Effects of Gas Temperature Fluctuations on the Evolution of

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Ind. Eng. Chem. Res. 2009, 48, 2206–2211

Effects of Gas Temperature Fluctuations on the Evolution of Nitrogenous Species during Coal Devolatilization Hongtao Zhang and Jian Zhang* Department of Engineering Mechanics, Tsinghua UniVersity, Beijing 100084, China

The effects of gas temperature fluctuations on the instantaneous evolution processes of nitrogenous species were investigated for pulverized coal particles undergoing devolatilization in a hot gas. The instantaneous mass variations of nitrogenous species released from the particles with diameters of 10-50 µm were computed for different conditions. The instantaneous gas temperature was varied with time either in a simple harmonic way or in a random way. The calculated results showed that, under different time-average gas temperatures, the HCN evolution behaviors of particles with different diameters were all affected by the gas temperature fluctuations. The gas temperature fluctuations led to more rapid HCN release from the pulverized coal particles compared to the results obtained without gas temperature fluctuations. The effects were further enhanced by increasing the amplitude or intensity of the gas temperature fluctuations. 1. Introduction Emission of nitric oxide (NO) from coal combustion continues to be a major environmental concern. Limitations on acceptable levels of NO emissions present stringent requirements for coal combustion technology. In a pulverized coal-fired furnace or combustor, the majority of nitric oxide is formed from nitrogen bound in the coal. Nitrogen in the coal is released as volatile species during the coal devolatilization process. The residual nitrogen in the char is converted to NO during the combustion of coal char. A proper description of the evolution of the nitrogen species in pulverized coal particles is essential for the prediction of NO emissions from a furnace or combustor. The reaction and pollution behaviors of pulverized coal particles in a furnace are influenced by many factors. It is noted that pulverized coal particles are exposed to a turbulent gas flow field along their pathway. Both the gas velocity and the gas temperature exhibit turbulent fluctuations in the flow field. The typical sizes of pulverized coal particles are around 10-100 µm. Their relaxation time for velocity is comparable to the turbulent time scale of gas flow. Furthermore, the particle relaxation time for temperature has the same order of magnitude as the particle relaxation time for velocity. Thus, the gas turbulent fluctuations will affect not only the instantaneous particle velocity and motion but also the instantaneous particle temperature.1 The nitrogenous species released as volatiles contribute appreciable amounts of NO emissions during pulverized coal combustion. The rates of coal devolatilization and nitrogenous species evolution are strongly dependent on the particle temperature. Because the instantaneous particle temperature is affected by the turbulent fluctuations of the gas temperature, the variation in the instantaneous particle temperature can further influence the evolution of nitrogenous species from pulverized coal particles during devolatilization. However, such a study has never been pursued before. To provide a basis for better prediction of NO emissions from a furnace or combustor, the effects of gas temperature fluctuations on the instantaneous nitrogenous species evolution of pulverized coal particles were explored in the current work. The instantaneous particle devolatilization and nitrogenous species release processes were * To whom correspondence should be addressed. E-mail: jianzhang@ mail.tsinghua.edu.cn.

computed numerically. The current investigation focuses on a single particle suspended in a hot gas stream, where the gas has a uniform but fluctuating temperature. 2. Instantaneous Governing Equations for the Evolution of Nitrogenous Species during Coal Devolatilization The evolution of nitrogenous species from a pulverized coal particle during devolatilization are considered in the present analysis. The instantaneous particle energy equation was formulated by taking into account the convective heat transfer between the gas and particle phases, the radiative heat transfer between the combustor wall and the particle, and the pyrolysis heat loss. This is expressed by2 6εkσb m ˙ v∆hv dTk 1 ) (T - Tk) + (T 4 - Tk4) + (1) dt τTk FpkdkCpk w mkCpk In the above equation, εk and Tw represent the particle emissivity and the combustor wall temperature, respectively, and τTk is the particle relaxation time for temperature. τTk is defined as τTk )

FpkCpkdk2 exp(Bk) - 1 6Nukλ Bk

(2)

where Bk is the dimensionless rate of variation of the particle mass and Nuk is the Nusselt number for gas-particle convective heat transfer. The primary nitrogenous gas compounds released during coal devolatilization are HCN and NH3. Different models for quantitatively predicting the rates of evolution of individual volatile species from coal particles have been proposed. They include the FG-DVC (functional group-depolymerization, vaporization, and cross-linking) model,3,4 the CPD (chemical percolation devolatilization) model,5 and the FLASHCHAIN model.6 Here, the FG-DVC model was employed to describe the instantaneous release rates of nitrogenous species during coal devolatilization. In the FG-DVC model, each functional group in the coal is divided into the non-tar-forming component and the potential-tar-forming component. The former releases nitrogenous gas compounds, and the latter releases tar as well as nitrogenous gas compounds.

10.1021/ie801076u CCC: $40.75  2009 American Chemical Society Published on Web 01/12/2009

Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 2207

The instantaneous mass fraction of each component is defined as its instantaneous mass divided by the initial mass of raw coal in the particle (mc0). Let X0 denote the mass fraction of the potential-tar-forming component in the coal, let X represent the remaining instantaneous mass fraction of the potential-tarforming component in the coal, and let Yi denote the instantaneous mass fraction of a functional group in the coal and tar. During the devolatilization of the pulverized coal particle, the instantaneous mass fraction of a functional group contained in the non-tar-forming component and the remaining potentialtar-forming component is thus given by Wi ) (1 - X0 + X)Yi

(3)

Its instantaneous rate of variation is calculated as dWi dYi dX ) (1 - X0 + X) + Yi dt dt dt

(4)

On the right-hand side of eq 4, the first and second terms represent the rates of mass variation of the ith functional group released as volatile gas species and converted to tar, respectively. Thus, the instantaneous rate of evolution of gas species from the ith functional group is obtained as dVi dYi ) -(1 - X0 + X) dt dt

(5)

where the instantaneous rate of mass variation of the ith functional group is given as

( )

dYi Ei ) -kiYi ) -AiYi exp dt RTk

(6)

The instantaneous rate of formation of tar is determined by

( )

Etar dX ) -ktarX ) -AtarX exp dt RTk

(7)

The instantaneous particle mass variation rate is obtained by summing the mass variation rate for each functional group in the coal as given by eq 4, yielding dmk )m ˙ v ) mc0 dt

∑ i

dWi dt

(8)

The diameter of the pulverized coal particle can be considered as undergoing no changes during the devolatilization process. The instantaneous particle material density is thus given as Fpk ) 6mk/πdk3. To investigate the effects of the gas temperature fluctuations on the release of nitrogenous species by the pulverized coal particle, the instantaneous gas temperature was assumed to follow a uniform spatial distribution but to fluctuate with time. Here, two different forms of gas temperature fluctuations were considered, as follows: (1) In the first case, the instantaneous gas temperature was assumed to vary with time in a simple harmonic way as j [1 + At sin(2πft)] T)T

(9)

j is the time-average gas temperature, At is the fluctuation where T amplitude of the gas temperature, and f represents the fluctuation frequency of the gas temperature. f was determined by the turbulent time scale, i.e., f ) 1/τT.

Table 1. Coal Analysis Data proximate analysis (wt %) VM FC ash moisture

31.1 56.2 11.3 1.4

ultimate analysis (wt % daf) C H N S O

82.1 5.6 1.7 2.4 8.2

(2) In the second case, the instantaneous gas temperature was assumed to vary with time in a random way. Its probability density function (PDF) was assumed to follow a uniform distribution given by p(T) )

1 [H(T - T-) - H(T - T+)] T+ - T-

(10)

where T+ and T- are two parameters and H(ξ) is Heaviside function. The value of H(ξ) is either 1 for ξ g 0 or 0 for ξ < 0. T+ and T- were calculated as j (1 + √3Bt) T+ ) T

(11)

j (1 - √3Bt) T- ) T

(12)

where Bt is the fluctuation intensity of the gas temperature. It j , where (T′2)1/2 is the root-meanis defined as Bt ) (T′2)1/2/T square of fluctuating gas temperature. Within an interval of the turbulent time scale, the instantaneous gas temperature was randomly selected as T ) (T+-T-)ζ+T-

(13)

where ζ is a random number whose PDF follows a uniform distribution between 0 and 1. 3. Calculation Conditions The instantaneous governing equations for the evolution of nitrogenous species from the pulverized coal particle during devolatilization were solved numerically by the finite difference method. The first-order explicit scheme7 was utilized for the discretization of each governing equation. The time step employed in the computations had to be quite small to ensure the accuracy of the results. A bituminous coal was chosen for the present study. Its proximate and ultimate analysis data8,9 are provided in Table 1. The kinetic rate constants and initial composition of functional groups and tar9 are listed in Table 2. All moisture was assumed to have evolved from the particle before devolatilization. During the coal devolatilization process, the gas volatile species evolved from the relevant extra-loose, loose, tight, and extra-tight functional groups in sequence as the particle temperature increased. The particle specific heat, emissivity, and initial material density were taken as Cpk ) 1090 J/(kg K), εk ) 0.8, and Fpk0 ) 1350 kg/m3, respectively. The instantaneous devolatilization and nitrogenous species evolution processes of the pulverized coal particle were calculated under different conditions. The time-average gas j ) was set to 900, 1000, or 1100 K. The fluctuation temperature (T amplitude (At) was chosen as 0, 0.1, or 0.2 for the harmonic fluctuations of the gas temperature, and the fluctuation intensity of the gas temperature (Bt) was taken to be 0, 0.0707, or 0.1414 for the random fluctuations of the gas temperature. The particle had a diameter of 10, 30, or 50 µm. For all calculations, the fluctuation frequency of the gas temperature was 100 Hz, the gas-particle relative velocity was 0, the particle initial tem-

2208 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 2. Kinetic Rate Constants and Initial Composition for Functional Groups and Tar kinetic rate constants composition parameter 0

Y1 Y02 Y03 Y04 Y05 Y06 Y07 Y08 Y09 Y010 Y011 Y012 Y013 Y014 Y015 Y016 Y017 Y018 Y019 X0

CO2 extra loose CO2 loose CO2 tight H2O loose H2O tight CO ether loose CO ether tight HCN loose HCN tight NH3 CHx aliphatic methane extra loose methane loose methane tight H aromatic methanol CO extra tight C nonvolatile S organic tar

composition

A (1/s)

0.000 0.006 0.005 0.011 0.011 0.050 0.022 0.009 0.022 0.000 0.190 0.020 0.015 0.015 0.012 0.000 0.020 0.562 0.024 0.430

E/R (K) 18

0.56 × 10 0.65 × 1017 0.11 × 1016 0.22 × 1019 0.17 × 1014 0.14 × 1019 0.15 × 1016 0.17 × 1014 0.69 × 1013 0.12 × 1013 0.84 × 1015 0.84 × 1015 0.75 × 1014 0.34 × 1012 0.10 × 1015 0 0.20 × 1014 0

30 000 33 850 38 315 30 000 32 700 40 000 40 500 30 000 42 500 27 300 30 000 30 000 30 000 30 000 40 500 0 45 500 0

0.86 × 1015

27 700

perature was set at 300 K, and the combustor wall had a temperature of 300 K. The time step was taken as 10-5s. The calculation for each case was terminated at the end of coal devolatilization. The particle devolatilization time was determined by utilizing the two-parallel-reaction model.10 4. Results and Discussion Because the initial mass fraction of NH3 functional groups in the present coal sample was 0, the nitrogenous gas species released from the coal was only HCN. Figures 1-3 show the instantaneous mass variations of HCN evolved from the pulverized coal particle during devolatilization under the conditions of harmonic gas temperature fluctuations. Figures 4 and 5 present the instantaneous mass variations of HCN released from the pulverized coal particle during devolatilization in the hot gas with random temperature fluctuations. In all of these figures, the instantaneous HCN mass was divided by the corresponding initial mass of raw coal in the particle. Figure 1a-c presents the effects of the harmonic gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles with diameters of 10, 30, and 50 µm, respectively. The time-average gas temperature was 900 K for these results. The instantaneous HCN mass released from the particle increased with time during the devolatilization processes. As seen in Figure 1a, the gas temperature fluctuations had a distinct influence on the instantaneous HCN evolution of the pulverized coal particle with a diameter of 10 µm. Compared to the results without gas temperature fluctuations, the gas temperature fluctuations led to faster HCN release during devolatilization. An increase in the fluctuation amplitude of the gas temperature further promoted HCN release. At the time of 0.18 s, the instantaneous dimensionless HCN mass was 5.36 × 10-5 without the gas temperature fluctuations. It became 2.44 × 10-4 and 1.83 × 10-3 when the fluctuation amplitudes of the gas temperature were 0.1 and 0.2, respectively. Figure 1b shows that the instantaneous HCN evolution of the pulverized coal particle with a diameter of 30 µm was also considerably affected by the gas temperature fluctuations. The results with the gas temperature fluctuations were faster than those without the gas temperature fluctuations. The effects were further enhanced by the increase in the fluctuation amplitude of the gas temperature. The gas temperature fluctuations had a certain

Figure 1. Effect of harmonic gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles (Tj ) 900 K).

effect on the instantaneous HCN evolution of the pulverized coal particle with a diameter of 50 µm, as seen in Figure 1c. The HCN release became fast as the fluctuation amplitude of the gas temperature increased. It should be noted that previous studies have provided only results without gas temperature fluctuations.11 The influences of gas temperature fluctuations on the HCN evolution were revealed in the present investigation. Figure 2a-c shows the effects of the harmonic gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles with diameters of 10, 30, and 50 µm, respectively. The results were obtained for a time-average gas temperature of 1000 K. As a result of coal devolatilization, the mass of HCN released from the particle increased with time. It can be seen from Figure 2a that the gas temperature fluctuations led to faster HCN evolution from the pulverized coal particle with a diameter of 10 µm than occurred in the absence of gas temperature fluctuations. The effects became more evident as the fluctuation amplitude of the gas temperature increased from 0.1 to 0.2. At the time of 0.06 s, the instantaneous dimensionless




HCN mass reached 1.49 × 10-3 and 4.69 × 10-3 for gas temperature fluctuation amplitudes of 0.1 and 0.2, respectively, whereas it was 4.30 × 10-4 if gas temperature fluctuations were not considered. Figure 2b shows that the instantaneous HCN evolution of the pulverized coal particle with a diameter of 30 µm was obviously affected by the gas temperature fluctuations. Differences were found between the results with and without gas temperature fluctuations, as the former was faster than the latter. The gas temperature fluctuations also had a distinct effect on the instantaneous HCN evolution of the pulverized coal particle with a diameter of 50 µm, as seen in Figure 2c. Faster HCN release was found with gas temperature fluctuations than without them. The effects became large as the fluctuation amplitude of the gas temperature increased. Figure 3a-c presents the effects of the harmonic gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles with diameters of 10, 30, and 50 µm, respectively. The time-average gas temperature was 1100 K for these results. Because the time-average gas temperature

was relatively high, the HCN was released rapidly from the particles. Its instantaneous mass showed an increase with time. The gas temperature fluctuations had evident influences on the instantaneous HCN evolution of the pulverized coal particles with diameters of 10-50 µm. They led to faster HCN release from the particles during devolatilization than occurred without the gas temperature fluctuations. The effects were further enhanced by an increase in the fluctuation amplitude of the gas temperature. As seen in Figure 3c, the instantaneous dimensionless HCN mass released from the pulverized coal particle with a diameter of 50 µm was 2.04 × 10-3 without the gas temperature fluctuations at t ) 0.05 s, whereas it became 2.72 × 10-3 and 4.33 × 10-3 when the amplitudes of the gas temperature fluctuations were 0.1 and 0.2, respectively. The effects of gas temperature fluctuations on the HCN evolution of the pulverized coal particles were further investigated. To simulate a real gas environment for the devolatilization of pulverized coal particles, random fluctuations of the gas temperature are also employed in the present computations.

2210 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009

Figure 4. Effect of random gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles (Tj ) 900 K).

Figure 5. Effect of random gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles (Tj ) 1000 K).

Figure 4a-c shows the effects of random gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles with diameters of 10, 30, and 50 µm, respectively. The time-average gas temperature was 900 K for these results. Again, it can be seen that the gas temperature fluctuations had distinct influences on the instantaneous HCN evolution of the pulverized coal particles with diameters of 10-50 µm during devolatilization. The results obtained with the gas temperature fluctuations were obviously different from those without gas temperature fluctuations. The former exhibited faster HCN release from the particles than the latter. The effects were further enhanced by an increase in the fluctuation intensity of the gas temperature. The calculated results without the gas temperature fluctuations exhibited a smooth increase with time, whereas the instantaneous HCN mass with the gas temperature fluctuations increased with time unevenly. As seen in Figure 4b, the instantaneous dimensionless HCN mass released from the particle with a diameter of 30 µm was 3.49 × 10-5 without gas temperature fluctuations at a time of 0.16 s. It increased to 1.91 × 10-4 and 1.55 × 10-3 when the fluctuation intensities of the gas temperature were 0.0707 and 0.1414, respectively. Although the fluctuation form was different, the gas temperature fluctuations still imposed influences on the HCN release from the particles.

Figure 5a-c presents the effects of random gas temperature fluctuations on the instantaneous HCN evolution of pulverized coal particles with diameters of 10, 30, and 50 µm, respectively. The results were obtained for a time-average gas temperature of 1000 K. The gas temperature fluctuations had evident effects on the instantaneous HCN evolution of pulverized coal particles with different diameters. The HCN release from the particles was predicted to be faster with the gas temperature fluctuations than that without them. An increase in the fluctuation intensity of the gas temperature led to faster HCN release. Figure 5a shows that, at the time of 0.04 s, the instantaneous dimensionless HCN mass released from the particle with a diameter of 10 µm reached 1.37 × 10-3 and 4.88 × 10-3 for gas temperature fluctuation intensities of 0.0707 and 0.1414, respectively. In contrast, it was 2.84 × 10-4 if the gas temperature fluctuations were not considered. The results further elucidate the influences of gas temperature fluctuations on the HCN evolution of pulverized coal particles, which has not been reported previously. 5. Conclusions The instantaneous devolatilization and HCN evolution processes of a pulverized coal particle in a hot gas with temperature fluctuations were investigated. The gas temperature had time-


average values of 900-1100 K and fluctuated in two different forms. The following conclusions were reached: (1) The instantaneous HCN evolution processes of pulverized coal particles with diameters of 10-50 µm are all affected by the gas temperature fluctuations during devolatilization. The HCN releases at higher rate with gas temperature fluctuations than that without them. (2) The fluctuation amplitude or intensity of the gas temperature has evident effects on the instantaneous HCN evolution of particles with different diameters. Higher amplitude or intensity leads to more rapid HCN release from the particles. (3) For both harmonic and random fluctuations of the gas temperature, the instantaneous HCN mass released from the pulverized coal particles during devolatilization is influenced by the gas temperature fluctuations. (4) The effects of gas temperature fluctuations on the HCN evolution during coal devolatilization were revealed by the present investigation. They should be taken into account in the prediction of NO emissions in practical pulverized coal combustion systems. Acknowledgment This study was supported by National Natural Science Foundation of China under Grant 50576044. Nomenclature A ) pre-exponential factor (1/s) At ) fluctuation amplitude of gas temperature Bk ) dimensionless rate of variation of particle mass Bt ) fluctuation intensity of gas temperature Cpk ) particle specific heat [J/(kg K)] dk ) particle diameter (m) E ) activation energy (J/mol) f ) fluctuation frequency of gas temperature (Hz) mc0 ) initial mass of raw coal in particle (kg) mHCN ) HCN instantaneous mass released from particle (kg) mk ) instantaneous particle mass (kg) m ˙ v ) devolatilization reaction rate (kg/s) Nuk ) particle Nusselt number R ) universal gas constant [J/(mol K)] t ) time (s) T ) instantaneous gas temperature (K) Tk ) instantaneous particle temperature (K) Tw ) wall temperature (K) X ) mass fraction of potential-tar-forming component in coal Yi ) mass fraction of ith functional group in coal and tar

Greek Symbols ∆hv ) heat of pyrolysis reaction (J/kg) εk ) particle emissivity λ ) gas thermal conductivity [W/(m K)] Fpk ) instantaneous particle material density (kg/m3) σb ) Stefan-Boltzmann constant [5.67 × 10-8 W/(m2 K4)] τT ) turbulent time scale (s) τTk ) particle relaxation time for temperature (s) ζ ) random number Superscripts 0 ) initial jx ) time-average of quantity x

Literature Cited (1) Shang, Q.; Zhang, J.; Zhou, L. X. Instantaneous Response of Pulverized Coal Particles to Fluctuating Temperature in a Hot Gas Flow. Chem. Eng. Commun. 2006, 193, 1397–1413. (2) Zhang, J.; Nieh, S. Comprehensive Modelling of Pulverized Coal Combustion in a Vortex Combustor. Fuel 1997, 76, 123–131. (3) Solomon, P. R.; Hamblen, D. G. Pyrolysis. In Chemistry of Coal ConVersion; Schlosberg, R. H., Ed.; Plenum Press: New York, 1985; pp 121-251. (4) Solomon, P. R.; Hamblen, D. G.; Garangelo, R. M.; Serio, M. A.; Deshpande, G. V. General Model of Coal Devolatilization. Energy Fuels 1988, 2, 405–422. (5) Grant, D. M.; Pugmire, R. J.; Fletcher, T. H.; Kerstein, A. R. Chemical Model of Coal Devolatilization Using Percolation Lattice Statistics. Energy Fuels 1989, 3, 175–186. (6) Niksa, S. FLASHCHAIN Theory for Rapid Coal Devolatilization Kinetics. 6. Predicting the Evolution of Fuel Nitrogen from Various Coals. Energy Fuels 1995, 9, 467–468. (7) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Hemisphere Series on Computational Methods in Mechanics and Thermal Science; Hemisphere: Washington, DC, 1980. (8) Jones, J. M.; Pourkashanian, M.; Williams, A.; Rowlands, L.; Zhu, Q.; Thomas, K. M. Conversion of Char Nitrogen to NO During Combustion. J. Energy Inst. 2004, 77, 82–89. (9) Serio, M. A.; Hamblen, D. G.; Markham, J. R. Kinetics of Volatile Product Evolution in Coal Pyrolysis: Experiment and Therory. Energy Fuels 1987, 1, 138–152. (10) Ubhayakar, S. K.; Stickler, D. B.; von Rosenberg, C. W., Jr.; Gannon, R. E. Rapid Devolatilization of Pulverized Coal in Hot Combustion Gas. In Proceedings of the 16th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1976; pp 427-436. (11) Visona, S. P.; Stanmore, B. R. Modeling NOx Release from a Single Coal Particle I. Formation of NO from Volatile Nitrogen. Combust. Flame 1996, 105, 92–103.

ReceiVed for reView July 14, 2008 ReVised manuscript receiVed November 9, 2008 Accepted November 25, 2008 IE801076U

Effects of Gas Temperature Fluctuations on the Evolution of

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