Exploration on the stability conditions in bubble columns by noncooperative game theory

doi:10.1016/j.cjche.2022.05.004

中国化学工程学报 ›› 2022, Vol. 50 ›› Issue (10): 75-84.DOI: 10.1016/j.cjche.2022.05.004

• Fluid Dynamics and Transport Phenomena • 上一篇下一篇

Exploration on the stability conditions in bubble columns by noncooperative game theory

Jiachen Liu^1,2, Xiaoping Guan¹, Ning Yang^1,2

1 State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2022-02-13 修回日期:2022-05-14 出版日期:2022-10-28 发布日期:2023-01-04
通讯作者: Ning Yang,E-mail:nyang@ipe.ac.cn
基金资助:
The authors acknowledge the long-term support from National Natural Science Foundation of China (21925805, 22178354, 91834303) and the "Transformational Technologies for Clean Energy and Demonstration" Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDA21000000. We thank Yifen Mu and Zhixin Liu of Academy of Mathematics and Systems Science, Chinese Academy of Sciences for helpful discussion on game theory.

Exploration on the stability conditions in bubble columns by noncooperative game theory

Jiachen Liu^1,2, Xiaoping Guan¹, Ning Yang^1,2

1 State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-02-13 Revised:2022-05-14 Online:2022-10-28 Published:2023-01-04
Contact: Ning Yang,E-mail:nyang@ipe.ac.cn
Supported by:
The authors acknowledge the long-term support from National Natural Science Foundation of China (21925805, 22178354, 91834303) and the "Transformational Technologies for Clean Energy and Demonstration" Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDA21000000. We thank Yifen Mu and Zhixin Liu of Academy of Mathematics and Systems Science, Chinese Academy of Sciences for helpful discussion on game theory.

摘要/Abstract

摘要： The energy-minimization multiscale (EMMS) model, originally proposed for gas-solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e., the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas-liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas-solid and gas-liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

关键词: Bubble column, Flow regimes, Mesoscale, Noncooperative game theory

Abstract: The energy-minimization multiscale (EMMS) model, originally proposed for gas-solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e., the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas-liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas-solid and gas-liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

Key words: Bubble column, Flow regimes, Mesoscale, Noncooperative game theory

Jiachen Liu, Xiaoping Guan, Ning Yang. Exploration on the stability conditions in bubble columns by noncooperative game theory[J]. 中国化学工程学报, 2022, 50(10): 75-84.

Jiachen Liu, Xiaoping Guan, Ning Yang. Exploration on the stability conditions in bubble columns by noncooperative game theory[J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 75-84.

参考文献

[1] N. Yang, W. Wang, W. Ge, J.H. Li, Choosing structure-dependent drag coefficient in modeling gas-solid two-phase flow, China Particuology 1 (1) (2003) 38-41
[2] N. Yang, W. Wang, W. Ge, J.H. Li, Analysis of flow structure and calculation of drag coefficient for concurrent-up gas-solid flow, Chin. J. Chem. Eng. 11 (1) (2003) 79-84
[3] J.F. Davidson, Circulating fluidised bed hydrodynamics, Powder Technol. 113 (3) (2000) 249-260
[4] J. Yerushalmi, D.H. Turner, A.M. Squires, The fast fluidized bed, Ind. Eng. Chem. Proc. Des. Dev. 15 (1) (1976) 47-53
[5] J.W.A. de Swart, R. Krishna, Simulation of the transient and steady state behaviour of a bubble column slurry reactor for Fischer-Tropsch synthesis, Chem. Eng. Process. Process. Intensif. 41 (1) (2002) 35-47
[6] J.H. Li, Z.D. Zhang, W. Ge, Q.C. Sun, J. Yuan, A simple variational criterion for turbulent flow in pipe, Chem. Eng. Sci. 54 (8) (1999) 1151-1154
[7] J.H. Li, W.L. Huang, From multiscale to mesoscience:Addressing mesoscales in mesoregimes of different levels, Annu. Rev. Chem. Biomol. Eng. 9 (2018) 41-60
[8] J.H. Li, W. Ge, W. Wang, N. Yang, W.L. Huang, Focusing on mesoscales:From the energy-minimization multiscale model to mesoscience, Curr. Opin. Chem. Eng. 13 (2016) 10-23
[9] J.H. Li, M. Kwauk, Particle-Fluid Two-Phase Flow:The Energy-Minimization Multi-Scale Method, Metallurgical Industry Press, Beijing, 1994
[10] J.H. Li, Multi-scale modeling and method of energy minimization for particle-fluid two phase flow, Ph.D. Thesis. Institute of Chemical Metallurgy, Chinese Academy of Sciences, Beijing, 1987. (in Chinese)
[11] J.H. Chen, N. Yang, W. Ge, J.H. Li, Stability-driven structure evolution:Exploring the intrinsic similarity between gas-solid and gas-liquid systems, Chin. J. Chem. Eng. 20 (1) (2012) 167-177
[12] W. Ge, W. Wang, N. Yang, J.H. Li, M. Kwauk, F.G. Chen, J.H. Chen, X.J. Fang, L. Guo, X.F. He, X.H. Liu, Y.N. Liu, B.N. Lu, J. Wang, J.W. Wang, L.M. Wang, X.W. Wang, Q.G. Xiong, G.Z. Zhou, Meso-scale oriented simulation towards virtual process engineering (VPE)-The EMMS paradigm, Chem. Eng. Sci. 66 (19) (2011) 4426-4458
[13] N. Yang, J.H. Chen, W. Ge, J.H. Li, A conceptual model for analyzing the stability condition and regime transition in bubble columns, Chem. Eng. Sci. 65 (1) (2010) 517-526
[14] N. Yang, J.H. Chen, H. Zhao, W. Ge, J.H. Li, Explorations on the multi-scale flow structure and stability condition in bubble columns, Chem. Eng. Sci. 62 (24) (2007) 6978-6991
[15] H. Zhao, Multi-scale modeling of gas-liquid (slurry) reactors, Ph.D. Thesis. Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 2006. (in Chinese)
[16] Y. Li, Y.F. Mu, S. Yuan, L. Guo, The game theoretical approach for multi-phase complex systems in chemical engineering, J. Syst. Sci. Complex. 30 (1) (2017) 4-19
[17] S. Yuan, Y.F. Mu, X.P. Guan, Z.X. Liu, J.H. Chen, N. Yang, L. Zhang, Game-theoretical explorations of the mesoscale flow structure and regime transitions in bubble columns, Particuology 48 (2020) 100-108
[18] W. Ge, J.H. Li, Physical mapping of fluidization regimes-The EMMS approach, Chem. Eng. Sci. 57 (18) (2002) 3993-4004
[19] J.H. Li, L.X. Wen, W. Ge, H.P. Cui, J.Q. Ren, Dissipative structure in concurrent-up gas-solid flow, Chem. Eng. Sci. 53 (19) (1998) 3367-3379
[20] C. Han, J.H. Chen, Mesoregime-oriented investigation of flow regime transition in bubble columns, Ind. Eng. Chem. Res. 58 (31) (2019) 14424-14435
[21] W. Ge, F.G. Chen, J. Gao, S.Q. Gao, J. Huang, X.X. Liu, Y. Ren, Q.C. Sun, L.M. Wang, W. Wang, N. Yang, J.Y. Zhang, H. Zhao, G.Z. Zhou, J.H. Li, Analytical multi-scale method for multi-phase complex systems in process engineering-Bridging reductionism and holism, Chem. Eng. Sci. 62 (13) (2007) 3346-3377
[22] M.J. Du, S.W. Hu, J.H. Chen, X.H. Liu, W. Ge, Extremum characteristics of energy consumption in fluidization analyzed by using EMMS, Chem. Eng. J. 342 (2018) 386-394
[23] X.P. Guan, N. Yang, Modeling of co-current and counter-current bubble columns with an extended EMMS approach, Particuology 44 (2019) 126-135
[24] H.A. Luo, H.F. Svendsen, Theoretical model for drop and bubble breakup in turbulent dispersions, AIChE J. 42 (5) (1996) 1225-1233
[25] Y.H. Wang, Q. Xiao, N. Yang, J.H. Li, In-depth exploration of the dual-bubble-size model for bubble columns, Ind. Eng. Chem. Res. 51 (4) (2012) 2077-2083
[26] N. Yang, Z.Y. Wu, J.H. Chen, Y.H. Wang, J.H. Li, Multi-scale analysis of gas-liquid interaction and CFD simulation of gas-liquid flow in bubble columns, Chem. Eng. Sci. 66 (14) (2011) 3212-3222
[27] X.D. Jiang, N. Yang, B.L. Yang, Computational fluid dynamics simulation of hydrodynamics in the riser of an external loop airlift reactor, Particuology 27 (2016) 95-101
[28] Q. Xiao, N. Yang, J.H. Li, Stability-constrained multi-fluid CFD models for gas-liquid flow in bubble columns, Chem. Eng. Sci. 100 (2013) 279-292
[29] X.P. Guan, N. Yang, CFD simulation of bubble column hydrodynamics with a novel drag model based on EMMS approach, Chem. Eng. Sci. 243 (2021) 116758
[30] T.C. Koopmans, Activity Analysis of Production and Allocation, John Wiley, New York, 1951
[31] Y. Mo, M.J. Du, W. Ge, P.W. Zhang, Analysis of the energy-minimization multiscale model with multiobjective optimization, Particuology 48 (2020) 109-115
[32] J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1955
[33] D. Fudenberg, J. Tirole, Game Theory, MIT Press, Cambridge, Massachusetts, 1991
[34] J.H. Chen, N. Yang, W. Ge, J.H. Li, Modeling of regime transition in bubble columns with stability condition, Ind. Eng. Chem. Res. 48 (1) (2009) 290-301
[35] R.F. Mudde, W.K. Harteveld, H.E.A. van den Akker, Uniform flow in bubble columns, Ind. Eng. Chem. Res. 48 (1) (2009) 148-158
[36] E. Camarasa, C. Vial, S. Poncin, G. Wild, N. Midoux, J. Bouillard, Influence of coalescence behaviour of the liquid and of gas sparging on hydrodynamics and bubble characteristics in a bubble column, Chem. Eng. Process. Process. Intensif. 38 (4-6) (1999) 329-344

Exploration on the stability conditions in bubble columns by noncooperative game theory

Exploration on the stability conditions in bubble columns by noncooperative game theory

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