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Home > Journals > SCIREA Journal of Energy > Archive > Paper Information

Critical Condition for the Mass Burning Rate Constant of a Carbon Particle Activated; Comparisons with Experimental Results

Volume 5, Issue 2, April 2020    |    PP. 32-59    |PDF (2040 K)|    Pub. Date: October 12, 2020
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Atsushi Makino, Department of Mechanical Engineering, Faculty of Engineering, Aichi Institute of Technology, Toyota, Aichi, Japan

Relevant to the activation of solid fuel particles, critical condition for the mass burning rate constant, above which particle combustion can successfully be accomplished has been obtained. Use has been made of the asymptotics, with focusing on the temporal variation of the particle temperature in the plateau stage. It has been confirmed that there exists a useful parameter, consisting of particle diameter and combustion rate, which mainly depends on the ambient temperature. It is seen that the critical condition separates regions, upper half of which corresponds to that for particle combustion with surface reactions activated. In addition, existence of the cut-off temperature, with respect to the ambient temperature, has been confirmed, above which the particle combustion can only be accomplished. Appropriateness and/or usefulness of this critical condition has further been examined, by use of such experimental data in the literature as are reported to burn in the quiescent environment. Experimental data used are those from semi-anthracite to low-rank coal char, as well as petroleum coke. A fair degree of agreement has been demonstrated, indicating that excessively smaller particles are unfavorable to the particle combustion. This fair agreement further suggests that the formulation, from which the critical condition has been derived, has captured the essential feature of the particle combustion that has not been elucidated. It has been confirmed again that the reduction in particle size does not necessarily favor the particle combustion, which is inconsistent with the premise prevailed.

heterogeneous combustion; char combustion; critical condition for particle activation; particle size; mass burning rate constant; cut-off temperature.

Cite this paper
Atsushi Makino, Critical Condition for the Mass Burning Rate Constant of a Carbon Particle Activated; Comparisons with Experimental Results, SCIREA Journal of Energy. Vol. 5 , No. 2 , 2020 , pp. 32 - 59 .


[ 1 ] P. L. Walker, Jr., F. Rusinko, Jr., and L. G. Austin, Gas reaction of carbon, In: D. D. Eley, P. W. Selwood, & P. B. Weisz (Eds.), Advances in Catalysis and Related Subjects, Vol. 11, Academic, New York, 1959, pp. 133-221.
[ 2 ] L. N. Khitrin, The Physics of Combustion and Explosion, Israel Program for Scientific Translations, Jerusalem, 1962, pp. 353-437.
[ 3 ] M. F. Mulcahy and I. W. Smith, Kinetics of combustion of pulverized fuel: A review of theory and experiment. Rev. Pure and Appl. Chem., 19 (1) (1969) 81-108.
[ 4 ] R. H. Essenhigh, Fundamentals of coal combustion, In: M. A. Elliott (Ed.), Chemistry of Coal Utilization, Wiley-Interscience, New York, 1981, pp. 1153-1312.
[ 5 ] I. W. Smith, The combustion rates of coal char: A Review, Nineteenth Symp. (Int.) Combust., 1982, pp. 1045-1065.
[ 6 ] K. Annamalai, and W. Ryan, Interactive processes in gasification and combustion - II. Isolated carbon, coal and porous char particles. Prog. Energy Combust. Sci., 19 (5) (1993) 383-446.
[ 7 ] K. Annamalai, W. Ryan, and S. Dhanapalan, Interactive processes in gasification and combustion - Part III: Coal/char particle arrays, streams and clouds. Prog. Energy Combust. Sci., 20 (6) (1994) 487-618.
[ 8 ] K. Annamalai and I. K. Puri, Combustion Science and Engineering, CRC, Baco Raton, 2007, pp. 608-620.
[ 9 ] V. M. Tret'yakov (Cited by Khitrin, L. N. [2]).
[ 10 ] S. Bandyopadhyay and D. Bhaduri, Prediction of ignition temperature of a single coal particle, Combust Flame, 18 (1972) 411-415.
[ 11 ] A. Makino, Critical size for the particle burn-out of solid carbon and/or boron as the high-energy-density fuel, Combust. Flame, 160 (2013) 742-744.
[ 12 ] D. A. Frank-Kamenetsukii, Diffusion and Heat Transfer in Chemical Kinetics, 2nd Ed., Plenum, New York, 1969, pp. 349-357.
[ 13 ] I. Glassman, Combustion, 3rd Ed., Academic, San Diego, 1996, pp. 330-340.
[ 14 ] A. Makino and M. Shintomi, Critical condition related to the activation of solid fuel particles; comparisons with experimental results for char combustion in a quiescent environment, Combust. Flame, 162 (2015) 3156-3165.
[ 15 ] A. Makino, Critical condition for the particle combustion of carbon, activated in a hot, quiescent environment; comparisons with experimental results, Combust. Sci. Technol., 189 (2017) 991-1012.
[ 16 ] R. H. Essenhigh and M. W. Thring, Measurement of Burning Times of Single Coal Particles, Paper 29, Proc. Residential Conf. on Science in the Use of Coal, Sheffield (1958).
[ 17 ] B. D. Katsnel’son and I. Ya. Marone, Effects of Pressure and Oxygen concentration on the Ignition and Combustion of Pulverized Coal Particles. Teploenergetika, 11 (1964) 11-15 (in Russian).
[ 18 ] I. P. Ivanova and V. L. Babii, A Study of the Burn-out Mechanism of Coal Particles, Thermal Engineering, 13 (4) (1966) 70-76.
[ 19 ] M. A. Field, Rate of Combustion of Size-graded Fractions of Char from a Low-rank Coal between 1200OK and 2000 OK, Combust. Flame, 13 (1969) 237-252.
[ 20 ] M. A. Field, Measurements of the Effect of Rank on Combustion Rates of Pulverized Coal, Combust. Flame, 14 (1970) 237-248.
[ 21 ] I. W. Smith, Kinetics of Combustion of Size-graded Pulverized Fuels in the Temperature Range 1200-2270 OK, Combust. Flame, 17 (1971) 303-314.
[ 22 ] I. W. Smith, The Kinetics of Combustion of Pulverized Semi-anthracite in the Temperature Range 1400-2200 OK, Combust. Flame, 17 (1971) 421-428.
[ 23 ] R. J. Hamor, I. W. Smith, and R. J. Tyler, Kinetics of Combustion of a Pulverized Brown Coal Char between 630 and 2200 K. Combust. Flame, 21 (1973) 153-162.
[ 24 ] I. W. Smith and R. J. Tyler, The Reactivity of a Porous Brown Coal Char to Oxygen between 630 and 1812oK. Combust Sci. Technol., 9 (1) (1974) 87-94.
[ 25 ] R. E. Mitchell and W. J. McLean, On the Temperature and Reaction Rate of Burning Pulverized Fuels. Nineteenth Symp. (Int.) on Combust., The Combust. Inst., 1982, pp. 1113-1122.
[ 26 ] G. J. Goetz, N. Y. Nsakala, R. L. Patel, and T. C. Lao, Combustion and Gasification Characteristics of Chars from Four Commercially Significant Coals of Different Rank. (Final Report, Sept. 1982). EPRI-AP-2601, Electric Power Research Institute, Palo Alto, CA.
[ 27 ] W. F. Wells, S. K. Kramer, L. D. Smoot, and A. U. Blackham, Reactivity and Combustion of Coal Chars. Twentieth Symp. (Int.) on Combust., The Combust. Inst., 1984, pp. 1539-1546.
[ 28 ] P. A. Bejarano and Y. A. Levendis, Single-coal-particle combustion in O2/N2 and O2/CO2 environments. Combust Flame, 153 (2008) 270-287.
[ 29 ] A. Makino, Critical Condition for the combustion Rate of a Carbon Particle to be Activated; Theory and Experimental Comparisons. Combust. Sci. Technol. 191 (2019) 607-628. An open access publication at https://doi.org/10.1080/00102202.2018.1511543
[ 30 ] J. R. Arthur, Reactions between Carbon and Oxygen, Trans. Faraday Soc., 47 (1951) 164-178.
[ 31 ] A. Makino, Mass Transfer Related to Heterogeneous Combustion of Solid Carbon in the Forward Stagnation Region - Part 1 - Combustion Rate and Flame Structure, in: Jozef Markoš (Ed.), Mass Transfer in Chemical Engineering Processes, InTech, 2011, pp. 251-282. .
[ 32 ] A. Makino, An Attempt for Applying Formulation of the Carbon Combustion in the Stagnation Flowfield to Some Experimental Comparisons Related to the Boundary Layer Combustion, Combust. Flame, 161 (6) (2014) 1537-1546.
[ 33 ] S. K. Ubhayakar and F. A. Williams, Burning and Extinction of a Laser-ignited Carbon Particle in Quiescent Mixtures of Oxygen and Nitrogen, J. Electrochem. Soc., 123 (5) (1976) 747-756.
[ 34 ] H. S. Caram and N. R. Amundson, Diffusion and Reaction in a Stagnant Boundary Layer about a Carbon Particle, Ind. Eng. Chem., Fundam., 16 (2) (1977) 171-181.
[ 35 ] E. Mon and N. R. Amundson, Diffusion and Reaction in a Stagnant Boundary Layer about a Carbon Particle. 2. An Extension, Ind. Eng. Chem., Fundam., 17 (4) (1978) 313-321.
[ 36 ] P. A. Libby and T. R. Blake, Theoretical Study of Burning Carbon Particles, Combust. Flame, 36 (1) (1979) 139-169.
[ 37 ] P. A. Libby and T. R. Blake, Burning Carbon Particles in the Presence of Water Vapor, Combust. Flame, 41 (1) (1981) 123-147.
[ 38 ] I. Glassman, The burning of carbon char particles. Combustion, 3rd Ed., Academic, San Diego, 1996, pp. 462-466.
[ 39 ] A. Makino, An Approximate Explicit Expression for the Combustion Rate of a Small Carbon Particle, Combust. Flame, 90 (2) (1992) 143-154.
[ 40 ] A. Makino and C. K. Law, An Analysis of the Transient Combustion and Burnout Time of Carbon Particles, Proc. Combust. Inst., 32 (2) (2009) 2067-2074.
[ 41 ] T. W. Lester, W. Randall Seeker, and J. F. Merklin, The Influence of Oxygen and Total Pressure on the Surface Oxidation Rate of Bituminous Coal, Eighteenth Symp. (Int.) on Combust., The Combust. Inst., 1981, pp. 1257-1265.
[ 42 ] A. Makino, N. Araki, and Y. Mihara, Combustion of Artificial Graphite in Stagnation Flow: Estimation of Global Kinetic Parameters from Experimental Results. Combust. Flame, 96 (3) (1994) 261-274.