Quasi-stationary Task on the Concentration Field of a Reacting Gas in the Vicinity of the Burning Coal Particle


When developing coal deposit, the coal dust is formed. Mixing with the atmosphere of the mine workings, it forms the dust-gas-air mixtures that are prone to chemical reactions in various forms. As a rule, such mixtures are neutralized in the dust source area. However, in the coal mines the danger remains related to the normal combustion turning into the detonation of the coal dust. It can be both in the composition of the dust-gas-air mixture, and in the form of the settled layers suspended in the atmosphere of the workings by a methane explosion. In this case there is a risk of a multiple increase in the explosion power due to the ignition of the coal particles as and when the burning spreads through the working.

Coal particles burning is considered as a stationary process. However, under certain conditions it becomes necessary to consider accounting the non-stationarity of its flow. This circumstance significantly complicates the consideration of the burning process.

Quasi-stationary problem that considers the change in the concentration fields of the reacting gas around a coal particle at different time intervals is studied in the article. The formulas are obtained for determining the concentrations of the reacting gas in the vicinity of the burning coal particle and on its surface. Based on the law of mass conservation of the substances involved in the burning reaction, the formula was found for calculating the radius of the burning coal particle over time. The formula is also derived for determining the complete burning time of the coal particle. The graphs are constructed concerning the dependences of the coal particle burnout time on the number of its parameters. The concentration fields of the reacting gas around the coal particle at various stages of its burning are revealed.

1. Frank-Kamenetskiy D.A. Diffusion and Heat Transfer in the Chemical Kinetics. Moscow: Nauka, 1987. 502 p. (In Russ.).
2. Kantorovich B.V. Fundamentals of the theory of burning and gasification of the solid fuel. Moscow: Kniga po trebovaniyu, 2013. 600 p. (In Russ.).
3. Vilenskiy T.V., Khzmalyan D.M. Dynamics of the pulverized fuel burning. Moscow: Nauka, 1978. 248 p. (In Russ.).
4. Lindenau N.I., Maevskaya V.M., Krylov V.F. Origin, prevention and extinguishing of the endogenous fires in the coal mines. Moscow: Nedra, 1977. 319 p. (In Russ.).
5. Chanyshev A.I. A method to determine a body’s thermal state. Journal of Mining Science. 2012. Vol. 48. pp. 660–668. DOI: 10.1134/S1062739148040107
6. Cherdantsev S.V., Lee Khi Un, Filatov Yu.M., Shlapakov P.A. Analysis of Combustion Process of Microheterogeneous Dust and Gas Mixtures in the Mine Workings. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2017. № 11. pp. 10–15. (In Russ.). DOI: 10.24000/0409-2961-2017-11-10-15
7. Cherdantsev S.V., Filatov Yu.M., Shlapakov P.A. Modes of diffusion combustion of fine dust-gas-air mixtures in the atmosphere of mine workings. Ugol = Coal. 2020. № 2. pp. 27–32. (In Russ.). DOI: 10.18796/0041-5790-2020-2-27-32
8. Shevchuk V.G., Kondratev E.N., Zolotko A.N., Sidorov A.E., Oparin A.S. Wave regimes of dust combustion. Combustion, Explosion, and Shock Waves. 2014. Vol. 50. pp. 80–86. DOI: 10.1134/S0010508214010109
9. Sidorov A.E., Shevchuk V.G. Laminar flame in fine-particle dusts// Combustion, Explosion, and Shock Waves. 2011. Vol. 47. pp. 518–522. DOI: 10.1134/S0010508211050042
10. Sidorov A.E., Shevchuk V.G., Kondratev E.N. Conductive-radiative model of a laminar flame in dust suspensions. Combustion, Explosion, and Shock Waves. 2013. Vol. 49. pp. 257–263. DOI: 10.1134/S0010508213030015
11. Cherdantsev S.V., Shlapakov P.A., Erastov A.Yu., Khaymin S.A., Lebedev K.S., Kolykhalov V.V., Shlapakov E.A. Process simulation of the reactant gas molecular diffusion to a poor-dispersion coal at rest in mine opening. Vestnik Nauchnogo tsentra VostNII po promyshlennoy i ekologicheskoy bezopasnosti = Bulletin of Scientific Centre VostNII for Industrial and Environmental Safety. 2017. № 4. pp. 13–21. (In Russ.).
12. Koshlyakov N.S., Gliner E.B., Smirnov M.M. Equations in the partial derivatives of the mathematical physics. Moscow: Vysshaya shkola, 1970. 712 p. (In Russ.). 
DOI: 10.24000/0409-2961-2022-3-7-13
Year: 2022
Issue num: March
Keywords : the Arrhenius law coal particles stoichiometric coefficients spherical coordinates diffusion coefficients quasi-stationary task burning time