Bubble size modeling approach for the simulation of bubble columns

doi:10.1016/j.cjche.2022.02.005

Abstract

Abstract: The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.

Key words: Bubble column, Bubble size modeling, Numerical simulation, Population balance equations, Computational efficiency

摘要： The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.

关键词: Bubble column, Bubble size modeling, Numerical simulation, Population balance equations, Computational efficiency

Xibao Zhang, Zhenghong Luo. Bubble size modeling approach for the simulation of bubble columns[J]. Chinese Journal of Chemical Engineering, 2023, 53(1): 194-200.

Xibao Zhang, Zhenghong Luo. Bubble size modeling approach for the simulation of bubble columns[J]. 中国化学工程学报, 2023, 53(1): 194-200.

References

[1] A.R. Sarhan, J. Naser, G. Brooks, CFD simulation on influence of suspended solid particles on bubbles' coalescence rate in flotation cell, Int. J. Miner. Process. 146 (2016) 54–64.
[2] A.R. Sarhan, J. Naser, G. Brooks, CFD modeling of bubble column: Influence of physico–chemical properties of the gas/liquid phases properties on bubble formation, Sep. Purif. Technol. 201 (2018) 130–138.
[3] A.R. Sarhan, J. Naser, G. Brooks, Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column, Particuology 36 (2018) 82-95.
[4] W. Su, X.G. Shi, Y.Y. Wu, J.S. Gao, X.Y. Lan, Simulation on the effect of particle on flow hydrodynamics in a slurry bed, Powder. Technol. 361 (2020) 1006–1020.
[5] L.J. Xu, B.R. Yuan, H.Y. Ni, C.X. Chen, Numerical simulation of bubble column flows in churn-turbulent regime: Comparison of bubble size models, Ind. Eng. Chem. Res. 52 (20) (2013) 6794–6802.
[6] X.F. Guo, Q. Zhou, J. Li, C.X. Chen, Implementation of an improved bubble breakup model for TFM–PBM simulations of gas–liquid flows in bubble columns, Chem. Eng. Sci. 152 (2016) 255-266.
[7] G.Y. Yang, H.H. Zhang, J.J. Luo, T.F. Wang, Drag force of bubble swarms and numerical simulations of a bubble column with a CFD–PBM coupled model, Chem. Eng. Sci. 192 (2018) 714-724.
[8] H.H. Zhang, A. Sayyar, Y.L. Wang, T.F. Wang, Generality of the CFD–PBM coupled model for bubble column simulation, Chem. Eng. Sci. 219(2020) 115514.
[9] H.H. Zhang, K.Y. Guo, Y.L. Wang, A. Sayyar, T.F. Wang, Numerical simulations of the effect of liquid viscosity on gas–liquid mass transfer of a bubble column with a CFD–PBM coupled model, Int. J. Heat. Mass. Transf. 161 (2020) 120229.
[10] N. Yang, Q. Xiao, A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors, Chem. Eng. Sci. 170 (2017) 241-250.
[11] M. An, X.P. Guan, N. Yang, Modeling the effects of solid particles in CFD–PBM simulation of slurry bubble columns, Chem. Eng. Sci. 223 (2020) 115743.
[12] P. Yan, H.B. Jin, G.X. He, X.Y. Guo, L. Ma, S.H. Yang, R.Y. Zhang, Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD–PBM coupled model, Chem. Eng. Res. Des. 154(2020) 47–59.
[13] X.P. Shang, B.F. Ng, M.P. Wan, S.R. Ding, Investigation of CFD–PBM simulations based on fixed pivot method: Influence of the moment closure, Chem. Eng. J. 382 (2020) 122882.
[14] W.B. Shi, X.G. Yang, M. Sommerfeld, J. Yang, X.Y. Cai, G. Li, Y. Zong, Modelling of mass transfer for gas–liquid two-phase flow in bubble column reactor with a bubble breakage model considering bubble-induced turbulence, Chem. Eng. J. 371 (2019) 470-485.
[15] Z.B. Huang, D.D. McClure, G.W. Barton, D.F. Fletcher, J.M. Kavanagh, Assessment of the impact of bubble size modelling in CFD simulations of alternative bubble column configurations operating in the heterogeneous regime, Chem. Eng. Sci. 186 (2018) 88-101.
[16] X.B. Zhang, Z.H. Luo, Effects of bubble coalescence and breakup models on the simulation of bubble columns, Chem. Eng. Sci. 226 (2020) 115850.
[17] S.G. Gong, N.N. Gao, L.C. Han, H.A. Luo, A theoretical model for bubble coalescence by coupling film drainage with approach processes, Chem. Eng. Sci. 213 (2020) 115387.
[18] L.C. Han, J. Fu, M. Li, S.G. Gong, N.N. Gao, C. Zhang, H.A. Luo, A theoretical unsteady-state model for kL of bubbles based on the framework of wide energy spectrum, AIChE J. 62 (4) (2016) 1007-1022.
[19] J. Solsvik, H.A. Jakobsen, Development of fluid particle breakup and coalescence closure models for the complete energy spectrum of isotropic turbulence, Ind. Eng. Chem. Res. 55 (5) (2016) 1449–1460.
[20] C.T. Xing, T.F. Wang, K.Y. Guo, J.F. Wang, A unified theoretical model for breakup of bubbles and droplets in turbulent flows, AIChE J. 61(4) (2015) 1391-1403.
[21] G.Y. Yang, K.Y. Guo, T.F. Wang, Numerical simulation of the bubble column at elevated pressure with a CFD–PBM coupled model, Chem. Eng. Sci.170 (2017) 251-262.
[22] 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.
[23] A. H. Syed, M. Boulet, T. Melchiori, J.M. Lavoie, CFD simulation of a slurry bubble column: Effect of population balance kernels, Comput. Fluids 175 (2018) 167-179.
[24] P. Chen, J. Sanyal, M.P. Duduković, Numerical simulation of bubble columns flows: Effect of different breakup and coalescence closures, Chem. Eng. Sci. 60 (4) (2005) 1085-1101.
[25] K. Ekambara, K. Nandakumar, J.B. Joshi, CFD simulation of bubble column reactor using population balance, Ind. Eng. Chem. Res. 47 (21) (2008) 8505-8516.
[26] J.W. Chen, P. Gupta, S. Degaleesan, M.H. Al-Dahhan, M.P. Duduković, B.A. Toseland, Gas holdup distributions in large-diameter bubble columns measured by computed tomography, Flow. Meas. Instrum. 9 (2) (1998) 91-101.
[27] H. Al-Naseri, J.P. Schlegel, M.H. Al-Dahhan, The effects of internals and low aspect ratio on the fully developed flow region and bubble properties in a pilot-plant bubble column, Exp. Therm. Fluid. Sci. 104 (2019) 284-301.
[28] A.J. Sultan, L.S. Sabri, M.H. Al-Dahhan, Investigating the influence of the configuration of the bundle of heat exchanging tubes and column size on the gas holdup distributions in bubble columns via gamma-ray computed tomography, Exp. Therm. Fluid. Sci. 98 (2018) 68-85.
[29] M. Ishii, N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J. 25 (5) (1979) 843–855.
[30] A. Tomiyama, H. Tamai, I. Zun, S. Hosokawa, Transverse migration of single bubbles in simple shear flows, Chem. Eng. Sci. 57(11) (2002) 1849-1858.
[31] T. Frank, P.J. Zwart, E. Krepper, H.M. Prasser, D. Lucas, Validation of CFD models for mono- and polydisperse air–water two-phase flows in pipes, Nucl. Eng. Des. 238 (3) (2008) 647-659.
[32] A.D. Burns, T. Frank, I. Hamill, J.M. Shi, The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows, In: Proceedings of the 5th International Conference on Multiphase Flow, Yokohama, Japan, 2004.
[33] M. Pourtousi, J.N. Sahu, P. Ganesan, Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column, Chem. Eng. Process.: Process. Intensif. 75 (2014) 38-47.
[34] R.M.A. Masood, A. Delgado, Numerical investigation of the interphase forces and turbulence closure in 3D square bubble columns, Chem. Eng. Sci. 108 (2014) 154-168.
[35] R.F. Mudde, O. Simonin, Two- and three-dimensional simulations of a bubble plume using a two-fluid model, Chem. Eng. Sci. 54 (21) (1999) 5061–5069.
[36] M.J. Prince, H.W. Blanch, Bubble coalescence and break-up in air-sparged bubble columns, AIChE J. 36 (10) (1990) 1485-1499.
[37] H.A. Luo, Coalescence, breakup and liquid circulation in bubble column reactors, Ph.D. Thesis, Norwegian Institute of Technology, Trondheim, Norway, 1993.
[38] H.A. Luo, H.F. Svendsen, Theoretical model for drop and bubble breakup in turbulent dispersions, AIChE J. 42 (5) (1996) 1225-233.
[39] L.C. Han, Study on the behaviors of the mass transfer, breakup and coalescence of fluid particles in multiphase flows reactors, Ph.D. Thesis, Xiangtan University, China, 2010.
[40] X.B. Zhang, W.C. Yan, Z.H. Luo, Numerical simulation of local bubble size distribution in bubble columns operated at heterogeneous regime, Chem. Eng. Sci. 231 (2021) 116266.
[41] X.P. Guan, N. Yang, Bubble properties measurement in bubble columns: From homogeneous to heterogeneous regime, Chem. Eng. Res. Des.127 (2017) 103-112.
[42] C. Han, X.P. Guan, N. Yang, Structure evolution and demarcation of small and large bubbles in bubble columns, Ind. Eng. Chem. Res. 57 (25) (2018) 8529-8540.