Devolatilization Characteristics of Coal Particles Heated with a CO2

Energy Fuels 2010, 24, 18–28 Published on Web 09/15/2009

: DOI:10.1021/ef900519b

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Devolatilization Characteristics of Coal Particles Heated with a CO2 Laser Controlled by Double Shutters: A Simulation Investigation† Hong Gao,*,‡ Jicheng He,§ and Masakatsu Nomura

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‡ Department of Thermal Energy and Power Engineering, Vehicle and Energy College, Yanshan University, 438 West Hebei Avenue, Qinhuangdao, Hebei, 066004, People’s Republic of China, §Department of Thermal Energy Engineering, Northeastern University, 11-Alley 3, Wenhua Road, Heping District, Shenyang, Liaoning,110004, People’s Republic of China, and Department of Applied Chemistry, Faculty of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan. †Presented at the 2009 Sino-Australian Symposium on Advanced Coal and Biomass Utilisation Technologies.

Received May 24, 2009. Revised Manuscript Received July 29, 2009

An empirical model was established based on measurements of devolatilization characteristics of coal particles (18.7%, 32.7%, and 43.0% VM; 0.14, 0.20, and 0.30 mm, respectively) heated at a heating rate of 103-104 K/s by a well-controlled CO2 laser with double shutters and a high-accuracy two-color pyrometer. The conclusions obtained are as follows: (1) particle temperature (Tp), volatile yield (V), heating rate (HR), and in situ energy density flux (Fed) during devolatilization can be well-predicted by solving an energy conservation equation and a devolatilization rate equation with two competing reaction rates; (2) the preexponential factor and activation energy of the two reactions are A1 = (1.7249-1.8936)
102 s-1, E1 = (2.6248-3.5447)
104 J/mol, A2=2.6
106 s-1, and E2=1.6740
105 J/mol, respectively, which are obtained by fitting our experiment data; (3) the final volatile yield (Vf) is dependent on the laser intensity (QL), the particle size (Dn), and the proximate volatile matter content (V0), and it can be well-predicted by a regressive equation of Vf with QL, Dn, and V0; (4) a modified Merrick’s heat capacity correlation can be used to predict the temperature history of coal particles heated at a rate of 103-104 K/s with excellent agreement; (5) the heats of devolatilization, which are given as -0.5244, -0.6629, and - 0.7348 MJ/kg for the three coals used in this study, are suitable values for predictions; (6) the sum of the heat of devolatilization (ΔHd) and energy loss per unit mass volatile yield (ΔHvl), which can be represented as ΔHd þ ΔHvl=-0.01046 MJ/kg, is a suitable value for predicting particle temperatures and volatile yields for all three coals; (7) the measured histories of weight loss are imperative for predicting the temperature and the devolatilization kinetics of coal particles heated at a high heating rate; and (8) the swellingshrinking ratios, absorptivity, emissivity, thermal capacity, and heat of devolatilization of coal particles at high heating rates should be measured for better predictions.

few classical model studies3-17 correlate the total weight loss and tar yields versus temperature or pressure; however, all of these models are contradicted by the observed absence of size dependence, and several other inconsistencies with observed behavior remain unresolved. In the second modeling category, coal is recognized as a cross-linked macromolecular network, and devolatilization is explicitly analyzed as a bona fide depolymerization. Therefore, these models necessarily include a postulated submodel for coal structure and constitution. Several investigators have used statistical methods to predict how the coal structure behaves when subjected to thermally induced bridge breaking, cross-linking, and mass-transport processes. Gavalas et al.18

Introduction Generally speaking, model studies on the devolatilization of coal fall into two primary categories: classical theory and the theory of depolymerization of macromolecular structure of coal. The classical devolatilization theory began with the pioneering work of Howard and co-workers at MIT and has been well-reviewed by Howard1 and Suuberg.2 Quite a *Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Howard, J. B. In Chemistry of Coal Utilization, 2nd Supplementary Volume; Elliot, M. A., Ed.; Wiley: New York, 1981; Chapter 12. (2) Suuberg, E. M.; Schlosberg, R. H. In Chemistry of Coal Conversion; Plenum Press: New York, 1985; Chapter 4. (3) Kobayashi, H. J.; Howard, B.; Sarofim, A. F. In 16th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1977; p 411. (4) Anthony, D. B.; Howard, J. B.; Hottel, H. C.; Meissner, H. P. In 15th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1975; p 1303. (5) Ubhayakar, S. K.; Stickler, D. B.; Rosenberg, C. W. Gannon, R. E. In 16th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1977; p 427. (6) Suuberg, E. M.; Peters, W. A.; Howard, J. B. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 37. (7) Smoot, L. D.; Pratt, D. T. Pulverized-Coal Combustion and Gasification, Plenum Press: New York, 1979. (8) Merrick, D. Fuel 1983, 62, 534. r 2009 American Chemical Society

(9) Merrick, D. Fuel 1983, 62, 540. (10) Merrick, D. Fuel 1983, 62, 547. (11) Maloney, D. J.; Jenkins, R. G. In 20th International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1984; p 1435. (12) Fong, W. S.; Khalil, Y. F.; Peters, W. A.; Howard, J. B. Fuel 1986, 65, 195. (13) Morgan, M. E.; Jenkins, R. G. Fuel 1986, 65, 757. (14) Oh, M. S.; Peter, W. A.; Howard, J. B. AIChE J. 1989, 35, 775. (15) Fu, W.; Zhang, Y.; Han, H.; Wang, D. Fuel 1989, 68, 505. (16) Zhang, Y. P.; Mou, J.; Fu, W. B. Fuel 1990, 69, 401. (17) Fu, W. B.; Yu, W. D. Fuel 1992, 71, 793. (18) Gavalas, G. R.; Cheong, P. H.; Jain, R. Ind. Eng. Chem. Fundam. 1981, 20, 122.

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used statistical methods to predict the release of monomers from a randomly connected network. The model of Niksa and Kerstein applied percolation theory in a model called DISARAY,19 which extended their previous model that had been built on chain statistics.20,21 Grant et al.22 applied percolation theory in a model called chemical percolation devolatilization (CPD). Solomon et al.23-25 used Monte Carlo methods in a network model called the devolatilization, vaporization, and cross-linking (DVC) model. This was their previous model for linear polymers.26,27 The DVC model was combined with their functional group (FG) model27,28 to produce the general FG-DVC pyrolysis model. Kerstein29 and Niksa30-35 used FLASHCHAIN theory for rapid coal devolatilization. As mentioned by Niksa,29 the depolymerization models depart from classical theory in two respects: (1) no model includes secondary redeposition of released volatile into solid residues within the char (instead, char formation is treated as the reintegration of potential tar precursors in the condensed phase); and (2) explicit submodels of coal structure and constitution are the basis for a bona fide depolymerization and cross-linking mechanism. The performance of these models clearly surpasses earlier milestones. For any particular coal type, the pressure, temperature, heating rate, reaction time, and particle size can be correlated with depolymerization models. Although yields and tar molecule weight distribution are available, a coherent theory for coal type effects is the principal remaining imperative for the characterization of devolatilization rates and yields. Mass-transport resistance for pulverized coals has often been neglected for the models. In addition, it is difficult to determine some important parameters in these models. So far, the applications of classical models and depolymerization models to the devolatilization of coal particles heated with a special heating source, such as a laser, remain challenging work. Maloney and co-workers36 developed a novel system that incorporates an electrodynamics balance and a pulsed-laser radiation source to isolate and rapidly heat individual particles, for monitoring rapid changes in particle size and temperature during coal devolatilization at heating rates representative of high-intensity combustion environments. Measured temperature histories were compared with theoretical estimates of the temperature response of rapidly

heated coal and carbon particles. Measurements and model predictions for 135-μm-diameter carbon spheres were in excellent agreement using property data correlation commonly applied in modeling coal devolatilization and combustion behavior. However, model predictions for coal particles significantly underestimated (on the order of 50%) the observed heating rates for coal particles with diameters of 115 μm, using the same property correlation. Potential reasons for this may include inadequate understanding of relevant coal mass and heat transfer, as well as failure to account for the changes in particle size and shape, which lead to large errors in the predicted temperature histories and associated devolatilization rates. After careful analysis and comparison with the work of Fletcher37 and Solomon et al.,38 they concluded that these differences were due in large part to the thermal properties, particle shape, and mass assumptions that were applied in their modeling. Sampath et al.39 investigated the impact of particle shape and mass, characterized external surface area, volume, mass, and density of individual coal particles prior to measuring their temperature response under rapid heating conditions. They indicated that the large discrepancies between temperature measurements and model predictions reported by Maloney et al.36 and others37,38 were predominantly due to the thermal property assumptions used to model the coal behavior. Maloney et al.40 critically evaluated the thermal property assumptions applied in coal combustion modeling and indicated that existing thermal property data such as that of Merrick9 have exhibited a steady increase in heat capacity and thermal conductivity with increasing temperature and are limited to slow heating conditions. They found that the application of thermal property correlations based on these data resulted in substantial underprediction of the rise in coal temperature when compared with corresponding measurements at combustion-level heat fluxes. They hypothesized that, at combustion-level heating rates (104-105 K/s), coal structural changes are delayed, and attendant increases in heat capacity and thermal conductivity are pushed to higher temperatures or require significant hold times to become manifest. Sampath et al.41 determined that, until the point when volatile evolution commences, the application of room-temperature values for coal heat capacity, thermal conductivity, and a heat of devolatilization of -250 cal/g (or -1.046
106 J/kg) as fit parameters yield excellent agreement between measurements and model projections. Maswadeh et al.42 developed a laser devolatilization gas chromatography/mass spectrometry (GC/MS) technique for single coal particles to identify substantial numbers of pyrolysis products from single coal particles in the size range of 50150 μm. Reliable temperature/time profiles of single coal particles during rapid laser heating were obtained using a specially designed two-wavelength radiation thermometer module with an integral video microscope. Note that the coal tar yield obtained in this work exhibit rather scattered results

(19) Niksa, S.; Kerstein, A. R. Fuel 1986, 66, 1389. (20) Niksa, S.; Kerstein, A. R. Combust. Flame 1986, 66, 95. (21) Niksa, S. Combust. Flame 1986, 66, 111. (22) Grant, D. M.; Pugmire, R. J.; Fletcher, T. H.; Kerstein, A. R. Energy Fuels 1989, 3, 175. (23) Squire, K. R.; Solomon, P. R.; Ditarant, M. B.; Carangelo, R. M. Am. Chem. Soc,. Div. Fuel Chem., Prepr. 1985, 30 (1), 186. (24) Solomon, P. R.; Squire, K. R.; Carangelo, R. M. In Proceedings of the International Conference on Coal Science; Pergamon Press: Sydney, Australia, 1985; p 945. (25) Solomon, P. R.; Squire, K. R. Am. Chem. Soc., Div. Fuel Chem., Prepr. 1985, 30 (4), 47. (26) Solomon, P. R.; King, H. H. Fuel 1984, 63, 1320. (27) Solomon, P. R.; Hamblen, D. G.; Carangelo, R. M. Combust. Flame 1988, 71, 137. (28) Solomon, P. R.; Hamblen, D. G.; Carangelo, R. M. Energy Fuels 1988, 2, 405. (29) Niksa, S.; Kerstein, A. R. Energy Fuels 1991, 5, 647. (30) Niksa, S. Energy Fuels 1991, 5, 665. (31) Niksa, S. Energy Fuels 1991, 5, 673. (31) Niksa, S. Energy Fuels 1991, 5, 673. (32) Niksa, S. Energy Fuels 1994, 8, 659. (33) Niksa, S. Energy Fuels 1994, 8, 671. (34) Niksa, S. Energy Fuels 1995, 9, 467. (35) Niksa, S. Energy Fuels 1996, 10, 173. (36) Maloney, D. J.; Monazam, E. R.; Woodruff, S. D.; Lawson, L. O. Combust. Flame 1991, 84, 220.

(37) Fletcher, T. H. Combust. Sci. Technol. 1989, 63, 89. (38) Solomon, P. R.; Serio, M. A.; Carangelo, R. M.; Markham, J. R. Fuel 1986, 65, 182. (39) Sampath, R.; Maloney, D. J.; Zondlo, J. W.; Woodruff, S. D.; Yeboah, Y. D. In 26th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1996; p 3179. (40) Maloney, D. J.; Sampath, R.; Zondlo, J. W. Combust. Flame 1999, 116, 94. (41) Sampath, R.; Maloney, D. J.; Zondlo, J. W. In 27th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1998; p 2915. (42) Maswadeh, W.; Arnold, N. S.; McClennen, W. H.; Tripathi, J. D.; Meuzelaar, H. L. C. Energy Fuels 1993, 7, 100.

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((20% uncertainty at the 95% confidence level), which, to a large extent, is due to the particle size and shape variations and also the considerable amount of heterogeneity between different coal particles. Gao et al.43 quantitatively studied the swelling characteristics (time-resolved swelling ratio, interval time between swelling and shrinking of bubble, etc.) of coal particles heated using the CO2 laser heating system via the combined application of a high-speed video camera with an image analysis system under atmospheric pressure in nitrogen. They observed that the swelling characteristics of coal particles were dependent on laser intensity, particle size, and coal properties. The swelling changes under laser heating were incorporated into the density calculation of coal particles on heating. Bhattacharya and Wall44 investigated the development of emittance of coal particles during devolatilization and char particles (45-125 μm) at temperatures of 473-1273 K and discussed the magnitude of potential errors in pyrometric temperature measurement. Recently, Tripathi et al.45,46 measured and modeled temperature profiles of individual carbonaceous particles and coal particles from three types of different rank coals, using a CO2 laser pyrolysis system with a two-color micropyrometry under pulverized coal combustion conditions. They predicted that the intraparticle gradients between the surface temperature and the bulk average radius temperature fall within the estimated errors range (100 K) of two-color pyrometry measurements and thus can be ignored for the particle size range of 80-120 μm. They indicated that using measured temperature histories was more reliable than using predicted average bulk temperatures for kinetics calculation. Gao et al.47 published their results on the devolatilization characteristics of coal particles heated with a CO2 laser, in which they investigated the group features rather than a single particle to avoid the potential problems caused by heterogeneities of coal particles and supplied reliable data which could be used for temperature and kinetics calculations under laser heating conditions. More recently, Biagini et al.48 studied the specific heat, size, and shape distribution, and density variation of low- and high-volatile-matter coal particles after devolatilization with CO2 laser in an electrodynamic balance (EDB). They indicated that the knowledge of properties of chars after severe devolatilization is crucial for both modeling purposes and practical applications. The devolatilization of coal particles is significantly affected by the operating conditions used, with a direct influence on the particle temperature, volatile yield, and subsequent char gasification or combustion step. In addition, model investigation faces a challenge, because few data can be found in the literature about thermal properties of coal and chars under severe thermal conditions that are similar to industry practices. Generally, the conditions used in laboratory facilities, such as a thermogravimetry (TG) balance (low temperature, low heating rate (HR), long residence time), are extremely different from those encountered in full-scale plants, so that parameters obtained cannot be directly applied for design purposes or comprehensive modeling.

Devolatilization processes play a very important role in coal gasification and combustion, and it is generally agreed that the chemical differences among the different coals affect the gasification and combustion rates, primarily through their devolatilization behaviors. The extent of coal devolatilization during gasification and combustion also has a strong effect on char reactivity. For these reasons, it is critical to predict temperature and weight loss of coal particles during devolatilization at high heating rates that are similar to industry reality. Over the past 30 years, models of coal devolatilization moved from simple empirical expressions of total mass release, involving one or two rate expressions,3-5 to more-complex descriptions of the chemical and physical processes.19-35 Nevertheless, simple models, such as that developed by Kobayashi et al.3 and Ubhayakar et al.,5 still have importance and are valuable in practical applications.49,50 The objective of this work is to present and discuss a simple empirical kinetic model that describes the devolatilization process of coal particles heated with CO2 laser at a high heating rate (103-104 K/s) and under pyrolysis conditions. In this model, the well-known classical two-competing reaction mechanism proposed by Kobayashi et al.3 was used; the proximate volatile matter content, coal particle size, laser intensity, and in situ energy density per surface area of coal particles were incorporated. The kinetics data for the devolatilization were obtained by analyzing the experimental data.47 The major reason for this interest in obtaining a better understanding of the pyrolysis, gasification, and combustion of coal lies in the increasing concern for the environmental impact of large-scale gasification and combustion processes. Another reason for this work is to solve some problems that remain from our early work.47 Formation of Simulation Model. As discussed in our earlier paper,47 the devolatilization rate is dependent on the volatile matter content, particle size, particle temperature, laser intensity, and heating rate. If a model that includes these parameters can be established, the predictions for the devolatilization process of coal particles under laser heating conditions will become possible. So far, two general models were proposed, one of which, developed by Fu et al.,15 belongs to a classical model. The kinetics data are not dependent on coal rank, but rather only on the final particle temperature or furnace temperature. However, the final temperature of coal particles heated with a laser is unknown before heating. Another general model, the so-called FG-DVC model, belongs to a depolymerization model, in which there are some difficulties in obtaining optimum adjustable parameters. Considering the simplicity and practicality of the model for application, a relatively simple two-competing-reaction scheme proposed by Kobayashi et al.3 was used to establish an empirical model under laser heating conditions and the model parameters were obtained by fitting our experimental data.47 To establish the model, the following assumptions were made: (1) A spherical coal particle is heated by a CO2 laser from one side with a cross section of πDC2/4;40,43,51

(43) Gao, H.; Murata, S.; Nomura, M.; Ishigaki, M.; Qu, M.; Tokuda, M. Energy Fuels 1997, 11, 730. (44) Bhattacharya, S. P.; Wall, T. F. Fuel 1999, 78, 511. (45) Tripathi, A.; Vaughn, C. L.; Maswadeh, W.; Meuzelaar, H. L. C. Thermochim. Acta 2002, 388, 183. (46) Tripathi, A.; Vaughn, C. L.; Maswadeh, W.; Meuzelaar, H. L. C. Thermochim. Acta 2002, 388, 199. (47) Gao, H.; Qu, M.; Ishigaki, M. Energy Fuels 2006, 20 (5), 2072. (48) Biagini, E.; Pintus, S.; Tognotti, L. Proc. Combust. Inst. 2005, 30, 2205.

(49) Mondal, S. S. Int. J. Therm. Sci. 2008, 47, 1442. (50) Higuera, F. J. Combust. Flame 2009, 156, 1023. (51) Maloney, D. J.; Lawson, L. O.; Fasching, G. E.; Monazam, E. R. Rev. Sci. Instrum. 1995, 66, 3615.

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(2) The sphericity correction factor is 0.75 for all coal particles, irrespective of coal rank and particle size;46 (3) Convective and radiative heat losses are taken on an entire spherical particle surface (πDC2);40,43,46,51 (4) Conductive heat losses from the particle surface to the sample plate are neglected; (5) The devolatilization of coal particles consists of two competing reactions;3,5,49,50 and (6) The devolatilization reactions are exothermic.9,51 Based on the aforementioned assumptions, a model to describe the devolatilization process of coal particles in nitrogen under laser heating conditions is established. Energy Conservation Equation and In Situ Energy Density Flux (Fed). The transient temperature and heating rate of coal particles are calculated using the energy conservation equation that is decribed by eq 1; the net energy received per unit area of coal particles (expressed in terms of W/m2), Fed is evaluated by eq 2. h i 6 ð1=4ÞRQL -hBFC ðTp -Tb Þ -εσðTp 4 -Tb 4 Þ dTp ¼ dt SCF FDc Cpc dV ΔHd þΔHvl dt Cpc 1 Fed ¼ RQL -hBFC ðTp -Tb Þ -εσðTp 4 -Tb 4 Þ 4 1 dV SCF FDc ðΔHd þΔHvl Þ 6 dt

The convective heat-transfer coefficient h is calculated using eq 4: NNu Kg ð4Þ h ðW m-2 K-1 Þ ¼ Dc The Nusselt number NNu is calculated using eq 5: NNu ¼ 2:6þ0:6ðNRe Þ1=2 ðNPr Þ1=3

The Reynolds number (NRe) and the Prandtl number (NPr) are calculated using eqs 6 and 7, respectively: NRe ¼

Dc F g u μg

ð6Þ

NPr ¼

Cg 3 μg Kg

ð7Þ

where Fg, Cg, μg, u, and Kg are, respectively, the density, specific heat capacity, viscosity, velocity, and thermal conductivity of the surrounding nitrogen gas. These parameters are determined using the average of the surface temperature of the particles (Tp) and the surrounding gas temperature (Tg): (Tg þ Tp)/2. To determine the heat-transfer coefficient (hBFC), we used the method outlined by Bird et al.52 and modified by Fletcher et al.53 It is calculated using eqs 8 and 9:

ð1Þ

hBFC ðW m-2 K-1 Þ ¼ ð2Þ B ¼

where dTp/dt is the instant heating rate and dV/dt is the instant volatile yield rate. The parameters are defined as follows: Cpc is the solid (coal and char) heat capacity (expressed in units of J kg-1 K-1); DC is the diameter of the coal particle (given in meters); hBFC is the convective heat-transfer coefficient with blow factor correction at the coal particle surface (given in terms of W m-2 K-1); ΔHd is the heat of devolatilization (given in units of J/kg), which is generally exothermic;9 ΔHvl is the energy loss per unit mass volatile yield (also given in units of J/kg); SCF is the sphericity correction factor for coal particles; Tb is the temperature of the gas boundary layer surrounding a coal particle with an average surrounding gas temperature (Tg) and coal particle temperature (Tp); QL is the laser intensity (given in units of W/m2); R, ε, and F represent the absorptivity, emissivity, and density (kg/m3) of coal particles, respectively; and σ is the Stefan-Boltzmann constant (σ=5.669
10-8 W m-2 K-4). The other parameters used in eqs 1 and 2 are determined in the following paragraphs. The density of coal particles upon heating is described using eq 3, and the change in density is affected by the change in particle size and volatile yield during devolatilization: F ð1 -VÞ F ¼ 0 rvs

ð5Þ

hB eB -1 

 Cg dmc 2πDc Kg dt

ð8Þ ð9Þ

where B is the transfer number for convective heat transfer and mc is the mass of the coal particle. The specific heat capacity (Cpc) of as-received coal is calculated with Merrick’s model.9 The specific heat of dry ash-free (daf) coal (c1, expressed in terms of J kg-1 K-1) is calculated using eqs 10 and 11:9 2 ! !3   R 4 389 1800 5 g1 þ2g1 c1 ¼ ð10Þ a Tp Tp g1 ðZÞ ¼

expðZÞ ½expðZÞ -1=Z2

ð11Þ

where a is the mean atomic weight, g1 is the Einstein specific heat function, R is the gas constant (R=8.314 J mol-1 K-1), and Z is a dummy variable. The specific heat of the ash (c2, expressed in units of J kg-1 -1 K ) is calculated using eq 12.9 c2 ¼ 754þ0:586Tp ð12Þ The specific heat of moisture (c3) has a value of 4187 J kg-1 K . The specific heat capacity (Cpc) of as-received coal is calculated using eq 13:9 3 X Cpc ðJ kg-1 K-1 Þ ¼ wi ci ð13Þ -1 9

ð3Þ

where F0 is the initial density of the coal particles; V the volatile yield; the rvs is a volume swelling ratio of coal particles on heating, which is measured by applying the method used in our early work.43 The absorptivity is taken as 0.9843 for K coal, 0.8702 for W coal, and 0.8269 for P coal, respectively. (Note: W coal denotes a South African highly volatile weak cooking coal called Witbank; K coal denotes a Rosier bituminous coal, and P coal denotes an Indonesia bituminous coal called Prima.)

i ¼1

where wi represents the mass fractions in the as-received coal of daf coal, ash, and moisture. (52) Bird, R. D.; Steward, W. E.; Lightfoot, E. N.; Transport Phenomena; Wiley: New York, 1960. (53) Fletcher, T. H. Combust. Sci. Technol. 1989, 63, 89.

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in which a pair of reactions with different rate parameters and volatile yields competes to pyrolyze the raw coal.

where R1 and R2 are mass stoichiometric coefficients. At lower temperatures, the first reaction is dominated by the yield of R1. At higher temperatures, the second reaction is dominated by the yield of R2. V1 and V2 are the volatile yields at low temperature and high temperature, respectively; R1 and R2 are the residues at low temperature and high temperature, respectively. The para1 meters k1 and k2 are rate constants:k1 ¼ A1 expð -E RT Þ and -E2 k2 ¼ A2 expð RT Þ. The overall weight loss (ΔW) was calculated 2 k2 as ΔW ¼ ðR1 kk11 þR þk2 Þf1 -exp½ -ðk1 þk2 Þtg. The advantages of this model are (i) its simplicity for practical applications, in which only four parameters are needed; (ii) the model will be reduced to a single reaction at relative low temperature or when the second one is much slower than the first one; and (iii) the model has adequate empirical correlation with experimental data. In this study, the two-competing-reaction scheme proposed by Kobayashi et al.3 was used. The rate equations are shown in eqs 15-17. dV dt

ðs -1 Þ ¼ ðk1 þk2 ÞðVf -VÞ

(15)

-E1 Þ k1 ðs -1 Þ ¼ A1 expð RT p

(16)

-E2 k2 ðs -1 Þ ¼ A2 expð RT Þ p

(17)

where k1 and k2 are the reaction rates (given in units of s-1) at low temperature and high temperature, respectively. A1 and A2 are pre-exponential factors (given in the unit of s-1), and E1 and E2 are the activation energy of the two rate equations (given in units of J/mol). V and Vf are the volatile yield at time t and final volatile yield, respectively; R is the gas constant (R=8.314 J mol-1 K-1), and Tp is the temperature of coal particles (given in Kelvin). The values of A1 and E1 are dependent on V0, Dc, and QL; they are calculated using eq 18, which is obtained by fitting the measured data42 using the procedure shown in Figure 1. 0:011QL0:2 0:1 0:7 0 Dc

A1 ðs -1 Þ ¼ 120þ V E1 ðJ=molÞ ¼

(18)

QL mE1 1:0159ð10 Dn nE1 V0 lmE1 6Þ

QL 2 QL mE1 ¼ -0:084ð10 6 Þ þ0:3038ð 6 Þþ0:7524 10

nE1 ¼ 3:9167Dn 2 þ1:6867Dn þ0:5060 lE1 ¼ 0:001236V0 -0:1133V0 þ5:5805 2

(19) ðR2 ¼ 1:0000Þ(20) ðR2 ¼ 1:0000Þ ðR ¼ 1:0000Þ 2

(21) (22)

The following ranges/values were used in this study: A1 = (1.7249-1.8936)
102 s-1, E1=(2.6248-3.5447)
104 J/mol, A2 =2.6
106 s-1, and E2 =1.6740
105 J/mol. Final Volatile Matter Yield (Vf). The parameter Vf is calculated using eq 23, which is obtained by fitting measured data,47 using the procedure shown in Figure 1. QL ð23Þ Vf ð%Þ ¼ ð 6 ÞmVf Dn nVf V0 lVf 10

Figure 1. Procedure for obtaining model parameters by fitting experiment data.

Devolatilization Rate Equation. Kobayashi and coworkers3,54,55 proposed the two-competing-reaction model described by eq 14 based on their experimental investigation, (54) Kobayashi, H. M.S. Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute Technology, Cambridge, MA, 1972. (55) Kobayashi, H. Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute Technology, Cambridge, MA, 1976.

where mVf, nVf, and lVf are calculated using the regression equations given in eqs 24-26: 22

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Table 1. Ultimate and Proximate Analysis of Three Coalsa Ultimate Analysis (wt %, daf)

Proximate Analysis (wt %, db)

coal

C

H

N

S

Ob

VM

FC

Ash

K W P

87.6 83.9 81.2

3.9 5.0 5.9

1.5 2.1 1.3

0.5 0.8 0.4

6.5 8.2 11.2

18.7 32.7 43.0

71.7 59.9 53.5

9.6 7.4 3.5

a W coal = a South African highly volatile weak cooking coal, Witbank; K coal=a Rosier bituminous coal; and P coal=an Indonesia bituminous coal, Prima. b Determined by difference.

mVf ¼ 0:1667ð

QL 2 QL Þ -1:1722ð 6 Þþ2:6073 106 10 ðR2 ¼ 1:0000Þ

ð24Þ

nVf ¼ 12:844Dn 2 -4:1669Dn þ1:3196 ðR2 ¼ 1:0000Þ lVf ¼ -0:0058V0 þ1:4958

ðR2 ¼ 0:9997Þ

ð25Þ ð26Þ

Dn is the diameter of coal particle (in millimeters), and V0 represents the volatile matter content (expressed as a percentage). In this study, the measured data47 were used to validate the utility of the proposed model (described by eqs 1-26). The heat capacity (Cpc) and thermal conductivity (Kp) of three coals were calculated based on the works of Merrick9 and Badzioch et al.56 In addition, Merrick9 predicted that the total heats of reaction for the standard 15, 25, and 35 wt % VM coals were exothermic reactions of 0.465, 0.616, and 0.653 MJ/kg, respectively. Based on these data, in this study, the heat of devolatilization (ΔHd) values were assumed to be -5.2438
105, -6.6292
105, and -7.3480
105 J/kg for K, W, and P coals, respectively. Since heat capacity data for coal volatiles (Cpv) at elevated temperatures are not available, the energy loss per unit mass volatile yield (ΔHvl) values were taken to be 5.1392
105, 6.5246
105, and 7.2434
105 J/kg for K, W, and P coals, respectively. Consequently, the sum of ΔHd and ΔHvl is -1.0460
104 J/kg for all three coals. A South African highly volatile weak cooking coal, Witbank (W), a Rosier bituminous coal (K), and an Indonesia bituminous coal, Prima (P), were used as raw coals. The coals were crushed and sieved to give samples with three ranges of particle size: 0.14, 0.20, and 0.30 mm. To avoid the obvious difference in size, shape, and mineral matters, we carefully selected experimental samples using a clean stainless steel needle under a microscope. The sphericity correction factor (SCF) is assumed to be 0.75 for all three coals.46 The proximate and ultimate analyses of three coals are shown in Table 1. The weight loss of single particles was not measured directly in our experiment.47 In each experiment, 0.3-mg samples of a given size were placed uniformly on the surface of the sample plate within a cross-sectional area 3 mm in diameter. The same experiment was performed at least 30 times to obtain ∼10 mg samples; the samples were weighed using a high-sensitivity electronic balance, and the weight loss was determined for the experimental conditions. Therefore, the measured particle temperature and weight loss are group features.

Figure 2. Comparison of predicted particle temperatures and volatile yield (V) with the measured particle temperatures of W coal under different laser intensity (QL) values.

Our experiments47 indicated that the measured temperature differences with different particle numbers (5, 10, and 20 particles) were within the system error; therefore, particle number does not affect temperature measurements. The established model is based on “single particles”, which should be a representative of a given coal. To compare predictions with measurements, the measured particle temperature and weight loss also must be representative for the coal. The energy conservation (described by eq 1) and the devolatilization rate (described by eq 15), with the related parameters for coal particles of three different ranks (18.7%, 32.7%, and 43.0% VM) with different size (0.14, 0.20, and 0.30 mm) under three different laser intensities (1.85, 2.59, and 3.70 MW/m2), were solved using the library function ode45 that was supplied in Matlab software (Matlab V7.4). Results and Discussions Comparison of Predicted Particle Temperature (Tp,c) and Volatile Yield (V) under Different Laser Intensity (QL) with Measured Data. Predicted and measured histories of the volatile yield and particle temperature of 0.20-mm W coal (32.7% VM) particles heated with different laser intensity (QL=1.85, 2.59, and 3.70 MW/m2) are respectively shown in Figures 2a, 2b, and 2c. The predicted histories of the volatile

(56) Badzioch, S.; Gregory, D. R.; Field, M. A. Fuel 1964, 43, 267.

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Energy Fuels 2010, 24, 18–28

: DOI:10.1021/ef900519b

Gao et al.

Table 2. Differences (%) between Measured and Predicted Particle Temperatures under Three Laser Intensity (W Coal, V0=32.7%, Dn=0.20 mm)

Table 3. Differences (%) between Measured and Predicted Particle Temperatures of Three Particle Sizes (W Coal, V0=32.7%, QL=1.85 MW/m2)

(Tp,c - Tp,m)/Tp,m
100 (%)

(Tp,c - Tp,m)/Tp,m
100 (%)

heating time (ms)

QL= 1.85 MW/m2

QL= 2.59 MW/m2

QL= 3.70 MW/m2 a

heating time (ms)

Dn=0.14 (mm)

Dn=0.20 (mm)

Dn=0.30 (mm)

100 200 300 400 500

-4.93 1.38 0.79 1.65 -0.26

-7.69 5.67 5.11 2.13 -1.50

-9.05 5.10 1.12 1.21 1.22

100 200 300 400 500

-4.89 0.64 -0.48 1.15 -0.30

-4.93 1.38 0.79 1.65 -0.26

-5.94 1.18 3.98 4.91 0.77

a At this laser intensity, Merrick’s heat capacity correlation9 is given as Cpc
1.6.

Table 4. Differences (%) between Measured and Predicted Particle Temperatures of Three Coals (QL=1.85 MW/m2, Dn=0.20 mm)

yield (V) and particle temperature (Tp) agree quite well with the measured data, although there are somewhat underpredictions or overpredictions. The differences between the predicted particle temperature (Tp,c) and the measured parT -T ticle temperature (Tp,m), difference ð%Þ ¼ p;cTp;m p;m
100 are summarized in Table 2. The differences change from -4.93% to 1.65% for a laser intensity of QL=1.85 MW/m2, from -7.69% to 5.67% for a laser intensity of QL = 2.59 MW/m2, and from -9.05% to 5.10% for a laser intensity of QL = 3.70 MW/m2. The temperatures that are underestimated at 100 ms increase as the QL value increases, and the effect of QL becomes irregular after 200 ms. These results may be related to the different heating rates under different QL values. The maximum heating rates are 1.0916
104, 1.5281
104, and 1.3644
104K/s for 1.85, 2.59, and 3.70 MW/m2, respectively. Note that Merrick’s heat capacity correlation9 was multiplied by a factor of 1.6 for the QL = 3.70 MW/m2 condition, which caused somewhat of a decrease in the maximum heating rate. These results show that the higher the QL value, the larger the difference becomes during the early stage of heating. Sampath et al.41 determined that the application of room-temperature values for the coal’s heat capacity, thermal conductivity, and heat of devolatilization (-250 cal/g, or -1.046
106 J/kg) as fit parameters yielded excellent agreement between the measurements and the model projections. Our predictions indicate that Merrick’s heat capacity correlation is suitable for most cases of W coal, except for the QL =3.70 MW/m2 condition, in which the correlation is multiplied by 1.6. Note that the heats of devolatilization used in this study are -5.2438
105, -6.6292
105, and -7.3480
105 J/kg for K, W, and P coasl, respectively. These data are on the same order of Merrick’s data and somewhat less than data of Sampath et al.41 In addition, the energy loss per unit mass volatile yield (ΔHvl) values used in this model are 5.1392
105, 6.5246
105, and 7.2434
105 J/kg for K, W, and P coals, respectively; the sum of ΔHd and ΔHvl is -1.0460
104 J/kg for all three coals. Moreover, in this study, the thermal conductivity (Kp) of the coal particles was also temperature-dependent.56 Comparison of the Predicted Histories of Particle Temperature (Tp,c) and Volatile Yield (V) with Measured Data under Different Particle Sizes (Dn). Predicted and measured histories of the volatile yield and particle temperature of W coal with different particle sizes, heated at the same laser intensity (QL =1.85 MW/m2) are shown in Figures 2a (Dn = 0.20 mm), 3a (Dn =0.14 mm), and 3b (Dn =0.30 mm). The difference data (given as a percentage, (Tp,c - Tp,m)/Tp,m
100) are summarized in Table 3. The differences range from -4.89% to 1.15% for the 0.14-mm W coal particles, from

(Tp,c - Tp,m)/Tp,m
100 (%) heating time (ms)

K coal, V0= 18.7%a

W coal, V0= 32.7%

P coal, V0= 43.0% b

100 200 300 400 500

3.09 -2.03 1.00 0.34 0.14

-4.93 1.38 0.79 1.65 -0.26

-1.90 -1.28 1.20 0.73 0.28

a At this VM content, Merrick’s heat capacity correlation is given as Cpc
0.70. b At this VM content, Merrick’s heat capacity correlation is given as Cpc
0.75.

-4.93% to 1.65% for the 0.20-mm W coal particles, and from -5.94% to 4.91% for the 0.30-mm W coal particles. The predicted particle temperatures and volatile yields agree quite well with the measured data. As shown in Table 3, the underpredicted temperature increases as the particle size increases at 100 ms; after 300 ms, the differences for the 0.30-mm W coal particles are larger than those of the 0.14and 0.20-mm W coal particles. Maloney et al.36 indicated that a marked intraparticle temperature gradient might exist. Tripathi et al.46 reported that the intraparticle temperature gradient in three 0.12-mm coal particles was P > W. Note that the Merrick’s thermal capacity correlation9 was multiplied by a factor of 0.70 for K coal and a factor of 0.75 for P coal; the Merrick’s thermal capacity correlation9 was without modification for W coal. These results suggest that the thermal capacity of K coal and P coal particles might

Figure 12. Predicted histories of Fed and HR with time under different particle size (Dn) values.

temperature, heating rate, devolatilization rate, final volatile yield, and other thermal properties are all related to it. The histories of Fed with heating time under different QL, Dn, and V0 values are respectively shown in Figures 11, 12, and 13. As shown in Figure 11, it is apparent that high QL values lead to high Fed; Fed decreases as the heating time increases and gradually reaches an equilibrium state, at which point Fed is a constant. The times required to arrive at the state are 700 ms under 1.85 and 2.59 MW/m2 conditions, but only 520 ms at QL =3.70 MW/m2. The Fed values at the equilibrium state are 2.4658
105, 4.2285
105, and 7.1383
105 W/ m2 at QL =1.85, 2.59, and 3.70 MW/m2, respectively. As shown in Figure 12, particle size has a great and complex effect on Fed. Generally, large particle sizes lead to a lower decreasing rate of Fed and higher equilibrium Fed value, which supports the results that the large particles have longer duration times at high heating rates and higher final temperatures. The time required to arrive at the equilibrium state was 730, 700, and 580 ms for the 0.14-, 0.20-, and 0.30-mm particles, respectively. The values of Fed values at the equilibrium state are 1.5651
105, 2.4658
105, and 3.6304
105 W/m2 for the 0.14-, 0.20-, and 0.30-mm particles, respectively. In the case of the 0.30-mm particles, a peak appears in the Fed curve, which is even higher than the initial Fed. This phenomenon is related to the combined heat (ΔHd þ ΔHvl=-1.0460
104 J/kg) and particle size (Dc) in eq 2. If Dc is larger than 0.239 mm, a peak appears in the Fed curve. This interesting phenomenon should be validated by experiments in the future. 27

Energy Fuels 2010, 24, 18–28

: DOI:10.1021/ef900519b

Gao et al.

be partially “frozen”; such results are partially similar to those of Maloney et al.40 After 450 ms, the HR values exhibit no notable differences among the three coals.

A2 = pre-exponential factor of rate equation at high temperature (s-1) B=transfer number for convective heat transfer c1 =specific heat of dry ash-free (daf) coal (J kg-1 K-1) c2 =specific heat of ash (J kg-1 K-1) c3 =specific heat of moisture (J kg-1 K-1) Cg =specific heat capacity of surrounding nitrogen (J kg-1 K-1) Cp =specific heat capacity of coal particles (J kg-1 K-1) Cpc =specific heat capacity of coal and char (J kg-1 K-1) Cpv =volatile heat capacity (J kg-1 K-1) Dc =diameter of coal particle (m) Dn =diameter of coal particle (mm) E1=activation energy of rate equation at low temperature (J/mol) E2 =activation energy of rate equation at high temperature (J/mol) Fed =in situ energy density flux (W/m2) g1 =Einstein specific heat function hBFC=convective heat-transfer coefficient with blow factor correction at coal particle surface (W m-2 K-1) ΔHd =heat of devolatilization reactions (J/kg) ΔHvl =energy loss per unit mass volatile yield (J/kg) HR=heating rate of coal particle (K/s) HR100 ms =heating rate of coal particle at 100 ms (K/s) k1 =reaction rate at low temperature (s-1) k2 =reaction rate at high temperature (s-1) Kg =thermal conductivity of nitrogen (W m-1 K-1) Kp =thermal conductivity of coal (W m-1 K-1) mc =mass of coal particle (kg) NNu =Nusselt number NRe =Reynolds number NPr =Prandtl number QL =laser intensity (W/m2) rvs =volume swelling ratio of coal particles upon heating R=gas constant; R=8.314 J mol-1 K-1 SCF =sphericity correction factor Tp =particle temperature (K) Tb = temperature of gas boundary layer surrounding a coal particle (K) Tp,c =predicted particle temperature (K) Tp,m =measured particle temperature (K) Ta =ambient gas temperature (K) u=velocity of nitrogen (m/s) V0 =volatile matter (VM) content (%) V1 =volatile yield at low temperature (%) V2 =volatile yield at high temperature (%) Vf =final volatile matter yield (%) wi =mass fractions in the as-received coal of the dry ashfree (daf) coal, ash, and moisture (%) ΔW=overall weight loss (%) Z=dummy variable

Summary and Conclusions In this study, an empirical model for coal devolatilization under CO2 laser conditions was proposed, based on the measurements of devolatilization characteristics of three types of coals (18.7%, 32.7%, 43.0% VM) with particle sizes of 0.14, 0.20, and 0.30 mm, heated at 103-104 K/s by a wellcontrolled CO2 laser under three laser intensities (1.85, 2.59, and 3.70 MW/m2). The comparisons between predictions and measured data for the three coals under various heating conditions indicate that this model is effective and useful. The important results obtained are as follows. (1) Particle temperature (Tp), volatile yield (V), heating rate (HR), and in situ energy density flux (Fed) during devolatilization can be well predicted by solving an energy conservation equation and a devolatilization rate equation with two competing reaction rates using the proposed model. (2) The pre-exponential factors and activation energies of the two reactions are A1= (1.7249-1.8936)
102 s-1, E1 =(2.6248-3.5447)
104 J/mol, A2 =2.6
106 s-1, and E2 =1.6740
105 J/mol; these values are obtained by fitting our experiment data. (3) The final volatile yield (Vf) is dependent on laser intensity (QL), particle size (Dn), and proximate volatile matter content (V0); these parameters can be well predicted using the regressive equationVf ¼ QL mVf Dn nVf V0 lVf . (4) A modified Merrick’s heat capacity correlation could be used to predict the temperature history of coal particles heated at a rate of 103-104 K/s with excellent agreement. (5) The heat of devolatilization (Hd) values, which are -0.5244, -0.6629, and -0.7348 MJ/kg, calculated based on Merrick’s work9 for the three coals, are reasonable values for predicting the particle temperatures. (6) The value of ΔHd þ ΔHvl=-0.01046 MJ/kg is a suitable value for predicting particle temperatures and volatile yields for all three coals. (7) Predictions indicate that the measured histories of weight loss are imperative for predicting the temperature and devolatilization kinetics of coal particles heated with a CO2 laser at high heating rates. (8) To get more precise predictions, the data measured using a wider range rank of coals under a wider range of experimental conditions are needed and some important in situ properties (such as swelling-shrinking ratios, absorptivity, emissivity, thermal capacity, and heat of devolatilization) of coal particles at high heating rates should be measured. Acknowledgment. We thank the Institute for Advanced Materials Processing (Tohoku University, Japan) for its support in finance and experimental apparatus; this is where the experiments were performed. This work was also partially supported by Yanshan University (B255).

Greek Symbols R=absorptivity of coal particle ε=emissivity of coal particle μg =viscosity of nitrogen gas (kg m-1 s-1) F=density of coal particle (kg/m3) F0 =initial density of coal particle (kg/m3) Fg =density of nitrogen (kg/m3) σ=Stefan-Boltzmann constant; σ=5.669
10-8 W m-2 K-4

Nomenclature Parameters a=mean atomic weight A1 = pre-exponential factor of rate equation at low temperature (s-1)

28