Study of the pore space of iron ore pellets using a cellular automaton model

Strengthening the role of pellets as an iron ore raw material sets the task of ensuring their high quality. One of the most important factors affecting the structure and metallurgical properties of pellets are the structural features of the pore space. The relationship between the pore parame­ters (volume, specific surface area) and metallurgical properties is realized through the size of the surface in contact with the reducing agent gas and strength of the mineral pellet frame. The aim of the work is to study the mechanism of pore formation in pellets using the methodology of cellular automata. The study was conducted using two-dimensional cells with a square lattice and a Moore neighborhood. The calculated field value was 8064 cells. The simulation was performed in the MS Excel environment. Studies have shown that already at the third or fourth step, the pores are localized and their size is stabilized. According to the data obtained, at the second step of modeling, the largest pores are formed, which further grow due to the absorption of small voids. In addition, relict pores remain inside the solid, which could not assimilate with larger ones due to the stochastic nature of the process. Thus, the localization of pores in the structure is mainly determined by the first stage of structure transformation. For sinter and pellets, this is the granu­lation of the charge. At this stage, pores are isolated and localized. They have a statistical advantage (initial size, presence of other pores nearby) and during further heat treatment they grow due to the absorption of other pores. The specific surface area of pores in pellets due to sintering, determined using the cellular automaton model, is reduced by 3.0 – 3.5 times.

1. Petrov S.P. Ferrous Metallurgy in Asian Russia in the Second and Third Decades of the 21st Century. Novosibirsk: Institute of Economics and Industrial Engineering of the SB RAS; 2023:240. (In Russ.).

2. Budanov I.A. Macroeconomic prospects of metal production. Stal’. 2024;(6):47–53. (In Russ.).

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;(2):4–11. http://doi.org/10.17580/cisisr.2023.02.01

4. Yur’ev B.P., Spirin N.A., Sheshukov O.Yu., etc. Development of Technologies for Production of Iron Ore Pellets with High Metallurgical Properties. Nizhny Tagil: NTI UrFU; 2018:172. (In Russ.).

5. Mal’tseva V.E., Seleznev V.S., Chukin D.M. Heat Treatment of Raw Pellets: Technology and Schemes of Roasting Machines. Moscow: Metallurgizdat; 2023:719. (In Russ.).

6. Zhuravlev F.N., Malysheva T.Ya. Pellets from Ferruginous Quartzite Concentrates. Moscow: Metallurgiya; 1991:127. (In Russ.).

7. Malysheva T.Ya., Dolitskaya O.A. Petrography and Mineralogy of Iron Ore Raw Materials. Moscow: MISIS; 2004:422. (In Russ.).

8. Medvedeva A.V., Mordasov D.M., Mordasov M.M. Classification of control methods for materials porosity. Vestnik TGTU. 2012;18(3):749–754. (In Russ.).

9. 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;54(4):305–309. https://doi.org/10.3103/S0967091224700682

10. 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;(1):10–15. (In Russ.). https://doi.org/10.17580/chm.2025.01.02

11. 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;54(12):1145–1155. https://doi.org/10.3103/S0967091225700019

12. 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;213:108746. https://doi.org/10.1016/j.mineng.2024.108746

13. Nie H., Qi B., Li Y., Qiu D., Wei H., Hammam A., Ah­­med A., Yu Y. Structure analysis of pellets with different reduction degrees using X-ray micro-computed tomography. Steel Research International. 2023;94(1):2200241. https://doi.org/10.1002/srin.202200241

14. Bersenev I.S., Vokhmyakova I.S., Ozornin N.K., Pokolenko S.I., Sabirov E.R., Spirin N.A. Porosity of iron-ore pellets at different stages of roasting and reduction. Steel in Translation. 2023;53(12):1137–1143. https://doi.org/10.3103/S096709122370002X

15. 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;53(11):1018–1022. https://doi.org/10.3103/S0967091223110062

16. Usol’tsev D.Yu., 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;52(10):859–863. https://doi.org/10.3103/S0967091222090133

17. Berman Yu.L. The Main Patterns of Pellet Production. Chelyabinsk: Metallurgiya; 1991:184. (In Russ.).

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;180:107459. https://doi.org/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. Physical Sciences / Physics, Engineering. 2021;63(4):3–7. https://doi.org/10.31276/VJSTE.63(4).03-07

20. Belous D.D., Tyrtyshnikov A.Yu., Gordienko M.G. Cellular-automaton approach to predict the changes of the pore size distribution during the purolysis process. Uspekhi v khimii i khimicheskoi tekhnologii. 2016;XXX(4):108–110. (In Russ.).

21. Kuchinsky N.A., Vasetsky A.M., Kenig E.Ya., Koltso­­va E.M. Cellular automata for mathematical modeling of coating formation on the granules. Fundamental'nye issledovaniya. 2013;(4):1069-1073. (In Russ.).

22. Bandman O.L. Parallel implementation of cellular auto­mata algorithms for simulation of spatial dynamics. Sibirskii zhurnal vychislitel’noi matematiki. 2007;10(4):335–348. (In Russ.).

23. Wolfram S. Twenty problems in the theory of cellular auto­mata. Physica Scripta. 1985;T9:170–183. https://doi.org/10.1088/0031-8949/1985/T9/029

24. Gu С., 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;49: 91–105. https://doi.org/10.1016/j.jmst.2020.02.028

25. 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;206:103921. https://doi.org/10.1016/j.advengsoft.2025.103921

26. 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;26:104669. https://doi.org/10.1016/j.rineng.2025.104669

27. Lian Y., Lin S., Yan W., Liu W.K., Wagner G.J. A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing. Computational Mechanics. 2018;61:543–558. https://doi.org/10.1007/s00466-017-1535-8

28. 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;9(1):57. https://doi.org/10.3390/met9010057

29. 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. Mate­rials & Design. 2017;113:369–376. http://dx.doi.org/10.1016/j.matdes.2016.10.031

30. 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;29(6):1950–1958. https://doi.org/10.1016/j.msec.2009.03.003

31. Beketov S.M., Zubkova D.A., Red’ko S.G. Evolutionary methods of optimization of digital models of organizational systems: A literary review. Perm National Research Polytechnic University Bulletin. Electrotechnics, Information Technologies, Control Systems. 2024:(52);45–75. (In Russ.).

32. Pavlovets V.M. Development of equipment and techno­logy for pelletizing iron ore charge in production of pellets. Izvestiya. Ferrous Metallurgy. 2023;66(5):529–537. https://doi.org/10.17073/0368-0797-2023-5-529-537