Experimental and Modeling Study on Char Combustion - Energy

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Experimental and Modeling Study on Char Combustion J. Yu* and M. C. Zhang Institute of Thermal Energy Engineering, School of Mechanical Engineering, Shanghai Jiaotong UniVersity, Shanghai, 200240, China ReceiVed January 8, 2009. ReVised Manuscript ReceiVed April 14, 2009

In this study, on the basis of experimental verifications with an FTIR online measurement system, theoretical calculations by using the strict continuous-film model were first compared with those by the simple singlefilm model that is still widely used in mathematical modeling of pulverized coal flames. The results indicated that the single-film model has some significant errors in its predictions of the ignition temperature and the combustion following ignition and hence should have some restrictions on its application. Then an improved char combustion model has been presented, taking into consideration the influence of the finite-rate heterogeneous reduction and oxidation reactions. This model gives the explicit algebraic expressions for the overall rate of combustion, the surface temperature of the particle, and the gas temperature at the flame sheet. Compared with the single-film model, predictions by the present model were in much better agreement with those predicted by the continuous-film model and the experimental data. The novel model is also much easier to be integrated into the comprehensive computing codes for industrial pulverized coal flame than the continuous-film model.

1. Introduction Coal is a vital energy resource, and its use is projected to increase in the foreseeable future. Coal is responsible for about 39% of the electricity generated in the world, and in China this figure exceeds 65%.1 Much of electricity is generated by means of the combustion of pulverized coal. There is a necessity to look for the most efficient combustion condition in terms of rationally using coal. Various experimental techniques have been developed to study the combustion of pulverized coal/char under conditions related to a pulverized coal furnace. However, because the experiments are generally expensive, numerical simulation becomes more and more important in decreasing experimental cost, optimizing design, and improving operation. A detailed review can be found in refs 2 and 3. Most of the mathematical models developed focus on comprehensively describing the processes in the furnace including the flow, combustion, and heat transfer. As a main combustion submodel, accurate prediction for the char combustion is important in terms of the ignition and burnout of pulverized coal. A series of investigations on the combustion model for a char particle have been carried out, and many valuable theoretical results have been obtained. For the combustion of a char particle in an ambience with high temperature (>1000 K), the dominant heterogeneous reactions at the particle surface are4 2C(s) + O2 f 2CO

(I)

C(s) + CO2 f 2CO

(II)

* To whom correspondence should be addressed. E-mail: yujuan@ sjtu.edu.cn. Fax: 86-21-34206115. (1) IEA; World Energy Outlook 2007; Paris, France, 2007. (2) Eaton, A. M.; Smoot, L. D.; Hill, S. C.; Eatough, C. N. Prog. Energy Combust. Sci. 1999, 25, 387–436. (3) Williams, A.; Backreedy, R.; Habib, R.; Jones, J. M.; Pourkashanian, M. Fuel 2002, 81, 605–618. (4) Lee, J. C.; Yetter, R. A.; Dryer, F. L. Combust. Flame 1995, 101, 387–398.

while the homogeneous reaction in the gas surrounding the particle is (III) CO + 1/2O2 f CO2 The effects of surface reactions I and II and CO volumetric reaction III are simultaneously described in the continuous-film model.5-7 The continuous-film model could faithfully reflect the combustion conditions and process. However, from the viewpoint of engineering application, it is not popularly used because of their complexity and difficulty to be coupled into the comprehensive computing code for pulverized coal flames. Therefore, more simplified models were presented for engineering application. The single-film model,8 which assumes either CO or CO2, is the product formed at the particle surface, and any CO formed is oxidized only in the free stream and is widely used in the area of combustion kinetics of char and mathematical modeling of pulverized coal flames. By using the single-film model, it is easy to resolve the highly nonlinear coupling between the chemical reactions, the heat transfer, and the mass transfer. But the burnout was overpredicted to a certain degree when the single-film was used for the combustion of a char particle.9 The double-film model, presented by Burke and Shumann,10 assumes the conversion of CO to CO2 at a flame sheet in the boundary layer and prevents any O2 from reaching the particle surface, thus allowing reaction II to govern the heterogeneous reaction rate. It can be seen that the double-film model represents a limiting case with infinitely fast rates for (5) Amundson, N. R.; Mon, S. Diffusion and reaction in carbon burning. In Dynamics and modelling of reactiVe systems; Academic Press, 1980; pp 353-374. (6) Daniel Hsuen, H. K.; Sotirchos, S. V. Chem. Eng. Sci. 1989, 44, 2653–2665. (7) Yu, J.; Zhang, M. C.; Zhang, J. Proc. Combust. Inst. 2009, 32, 2037– 2042. (8) Field, M. A.; Gill, D. W.; Morgan, B. B.; Hawksley, P. G. W. Combustion of pulVerized coal; Leatherhead: England, BCURA, 1967. (9) Sheng, C. D.; Moghtaderi, B.; Gupta, R.; Wall, T. F. Fuel 2004, 83, 1543–1552. (10) Burke, S. P.; Schuman, T. E. W. Proc. Int. Conf. Bituminous Coal 1932, 2, 485–509.

10.1021/ef900018b CCC: $40.75  2009 American Chemical Society Published on Web 04/29/2009

Experimental and Modeling Study on Char Combustion

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Figure 1. Schematic of the FTIR measurement system. 1, flue gas duct; 2, transparent wall reactor; 3, electric heater; 4, bracket; 5, lift device; 6, FTIR.

reactions II and III. In some other models, surface reactions I and II are simultaneously taken into account.11,12 It can be seen that these models would have restrictions in their applications because of neglect, to some extent, of the physical reality of char combustion. Therefore, it looks attractive for the researchers to develop a model, both rationally reflecting the physical reality and being suitable to engineering application. Some efforts have been made to achieve the aim mentioned above by the authors. A new simplified method called the Moving Flame Front (MFF) model was put forward.13 In this model, the combustion rate and the surface temperature are expressed in algebraic forms, so the computational effort is greatly decreased. In spite of its simplicity, predictions of this model faithfully reproduce many of the characteristics obtained by the continuous-film model. Good agreement was obtained between the model predictions and the experimental measurements of Young and Niksa,14 which could not be obtained using the customary single-film model. However, since emphasis in the MFF model was placed on the influence of CO oxidation on the ignition of a carbon particle, the heterogeneous reduction of CO2 (reaction II), which becomes important at even higher temperatures, was neglected. Thus, the objectives of the present work were to compare the discrepancy between the continuous film and the single film based on experimental data obtained by using a Fourier Transform Infrared spectroscopy (FTIR) online temperature measuring system and then to develop a char combustion model, considering the effects of heterogeneous reduction and oxidation on the combustion of a char particle, and to compare the model predictions with those of other combustion models and the experimental data. 2. Experimental Section 2.1. Sample. A Chinese bituminous coal from Shenfu was used in the experiments. The proximate analysis data of the coal are 3.58% moisture, 14.64% ash, 28.57% volatile matter, and 53.22% fixed carbon in the air-dry basis. The coal was pulverized to a mean particle diameter of 50 µm.The coal particles were devolatilized in a muffle furnace at 1183 K for 7 min in the absence of air to ensure complete annealing. It appears that a little swelling occurs during devolatilization. So the char particles prepared from the coal were resieved, and the sizes used in the experiments were 64-90 µm

(average size: 77 µm). The proximate analysis values of the char sample are 3.63% moisture, 20.47% ash, 2.10% volatile matter, and 73.80% fixed carbon in the air-dry basis. The kinetic parameters of the surface oxidation reaction I were measured using a drop tube furnace. The frequency factor was determined to be kO,s ) 6.2 × 106 m/s, and the activation energy was 184 kJ/mol.15 For reaction II, the activation energy of 270 kJ/ mol was taken from ref , and the frequency factor was considered to be ten times kO,s, i.e., kP,s ) 6.2 × 107 m/s. For reaction III, the activation energy of 113 kJ/mol and frequency factor of 1.4 × 109 (m3/mol)1/2/s17 were used. 2.2. Experimental System. An experimental system (see Figure 1) was established to measure the particle temperature.15 It mainly consists of an FTIR spectrometer, an electric heater, and a reactor. The FTIR, Bruker model EQUINOX 55, was used with a selected spectral resolution of 4 cm-1, giving a spectral range from 500 to 6500 cm-1. The transfer optics of FTIR is shown in Figure 2, and the transmission and emission measurements for a multiphase reacting flow can be performed to determine the temperatures of particle and combustion gas species, according to the method developed by Solomon and co-workers.18,19 This method is described briefly as follows. For a dilute, homogeneous, and optically thin medium containing gases and soot with absorption coefficients Rνg and Rνs and particles of geometrical cross sections, A, at a density of N particles (cm-3), the transmittance, τν, is given by

τν ) exp[-(Rgν + Rsν + NAFνt)L]

(1)

(11) Gibb, J. Combustion of residual char remaining after devolatilization. In Lecture at course of pulVerised coal combustion; Imperial College: London, 1985. (12) Shen, Y. S.; Guo, B. Y.; Yu, A. B.; Zulli, P. A. Fuel 2009, 88, 255–263. (13) Zhang, M. C.; Yu, J.; Xu, X. C. Combust. Flame 2005, 143, 150– 158. (14) Young, B. C.; Niksa, S. Fuel 1988, 67, 155–164. (15) Yu J. Study and modelling on the interaction of Volatile flame, CO flame and char particle combustion; Shanghai Jiaotong University: Shanghai, China, 2003. (16) Essenhigh, R. H. Chemistry of coal utilization; Elliot M. A., Ed.; Wiley-Interscience Press: New York, 1981; Second Supplementary Volume, pp 1153-1312. (17) Howard, J. B.; Williams, G. C.; Fine, D. H. Proc. Combust. Inst. 1973, 14, 975–986. (18) Solomon, P. R.; Best, P. E.; Carangelo, R. M.; et al. Proc. Combust. Inst. 1986, 21, 1763–1771. (19) Solomon, P. R.; Carangelo, R. M.; Best, P. E.; Markham, J. R.; Hamblen, D. G. Fuel 1987, 66, 897–908.

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Figure 2. Transfer optics of FTIR spectrometer. 1, infrared light supply; 2, moveable optic; 3, Michelson’s interferometer; 4, measurement chamber; 5, detector.

where Fνt is the ratio of the total cross section (extinction) to geometric cross section and L is the path length. The power from the sample with background subtracted, Sν, is measured and converted back to the sample radiation, Rν, in the following way

Rν ) Sν /Wν

(2)

where Wν is the response function of the instrument that is determined by means of the emission spectrum of a standard blackbody emitter. The radiation is the sum of gas, soot, particle, and reactor wall radiation

Rν ) [RgνRbν(Tg) + RsνRbν(Ts) + NAενRbν(Tp) + NAFs′ν Rbν(Tw)](1 - τν) Rgν + Rsν + NAFtν (3) Rbν(Tg),

Rbν(Ts),

Rbν(Tp),

Rbν(Tw)

where and are the blackbody emission spectra at the temperatures Tg, Ts, Tp, and Tw of the gas, soot, particle, and wall, respectively. εν is the particle’s spectral emittance, and Fνs′ is the cross section for scattering radiation into the spectrometer. Zero scattering is assumed for soot particles in the IR region. If Tw is room temperature, Fνs′ may be neglected. The normalized radiation, Rνn, which is defined as the radiance divided by (1 - τν), is given by

Rnν )

Rν ) 1 - τν RgνRbν(Tg)

+

RsνRbν(Ts) + NAενRbν(Tp) Rgν + Rsν + NAFtν

+

NAFs′ν Rbν(Tw)

Figure 3. Spectra for candle flame: (a)1 - τν; (b) emission spectrum; (c) normalized radiance.

(4)

The normalized radiation is the main experimental result we interpret. For gas samples, measurements are restricted to the narrow band spectral region. For soot and particles, the radiation is a continuum spectrum. If Tw is low enough, the radiance comes from the contributions of char, gases, and ash for the char flame. Because the measurement locations selected are far away from the burnout region, the radiance from ash is neglected. Thus, if comparing the normalized radiance to theoretical blackbody curves in the region excluding the spectrum containing the CO2 and H2O band according to the following equation, the particle temperature along the line-of-sight will be obtained

Rnν )

ενRbν(Tp) Ftν

) MRbν(Tp)

(5)

where the blackbody, M, is the constant fraction of the theoretical blackbody which produces the best match in shape and amplitude to the experimental data. The two parameters, Tp and M, were determined by the nonlinear regression method. The electric heater provides a hot circumstance for the reactor. The heating elements are four resistance wires, and the total power of the electric heater is up to 8 kW. Knob insulators are packed among the heating elements to sustain the heating elements and enhance the heat exchange between the elements and the gas. The electric heater is controlled by two transformers. The reactor is an octagonal stainless steel enclosure with two movable KBr windows to allow access to the flame by the beam of the FTIR spectrometer. A flow of ambient air along the inside of the enclosure keeps the KBr windows overheating. The flue gas is exhausted from the duct at the top of the reactor. The lift device is used to change the measurement location by lifting/lowering the heater and the reactor along the lines of height.



Figure 5. Photograph of the char flame.

Figure 4. Spectra for clay particles: (a) 1 - τν; (b) emission spectrum; (c) normalized radiance.

The accuracy of temperature measurement was evaluated for the experimental system. Figure 3 is the detected spectra of a candle flame. From the normalized spectrum, we can see that there is a clear solid radiation continuum curve in regions of no gases radiation bands. It is in accordance with the fact that a large quantity of soot particles exist in the candle flame. The fitting curve by implementing the method stated above agrees closely with the measured continuum spectrum, and the temperature of soot, 1196 K, was obtained. Comparing with the temperature of a candle flame, 1214 K, that was measured by a nonintrusive IR pyrometer with an accuracy of (0.5%, the temperature fitted is satisfactory. Figure 4 is the spectra of clay particles that are nonreactive and have little change in physical properties during a medium heating. The clay particles with an average diameter of 77 µm were entrained by cold air and injected into the reactor. The ambient air temperature is about 873 K, and the calculation indicates the temperature of clay

particles approaches it at a location of 6 cm above the injector. The scheduled measurement location was 16 cm. The temperature of the particle fitted from the normalized spectrum was 831 K that agrees well with the gas temperature of 867 K measured by a type-K thermocouple (accuracy: (0.4%). Temperature measurements appear to be accurate to less than (40 K, depending mainly on the particle concentration in the detection volume. When the concentration is low, the radiation fluctuates during the scans and may seriously distort the spectra. So 24 scans per spectrum were performed to obtain a sufficiently good S/N ratio and to avoid the distortion of the spectra caused by flicker. 2.3. Procedure. The experiment was started by heating the oxidizing gas to the required temperature. The gas is passed through the electric heater and enters the bottom of the reactor. The gas temperature was checked using a type-K thermocouple located in the reactor center-line. With the ambient hot gas conditions established, the transmission and emission measurements were performed to obtain the background spectra, which will be used in the data processing. Then the char particles entrained in a cold carrier dry air were injected into the reactor through a coaxial 5 mm diameter tube. The feed rates for char particles, the carrier gas, and the hot gas were 0.2 ∼ 0.3 g/min, 300 mL/min, and 10 m3/h, respectively. Figure 5 shows one of the photographs of char flames. The calculation and the experimental observations indicate that the requirement that the sample be optically thin and dilute was satisfied. The primary measurement in each experiment was the variation of particle temperature with height/time as the char particles oxidized in the reactor. The ambient oxygen partial pressure was 0.21 atm. The gas temperature was in the range of 973 ∼ 1273 K. The measurement locations were at the distances of 2, 3, 4, 5, 6, and 7 cm above the char particle injector. Each experiment was repeated twice. Figure 6 is the normalized radiance spectra and the fitting particle temperatures for several positions above the char injection nozzle. From it, we can see that 2 cm above the nozzle is in the region prior to ignition, 5 cm is at the beginning of the ignition, and 6 and 7 cm are in the ignition region and show a bright flame. The measurements agree well with the observations.

3. Continuous-film Model 3.1. Description. The combustion model for a char particle used in the present study was developed by Makino and

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Figure 6. Normalized radiance spectra (T∞ ) 1163 K). Solid line: to fit particle temperature. Dashed line: to fit CO2 temperature.

the boundary layer of a char particle, CO + 1/2O2 f CO2, is also considered. Then, a semianalytical, seminumerical model, which takes chemical reactions, heat, and mass transfer into account, was established Y˜F + Y˜P ) YÕ + Y˜P )

(Y˜P,∞ + δβ) + (Y˜P,∞ - δ)βξ 1+β

(6)

(YÕ,∞ + Y˜P,∞ - δβ) + (YÕ,∞ + Y˜P,∞ + δ)βξ 1+β (7)

Y˜P - T˜ ) -T˜s + (Y˜P,∞ - T˜∞ + T˜s)ξ + (1 - ξ) × Y˜P,∞ - T˜∞ + T˜s + γ Figure 7. Particle lifetime as a function of the initial surface Damkohler number.

1 + β + Das2(T˜∞ /T˜s)exp(-θs,C-CO2 /T˜s)/(dξ/dr˜)s

Law.20

It is established on the basis of the following assumptions: (a) Spherical symmetry exists. (b) The char particle is burned in a quiescent environment. (c) The physical properties of char and gas are constant. (d) The particle temperature is uniform throughout the solid. (e) The Lewis number is unity, i.e., Le ) 1. (f) The primary product of the heterogeneous reaction at the residual char particle surface is mainly CO. Consequently, the dominating surface reactions are 2C + O2 f 2CO and C + CO2 f 2CO. The further oxidation of CO in (20) Makino, A.; Law, C. K. Proc. Combust. Inst. 1986, 21, 183–191.

(8)

1 + βξ YÑ ) YÑ,∞ 1+β

(9)

L(T˜) ) Dagwg

(10)

where m ˜ ) m/(4πrsF∞D∞), r˜ ) r/rs, T˜ ) (RFcpT)/HCO, θ ) (RFcpE)/(RHCO), RF ) (νPMP)/(νFMF), RO ) (νPMP)/(νOMO), RP ) (νPMP)/(νPMP) ) 1, δ ) MP/MC, Y˜F ) RFYF, YÕ ) ROYO, Y˜P ) YP, YÑ ) YN, ξ ) (e-m˜/r˜ - e-m˜)/(1 - e-m˜), β ) em˜ - 1, γ ) ˜ - 2r˜)/r˜2][d/(dr˜)] - [d2/ [(dT˜)/(dr˜)]s/[(dξ)/(dr˜)]s, and L( · ) ) {[(m (dr˜2)]}( · ) is the spherically symmetric convective-diffusive operator and Damkohler numbers for the gas-phase reaction are Dag )

[( )

rs2 F∞ kg D∞ νPMP

(νF+νO-1)

]

νFνFνOνO

(11)



Figure 8. Particle temperature, combustion rate, and radius as a function of time (T∞ ) 1133 K).

()

T˜∞ wg ) T˜

(νF+νO)

Y˜FνFYÕνO exp(-θg /T˜)

(12)

The transient variation of particle temperature is determined by the energy conservation equation

( )

c˜s dT˜ dT˜ - R20 ) 3 dτ dr˜

(

exp -

)

s

()

+m ˜ (1 - c˜s)T˜s - QDas1

() (

T˜∞ YÕ,s T˜s

)

θs,C-CO2 θs,C-O T˜∞ - (Q - 1)Das2 Y˜P,s exp + T˜s T˜s T˜s εR0(T˜s4 - T˜∞4 )/Bo (13)

2 where τ ) F∞D∞t/(Fsrs0 ), c˜s ) cs/cp, Q ) MCHC/(MFHCO), Bo ) 3 (F∞D∞cp)(cpRF/HCO) /(rs0σ), and R0 ) 1. The transient variation of particle radius is

dR2 ) -2m ˜ dτ

(14)


where R ) rs/rs0. 3.2. Comparison. Figure 7 shows variation of the particle lifetime as a function of the initial surface Damkohler number Das0. Comparisons were made between the calculations and the experimental results from ref 21 where the sample is lignite char with a size range of 160 ∼ 300 µm. The initial gas Damkohler number Dag0 was taken as 3.9 × 104. It can be seen that the particle lifetime decreases with increasing the initial surface Damkohler number, and the comparison is reasonable as far as the variation trend is concerned. 4. Results and Analysis Figures 8-10 are the temporal variations of particle temperature, dimensionless combustion rate, and particle size at ambient gas temperatures from 1133 to 1183 K. The particle temperatures calculated agree well with those measured. At (21) Ivanova, I. P.; Babii, V. L. Therm. Eng. 1966, 13, 70–76.

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lower temperature (T∞ ) 1133 K), the main surface reaction is 2C + O2 f 2CO, and the reduction reaction C + CO2 f 2CO has little effect on the combustion rate. The particle temperature could be higher than 1133 K, but under this ambient gas temperature the particle cannot be ignited yet. With the ambient temperature increasing (T∞ ) 1163 K), when the particle is heated to a sufficiently high temperature, the oxidation reaction is sped up and the gas-phase reaction CO + 1/2O2 f CO2 ignites. This can be seen from Figure 11. Figure 11 gives the temperature profiles and concentration profiles in the boundary layer of the particle. Prior to the particle ignition, the concentration field in the boundary layer of the particle hardly changes. After ignition, the gas temperature in the vicinity of the particle is far higher than the ambient gas temperature, and the concentrations of O2 and CO sharply decrease, indicating the establishment of a CO flame. Because the CO gas-phase reaction consumes the amount of O2 that can reach the particle surface, consequently the surface oxidation reaction quenches (see Figure 9). With a continuous increase in particle temperature, the reduction reaction is activated because of the abundance of CO2 generated by the gas-phase reaction. However, with the diminishment of the particle size, the gas-phase Damkohler number, which is sensitive to the square of particle radius, eventually becomes so small that the gas phase is extinguished. The surface oxidation reaction again dominates over the reduction reaction. At 1183 K, the characteristics of the combustion processes are the same as those at 1163 K, and the combustions are more violent. Figure 12 is an ignition diagram for a char particle with a diameter of 77 µm and ambient oxygen partial pressure of 0.21 atm. The experimental conditions and the kinetic parameters used in the models are stated in the Experimental Section. It can be seen that good agreement is achieved between the rigid continuous-film model and the experimental data in terms of

the temperature of the particle. However, the single-film model, still widely used in the combustion simulations, has some significant errors in its predictions of the ignition temperature (absolute error: about 115 K) and the temperatures following ignition (absolute error: e260 K) and hence should have some restrictions on its application. 5. Improved Char Combustion Model 5.1. Description. The possible reactions, including those occurring in the boundary layer of the carbon particle, are reactions I, II, and III. The model is formulated as Kd,O2 ) 2MCDm,O2 /(aRTm) ) 4MCDm,O2 /(xRTm)

(15)

Ks,O2 ) k' exp[-E'/(RTs)]

(16)

Kd,CO2 ) MCDm,CO2 /(aRTm) ) 2MCDm,CO2 /(xRTm)

(17)

Ks,CO2 ) k'' exp[-E''/(RTs)]

(18)

q) Pg,O2 +

1 1 a + 1Ks,O2 Kd,O2 b

(

1 Ks,CO2

1 Ks,O2

+

1 Kd,O2

(1 + ba ) -

+

[

1 1 Ks,O2

1 Ks,CO2

a b

Pg,CO2

) 1 a + 1- ) K ( b a 1 a bK + (1 - b ) K

Kd,CO2

(

)

1-

d,O2

d,CO2

]

d,CO2

(19)


Pg,CO2 + q'' )

1 Ks,CO2

+

aq bKd,CO2 1

Kd,CO2

(

1-


obtained. The detailed derivation of this model can be found in the Appendix. a b

(20)

)

q' ) q - q''

(21)

a a + (qH′′′ Ts ) Tg + (q'H' + q''H'' - Hr) 1 b λm

(

)

Hr)

a2 bλm

(22)

where Hr ) εσ(Ts4 - Tw4) Tf ) Tg + (qH′′′ - Hr)

a2 bλm

(23)

The location of the flame front b is determined according to the different combustion conditions. b is obtained by 2a , 1 + Kd,O2 /Ks,O2 b ) a,

b)

when Kd,O2 e Ks,O2 when Kd,O2 > Ks,O2

(24)

Considering the density to be a constant and the particle diameter varying, it yields 2q dx )dt Fs

(25)

Then the transient history of char particle combustion can be

5.2. Limiting Cases. 5.2.1. Kinetic Control of Surface Oxidation. When the combustion of a char particle is kinetically controlled, there is Ks,O2 , Kd,O2, and the reaction rate of surface reduction is zero, i.e., Ks,CO2 ) 0. Therefore, the overall combustion rate q ) Ks,O2Pg,O2 is obtained from the improved model, which is in accordance with the result given by the single-film model under kinetic control. 5.2.2. Complete Diffusion Control. At extremely high temperature, the combustion process is under diffusion control of CO2. Under this condition, Ks,O2 f ∞ and Ks,CO2 f ∞. This combustion state is that described by the double-film model. The combustion rate q ) Kd,O2Pg,O2 + Kd,CO2Pg,CO2 is obtained from the improved model, which is the theoretical maximum value for the combustion system. 5.2.3. Partial Diffusion Control. At an appropriately high temperature and for a certain particle size, if the reaction rate of CO2 reduction is very slow (Ks,CO2 f 0) and the reaction rate of surface oxidation greatly exceeds the diffusion rate of O2 (Ks,O2 . Kd,O2), the reaction is under partial diffusion control. Under this condition, the combustion rate is q ) 2Kd,O2Pg,O2/3, which shows that the combustion rate under O2 diffusion control region is 2/3 times less than the theoretical maximum when there is no CO2 in the ambient gas. 5.3. Comparisons. Transient particle heating is an important process in its combustion because the particle temperature has importance on the relative contributions of the various reactions

Figure 11. Temperature profiles and concentration profiles in the boundary layer of particle.

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It can be seen that good agreement was achieved between the improved model and the rigid continuous-film model in predicting the temperature of the particle. To obtain these results, the computation time for the complete curve using the continuousfilm model was about 50 h, while only 1∼2 s were needed using the improved model. The predictions by both the continuousfilm model and the improved model also agree well with the measured data. And what’s more, it is much easier for the present model to be integrated into the comprehensive computing codes of industrial pulverized coal flame than the continuousfilm model. 6. Conclusions Figure 12. Comparisons of the curves calculated by models with the experimental data from the present work.

Figure 13. Comparisons between experimental data and calculated curves.

Figure 14. Comparisons of calculations with experimental data from the present work.

which determine the particle combustion rate. Figure 13 gives the experimental data and the calculations using the improved model presented above at the same conditions. The experimental conditions and the kinetic parameters used in the model are stated in the Experimental Section. The devolatilized char ignites at 1163 K. The higher the ambient temperature, the shorter the burnout time and the higher the particle temperature will be. Comparisons between the measurement and the predictions for all cases are shown in Figure 14. It can be seen that (10% error is obtained for most data points, indicating the predictions reasonably agree with the experimental data. Comparisons were performed among different char combustion models for a char particle with a diameter of 77 µm and ambient oxygen partial pressure of 0.21 atm (see Figure 12). Three kinds of models, continuous-film model, single-film model, and the present improved model, were used to calculate the ignition and combustion at different ambient temperatures.

An FTIR experimental system was established for online temperature measurement. The calculations by using rigid continuous film satisfactorily agree with the experimental data. The calculations by using the single-film model, still widely used in combustion modeling, have some significant errors in its predictions for the ignition temperature and the combustion following ignition, compared to the experimental results. Therefore, the single-film model should have some restrictions on its application, and it is necessary to develop a novel combustion model for a char particle considering most of the physicochemical processes involved. Taking into consideration the influences of volumetric reaction of CO, finite-rate heterogeneous oxidation of O2, and reduction of CO2, an improved combustion model was put forward in this work. Explicit algebraic expressions for the overall rate of combustion, the surface temperature of the particle, and the gas temperature at the flame sheet were given by this model. The transition to various limiting combustion conditions can be easily obtained using the improved model. Compared with the single-film model, predictions for particle temperature by the improved model were in much better agreement with those predicted by the rigid continuous-film model and the experimental data, while the computation time of the improved model is much shorter than that using the continuous-film model. In addition, the improved model is much easier to be integrated into the comprehensive computing codes for industrial pulverized coal flame than the continuous-film model. Acknowledgment. The authors of this paper gratefully acknowledge financial support from The Special Fund of The Key Fundamental Research of China, Grants No. 2004CB217703 and No. 2006CB200303, and the great help from Prof. P.M. Walsh in the University of Alabama, USA, in preparing the manuscript.

Appendix Derivation of Improved Char Combustion Model. Considering reactions I-III and assuming an infinitesimally thin flame sheet is formed around the char particle due to the homogeneous oxidation of CO, it is assumed that the carbon particle is a uniform sphere and is burned in a quiescent atmosphere. Neglecting the effects of Stefan flow, the diffusion flux of oxygen for the surface oxidation (reaction I) is GO2(r) )

DO2MO2 dPO2

(A1) RT dr Since there is no oxygen consumed in [a, b], the spherical shell between a and b, the diffusion flux of oxygen should satisfy the following equation (see Figure A1a)



Pg,O2 - Pf,O2 )

2a(q' + q'') bKd,O2

(A8)

By resolving eq A5 and eq A8 simultaneously, also Pg,O2 - Ps,O2 )

q' a (q' + q'') 2a 1+ Kd,O2 b Kd,O2 b

(

)

(A9)

The partial pressure of oxygen at the particle surface is Figure A1. Partial pressure profiles of gaseous species in the boundary layer of the particle.

q' Ks,O2

Ps,O2 )

where Ks,O2 ) k′ exp[-E′/(RTs)], then Pg,O2 ) q'

[

1 1 a + 1Ks,O2 Kd,O2 b

(

)] + (q' + q'') bK2a

d,O2

(A10)

Finally, the overall combustion rate of carbon, q, is expressed as q ) q' + q'' ) Figure A2. Temperature profile in the boundary layer of the particle.

4πr2GO2(r) ) 4πa2GO2(a)

(A2)

Substituting eq A2 into eq A1, and integrating from a to b, using average values for the constants Tm and Dm, yields Pf,O2 - Ps,O2 )

aGO2(a)RTm Dm,O2MO2

(1 - ba )

(A3)

If the consumption rate of carbon by surface oxidation (reaction I) is q ′, then we have q'MO2

GO2(a) )

(A4)

2MC

Pf,O2 - Ps,O2

Pg,O2 + q''

(

q)

)

2MCDm,O2 aRTm

)

4MCDm,O2 xRTm

then Pf,O2 - Ps,O2 )

q' a 1Kd,O2 b

(

)

(A5)

Similarly, in [b,∞], the space outside the flame front, 4rπ2GO2(r) ) 4bπ2GO2(b). Integrating eq A1 from b to ∞ yields Pg,O2 - Pf,O2 )

bGO2(b)RTm Dm,O2MO2

(A6)

Since all of the CO at the flame sheet burns to CO2, the mass flux of O2 arriving at the flame front is GO2(b) )

a2(q' + q'')MO2 MCb2

1

[

Ks,O2

Let Kd,O2 )

[

q' 1 1 a + 1q' + q'' Ks,O2 Kd,O2 b

(A7)

where q ′′ is the consumption rate of carbon by the heterogeneous reduction of CO2 (reaction I). Putting eq A7 into eq A6, we have

(

)] + bK2a

d,O2

(A11)

In eq A11, 1/Ks,O2, (1 - a/b)/Kd,O2, and 2a/(bKd,O2) represent the resistance of the surface oxidation reaction, the resistance of oxygen diffusion between the surface and the flame sheet, and the resistance of oxygen diffusion outside the flame sheet, respectively. It can be seen from this equation, compared with the case of no reduction being considered (i.e., q ′′ ) 0), that the heterogeneous reduction of CO2 reduces, equivalently, the resistance of the surface oxidation reaction and the resistance of oxygen diffusion between the surface and the flame sheet by the factor q ′/(q ′ + q ′′). By rearranging eq A11, q can also be expressed as

Equation A3 then becomes aq'RTm a ) 12MCDm,O2 b

Pg,O2

1 1 a + 1Ks,O2 Kd,O2 b

(

+

1 Kd,O2

(1 + ba )

)]

(A12)

Equation A12 shows that the combustion rate of carbon, considering the heterogeneous reduction of CO2, is equivalent in form (only in form, since the particle temperature and then Ks,O2 will change) to the case of only surface oxidation considered, but the effective oxygen partial pressure in the ambient gas is increased by an amount q ′′[1/(Ks,O2) + 1/(Kd,O2)(1 - a/b)]. In a similar way, for the heterogeneous reduction of CO2 (reaction II), from the diffusion equation for CO2 in [a, b] (see Figure A1b), one can write Pf,CO2 - Ps,CO2 )

q'' a 1Kd,CO2 b

(

)

(A13)

where Ps,CO2 ) q ′′/Ks,CO2, Ks,CO2 ) k′′ exp(-E′′/R0Ts), Kd,CO2 ) (MCDm,CO2)/(aRTm) ) (2MCDm,CO2)/(xRTm). Then q'' )

Pf,CO2 1 Ks,CO2

+

1 Kd,CO2

(1 - ba )

(A14)

In the region [b, ∞], the relationship between the outward diffusion of CO2 and the inward diffusion of O2 is

2884


Pf,CO2 - Pg,CO2

GCO2(b)MO2Dm,O2

)

Pg,O2 - Pf,O2

Yu and Zhang

GO2(b)MCO2Dm,CO2

)

no consumption of CO and O2 by the reaction, the partial pressures of CO and O2 at the flame front are

Dm,O2 Dm,CO2

Pf,CO ) Pg,CO +

thus Dm,O2

Pf,CO2 ) Pg,CO2 +

Dm,CO2

(Pg,O2 - Pf,O2) ) Pg,CO2 +

Pf,O2 ) Pg,O2 -

2aq Dm,O2 bKd,O2 Dm,CO2

(A15)

Since Kd,CO2 ) Kd,O2Dm,CO2/2Dm,O2, finally Pf,CO2 an be written as aq bKd,CO2

Pf,CO2 ) Pg,CO2 +

(A16)

q'' )

1 Ks,CO2

+

Kd,CO2

a 1b

(

aq bKd,CO2

Pg,O2 +

1 Ks,CO2

q)

+

1

(A17)

)

Kd,CO2

1 1 a + 1Kd,O2 b a Ks,O2 1b

(

(

1 1 a + 1+ Ks,O2 Kd,O2 b

(

)]

) (A18)

and finally q) 1 Pg,O2 +

Ks,O2 1 Ks,CO2

1 Ks,O2

+

1 Kd,O2

(

a 1+ b

)

+ +

[

1 Kd,O2 1

(

1-

1 Ks,O2 1 Ks,CO2

)

a b

Pg,CO2

) 1 a + 1- ) K ( b a 1 a bK + (1 - b ) K

Kd,CO2

(

a b

1-

]

d,O2

d,CO2

d,CO2

(A19)

The surface temperature of the char particle can also be derived similarly (for the notation see Figure A2). The result is

(

Ts ) Tg + (q'H' + q''H'' - Hr) 1 -

a a + (qH′′′ b λm

)

Hr)

a2 bλm

(A20)

where Hr ) εσ(Ts4 - Tw4). Th temperature of the flame is Tf ) Tg + (qH′′′ - Hr)

a2 bλm

(

(A21)

The condition for locating the flame front b in the model is “the fastest rate of CO combustion” (or “the most faVorable place for CO oxidation”). Under a hypothetical condition of

)]

(A23)

)

(A24)

From eq 24, the location of the flame front b can be obtained directly. b)

)[

[

(A22)

1 2aq 1 a ) + 1q bKd,O2 Ks,O2 Kd,O2 b

(

Putting eq A17 into eq A12 yields Pg,CO2 +

)

1 1 a 1 a + 1) Ks,O2 Kd,O2 b Kd,O2 b

aq + bKd,CO2 1

) (

1 a 1 a q≈2 q Kd,CO b Kd,O2 b

where Kd,CO is defined as MCDm,CO/aRTm ) 2MCDm,CO/xRTm, and physically also Dm,CO ≈ Dm,O2. The reaction I is first-order in CO and 0.3th-order in O2. So, the position most favorable for CO oxidation should have a higher Pf,CO than Pf,O2. Then, it is simply assumed that Pf,CO is twice Pf,O2, which have been applied in the homogeneous ignition model by Annamalai. The location of the flame front b is obtained by

Substituting the above equation into eq A14 gives Pg,CO2

(

2a Kd,O2 1+ Ks,O2

(A25)

The condition for the equation to satisfy is Kd,O2 e Ks,O2. When Kd,O2 > Ks,O2, b < a would be obtained, which is physically unrealistic. Therefore, in this case, b ) a is taken. In conclusion, the location of the flame front b can be written as 2a , 1 + Kd,O2 /Ks,O2 b ) a,

b)

when Kd,O2 e Ks,O2 when Kd,O2 > Ks,O2

(A26)

It is very attractive that the expression for the flame location is simple and explicit and makes it possible to establish a fully explicit model for the combustion of a carbon particle. Considering the density to be a constant and the particle diameter varying, it yields 2q dx )dt Fs

(A27)

Then, the transient history of char particle combustion can be obtained. Nomenclature a ) Radius of particle (m) b ) Radius of flame front (m) c ) Specific heat (J kg-1 K-1) D ) Diffusion coefficient (m2 s-1) E ) Activation energy of surface reaction (J mol-1) G ) Diffusive mass flux, (kg m-2 s-1) H ) Heat of reaction (J kg(C)-1) HCO ) Heat of reaction for CO + 1/2O2 f CO2 (J kg(C)-1) Hr ) Radiative heat flux leaving particle surface (kW m-2) k ) Pre-exponential factor of surface reaction (m s-1 or kg m-2 s-1 Pa-1) K ) Reaction rate coefficient (kg m-2 s-1 Pa-1) m ) Mass flux corresponding to combustion rate (kg s-1) M ) Molecular weight (kg kmol-1) P ) Partial pressure (Pa or atm) q ) Overall reaction rate of carbon per unit surface area (kg m-2 s-1) Q ) Conductive heat flux (kW m-2)

Experimental and Modeling Study on Char Combustion r ) Radial distance from carbon particle (m) R ) Universal gas constant (J mol-1 K-1) S ) Surface area of particle (m2) t ) Time (s) T ) Temperature (K) w ) Reaction rate (kg m-2 s-1or kg m-3 s-1) x ) Diameter of particle (m) Y ) Mass fraction, / R ) Stoichiometric mass ratio of product (CO2) to reactant ε ) Emissivity of particle surface λ ) Thermal conductivity (W m-1 K-1) ν ) Stoichiometric coefficient or reaction order F ) Density (kg m-3) σ ) Stefan-Boltzmann constant (W m-2 K-4)

Energy & Fuels, Vol. 23, 2009 2885 N ) N2 O ) O2 p ) Constant pressure P ) CO2 r ) Radiation s ) Particle surface or soot ν ) wavenumber w ) wall surface CO-O ) Reaction 2CO + O2 f 2CO2 C-O ) Reaction 2C + O2 f 2CO C-CO2 ) Reaction C + CO2 f 2CO 0 ) Initial value ∞ ) ambient Superscripts

Subscripts C ) Carbon d ) Diffusion f ) Flame front F ) CO g ) Gas m ) Averaged

b ) blackbody ′ ) Reaction 2C + O2 f 2CO ′′ ) Reaction C + CO2f 2CO ′′′ ) Reaction C + O2 f CO2 ∼ ) Dimensionless quantity EF900018B

Experimental and Modeling Study on Char Combustion - Energy

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