DOI: 10.52150/2522-9117-2026-40-019
M. H. Ivancha1, Senior Researcher, ORCID 0000-0002-5366-9328
V. I. Vіshnyakov1, Researcher, ORCID 0000-0002-5538-6962
I. H. Muravyova1,*, D. Sc. (Tech.), Leading Researcher, ORCID 0000-0001-5926-7787
L. I. Garmash1, Ph. D. (Tech.), Senior Researcher, ORCID 0000-0002-6873-6685
V. R. Shcherbachov1, Junior Researcher, Ph. D. Student, ORCID 0000-0002-6734-0451
O. O. Biloshapka1, Junior Researcher, ORCID 0000-0003-3103-0512
K. P. Yermolina1, Leading Engineer, ORCID 0000-0001-6819-9886
1 Iron and Steel Institute of Z. I. Nekrasov National Academy of Sciences of Ukraine
* Corresponding author: irinamuravyova@gmail.com
CALCULATION METHODS AND MATHEMATICAL MODELS OF THE DISTRIBUTION OF CHARGE MATERIALS ON THE TOP OF A BLAST FURNACE, USED IN TECHNOLOGICAL AND RESEARCH PRACTICE
Abstract. Increasing the efficiency of using the reducing capacity of gases in a blast furnace, optimizing the processes of slag formation and lining, forming a rational configuration and dimensions of the cohesive zone and, as a result, improving the technical and economic indicators of smelting as a whole is ensured, first of all, by rational distribution of charge materials on the top. Analysis of known calculation methods and mathematical models of the distribution of charge materials on the top of a blast furnace, which are used in technological and research practice, showed that mathematical modeling using the results of experimental studies remains the main way to obtain information about the distribution of charge materials. Instrumental means of controlling the distribution of charge components do not currently exist. A feature of known mathematical models is that with their use the distribution of two charge components was predicted – the iron ore part and coke. Modern blast furnace charge conditions are characterized by a significant expansion of the raw material base and the component composition of charge materials loaded into the blast furnace. When these components are unloaded onto the surface of the backfill, a mixture layer is formed, the composition of which differs significantly in different zones of the top. The difference in the composition of the mixtures determines the corresponding difference in the high-temperature properties of the iron ore part of the charge and the properties of the melts along the cross-section of the blast furnace. Analysis of previously performed research in the field of developing mathematical models and methods for calculating distribution characteristics showed that a significant part of the work is devoted to the distribution of the iron ore and carbon-containing parts of the charge as a whole, without assessing the distribution of the components included in it. In this regard, problems are becoming particularly relevant, the solution of which is aimed at creating a complex mathematical model of blast furnace loading, which includes models of a number of processes of forming multicomponent portions of charge materials, their movement along the loading path and in the working space of the blast furnace, as well as their distribution on the surface of the backfill.
Key words: blast furnace, mathematical models, multicomponent charge, component distribution in zones.
For citation: Ivancha, M. H., Vіshnyakov, V. I., Muravyova, I. H., Garmash, L. I., Shcherbachov, V. R., Biloshapka, O. O., & Yermolina, K. P. (2026). Calculation methods and mathematical models of the distribution of charge materials on the top of a blast furnace, used in technological and research practice. Fundamental and applied problems of ferrous metallurgy, 40, 290-319. https://doi.org/10.52150/2522-9117-2026-40-019
References
- Bolshakov, V. I. (2007). Tehnologiya vysokoeffektivnoj energosberegayushej domennoj plavki. Nauk. dumka.
- Bolshakov, V. I., Muraveva, I. G., Beloshapka, E. A., & Varivoda, I. E. (2004). Matematicheskie modeli radialnogo raspredeleniya shihty v domennyh pechah. Sbornik nauchnyh trudov IChM «Fundamental’nye i prikladnye problemy chernoj metallurgii» (No. 8, pp. 86–102). Dnepropetrovsk.
- Tovarovskij, I. G. (2009). Domennaya plavka: Monografiya (2nd ed.). Porogi.
- Gruzinov, V. K. (1960). Upravlenie gazovym potokom v domennoj pechi programmoj zagruzkoj. Metallurgizdat.
- Nikolaj, E. I., Plastinin, B. G., Gruzinov, V. K., & Osinceva, N. L. (1972). K voprosu ocenki haraktera padeniya materialov s bol’shogo konusa. Trudy khimiko-metallurgicheskogo instituta. Akademiya nauk Kazakhskoj SSR, 13, 74–79.
- Osinceva, N. L., Gruzinov, V. K., & Ozolina, Z. M. (1974). Dvizhenie materialov domennoj shihty pri ssypanii s konusov zasypnyh ustrojstv. Trudy khimiko-metallurgicheskogo instituta. Akademiya nauk Kazakhskoj SSR, 26, 32–40.
- Babarykin, N. N. (1963). Osnovnye zakonomernosti raspredeleniya materialov na koloshnike domennoj pechi. Sb. Domennyj process po novejshim issledovaniyam (pp. 84–102). Metallurgizdat.
- Klempert, V. M., Frenkel’, M. M., & Grishkova, A. A. (1993). Kontrol’ i upravlenie gazoraspredeleniem domennoj pechi. Metallurgiya.
- Bolshakov, V. I. (2006). Upravlenie zagruzkoj, raspredeleniem shihty i gazov v domennoj pechi. Poznanie processov domennoj plavki (pp. 87–109). Porogi.
- Loginov, V. I., Glushenko, I. M., & Bekhter, E. I. (1986). Povyshenie effektivnosti ispol’zovaniya koksa v narodnom khozyajstve. Metallurgiya.
- Tarasov, V. P. (1990). Gazodinamika domennogo processa. Metallurgiya.
- Eksperimental’noe i teoreticheskoe issledovanie ssypaniya materialov s bol’shogo konusa i izmeneniya ugla ikh otskoka v shakhte domennoj pechi [Translation VCP No. E-08999]. (1993, May 24).
- Kajiwara, Y., Jimbo, T., & Sakai, T. (1983). Development of a simulation model for burden distribution at blast furnace top. Transactions of the Iron and Steel Institute of Japan, 23(12), 1045–1052. https://doi.org/10.2355/isijinternational1966.23.1045
- Hinnela, J., & Saxén, H. (2001). Hybrid model of burden distribution in the blast furnace. Ironmaking Conference Proceedings, 49–56.
- Hinnela, J., Saxén, H., & Pettersson, F. (2003). Modeling of the blast furnace burden distribution by evolving neural networks. Industrial & Engineering Chemistry Research, 42(11), 2314–2323. https://doi.org/10.1021/ie0203779
- Pettersson, F., Hinnela, J., & Saxén, H. (2003). Evolutionary neural network modeling of blast furnace burden distribution. Materials and Manufacturing Processes, 18(3), 385–399. http://dx.doi.org/10.1081/AMP-120022017
- Kovshov, V. N. (1982). Formirovanie poverkhnosti zasypki domennoj pechi sovremennymi zagruzochnymi ustrojstvami. Soobshchenie 1 [Izvestiya vuzov. Chernaia metallurgiia, (12), 8–12.
- Tarakanov, A. K., Grinshtejn, N. Sh., Bajraka, M. N., et al. (1986). Avtomatizirovannyj vybor rezhima zagruzki domennoj pechi s zagruzochnym ustrojstvom lotkovogo tipa. Stal’, (5), 11–16.
- Tarakanov, A. K., Lyalyuk, V. P., Kassim, D. A., et al. (2018). Soglasovannoe upravlenie raspredeleniem shikhtovykh materialov na koloshnike i gazovogo potoka v gorné domennoj pechi. Stal’, (6), 2–5.
- Kröjc, L., & Bergman, B. (1988). Raspredelenie materialov v domennoj pechi, rabotayushchej s beskonusnym zasypnym apparatom. Chernye Metally, (19), 3–19.
- Kröjc, L., Gudenau, H. V., & Shtandish, N. (1991). Vliyanie na simmetriyu raspredeleniya materialov v domennoj pechi pri primenenii zasypnogo apparata s vrashchayushchimsya zhelobom. Chernye Metally, (3), 26–32.
- Yu, Y. W., Bai, C. G., Zhang, Z. R., Wang, F., Lv, D. G., & Pan, C. (2009). Theoretical calculation and validation of burden trajectory in bell-less top blast furnace. Ironmaking & Steelmaking, 36(7), 505–508. https://doi.org/10.1179/174328109X445705
- Teng, Z.-J., Cheng, S.-S., Du, P.-Y., & Guo, X.-B. (2013). Mathematical model of burden distribution for the bell-less top of a blast furnace. International Journal of Minerals, Metallurgy and Materials, 20(7), 620–626. https://doi.org/10.1007/s12613-013-0775-7
- Fu, D., Chen, Y., & Zhou, C. Q. (2015). Mathematical modeling of blast furnace burden distribution with non-uniform descending speed. Applied Mathematical Modelling, 39(23), 7554–7567. https://doi.org/10.1016/j.apm.2015.02.054
- Park, J.-I., Baek, U.-H., Jang, K.-S., Oh, H.-S., & Han, J.-W. (2011). Development of the burden distribution and gas flow model in the blast furnace shaft. ISIJ International, 51(10), 1617–1623. https://doi.org/10.2355/isijinternational.51.1617
- Yang, Y., Yin, Y., Wunsch, D., Zhang, S., Chen, X., Li, X., Cheng, S., Wu, M., & Liu, K.-Z. (2017). Development of blast furnace burden distribution process modeling and control. ISIJ International, 57(8), 1350–1363. https://doi.org/10.2355/isijinternational.ISIJINT-2017-002
- Zhao, G., Cheng, S., Xu, W., & Li, C. (2015). Comprehensive mathematical model for particle flow and circumferential burden distribution in charging process of bell-less top blast furnace with parallel hoppers. ISIJ International, 55(12), 2566–2575. https://doi.org/10.2355/isijinternational.ISIJINT-2015-342
- Gupta, P. K., Rao, A. S., Sekhar, V. R., Ranjan, M., & Naha, T. K. (2010). Burden distribution control and its optimization under high pellet operation. Ironmaking & Steelmaking, 37(3), 235–239. http://dx.doi.org/10.1179/174328109X422566
- Fojtík, D., Tuma, J., & Faruzel, P. (2021). Computer modelling of burden distribution in the blast furnace equipped by a bell-less top charging system. Ironmaking & Steelmaking, 48, 1226–1238. https://doi.org/10.1080/03019233.2021.1952829
- Li, M., Wei, H., Ge, Y., Xiao, G., & Yu, Y. (2020). A mathematical model combined with radar data for bell-less charging of a blast furnace. Processes, 8(2), Article 239. https://doi.org/10.3390/pr8020239
- Saxén, H., Helle, M., & Li, H. (2019). Mathematical model of burden distribution in the blast furnace. In F. Kongoli, P. Assis, M. C. Gomez-Marroquin, S. Kitayama, H. Konishi, A. Murao, S. Nomura, H. Ono, H. Saxén, K. Seto, & J. I. Tani (Eds.), Sustainable industrial processing summit (SIPS) 2019, Vol. 8: Usui international symposium/advanced sustainable iron and steel making (pp. 243–248). Montreal, Canada.
- Hinnela, J., Saxén, H., & Pettersson, F. A. (2003). Modeling of the blast furnace burden distribution by evolving neural networks. Industrial & Engineering Chemistry Research, 42(11), 2314–2323. https://doi.org/10.1021/ie0203779
- Park, J. I., Jung, J. H., Jo, M. K., Oh, H. S., & Han, J. W. (2011). Mathematical modeling of the burden distribution in the blast furnace shaft. Metals and Materials International, 17(3), 485–496. https://doi.org/10.1007/s12540-011-0629-7
- Shi, P. Y., Zhou, P., Fu, D., & Zhou, C. Q. (2016). Mathematical model for burden distribution in blast furnace. Ironmaking & Steelmaking, 43(1), 74–81. https://doi.org/10.1179/1743281215Y.0000000052
- Chen, J., Zuo, H., Xue, Q., & Wang, J. (2021). A review of burden distribution models of blast furnace. Powder Technology, 398, Article 117055. https://doi.org/10.1016/j.powtec.2021.117055
- Nag, S., Gupta, A., Paul, S., Gavel, D. J., & Aich, B. (2014). Prediction of heap shape in blast furnace burden distribution. ISIJ International, 54(7), 1517–1520. https://doi.org/10.2355/isijinternational.54.1517
- Agrawal, A. (2019). Blast furnace performance under varying pellet proportion. Transactions of the Indian Institute of Metals, 72, 777–787. https://doi.org/10.1007/s12666-018-1530-6
- Mitra, T. (2016). Modeling of burden distribution in the blast furnace [Doctoral dissertation, Åbo Akademi University]. Thermal and Flow Engineering Laboratory, Faculty of Science and Engineering. https://urn.fi/URN:ISBN:978-952-12-3420-0
- Li, Z., Kuang, S., Liu, S., Gan, J., Yu, A., Li, Y., & Mao, X. (2019). Numerical investigation of burden distribution in ironmaking blast furnace. Powder Technology, 353, 385–397. https://doi.org/10.1016/j.powtec.2019.05.047
- Chen, J., Zuo, H., Xue, Q., & Wang, J. (2022). A review of burden distribution models of blast furnace. Powder Technology, 398, Article 117055. https://doi.org/10.1016/j.powtec.2021.117055
- Roeplal, R., Pang, Y., Adema, A., Stel, J., & Schott, D. (2023). Modelling of phenomena affecting blast furnace burden permeability using the Discrete Element Method (DEM) – A review. Powder Technology, 415, Article 118161. https://doi.org/10.1016/j.powtec.2022.118161
- Yu, Y. W., & Saxén, H. (2011). Analysis of rapid flow of particles in and from an inclined chute using small-scale experiments and discrete element simulation. Ironmaking & Steelmaking, 38(6), 432–442. http://dx.doi.org/10.1179/1743281211Y.0000000015
- Narita, Y., Orimoto, T., Mio, H., & Nomura, S. (2017). DEM analysis of particle trajectory in circumferential direction at bell-less top. ISIJ International, 57(3), 429–434. https://doi.org/10.2355/isijinternational.ISIJINT-2016-560
- Ma, H., Xia, X., Zhou, L., & Xu, C. (2023). A comparative study of the performance of different particle models in simulating particle charging and burden distribution in a blast furnace within the DEM framework. Energies, 16(9), Article 3890. https://doi.org/10.3390/en16093890
- Ivancha, N. G., Muraveva, I. G., Vishnyakov, V. I., Sherbachev, V. R., & Ermolina, K. P. (2022). Povyshenie energoeffektivnosti domennoj plavki za schet vybora racional’nykh parametrov rezhima zagruzki mnogokomponentnoj shihty. Problems of the Regional Energetics, (2(54)), 53–62. https://doi.org/10.52254/1857-0070.2022.2-54.05
- Bolshakov, V. I., Ivancha, N. G., Muraveva, I. G., & Vishnyakov, V. I. (2012). Tekhnologicheskoe obosnovanie effektivnosti zagruzki mnogokomponentnykh smeshannykh porcij shikhtovykh materialov v domennuyu pech’. In Sb. nauchn. tr. IChM «Fundamental’nye i prikladnye problemy chernoj metallurgii» (No. 25, pp. 103–122).
- Dobroskok, V. A. (2007). Spetsial’nye sistemy zagruzki domennykh. Chernye Metally, (9), 13–21.
- Bukhval’der, J., Dobroskok, V. A., Lonardi, E., Goffin, R., Tillen, G., & Kyoler, S. (2008). Sovremennye tekhnologii zagruzki domennykh pechej [Modern blast furnace loading systems]. Chyornye metally, (9), 21–25. [In Russian]
- Nikitin, L. D., Dolinskij, V. A., Bugajov, S. F., Mar’yasov, M. F., Denisov, Yu. M., Chudnova, N. T., & Fyodorov, I. P. (2004). Formirovanie racional’noj struktury stolba shikhtovykh materialov v domennoj pechi [Formation of a rational structure of a column of charged materials in a blast furnace]. Metallurgist, (2), 26–28.
- Shepetovskij, E. A. (2003). Racional’noe formirovanie stolba shikhty v domennoj pechi [Rational formation of charge column in a blast furnace]. Steel, (5), 11–15. [In Russian]
- Yaroshevskij, S. L., Nozdrachev, V. A., Chebotarev, A. P., Rudenko, V. A., Feshchenko, S. A., Kuznetsov, A. M., Padalka, V. P., Hlaponin, N. S., & Kuzin, A. V. (2000). Effektivnost’ ispol’zovaniya koksa fraktsii men’she 40 mm v domennoj plavke [Efficiency of using coke fraction less than 40 mm in blast-furnace smelting]. Metallurgist, (12), 32–35. [In Russian]
- Litvinov, L. F., Yaroshevskij, S. L., Kuznetsov, A. M., Padalka, V. P., Hlaponin, N. S., & Kuzin, A. V. (2004). Effektivnost’ tekhnologii domennoj plavki pri zagruzke v pech’ koksovogo oreshka v smesi s zheleazorudnoj shikhtoj [Efficiency of using coke fraction less than 40 mm in blast-furnace smelting]. Metal and Casting of Ukraine, (12), 5–9. [In Russian]
- Yu, X., & Shen, Y. (2020). Model study of central coke charging on ironmaking blast furnace performance: Effects of charring pattern and nut coke. Powder Technology, 361, 124–135. https://doi.org/10.1016/j.powtec.2019.10.012
- Kashihara, Y., Iwai, Y., Ishiwata, N., Oyama, N., Matsuno, H., Horikoshi, H., Yamamoto, K., & Kuwabara, M. (2017). Development of new charging technique for mixing coke in ore layer at blast furnace with center feed type bell-less top. ISIJ International, 57(4), 665–672. https://doi.org/10.2355/isijinternational.ISIJINT-2016-613
- Matsui, Y., Sato, A., Oyama, T., & Matsuo, T. (2003). All pellets operation in Kobe No. 3 blast furnace under intensive coal injection. ISIJ International, 43(2), 166–174. https://doi.org/10.2355/isijinternational.43.166
- Kalinin, A. P., Zagainov, S. A., & Yaroshenko, Yu. G. (1985). Matematicheskaya model’ otsenki kachestvennykh kharakteristik potoka pri ikh tsiklicheskoj zagruzke i vygruzke iz bunkera. Izvestiya VUZov. Chernaia metallurgiia, (8), 95–98.
- Kalinin, A. P. (1990). Matematicheskie modeli dvizheniya shikhty i ee raspredeleniya na koloshnike domennoj pechi. Obzornaya informatsiya. Seriya «Podgotovka syrevykh materialov k metallurgicheskomu pererabotke i proizvodstvu chuguna» (No. 4, pp. 1–32). Institut “Chermetinformatsiya”.
- Malakhov, G. M. (1952). Vypusk rudy iz obrushennykh blokov. Metallurgizdat.
- Kvapil, R. (1961). Dvizhenie sypuchikh materialov v bunkerakh. Gosgorteorizdat.
- Panich, Yu. V., & Pajkin, M. Z. (1977). Matematicheskaya model’ zagruzki i istecheniya sypuchikh materialov iz nakopitel’nykh emkostej s tsel’yu usredneniya rud. Obogashchenie Rud, (3), 6–10.
- Kulikov, V. V. (1982). Vypusk rudy. Nedra.
- Nakano, K., Isei, Y., Natsui, T., Watanabe, K., & Kishino, T. (2020, March). Technical report tracking technique of burden materials for blast furnace with bell-less top by using RFID. Nippon Steel Technical Report, (123), 83–89. https://www.nipponsteel.com/en/tech/report/pdf/123-13.pdf
- Nakano, K., Sunahara, K., & Inada, T. (2010). Advanced supporting system for burden distribution control at blast furnace top. ISIJ International, 50(7), 994–999. https://doi.org/10.2355/isijinternational.50.994
- Kajiwara, Y., Jimbo, T., Joko, T., Aminaga, Y., & Inada, T. (1985). Development of a simulation model for burden distribution in bell-less charging based on full scale model experiments. Transactions of ISIJ, 71(2), 175–182. http://dx.doi.org/10.2355/tetsutohagane1955.71.2_175
- Tyuzyun, U., & Nedderman, R. (1985). Eksperimental’noe dokazatel’stvo kinematicheskogo modelirovaniya techenij granulirovannykh sred v otsutstvie soprotivleniya vozdukha. In Mekhanika granulirovannykh sred: Teoriya bystrykh dvizhenij: Sb. st. Ser. Mekhanika (pp. 193–209). Mir.
- Mio, H., Kadowaki, M., Matsuzaki, S., & Kunitomo, K. (2012). Development of particle flow simulator in the charging process of blast furnace by discrete element method. Minerals Engineering, 33, 27–33. http://dx.doi.org/10.1016/j.mineng.2012.01.002
- Kumar, R., Patel, C. M., Jana, A. K., & Gopireddy, S. R. (2018). Prediction of hopper discharge rate using combined discrete element method and artificial neural network. Advanced Powder Technology, 29(11), 2822–2834. https://doi.org/10.1016/j.apt.2018.08.002
- Chibwe, D. K. (2019). Optimized burden delivery for blast furnace operations [Doctoral dissertation, The University of Newcastle]. Faculty of Engineering and Built Environment.
- Bolshakov, V. I. (1990). Teoriya i praktika zagruzki domennykh pechej. Metallurgiya.
- Bolshakov, V. I., Semenov, Yu. S., Ivancha, N. G., Vishnyakov, V. I., Shumelchik, E. I., et al. (2012). Issledovanie parametrov potoka shikhtovykh materialov i ikh raspredeleniya na koloshnike sovremennoj domennoj pechi. Metallurgicheskaya i gornorudnaya promyshlennost’, (3), 87–92.
- Bolshakov, V. I., Bogachev, Yu. A., Vishnyakov, V. I., Ivancha, N. G., & Shuliko, S. T. (2008). Predpuskovye issledovaniya zagruzki i raspredeleniya shikhty v domennoj pechi bol’shogo ob”ema. Byulleten’ nauchno-tekhnicheskoj i ekonomicheskoj informatsii. Chernaya metallurgiya, (6(1302)), 39–44.
- Bolshakov, V. I., Varivoda, I. E., Roslik, N. A., & Shutylev, F. M. (1995). Vliyanie dvizheniya shikhty po traktam zagruzochnogo ustrojstva na okruzhnoye raspredeleniye v domennoj pechi. In Sb. Fundamental’nye i prikladnye problemy chernoj metallurgii (pp. 57–68). Naukova Dumka.
- Bolshakov, V. I., & Zarembo, A. Yu. (1990). Issledovanie dvizheniya materialov v shikhtovykh traktakh beskonusnykh zagruzochnykh ustrojstv. Obzornaya informatsiya. Ser. «Podgotovka syrevykh materialov k metallurgicheskomu pererabotke i proizvodstvu chuguna» (No. 2, pp. 1–9). Institut «Chermetinformatsiya».
- Bolshakov, V. I., & Zarembo, A. Yu. (1985). Traektorii dvizheniya shikhty v koloshnikovom prostranstve sovremennoj domennoj pechi. Byulleten’ CNIIChM. Chernaya metallurgiya, (20), 35–37.
- Bolshakov, V. I., Zarembo, A. Yu., & Salo, A. S. (1984). Metodika rascheta parametrov shoda shikhty s raspredelitel’nogo lotka. In Sb. MChM: Voprosy proizvodstva chuguna v domennykh pechakh (pp. 60–64). Metallurgiya.
- Bolshakov, V. I., Zarembo, A. Yu., & Ivancha, N. G. (2007). Dvizhenie shikhty v koloshnikovom prostranstve domennoj pechi pri zagruzke lotkovym raspredelitelem. Metallurgicheskaya i gornorudnaya promyshlennost, (4), 75–79.
- Bolshakov, V. I., Semenov, Yu. S., Lebed’, V. V., Shumelchik, E. I., & Vishnyakov, V. I. (2011). Model’ radial’nogo raspredeleniya shikhtovykh materialov na koloshnike domennoj pechi, oborudovannoj BZU. iSb. nauchn. tr. IChM «Fundamental’nye i prikladnye problemy chernoj metallurgii» (No. 23, pp. 52–62).
- Semenov, Yu. S., Shumelchik, E. I., Vishnyakov, V. I., Nasledov, A. V., Semen, I. Yu., & Zubenko, A. V. (2013). Model system for selecting and correcting charging programs for blast furnaces equipped with a bell-less charging apparatus. Metallurgist, 56(9–10), 652–657. https://doi.org/10.1007/s11015-013-9630-3
Рукопис надійшов до редакції / Received 22.10.2025
Рекомендовано до друку / Accepted 28.05.2026
Опубліковано / Published 30.05.2026


