Abstract
In chemical, petrochemical, and biochemical sectors, bubble columns are essential for facilitating critical reactions like methanation, oxidation, and hydrogenation. Gas hold-up is one of the most important operational parameters that has a significant impact on the performance and efficiency of these multiphase reactions. In order to improve the design and operational efficiency of bubble columns, it is imperative that the gas hold-up be precisely estimated. Creating a sophisticated predictive model with machine learning techniques is a promising solution for obtaining accurate and dependable estimations because of the intricate relationships and the unpredictable impact of numerous factors on gas hold-up. Therefore, this study explores the efficiency of four deep learning models, including the Recurrent Neural Network, Convolutional Neural Network, Long Short-Term Memory, and Gated Recurrent Unit in gas hold-up estimation. This study utilizes the Harris Hawk Optimization algorithm for hyperparameter fine-tuning and enhancing the model’s performance. The optimized Recurrent Neural Network model achieves markable results, attaining a test correlation coefficient of 0.995, root mean square error of 0.005 alongside a mean absolute error of 0.0054. Additionally, this study demonstrate that liquid height is the most influential variable in controlling gas hold-up by sensitivity indices approaching 1, which suggests that even slight variations in liquid height can lead to significant changes in gas retention.
Acknowledgments
We would like to take this opportunity to acknowledge that there are no individuals or organizations that require acknowledgment for their contributions to this work.
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Research ethics: Research involving Human Participants and Animals: The observational study conducted on medical staff needs no ethical code. Therefore, the above study was not required to acquire ethical code.
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Informed consent: This option is not necessary due to that the data were collected from the references.
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Author contributions: All authors contributed to the study’s conception and design. Data collection, simulation and analysis were performed by “Chonglin Fan and Qing Hu”. Also, the first draft of the manuscript was written by Chonglin Fan. Qing Hu commented on previous versions of the manuscript.
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Use of Large Language Models, AI and Machine Learning Tools: During the preparation of this work, the authors used Large Language Models, AI, and Machine Learning tools for tasks such as language refinement, data analysis, or figure generation, with all outputs being reviewed and validated by the authors to ensure accuracy and originality. After using these tools/services, the authors reviewed and edited the content and take full responsibility for the content of the published article.
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Conflict of interest: The authors declare no competing interests.
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Research funding: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
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Data availability: The authors do not have permission to share data.
References
1. Sun, H, Anderson, A, Albeshr, MF, Fahad Alrefaei, A, Hoang Le, Q, Gavurová, B, et al.. Chlorella vulgaris microalgae derived blends in micro gas turbine engines: a comprehensive environmental impact analysis for highway vehicle applications. Fuel 2024;355:129467. https://doi.org/10.1016/j.fuel.2023.129467.Search in Google Scholar
2. Oh, E. Prediction of gasification process via random forest regression model optimized with meta-heuristic algorithms. J Artif Intell Syst Model 2024;02:45–65. https://doi.org/10.22034/jaism.2024.445930.1026.Search in Google Scholar
3. Neviani, M, Bagnerini, P, Paladino, O. Gas bubble dynamics in airlift photo-bioreactors for microalgae cultivation by level set methods. Fuel 2021;292:120402. https://doi.org/10.1016/j.fuel.2021.120402.Search in Google Scholar
4. Gu, W, Theau, E, Anderson, AW, Fletcher, DF, Kavanagh, JM, McClure, DD. A modelling workflow for quantification of photobioreactor performance. Chem Eng J 2023;477:147032. https://doi.org/10.1016/j.cej.2023.147032.Search in Google Scholar
5. Luzi, G, McHardy, C. Modeling and simulation of photobioreactors with computational fluid Dynamics—a comprehensive review. Energies (Basel) 2022;15:3966. https://doi.org/10.3390/en15113966.Search in Google Scholar
6. Papacek, S, Jablonsky, J, Petera, K. Advanced integration of fluid dynamics and photosynthetic reaction kinetics for microalgae culture systems. BMC Syst Biol 2018;12:1–12. https://doi.org/10.1186/s12918-018-0611-9.Search in Google Scholar PubMed PubMed Central
7. Wang, G, Haringa, C, Noorman, H, Chu, J, Zhuang, Y. Developing a computational framework to advance bioprocess scale-up. Trends Biotechnol 2020;38:846–56. https://doi.org/10.1016/j.tibtech.2020.01.009.Search in Google Scholar PubMed
8. Lim, SH, Kwon, EH, Go, KS, Pham, HH, Nho, NS, Kim, KH, et al.. Estimation of the gas hold up and flow regime of a bubble column reactor for the slurry phase hydrocracking of heavy oil. Fuel 2023;338:127190. https://doi.org/10.1016/j.fuel.2022.127190.Search in Google Scholar
9. Clift, R, Grace, JR, Weber, ME. Bubbles, drops, and particles. Mineola, New york: Dover Publications, INC; 2005.Search in Google Scholar
10. Dobbelaere, MR, Plehiers, PP, Van de Vijver, R, Stevens, C, Van Geem, KM. Machine learning in chemical engineering: strengths, weaknesses, opportunities, and threats. Engineering 2021;7:1201–11. https://doi.org/10.1016/j.eng.2021.03.019.Search in Google Scholar
11. Schweidtmann, AM, Esche, E, Fischer, A, Kloft, M, Repke, J, Sager, S, et al.. Machine learning in chemical engineering: a perspective. Chem Ing Tech 2021;93:2029–39. https://doi.org/10.1002/cite.202100083.Search in Google Scholar
12. Venkatasubramanian, V. The promise of artificial intelligence in chemical engineering: is it here, finally? AIChE J 2019;65. https://doi.org/10.1002/aic.16489.Search in Google Scholar
13. Sun, W, Braatz, RD. Smart process analytics for predictive modeling. Comput Chem Eng 2021;144:107134. https://doi.org/10.1016/j.compchemeng.2020.107134.Search in Google Scholar
14. Fisher, OJ, Watson, NJ, Escrig, JE, Witt, R, Porcu, L, Bacon, D, et al.. Considerations, challenges and opportunities when developing data-driven models for process manufacturing systems. Comput Chem Eng 2020;140:106881. https://doi.org/10.1016/j.compchemeng.2020.106881.Search in Google Scholar
15. Hastie, T, Tibshirani, R, Friedman, JH, Friedman, JH. The elements of statistical learning: data mining, inference, and prediction. New York: Springer; 2009, vol. 2.10.1007/978-0-387-84858-7Search in Google Scholar
16. Al‐Masry, WA, Abdennour, A. Gas hold‐up estimation in bubble columns using passive acoustic waveforms with neural networks. J Chem Technol Biotechnol 2006;81:951–7. https://doi.org/10.1002/jctb.1475.Search in Google Scholar
17. Hazare, SR, Patil, CS, Vala, SV, Joshi, AJ, Joshi, JB, Vitankar, VS, et al.. Predictive analysis of gas hold-up in bubble column using machine learning methods. Chem Eng Res Des 2022;184:724–39. https://doi.org/10.1016/j.cherd.2022.06.007.Search in Google Scholar
18. Zhong, H, Sun, Z, Zhu, J, Zhang, C. Prediction of solid holdup in a gas–solid circulating fluidized bed riser by artificial neural networks. Ind Eng Chem Res 2021;60:3452–62. https://doi.org/10.1021/acs.iecr.0c05474.Search in Google Scholar
19. Shahhoseyni, S, Rahmani, M, Sivaram, A. Advanced modeling techniques for predicting gas holdup in bubble columns using machine learning. Fuel 2025;388:134449. https://doi.org/10.1016/j.fuel.2025.134449.Search in Google Scholar
20. Ranade, V, Marchini, S, Kipping, R, Ranade, N, Schubert, M. Estimation of gas hold-up in bubble columns using wall pressure fluctuations and machine learning. Chem Eng J 2024;500:157078. https://doi.org/10.1016/j.cej.2024.157078.Search in Google Scholar
21. Wilkinson, PM, Spek, AP, van Dierendonck, LL. Design parameters estimation for scale-up of high-pressure bubble columns. AIChE J 1992;38:544–54. https://doi.org/10.1002/aic.690380408.Search in Google Scholar
22. Akita, K, Yoshida, F. Gas holdup and volumetric mass transfer coefficient in bubble columns. Effects of liquid properties. Ind Eng Chem Process Des Dev 1973;12:76–80.https://doi.org/10.1021/I260045A015/ASSET/I260045A015.FP.PNG_V03.10.1021/i260045a015Search in Google Scholar
23. Anabtawi, MZA, Abu-Eishah, SI, Hilal, N, Nabhan, MBW. Hydrodynamic studies in both bi-dimensional and three-dimensional bubble columns with a single sparger. Chem Eng Process Process Intensif 2003;42:403–8.https://doi.org/10.1016/s0255-2701(02)00061-2.Search in Google Scholar
24. Heijnen, JJ, Van’t Riet, K. Mass transfer, mixing and heat transfer phenomena in low viscosity bubble column reactors. Chem Eng J 1984;28:B21–42.https://doi.org/10.1016/0300-9467(84)85025-x.Search in Google Scholar
25. Kadic, E, Heindel, TJ. An introduction to bioreactor hydrodynamics and gas-liquid mass transfer. Hoboken, NJ: John Wiley & Sons; 2014.10.1002/9781118869703Search in Google Scholar
26. Akita, K, Yoshida, F. Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns. Ind Eng Chem Process Des Dev 1974;13:84–91. https://doi.org/10.1021/i260049a016.Search in Google Scholar
27. Dey, R, Salem, FM. Gate-variants of gated recurrent unit (GRU) neural networks. In: 2017 IEEE 60th international midwest symposium on circuits and systems (MWSCAS). Piscataway, NJ: IEEE; 2017:1597–600 pp.10.1109/MWSCAS.2017.8053243Search in Google Scholar
28. Xiong, B, Fu, M, Cai, Q, Li, X, Lou, L, Ma, H, et al.. Forecasting ultra-short-term wind power by multiview gated recurrent unit neural network. Energy Sci Eng 2022;10:3972–86. https://doi.org/10.1002/ese3.1263.Search in Google Scholar
29. Zhu, Q, Tan, M. A novel activation function based recurrent neural networks and their applications on sentiment classification and dynamic problems solving. Front Neurorobot 2022;16:1022887. https://doi.org/10.3389/fnbot.2022.1022887.Search in Google Scholar PubMed PubMed Central
30. Kazmi, S, Gorgulu, B, Cevik, M, Baydogan, MG. A concurrent CNN-RNN approach for multi-step wind power forecasting. arXiv preprint arXiv:2301. 2023;00819:1–28. https://doi.org/10.48550/arXiv.2301.00819Search in Google Scholar
31. Jin, H, Oxner, M, Corballis, PM, Hayward, WG. Holistic face processing is influenced by non-conscious visual information. Br J Psychol 2022;113:300–26. https://doi.org/10.1111/bjop.12521.Search in Google Scholar PubMed
32. Liu, Q, Long, L, Yang, Q, Peng, H, Wang, J, Luo, X. LSTM-SNP: a long short-term memory model inspired from spiking neural P systems. Knowl Based Syst 2022;235:107656. https://doi.org/10.1016/j.knosys.2021.107656.Search in Google Scholar
33. O’shea, K, Nash, R. An introduction to convolutional neural networks. arXiv preprint arXiv:1511. 2015;08458:1–11. https://doi.org/10.48550/arXiv.1511.08458Search in Google Scholar
34. Kourounis, G, Elmahmudi, AA, Thomson, B, Hunter, J, Ugail, H, Wilson, C. Computer image analysis with artificial intelligence: a practical introduction to convolutional neural networks for medical professionals. Postgrad Med J 2023;99:1287–94. https://doi.org/10.1093/postmj/qgad095.Search in Google Scholar PubMed PubMed Central
35. Heidari, AA, Mirjalili, S, Faris, H, Aljarah, I, Mafarja, M, Chen, H. Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 2019;97:849–72. https://doi.org/10.1016/j.future.2019.02.028.Search in Google Scholar
36. Bansal, N, Bansal, A, Gupta, M. Analyzing the variability of RNN hyperparameters and architectures for HAR with wearable sensor data. In: 2024 3rd International conference on power electronics and IoT applications in renewable energy and its control (PARC). Piscataway, NJ: IEEE; 2024:232–7 pp.10.1109/PARC59193.2024.10486796Search in Google Scholar
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