NPVP TOREX, Yekaterinburg, Russia¹ ; Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia²

I. S. Bersenev, Cand. Eng., Head of the Research and Analysis Department¹, Associate Prof., Dept. of Iron and Alloy Metallurgy², e-mail: i.bersenev@torex-npvp.ru
E. R. Sabirov, Senior Engineer¹, Postgraduate Student², e-mail: e.sabirov@torex-npvp.ru

Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia

N. A. Spirin, Dr. Eng., Prof., Head of the Dept. of Thermal Physics and Informatics in Metallurgy, e-mail: n.a.spirin@urfu.ru

This paper presents a study of the effect of pore size in iron ore pellets on their strength using cellular automaton method. The relevance of this study is due to the increasing production and consumption of pellets, with porosity being one of the main factors influencing their properties. The aim of this study is to study crack formation in pellets using cellular automaton methodology and assess their relationship with pore size and strength. A cellular automaton approach was used to model the pore structure, which allows for the stochastic nature of pore formation and their evolution during heat treatment. Cellular automata are discrete mathematical models consisting of a grid of cells, each of which can be in one of a finite number of states. The cell states change according to predetermined rules, depending on neighboring cells. The simulation was conducted in a two-dimensional space with a square grid, where each cell could be in one of two states: 0 – pore, 1 – solid. The results showed that small pores (less than 0.26 mm) create a greater number of crack nuclei, which reduces pellet strength by 20–25 % compared to pellets with large pores (more than 0.26 mm). It was found that increasing pore surface area by decreasing pore size improves pellet reducibility, but simultaneously promotes the rapid initiation and propagation of cracks, reducing their strength. Thus, optimizing the metallurgical properties of pellets requires finding a rational combination of porous structure parameters.

1. Petrov S. P. Ferrous metallurgy of Asian Russia in the second and third decades of the 21st century. Novosibirsk : Institute of Economics and Industrial Engineering, Siberian Branch of the Russian Academy of Sciences, 2023. 240 p.
2. Budanov I. A. Macroeconomic prospects of metal production. Stal. 2024. No. 6. pp. 47–53.
3. Kapelyushin Yu. E. Comparative review on the technologies of briquetting, sintering, pelletizing and direct use of fines in processing of ore and technogenic materials. CIS Iron and Steel Review. 2023. Vol. 26. pp. 4–11.
4. Yuryev B. P., Spirin N. A., Sheshukov O. Yu. et al. Development of technologies for production of iron ore pellets with high metallurgical properties: scientific monograph. Nizhny Tagil : NTI (branch) of UrFU, 2018. 172 p.
5. Maltseva V. E., Seleznev V. S., Chukin D. M. Heat treatment of raw pellets: technology and schemes of roasting machines. Moscow : Metallurgizdat, 2023. 719 p.
6. Bersenev I. S., Sabirov E. R., Ishimbaev A. V., Matyukhin V. I. Study of the porosity of burnt pellets using the capillary-porous solids model. Steel in Translation. 2024. Vol. 54, No. 4. pp. 311–315.
7. Zhuravlev F. N., Malysheva T. Ya. Pellets from ferruginous quartzite concentrates. Moscow : Metallurgiya, 1991. 127 p.
8. Malysheva T. Ya., Dolitskaya O. A. Petrography and mineralogy of iron ore raw materials: textbook for university students. Moscow : MISIS, 2004. 422 p.
9. Bersenev I. S., Vokhmyakova I. S., Ozornin N. K., Pokopenko S. I., Sabirov E. R., Spirin N. A. Porosity of iron-ore pellets at different stages of roasting and reduction. Steel in Translation. 2023. Vol. 53, No. 12. pp. 1137–1143.
10. Bersenev I. S., Pokolenko S. I., Sabirov E. R., Spirin N. A., Borisenko A. V., Kurochkin A. R. Influence of the Iron Ore Pellets Macrostructure on Their Strength. Steel in Translation. 2023. Vol. 53, No. 11. pp. 1018–1022.
11. Usol’tsev D. Y., Bersenev I. S., Bardavelidze G. G., Sabirov E. R., Spirin N. A., Isaenko G. E. On the formation
of porosity in fluxed iron-ore pellets. Steel in Translation. 2022. Vol. 52, No. 10. pp. 859–863.
12. Berman Yu. L. Basic principles of pellet production. Chelyabinsk : Metallurgiya, 1991. 184 p.
13. Gruzdev A. I., Bersenev I. S., Chernov M. S., Pigarev S. P., Gridasov I. N., Pokolenko A. Yu., Sabirov E. R., Spirin N. A. Study of the pore space structure of iron ore pellets using computer tomography. Steel in Translation. 2024. Vol. 54, No. 12. pp. 1145–1155.
14. Cavaliere P., Sadeghi B., Dijon L., Laska A., Koszelow D. Three-dimensional characterization of porosity in iron ore pellets: A comprehensive study. Minerals Engineering. 2024. Vol. 213. 108746. DOI: 10.1016/j.mineng.2024.108746
15. Nie H., Qi B., Li Y., Qiu D., Wei H., Hammam A., Ahmed A., Yaowei Yu. Structure analysis of pellets with different reduction degrees using X-ray micro-computed tomography. Steel Res. Int. 2023. Vol. 94, Iss. 1. 2200241. DOI: 10.1002/srin.202200241
16. Medvedeva A. V., Mordasov D. M., Mordasov M. M. Classification of methods for monitoring the porosity of materials. Vestnik TGTU. 2012. Vol. 18, No. 3. pp. 749–754.
17. Bersenev I. S., Bizhanov A. M., Sabirov E. R., Spirin N. A. Determination of specific surface area of pore space of iron ore pellets. Chernye Metally. 2025. No. 1. pp. 10–15.
18. Scharm C., Küster F., Laabs M., Huang Q., Volkova O., Reinmöller M., Guhl S., Meyer B. Direct reduction of iron ore pellets by H2 and CO: In-situ investigation of the structural transformation and reduction progression caused by atmosphere and temperature. Minerals Engineering. 2022. Vol. 180. 107459. DOI: 10.1016/j.mineng.2022.107459
19. Nguyen C.-S., Nguyen T.-H., Nguyen S.-L., Bui A.-H. Study on the reducibility of iron ore pellets at high temperature. Vietnam Journal of Science, Technology and Engineering. 2021. Vol. 63, No. 4. pp. 3–7. DOI: 10.31276/VJSTE.63(4).03-07
20. Gilyarov V. L. Modeling of crack growth during the destruction of heterogeneous materials. Fizika tverdogo tela. 2011. Vol. 53, Iss. 4. pp. 707–710.
21. Belous D. D., Tyrtyshnikov A. Yu., Gordienko M. G. Cellular automata approach for predicting changes in pore size distribution during pyrolysis. Uspekhi v khimii i khimicheskoy tekhnologii. 2016. Vol. 30, No. 4. pp. 108–110.
22. Kuchinsky N. A., Vasetsky A. M., Kenig E. Ya., Koltsova E. M. Modeling the process of granule coating formation based on the cellular automata theory. Fundamentalnye issledovaniya. 2013. No. 4. pp. 1069–1073.
23. Bandman O. L. Parallel implementation of cellular automata algorithms for modeling spatial dynamics. Sibirskiy zhurnal vychislitelnoy matematiki. 2007. Vol. 10, No. 4. pp. 335–348.
24. Wolfram S. Twenty problems in the theory of cellular automata. Physica Scripta. 1985. Vol. T9. pp. 170–183.
25. Gu C., Ridgeway C. D., Cinkilic E., Lu Y., Luo A. A. Predicting gas and shrinkage porosity in solidification microstructure: A coupled three-dimensional cellular automaton model. Journal of Materials Science & Technology. 2020. Vol. 49. pp. 91–105. DOI: 10.1016/j.jmst.2020.02.028
26. Psakhye S. G., Korostelev S. Yu., Smolin A. Yu., Dmitriev A. I. et al. The method of movable cellular automaton as a tool of physical mesomechanics of materials. Fizicheskaya mezomekhanika. 1998. Vol. 1. No. 1. pp. 95-108.
27. Mendoza-Cuy A., Begambre-Carrillo O., Villalba-Morales J. D. Topology optimization of steel slotted dampers with the hybrid cellular automata technique. Advances in Engineering Software. 2025. Vol. 206. 103921. DOI: 10.1016/j.advengsoft.2025.103921
28. Bozsóki I., Illés B., Géczy A. Numerical simulation of Sn grain growth in composite solder joint using a modified cellular automaton model. Results in Engineering. 2025. Vol. 26. 104669. DOI: 10.1016/j.rineng.2025.104669
29. Lian Y., Lin S., Yan W. et al. A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing. Comput Mech. 2018. Vol. 61. pp. 543–558. DOI: 10.1007/s00466-017-1535-8
30. Guo Z., Zhou J., Yin Y., Shen X., Ji X. Numerical simulation of three-dimensional mesoscopic grain evolution: model development, validation, and application to nickel-based superalloys. Metals. 2019. Vol. 9, No. 1. 57. DOI: 10.3390/met9010057
31. Lopez-Botello O., Martinez-Hernandez U., Ramírez J., Pinna C., Mumtaz K. Two-dimensional simulation of grain structure growth within selective laser melted AA-2024. Mater. Des. 2017. Vol. 113. pp. 369–376.
32. Guo C., Sheng X., Chu C., Dong Y., Pu Y., Lin P. A cellular automaton simulation of the degradation of porous polylactide scaffold: I. Effect of porosity. Materials Science and Engineering: C. 2009. Vol. 29, Iss. 6. pp. 1950–1958. DOI: 10.1016/j.msec.2009.03.003
33. Vetyugov D. A., Matveeva T. N. Use of xanthan gum as part of bentonite-polymer binder for pelletizing of iron ore concentrate. Chernye Metally. 2024. No. 5. pp. 4–9.
34. Wang C., Xu C., Liu Z. Effect of organic binders on the activation and properties of indurated magnetite pellets. Int J Miner Metall Mater. 2021. Vol. 28. pp. 1145–1152.
35. Ma M., Qian L., Xuling C., Yan Z., Yongbin Y., Qiang Z. Reducing bentonite usage in iron ore pelletization through a novel polymer-type binder: Impact on pellet induration and metallurgical properties. Journal of Materials Research and Technology. 2024. Vol. 30. pp. 8019–8029.
36. Shupletsov Yu. P. Strength and deformability of rock massifs. Yekaterinburg : Izdatelstvo UrO RAN, 2004. 195 p.
37. Khopunov E. A. Selective destruction of mineral and technogenic raw materials (in beneficiation and metallurgy). Yekaterinburg : UIPTs, 2013. 429 p.
38. Bezerra E. T. V., Augusto K. S., Paciornik S. Discrimination of pores and cracks in iron ore pellets using deep learning neural networks. REM, Int. Eng. J. 2020. Vol. 73 (2). pp. 1–8. DOI: 10.1590/0370-44672019730119
39. Mikhalyuk A. V., Zakharov V. V. Relaxation effects in the dynamics of soils and rocks. Prikladnaya mekhanika i tekhnicheskaya fizika. 2000. Vol. 41, No. 3. pp. 202–212.
40. GOST 24765-81. Iron pellets. Method for the determination of compression strength. Introduced: 01.07.1981.