37 m3/h



5% 47% 46% 25% 37%

9% 51% 53% 32% 42% 38% 25% 26%

52% 53% 32% 43% 40% 26% 28%

16%

In all the reburning experiments, the axes of reburn fuel and burnout air injection tube, as well as the axis of primary air port, are positioned in the same horizontal plane. 2.2. Optimized Reburning Case. To obtain the optimized reburn configuration, a number of experiments have been previously performed against various experimental conditions. The base and reburning experimental conditions are shown in Table 3. In all the base and reburning cases, the overall furnace stoichiometry is maintained at 15% excess air. The amount of methane used for reburning experiments was, respectively, 10%, 15%, and 20% of the total thermal input for obtaining the optimized flow rate of methane. The optimized injection positions for the reburn fuel and burnout air were obtained by introducing methane and burnout air in the furnace from different test holes and measuring the lowest NOx exhaust emissions simultaneously. The results of the experiments are summarized in Table 4. Table 4 shows that the maximum 53% NO reduction can be achieved when methane is injected from no. 4 test hole and the burnout air is injected from no. 8 test hole simultaneously. As listed in Table 1, the optimized injection positions for methane and burnout air are, respectively, 0.95 and 2.35 m downstream from the burner exit plane for the current furnace configuration. As also shown in Table 4, the effects of methane flow rate on NO exhaust emission are also investigated in the experiments. Increasing the flow rate of methane from 1.37 to 2.17 m3/h results in obvious NO reduction, but a further increase of the flow rate to 3.08 m3/h does not show obviously larger NO reduction. Under the present experimental conditions, the appropriate flow rate of methane is 2.17 m3/h (∼15% of the total thermal input, as shown in Table 3). A full description of the base and reburning experiments, which achieved the optimized reburning case, can be found in ref 17. According to the optimized reburn configuration described above, the model developed in this study is applied to simulate the base and optimized reburning case. Then the predicted results are compared and analyzed with the experimental data to evaluate the model.

treated in Eulerian fashion and the latter treated in Lagrangian fashion. The gas-phase turbulence is simulated by the standard k- model. The code assumes the gaseous reactions are limited by the mixing rates of reactants and not by the reaction kinetics, and the local elemental composition is determined from the mixing of the inlet streams, which is tracked using a conserved scalar called the mixture fraction (f). The gas properties (i.e., density, temperature, and species concentrations) and any other conserved scalars can be calculated from the local value of the mixture fraction. Because the gas properties will fluctuate due to the turbulence, the local variance of the mixture fraction (g) and an assumed shape of the probability density function (beta PDF) are required to calculate time-averaged values of the gas properties. For the particle-turbulence interaction, the stochastic particle trajectory (SPT) model is used to simulate the two-phase flow of pulverized coal in the furnace. The turbulent velocity of the particle is determined by making a random selection from the probability density function of velocity. On the basis of the Lagrangian approach, each particle-size class is tracked through the gas field, and particle random trajectories and changing process are calculated. In this model, coal devolatilization is simulated by a firstorder single-reaction model and char particle combustion is expressed by a parallel process of surface kinetics and oxygen diffusion. For radiation heat transfer, the discrete transfer method, which is based on the direct solution of the radiation intensity transport equation, is used to simulate thermal radiation in the furnace. The radiative properties of the gas are computed using the wide-band model. More detailed descriptions of the program and its application can be found in refs 18-21. 3.2. NO Formation and Destruction Modeling. In this modeling approach, the amount of NO produced in the combustion process is characterized using the following steady-state transport equation:

3. Mathematical Model

This equation is general and accounts the convection, diffusion, production, and consumption of NO in the coal combustion

3.1. Combustion Modeling. A computational fluid dynamics program is used to predict turbulence, combustion, and heat transfer in the single-burner coal combustion furnace. The model, which is based on the finite volume discretization technique, solves the mass and momentum equations using the SIMPLER algorithm. The basic prediction procedure involves numerical solution of the time-averaged conservation equations for the gas phase and the particle phase, with the former being (17) Sheng, S.; Jun, X.; Song, H.; Xuexin, S.; Zhongxiao, Z.; Jimu, Z. Experimental research on denitration by use of gas reburn technology. J. Power Eng. 2004, 24, 884-888.

(

)

∂YNO ∂ ∂ (FuiYNO) ) FD + SNO ∂xi ∂xi ∂xi

(1)

(18) Jun, X.; Lushi, S.; Shiqiang, G.; Yuexia, L.; Xuexin, S. 3-D numerical simulation of NOx formation with PDF-ARRHENIUS model. Proceedings of the 3rd Asia-Pacific conference on combustion; Seoul, Korea, 2001; pp 632-635. (19) Jun, X.; Youhui, X.; Chuguang, Z.; Xuexin, S. Using PDFARRHENIUS to simulation 3-dimensionally NOx formation during coal combustion. Proc. CSEE 2002, 22, 156-160. (20) Minghou, X.; Jianwei, Y.; Shifa, D.; Handing, C. Simulation of gas temperature deviation in large-scale tangential coal fired utility boilers. Comput. Methods Appl. Mech. Eng. 1998, 155, 369-380. (21) Minghou, X.; Azevedo, J. L. T.; Carvalho, M. G. Modelling of the combustion process and NOx emission in a utility boiler. Fuel 2000, 179, 1611-1619.


Energy & Fuels, Vol. 20, No. 4, 2006 1437

The other sources’ contributions due to reaction pathways (1) and (2) (as shown in Figure 2) are

SHCN-1 ) -R1

SHCN-2 ) -R2

Figure 2. Submodels for fuel NO and reburning NO.

process. Because the concentration of NO is typically very small compared with the concentrations of other species of interest in the coal combustion process, the NO transport equation is commonly solved for a given combustion flow-field solution. The NO model is, therefore, typically employed in a “postprocessing” fashion. The source term, SNO in eq 1, is considered as contributions from the following predominant mechanisms: thermal NO, fuel NO, and reburning NO. The prompt NO is not considered in the present model because it is only significant in very fuel-rich systems and is a small portion of the total NO formed in most coal combustion systems.22 The models for fuel NO, reburning NO, and thermal NO are described subsequently. 3.2.1. Fuel NO Modeling. The nitrogen contained in coal is the most significant source of NO formed during combustion. For the fuel NO modeling, the global models proposed by De Soete23 and Smoot and Smith24 are considered as the base fuelNO mechanism of coal combustion. It is assumed that fuelbound nitrogen is distributed between the volatiles and the char. All the fuel-bound nitrogen evolves as HCN. The reaction pathway is described in Figure 2. This figure indicates that the fuel NO is produced in reaction pathway (1) but can be destroyed in reaction pathways (2) and (3). The following steady-state transport equation is required to track the species of HCN for the NO modeling:

(

)

∂YHCN ∂ ∂ (FuiYHCN) ) FD + SHCN ∂xi ∂xi ∂xi

(2)

The HCN source term, SHCN in eq 2, accounts all the production and consumption of HCN in the coal combustion process. It includes the contributions from the fuel NO mechanism (Sfuel,HCN) and reburning NO mechanism (Sreburn,HCN), which are described subsequently. The HCN source from the coal, ScoalfHCN, is related to the rate of volatile release and char burnout,

ScoalfHCN )

SvolYN,volMHCN ScYN,charMHCN + M NV M NV

(3)

where Svol is the source of volatiles originating from the coal particles into the gas phase (kg/s) and Sc is the char burnout rate (kg/s). YN,vol and YN,char are the mass fractions of nitrogen in the volatiles and char, respectively. MHCN and MN are the molecular weights of HCN and N (kg/mol). V is the cell volume (m3). (22) Fenimore, C. P. Studies of fuel-nitrogen in rich flame gases. 17th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1979; pp 661-669. (23) De Soete, G. G. Overall reaction rates of NO and N2 formation from fuel nitrogen. 15th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1975; pp 1093-1102. (24) Smoot, L. D.; Smith, P. J. NOx pollutant formation in a turbulent coal system. In Coal Combustion and Gasification; Plenum: New York, 1985.

MHCNp RT h MHCNp RT h

MNOp

SNO-1 ) R1

SNO-2 ) -R2

RT h MNOp RT h

(4)

(5)

(6)

(7)

R1 ) (3.5 × 1010)XHCNXOR 2 e-280 452/RT

(8)

R2 ) (3.0 × 1012)XHCNXNO e-251 151/RT

(9)

where R1 and R2 are the conversion rates of HCN (s-1). MNO is the molecular weight of NO (kg/mol). T is the instantaneous temperature, and T h is the mean temperature (K). Xi is the mole fraction of species i, and p is the pressure (Pa). The oxygen reaction order R is depends on experimental conditions.23 The source term of the heterogeneous reaction (reaction pathway (3) in Figure 2) of NO reduction on the char surface, SNO-3, is given by ref 25,

SNO-3 ) csABETMNOR3

(10)

R3 ) 230 e-142 737/RTh XNOpj

(11)

where cs is the concentration of particles (kg/m3), ABET is the BET surface area (m2/kg), and pj is the mean pressure (atm). The source terms for the transport eqs 2 and 1 due to fuel NO are as follows:

Sfuel,HCN ) ScoalfHCN + SHCN-1 + SHCN-2

(12)

Sfuel,NO ) SNO-1 + SNO-2 + SNO-3

(13)

3.2.2. Reburning NO Modeling. For the reburning mechanisms, it is found that such reactions, involving hydrocarbons, such as CH2, CH, and C, and NO mainly produce HCN compounds. Under the prevailing fuel-rich conditions, the reformed HCN reacts with any available NO to form a major reduction pathway. The approach to calculate the concentration of hydrocarbon radicals decomposed from reburn fuel is critical for simulating NO reduction by reburning. Because the hydrocarbon radical reactions are very fast compared with the slow nitrogen reactions, “partial equilibrium” assumptions13 can be introduced to calculate the concentrations of important radicals. In this study, the reburning NO model proposed by Kandamby et al.13 and Dimitriou et al.14 is applied for the reburning NO modeling. This model is evaluated by the authors for the present study. The reburning NO model based on the “partial equilibrium” approach adds reduction pathways (4) and (5) to the global fuel NO model, as shown in Figure 2. The additional (25) Levy, J. M.; Chan, L. K.; Sarofim, A. F.; Beer, J. M. NO/Char reactions at pulverized coal flame conditions. 18th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1981; pp 111-120.


Su et al.

reduction path accounts for the NO destruction in the fuel-rich reburn zone by hydrocarbon radicals. In the reburning reactions, the following three reactions are considered to be the most important reactions of NO reduction by CH radicals and for which the forward rate is dominant:2,14

NO + CH2 f HCN + OH

(R1)

NO + CH f HCN + O

(R2)

NO + C f CN + O

(R3)

The hydrocarbon radicals involved in the above reactions are formed from the following elementary reactions:

and the rate constants ka, kb, and kc for different reburn fuel types can be calculated according to refs 27-29. In this study, the rate constants ka, kb, and kc are calculated and evaluated by the authors subsequently. Therefore, the source terms for eqs 2 and 1 due to reburning NO reactions are given by

Sreburn,HCN ) MHCN Sreburn,NO ) MNO

d[HCN] ) R4MHCN dt

d[NO] ) -(R4 + R5)MNO dt

(20) (21)

CH4 + H T CH3 + H2

(R4)

CH3 + OH T CH2 + H2O

(R5)

3.2.3. Thermal NO Modeling. The formation of thermal NO is determined by the following three highly temperaturedependent chemical reactions known as the extended Zeldovich mechanism:30

CH2 + H T CH + H2

(R6)

N2 + O T NO + N

(R9)

CH + H T C + H2

(R7)

O2 + N T NO + O

(R10)

OH + N T NO + H

(R11)

The reactions R4-R7 can be considered, with reasonable accuracy, to be in “partial equilibrium” for hydrocarbon diffusion flames.14 The reactions R1-R3 may be globally described by the addition of pathways (4) and (5) in Figure 2, leading, respectively, to the formation of HCN and of minor intermediate nitrogen radicals. In the present model where methane is the reburn fuel, the global NO reduction rates for reaction pathways (4) and (5) can be expressed as

R4 ) (kaχ1 + kbχ12)χ2[CH4][NO]

(14)

R5 ) kcχ13χ2[CH4][NO]

(15)

k4k5 ka ) k1 k-4k-5

(16)

k4k5k6 k b ) k2 k-4k-5k-6

(17)

k4k5k6k7 kc ) k3 k-4k-5k-6k-7

(18)

χ2 )

[OH] k-8 ) k8 [H2O]

d[NO] ) k9[O][N2] + k10[N][O2] + k11[N][OH] dt k-9[NO][N] - k-10 [NO][O] - k-11[NO][H] (22) In the above expressions, k9, k10, and k11 are the forward rate constants for reactions R9-R11 and k-9, k-10, and k-11 are the corresponding reverse rate constants. The rate constants used in the model can be obtained from ref 30. To calculate the formation rates of NO, the concentrations of O and OH are required. OH concentration is determined by eq 19, and O concentration is estimated by

[O] ) 36.64T1/2[O2]1/2 e-27 123/T mol/m3

(23)

In the transport eq 1, the NO source term due to the thermal NO mechanism is

where k1, k2, and k3 are the rate constants for reactions R1-R3 and the forward and reverse rate constants for reactions R4R7 are k4-k7 and k-4-k-7, respectively. In addition, it is assumed that χ1 ) [H]/[H2] ) 1 because the H-radical concentration in the post-flame region of a hydrocarbon diffusion flame has been observed to be of the same order as [H2]. χ2 is estimated by considering the following reaction:14

OH + H2 T H2O + H

On the basis of the chemical reactions above, the thermal NO formation rate becomes30

(R8) (19)

The forward and reverse rate constants, k8 and k-8, for reaction R8 can be obtained from ref 26. The values for reaction rate constants k1, k2, and k3 can be taken from refs 27 and 28, (26) Glarborg, P.; Miller, J. A.; Kee, R. J. Kinetic modeling and sensitivity analysis on nitrogen oxide formation in well stirred reactors. Combust. Flame 1986, 65, 177-202.

Sthermal,NO ) MNO

d[NO] dt

(24)

where MNO is the molecular weight of NO (kg/mol) and d[NO]/ dt is computed from eq 22. 3.2.4. NO Formation in Turbulent Flows. The turbulent mixing process results in temporal fluctuations in temperature and species concentration that will influence the characteristics of the flame. The relationships among NO formation rate, temperature, and species concentration are highly nonlinear in a turbulent mixing process. Hence, if time-averaged composition and temperature are employed in any model to predict the mean NO formation rate, significant errors will result. Thus, temper(27) Bowman, C. T. Chemistry of gaseous pollutant formation and destruction. In Fossil Fuel Combustion; Bartok, W., Sarofim, A. F., Eds.; J. Wiley and Sons: Canada, 1991. (28) Dean, A. J.; Hanson, R. K., Bowman, C. T. A shock tube study of reactions of C atoms and CH with NO including product channel measurement. J. Phys. Chem. 1991, 95, 3180-3189. (29) Leung, K. M.; Lindsted, R. P. Detailed kinetic modeling of C1C3 alkane diffusion flames. Combust. Flame 1995, 102, 129-160. (30) Hill, S. C.; Smoot, L. D. Modeling of nitrogen oxides formation and destruction in combustion systems. Prog. Energy Combust. Sci. 2000, 26, 417-458.



Figure 3. Comparisons of measured and predicted temperatures for reburning case.

Figure 4. Comparisons of measured and predicted O2 concentrations for reburning case.

ature and composition fluctuations must be taken into account for the mean NO formation rate. In this study, an assumed shape of probability density function (beta PDF) in terms of a normalized temperature and oxygen species mass fraction is used to predict the NO emission.18,19 The PDF is used for weighting against the instantaneous rates of production of NO and subsequent integration over suitable ranges to obtain the mean turbulent reaction rate. In the case of the two-variable PDF, it is further assumed that the variables V1 and V2 are statistically independent, so that

ShNO )

∫∫SNO(V1,V2)P(V1,V2) dV1 dV2 ) ∫∫SNO(V1,V2)P(V1)P(V2) dV1 dV2

(25)

where ShNO is the mean rate of production of NO and SNO is the instantaneous rate of production of NO. P(V1,V2) are the PDF of the variables V1 and V2 (temperature and oxygen species mass fraction). The same treatment applies for the HCN source terms. 4. Results and Discussion 4.1. Profile Comparisons. For the reburning case shown in Figures 3 and 4, the profiles of predicted temperature and O2 concentration along the furnace centerline are compared with experimental data. Figures 5 and 6 show the comparisons of predicted and measured NO concentration along the furnace centerline for the base and reburning cases, respectively. In all these figures, the burner exit plane is at axial distance ) 4.0 m and the exit of the furnace is at axial distance ) 0 m for keeping the same direction with Figure 1a. As shown in Figures 3 and 4, the predicted temperature and O2 concentration match well with the experimental data,

Figure 5. Comparisons of measured and predicted NO concentrations for base case.

Figure 6. Comparisons of measured and predicted NO concentrations for reburning case.

although a small discrepancy is observed between the predicted and measured values. The explanation of this disparity is probably that the radiation heat transfer model used in the computation is not sufficiently accurate. The incorrect flowfield predictions may have caused the small differences between the measurements and predictions. Furthermore, relative error in measurement exists in experimental data because of an unstable coal feed rate and equipment measurement error. These experimental errors sometimes may account for a large part of the observed difference. Nevertheless, the consistency of predictions with the measurements shown in Figures 3 and 4 indicates that the modeling methodology deployed in this study is adequate to predict the overall flow-field properties and combustion behavior for the purposes of the reburning process study. Figure 5 shows that the computation predicts some NO reduction in the furnace for the base case without reburning. Part of this NO reduction is due to the effect of the combustion gas dilution of upstream flow. Additionally, the NO homogeneous reduction by HCN through reaction pathway (2), shown in Figure 2, and the NO heterogeneous reduction on the char surface may also cause the NO reduction in the downstream zone of the furnace. However, The NO simulation for the base case predicts a 296 mg/m3 (dry, 3% O2) exhaust emissions, which is in good agreement with the measured concentration of 315 mg/m3 (dry, 3% O2). Figure 6 shows the comparisons between the predicted and measured NO concentrations along the furnace centerline for the reburning case. The predicted NO concentration shows overall good agreement with the experimental data; nevertheless, it must be stated that the computation has somewhat underpredicted the NO concentration in the reburn zone. The accurate prediction of NO concentration, which is simulated in a


Su et al.

postprocessing fashion once a fully converged flow-field solution is obtained, is dependent on the quality of the flowfield solution. Incorrect upstream flame structure predicted by the CFD-based combustion model may have caused the difference between measurements and predictions. Furthermore, less O2 than observed is predicted near the CH4 injection position (as shown in Figure 4), which leads to the decomposition of more CH4 than observed to hydrocarbon radicals, rather than reaction with O2 to generate CO2 and H2O. These hydrocarbon radicals increase the reburning reaction rate and then lead to a lower predicted NO concentration than observed in the reburn zone. However, the general trend of predicted NO concentration is very similar to that measured, indicating that the present computational model for NO annihilation depicts quite well the behavior of NO reduction in the reburning process. Despite the small difference between the computed and measured values, the results of profile comparisons indicate that the present reburning reaction scheme is capable to predict quantitatively the NO reduction levels. 4.2. Effects of Reburning NO Model on the NO Predictions. To further examine the effects of the reburning NO model on the NO predictions, it is useful to investigate more reactions of nitrogen oxides with hydrocarbon radicals in reburning mechanisms. Some of the reburning process predictions with comprehensive combustion codes included more species of hydrocarbon radicals, such as CH3, in the reburning NO model.2,12,31 Therefore, the following possible reaction of nitrogen oxide with CH3 is added to the reburning NO model described above to investigate the effect of this reaction on predicted NO concentrations for the reburning process.

NO + CH3 f HCN + H2O

(R12)

On the basis of the “partial equilibrium” assumptions, R4 in eq 14 becomes

R′4 ) (kaχ1χ2 + kbχ12χ2 + kdχ1)[CH4][NO]

(26)

k4 kd ) k12 k-4

(27)

and

where kd is the rate constant for reaction R12 and can be taken from ref 27. Therefore, R4 in eqs 20 and 21 is replaced by R4′ to simulate the optimized reburning case in the single-burner furnace. All other parameters remain unchanged for the simulations. Figure 7 shows the effects of reaction R12 on the predicted NO concentrations for the reburning case. Figure 7 shows that there are not significant differences between the profiles of NO concentrations predicted by the model whether including or excluding reaction R12. For adding reaction R12 to the reburning NO model, the predicted NO concentration is somewhat less than the predicted NO concentration without reaction R12. This result is reasonable, because reaction R12 adds a reaction pathway of NO reduction in the reburning mechanisms. However, the results of comparisons shown in Figure 7 indicate that the contributions of reaction R12 on the NO reduction are not obvious for the present reburning NO model. Additionally, the predicted NO concentration is not sensitive to a large change in the value of rate constant (31) Weihong, Y.; Wlodzimierz, B. Mathematical modelling of NO emissions from high-temperature air combustion with nitrous oxide mechanism. Fuel Process. Technol. 2005, 86, 943-957.

Figure 7. Effect of reaction R12 on predicted NO concentrations for reburning case.

Figure 8. Effects of kinetic parameters on predicted NO concentrations for reburning case.

kd, which was derived because of reaction R12. For example, a multiplicative factor of 0.1 for the rate constant kd resulted in only ∼3% rise for the predicted NO concentration. This also indicates that reaction R12 does not have an important influence on the predicted NO concentration. Further, Figure 7 shows that a larger difference between measurements and predictions is observed by using the reburning NO model with reaction R12. Thus, it is reasonable and computationally economic to neglect reaction R12 in the present reburning NO model. This result is consistent with the conclusion of ref 28. As shown in Figures 6 and 7, some differences still exist between measurements and predictions. To investigate the sensitivity of the predicted NO concentration to the kinetic parameters in the reburning NO model and to obtain more accurate predicted results, variations of kinetic parameters ki (i ) a, b, c) are made to investigate the effects of these kinetic parameters on predicted NO concentrations. Figure 8 shows the predicted NO concentrations by the reburning NO model with ki′ (ki′ ) 0.4ki) and ki′′ (ki′′ ) 4ki). The predicted values are also compared with the experimental values. As shown in Figure 8, changes in the values of kinetic parameters ki (i ) a, b, c) have some certain effects on the predicted NO concentrations. A decrease in the value of ki to 0.4ki results in better agreement between measurements and predictions, and an increase in the value of ki to 4ki results in a larger difference between measurements and predictions. In this study, the kinetic parameters ki from refs 27-29 have underpredicted NO concentrations for the reburning case, especially in the reburn zone. Thus, decreasing the reaction rates of NO reduction (R4 and R5) in the reburning mechanisms is the reasonable way to modify these kinetic parameters.



Figure 9. Predicted O2 concentration profiles for base and reburning case.

Figure 10. Predicted NO concentration profiles for base and reburning case.

Figure 8 shows that a multiplicative factor of 0.4 for the kinetic parameters ki results in the best agreement between measured and predicted values. This factor is obtained from the modification for the reburning case in this study. Thereby, it cannot be extrapolated to other cases and experimental systems. The predicted NO concentration is sensitive to kinetic parameters in the present reburning NO model, and the more accurate kinetic parameters are required. The key issues to obtain the more general and accurate kinetic parameters rely on further studying of kinetic mechanisms and performing more experiments for the reburning process. However, the predicted results shown in Figure 8 indicate that the reburning NO model based on the “partial equilibrium” approach is capable to properly predict the NO reduction levels in the reburning process; nevertheless, it must state that this model has somewhat underpredicted the NO concentration with the kinetic parameters in refs 27-29. 4.3. Discussion on the Modeling Results. For the base and reburning cases, Figures 9 and 10 show the predicted profiles of O2 and NO concentration at the horizontal section in the furnace. That horizontal section is through the axes of reburn fuel and burnout air injection tube, as well as the axis of primary air port. For the predicted oxygen profiles, Figure 9b shows that an obvious oxygen-lean region (O2 ) 0%) is formed downstream to the methane injection station. It indicates that the computation is able to properly simulate the profiles of oxygen concentration in the furnace for the reburning process. It should be noted that the change of the oxygen concentration in the region near the methane injection position is faster, and the oxygen-lean region is formed earlier near the methane injection position. This is because the reburn fuel flow is deflected from its course due to the impingement of the mainstream flow. The deflected reburn fuel flow first consumes the oxygen in the region near the reburn

fuel injection position to form a local oxygen-lean zone. With the development of the turbulence flow, the reburn fuel can fully mix with the mainstream flow and react with the oxygen in the central region of the furnace. Thus, the oxygen-lean region extends to the central zone of the furnace and finally forms the reburn zone, as shown in Figure 9b. This result implies that the higher injection velocity of the reburn fuel stream is able to penetrate further into the furnace before it is consumed, which results in a large region where the reburning reactions have an effect. The symmetrical injection of reburn fuel from both sides of the furnace wall can strengthen the mixing of reburn fuel with mainstream flow to optimize the oxygen profiles in the reburn zone.2,14 However, the opposed injection of reburn fuel from both sides of the furnace wall is not deployed in the present reburn experiments because of the limitations of experimental conditions. Figure 10 shows the predicted NO concentration profiles for the reburning case. This figure clearly reveals that large NO reduction is obtained in the reburn zone by the computation. Figure 10 shows that the methane injection position is located in the region of the max NO concentration, which is beneficial to the NO reduction reactions.2 This predicted result proves that the present reburn fuel injection position resulting from a complete set of experiments is optimal for the current furnace configuration to obtain the max NO reduction. Figure 10b also show that a small quantity of NO regenerates in the vicinity of the burnout air admission station. That is due to the oxidation of the HCN transported from the reburn zone. This result indicates that the amount of injected methane (15% of the total thermal input) is sufficient for the NO reduction in the reburn zone and that too much methane (20% of the total thermal input) is unfavorable to total NO reduction, which accords with the results of the experiments described previously. This conclusion is also consistent with experimental observations by Chagger


Su et al.

et al.,32 who reported an upper limit in hydrocarbon gas percentage for the reburning reaction. Comparisons of predicted NO concentration profiles in Figure 10 reveal that the reduction of NO occurs above the reburn fuel admission station. The experimental measurements shown in Figure 6 also track this earlier NO reduction. This is a fact that a small quantity of hydrocarbon radicals is upstream transported because of the entrainment of the mainstream flow, and thus, the NO reduction mechanism is activated earlier in the computation. This earlier NO reduction is also predicted by Dimitriou et al.14 and observed by Xu et al.33 The results of mathematical modeling shown in Figures 9 and 10 reveal that the accurate simulations for the flame structure and the turbulent mixing of the reburn fuel with mainstream flow are very important to the NO concentration prediction. 4.4. Comparisons of Reburning Submodels. To further evaluate the reburning NO model based on the “partial equilibrium” approach in this study, it is very useful to compare this model with the global reburning reaction model proposed by Chen et al.12 Chen and co-workers12,34 have developed a global reburning reaction model for reaction R0 and successfully applied it to predict the reburning process. The rate expression of the global reburning reaction R0 was deduced from a combination of elemental reactions by correlating predicted species profiles from simple hydrocarbon laminar flames, and can be written as35

Rglobal,reburning ) k0XHCXNO

(28)

where XNO is the nitric oxide molar concentration and XHC is the sum of hydrocarbon molar concentrations. In this work, the following species are used to determine XHC and included with other species in the combustion chemistry calculation: CH4, CH3, CH2, and CH. The rate constant recommended by Chen et al.12 for the global reburning reaction R0 is

k0 ) (2.7 × 106) e-18 800/RT

(29)

The source term for the global reburning NO mechanism in the transport eq 1 can then be calculated as

Sglobal,reburning ) -Rglobal,reburning

MNOp RT h

(30)

Smoot et al.2 further evaluated this global reburning NO model and its parameters by comparison with data from two laboratory-scale, coal-fired diffusion flame gas reburning cases. The predicted NO profiles were consistent with measured results, but the rate constant for reaction R0 had to be modified by them. The rate constant recommended by Smoot et al.2 showed a significantly better agreement with the measured values and can be expressed as (32) Chagger, H. K.; Goddard, P. R.; Murdoch, P.; Williams, A. Effect of SO2 on the reduction of NOx by reburning with methane. Fuel 1991, 70, 1137-1142. (33) Xu, H. J.; Smoot, L. D.; Tree, D. R.; Hill, S. C. Prediction of nitric oxide destruction by advanced reburning. Energy Fuels 2001, 15, 541551. (34) Chen, W.; Smoot, L. D.; Fletcher, T. H.; Boardman, R. D. A computational method for determining global fuel-NO rate expressions. Part 1. Energy Fuels 1996, 10, 1036-1045. (35) Eaton1, A. M.; Smoot, L. D.; Hill, S. C. Components, formulations, solutions, evaluation, and application of comprehensive combustion models. Prog. Energy Combust. Sci. 1999, 25, 387-436.

k′0 ) (2.72 × 106) e-7 500/RT

(31)

In this study, both k0 and k0′ are applied in the global reburning reaction model to predict the optimized reburning case in the laboratory-scale single-burner furnace. The predicted NO profiles are then compared with the predicted results from the reburning NO model based on the “partial equilibrium” approach with ki′ (i ) a, b, c). In such way, the “partial equilibrium” reburning model can be validated. Figure 11 shows the comparisons of predicted NO concentration along the furnace centerline for the optimized reburning case. Figure 11 shows the effects of the rate constant for the global reburning reaction model on the predicted NO concentrations. Changes in the value of the rate constant for the global reburning reaction have a significant effect on the predicted NO concentrations, and the predicted NO concentrations obtained with k0′ show an obviously better agreement with the measured data than that obtained with k0. As shown in Figure 11, the general trend of NO concentration predicted by the reburning NO model based on the “partial equilibrium” approach is similar to that predicted by the global reburning reaction model with rate constant k0′; nevertheless, it must be stated that the former has somewhat underpredicted NO concentration and the latter has overpredicted NO concentration in the furnace. Both the NO concentrations predicted by the two models show good agreement with the measured values. This indicates that the “partial equilibrium” reburning model is capable to predict quantitatively the NO reduction levels in the reburning process, just like the global reburning reaction model, which was proved to be able to predict the reburning process successfully.2,12 The comparisons of the predicted NO concentrations in Figure 11 show that the simulation performed with the “partial equilibrium” reburning model resulted in the best agreement between the measured and predicted values. It could not be concluded that the reburning NO model based on the “partial equilibrium” approach is more accurate than the global reburning reaction model, because this advantage resulted from the comparisons for only one reburning case and the kinetic parameters ki′ used in this model were modified by the authors for the present study. However, one point that can be confirmed from the comparisons is that the reburning model based on the “partial equilibrium” approach provides reasonable predictions for the reburning process and does not require the specification of hydrocarbon radical concentrations in the model. The concentrations of hydrocarbon radicals are critical for reburning reactions but difficult to measure and accurately estimate in complex, turbulent diffusion flames.2,25 In the global reburning reaction model, the specification of hydrocarbon radicals for XHC is difficult with different reburn fuels.2,12 The hydrocarbons used to determine XHC in this study include only CH4, CH3, CH2, and CH. These hydrocarbons may not be accurate enough for the global reburning mechanisms and may have caused the differences between the measurements and predictions. On the basis of the above comparisons and analyses, it is believed that the reburning “partial equilibrium” model represents a useful technique to predict the reburning process in practical combustors. Inevitably, there are some predictive disparities, partially due to the inaccurate predicted flame structure and to experimental errors, but in view of the complexity of all that which has been predicted, these are remarkably small.


Figure 11. Effects of reburning NO submodel on the NO predictions.

5. Conclusions The NO model including the reburning reactions has been incorporated into a comprehensive combustion model to predict the NO reduction by the reburning process. The reburning NO submodel in this model, on the basis of the “partial equilibrium” approach, requires the solution of only two transport equations (eqs 1 and 2) to simulate the complicated physical and chemical processes inherent in the reburning technology. Further, this reburning NO submodel does not require the specification of hydrocarbon radical concentrations in its expression. Sensitivity analyses of the kinetic parameters ki in this reburning NO


submodel reveal that the predicted NO concentration is sensitive to these critical parameters, and the present model has somewhat underpredicted the NO concentration in the reburning process. However, profile comparisons show that the predicted temperature and oxygen concentration match well with the measurements, and the general trend of predicted NO concentration is very similar to that measured. These results indicate that the reburning NO model depicts quite well the observed behavior of NO annihilation in the reburning process and represents a useful technique to predict the reburning process in practical combustors. One can always surmise reasons for the difference between the prediction and the measurement, but significant further study is required to secure definitive arguments. The key issues to improve agreement rely on improving prediction of the flame structure and obtaining the more accurate kinetic parameters for the reburning NO model. Additionally, more experiments should be carried out to evaluate and modify the NO model. We can only express our opinion that the present development stage is in many ways sufficient, and the model presented in this study provides a basis for further studies. Acknowledgment. This research was conducted in the State Key Laboratory of Coal Combustion at Huazhong University of Science and Technology in China and financially supported by Grant No. 2002AA527054 from the National High Technology Research and Development Program of China (863 program). EF060026X

Mathematical Modeling of Nitric Oxide Destruction by Reburning

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