隨著全球暖化問題日益嚴峻，鋼鐵產業面臨巨大的減碳壓力。氫氣還原技術被視為最具潛力的低碳煉鐵解決方案，可減少高達85%的二氧化碳排放。然而，鐵礦還原反應涉及複雜的固氣反應機制，包括外部傳輸、內部擴散及化學反應等多重控制步驟，其動力學係數擬合面臨高維非線性優化挑戰、數值微分誤差放大、反應機制選擇困難等問題。
本研究開發了一套完整且自動化的鐵礦還原反應動力學係數分析方法。採用神經網路結合自動微分技術建立數據預處理方法，解決傳統數值微分的誤差累積問題，計算精度可達10⁻¹⁶。提出轉化率均勻取樣策略，確保整個反應過程的均勻表示，避免時間均勻取樣導致的數據分布不均問題。開發PSO-GD混合優化策略，結合粒子群優化的全域探索能力與梯度下降法的局部收斂精度，通過300個粒子的並行搜索克服傳統方法對初始係數值的強烈依賴性。構建基於策略模式的機制自動選擇架構，實現對多種反應機制組合的系統性測試與比較。
實驗驗證結果顯示，所開發方法成功應用於Fe2O3→Fe3O4、Fe3O4→FeO、FeO→Fe三個還原階段的動力學分析，擬合係數均保持在物理合理範圍內，相較於傳統梯度下降法在擬合精度和穩定性方面均有顯著提升。本研究建立的高度自動化、穩定可靠的動力學係數分析方法，為氫氣還原煉鐵技術的工業化發展提供重要的理論支撐和標準化分析工具。

Hydrogen-based reduction has emerged as the most promising low-carbon ironmaking technology, capable of reducing CO₂ emissions by up to 85%. However, iron ore reduction involves complex gas–solid mechanisms, and conventional kinetic modeling faces challenges such as high-dimensional nonlinear optimization, numerical errors, and mechanism identification.
This study develops a fully automated framework for kinetic parameter analysis. Neural networks with automatic differentiation are applied for data preprocessing, eliminating numerical differentiation errors and achieving high computational accuracy. A conversion-based sampling strategy ensures uniform data distribution across the reaction process. Furthermore, a hybrid Particle Swarm Optimization–Gradient Descent (PSO-GD) algorithm combines global exploration with local convergence accuracy, employing parallel computation with 300 particles to reduce dependency on initial parameters. A strategy-pattern-based framework is also introduced to systematically evaluate and compare multiple mechanisms.
Experimental validation confirms the applicability of the proposed method to the three-step reduction process (Fe2O3→Fe3O4、Fe3O4→FeO、FeO→Fe), with fitted parameters remaining physically reasonable. Compared with conventional approaches, the framework exhibits superior accuracy and stability, providing a reliable and automated methodology for kinetic analysis. This work offers theoretical support and standardized tools for advancing hydrogen-based ironmaking technologies toward industrial implementation.

[1] D. Wagner, "Etude expérimentale et modélisation de la réduction du minerai de fer par l'hydrogène," Institut National Polytechnique de Lorraine-INPL, 2008.
[2] A. Khawam and D. R. Flanagan, "Solid-state kinetic models: basics and mathematical fundamentals," The journal of physical chemistry B, vol. 110, no. 35, pp. 17315-17328, 2006.
[3] J. Hancock and J. Sharp, "Method of comparing solid‐state kinetic data and its application to the decomposition of kaolinite, brucite, and BaCO3," Journal of the American Ceramic Society, vol. 55, no. 2, pp. 74-77, 1972.
[4] F. Patisson and O. Mirgaux, "Hydrogen ironmaking: How it works," Metals, vol. 10, no. 7, p. 922, 2020.
[5] X. Jiang, L. Wang, and F. M. Shen, "Shaft furnace direct reduction technology-Midrex and Energiron," Advanced materials research, vol. 805, pp. 654-659, 2013.
[6] M. Atsushi, H. Uemura, and T. Sakaguchi, "MIDREX processes," Kobelco Technol Rev, vol. 29, no. 8, 2010.
[7] I. Kurunov, "The direct production of iron and alternatives to the blast furnace in iron metallurgy for the 21st century," Metallurgist, vol. 54, no. 5, pp. 335-342, 2010.
[8] H. Hamadeh, O. Mirgaux, and F. Patisson, "Detailed modeling of the direct reduction of iron ore in a shaft furnace," Materials, vol. 11, no. 10, p. 1865, 2018.
[9] J. D. Anderson and J. Wendt, Computational fluid dynamics. Springer, 1995.
[10] H. Jasak, "Error analysis and estimation in the Finite Volume method with applications to fluid flows," 1996.
[11] R. Eymard, T. Gallouët, and R. Herbin, "Finite volume methods," Handbook of numerical analysis, vol. 7, pp. 713-1018, 2000.
[12] H. Baolin, H. Zhang, L. Hongzhong, and Z. Qingshan, "Study on kinetics of iron oxide reduction by hydrogen," Chinese journal of chemical engineering, vol. 20, no. 1, pp. 10-17, 2012.
[13] A. Zare Ghadi, M. S. Valipour, S. M. Vahedi, and H. Y. Sohn, "A review on the modeling of gaseous reduction of iron oxide pellets," steel research international, vol. 91, no. 1, p. 1900270, 2020.
[14] S. Patankar, Numerical heat transfer and fluid flow. CRC press, 2018.
[15] S. Ruder, "An overview of gradient descent optimization algorithms," arXiv preprint arXiv:1609.04747, 2016.
[16] A. F. Villaverde, F. Fröhlich, D. Weindl, J. Hasenauer, and J. R. Banga, "Benchmarking optimization methods for parameter estimation in large kinetic models," Bioinformatics, vol. 35, no. 5, pp. 830-838, 2018, doi: 10.1093/bioinformatics/bty736.
[17] Y. Wang, S. Christley, E. Mjolsness, and X. Xie, "Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent," BMC systems biology, vol. 4, no. 1, p. 99, 2010.
[18] Y. Zhang, S. Wang, and G. Ji, "A comprehensive survey on particle swarm optimization algorithm and its applications," Mathematical problems in engineering, vol. 2015, no. 1, p. 931256, 2015.
[19] M. Schwaab, E. C. Biscaia Jr, J. L. Monteiro, and J. C. Pinto, "Nonlinear parameter estimation through particle swarm optimization," Chemical Engineering Science, vol. 63, no. 6, pp. 1542-1552, 2008.
[20] Z. Fu, Z. Wang, and G. Chen, "Enhanced parameter estimation with improved particle swarm optimization algorithm for cell culture process modeling," AIChE Journal, vol. 70, no. 4, p. e18388, 2024.
[21] E. El Rassy, A. Delaroque, P. Sambou, H. K. Chakravarty, and A. Matynia, "On the potential of the particle swarm algorithm for the optimization of detailed kinetic mechanisms. comparison with the genetic algorithm," The Journal of Physical Chemistry A, vol. 125, no. 23, pp. 5180-5189, 2021.
[22] D. J. Wales and J. P. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms," The Journal of Physical Chemistry A, vol. 101, no. 28, pp. 5111-5116, 1997.
[23] M. Baioletti, V. Santucci, and M. Tomassini, "A performance analysis of Basin hopping compared to established metaheuristics for global optimization," Journal of Global Optimization, vol. 89, no. 3, pp. 803-832, 2024.
[24] M. Goodridge, J. Moriarty, J. Vogrinc, and A. Zocca, "Hopping between distant basins," Journal of Global Optimization, vol. 84, no. 2, pp. 465-489, 2022.
[25] A. K. Pujari and S. D. Veeramachaneni, "Gradient based Hybridization of PSO," in Proceedings of the 2023 7th International Conference on Computer Science and Artificial Intelligence, 2023, pp. 353-360.
[26] Wikipedia. "龍格現象." https://zh.wikipedia.org/zh-tw/%E9%BE%99%E6%A0%BC%E7%8E%B0%E8%B1%A1 (accessed 7/15, 2025).
[27] scikit-learn. "Polynomial and Spline interpolation." https://scikit-learn.org/stable/auto_examples/linear_model/plot_polynomial_interpolation.html (accessed 7/15, 2025).
[28] D. Kapil. "Stochastic vs Batch Gradient Descent." https://medium.com/@divakar_239/stochastic-vs-batch-gradient-descent-8820568eada1 (accessed 7/15, 2025).
[29] M. Iljana, A. Abdelrahim, H. Bartusch, and T. Fabritius, "Reduction of acid iron ore pellets under simulated wall and center conditions in a blast furnace shaft," Minerals, vol. 12, no. 6, p. 741, 2022.
[30] A. Abdelrahim, M. Iljana, M. Omran, T. Vuolio, H. Bartusch, and T. Fabritius, "Influence of H₂–H₂O content on the reduction of acid iron ore pellets in a CO–CO₂–N₂ reducing atmosphere," 2020.
[31] L. Braun et al., "Following the structural changes of iron oxides during reduction under transient conditions," ChemSusChem, vol. 17, no. 24, p. e202401045, 2024.
[32] W. Zhang et al., "Thermodynamic analyses of iron oxides redox reactions," in Proceedings of the 8th Pacific Rim International Congress on Advanced Materials and Processing, 2013: Springer, pp. 777-789.
[33] R. TAKAHASHI, Y. TAKAHASHI, and Y. OMORI, "Operation and simulation of pressurized shaft furnace for direct reduction," Transactions of the Iron and Steel Institute of Japan, vol. 26, no. 9, pp. 765-774, 1986.