CFD-PBM耦合模型用于浆态床反应器的研究进展

doi:10.16085/j.issn.1000-6613.2025-0512

摘要/Abstract

摘要：

计算流体力学-群体平衡模型（CFD-PBM）由于结合了CFD预测流场信息和PBM计算气泡尺寸分布两方面的优势，被广泛应用于鼓泡塔反应器的数值模拟。但目前大多数研究工作主要针对常压下空气-水体系，其结果无法直接应用到高温、高压下操作的真实工业浆态床反应器中。本文从不同操作环境下气泡破碎及聚并行为建模角度出发，阐述了压力、黏度、表面张力及颗粒对流体力学行为影响的最新进展。模拟结果表明，CFD-PBM耦合模型可以准确描述浆态床内流体力学行为，与传统的经验关联式相比模型适用性更广。目前的模拟工作大多集中在实验室规模浆态床反应器的冷模研究，未来需要克服工业规模反应器多尺度耦合的难题，从而推动CFD-PBM耦合模型从实验室规模模拟向工业应用跨越。

关键词: 计算流体力学-群体平衡模型, 浆态床反应器, 气泡破碎, 气泡聚并, 多相流, 流体动力学

Abstract:

The computational fluid dynamics-population balance model (CFD-PBM), which integrates the advantages of CFD in predicting flow field with PBM in calculating bubble size distributions, has been widely applied in numerical simulations of bubble column reactors. However, most existing studies focus on ambient pressure air-water systems, limiting the direct applicability of their findings to industrial slurry reactors operated under high-temperature and high-pressure conditions. This review summarizes recent advances in understanding the effects of pressure, viscosity, surface tension, and particles on hydrodynamic behaviors, with a focus on modeling bubble breakup and coalescence under various operating conditions. Simulation results show that the CFD-PBM coupled model can effectively characterize hydrodynamic behaviors in slurry reactors and has wider applicability than the traditional empirical correlations. While current simulations predominantly address cold-mode laboratory-scale reactors, future investigations should focus on resolving multi-scale coupling challenges in industrial-scale systems. Such advancements are crucial for enabling the translation of the CFD-PBM framework from fundamental research to practical industrial applications.

Key words: computational fluid dynamics-population balance model (CFD-PBM), slurry reactors, bubble breakup, bubble coalescence, multiphase flow, hydrodynamics

中图分类号:

TQ021.1

沈宪琨, 贾志勇, 蓝晓程, 王铁峰. CFD-PBM耦合模型用于浆态床反应器的研究进展[J]. 化工进展, 2025, 44(8): 4408-4418.

SHEN Xiankun, JIA Zhiyong, LAN Xiaocheng, WANG Tiefeng. Progress on CFD-PBM coupled model for slurry reactors[J]. Chemical Industry and Engineering Progress, 2025, 44(8): 4408-4418.

图/表 9

图1 CFD-PBM耦合模型示意图[8]

图2 单个气泡的变形与破碎过程[28-29]

图3 气泡破碎过程内部气体流动示意图[34]

图4 压力/气体密度对气泡破碎的影响[28,34]

图5 液体黏度对湍流能谱各子区部分能量的影响[16]（ε=2.0m2/s3，k=0.2m2/s2）

图6 惯性子区能谱和全能谱下液体黏度对二阶结构函数和湍流涡数量密度的影响[42]（ε=2.0m2/s3，k=0.2m2/s2）

图7 不同液体黏度下由惯性子区能谱和全能谱计算的气泡破碎速率[42]（ε=2.0m2/s3，k=0.2m2/s2）

图8 液体表面张力对气泡破碎行为的影响[28]

图9 浆态床中不同颗粒效应对比[63]（αs=20%，ds=55μm，Ug=0.16m/s）

参考文献 63

[1]	AN Min, GAO Jingqi, WANG Tiankuo, et al. Particle effects on the hydrodynamics in slurry bubble column reactors: A review from multiscale mechanisms[J]. Particuology, 2024, 91: 176-189.
[2]	MAHMOUDI Sadra, HLAWITSCHKA Mark W. Effect of solid particles on the slurry bubble columns behavior—A review[J]. ChemBioEng Reviews, 2022, 9(1): 63-92.
[3]	GRANDE Giuseppe Actis, ROVERO Giorgio, SICARDI Silvio, et al. Degradation of residual dyes in textile wastewater by ozone: Comparison between mixed and bubble column reactors[J]. The Canadian Journal of Chemical Engineering, 2017, 95(2): 297-306.
[4]	WANG Xuqing, WEN Zhaoquan, ZHANG Xibao, et al. Numerical simulation of mass transfer characteristics of gas-liquid bubble columns and an improved mass transfer model[J]. Industrial & Engineering Chemistry Research, 2024, 63(18): 8473-8486.
[5]	VARALLO Nicolò, BESAGNI Giorgio, MEREU Riccardo. Computational fluid dynamics simulation of the heterogeneous regime in a large-scale bubble column[J]. Chemical Engineering Science, 2023, 280: 119090.
[6]	GUAN Xiaoping, YANG Ning. Bubble size distribution in a bubble column with vertical tube internals: Experiments and CFD-PBM simulations[J]. AIChE Journal, 2022, 68(9): e17755.
[7]	YAN Peng, JIN Haibo, HE Guangxiang, et al. Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model[J]. Chemical Engineering Research and Design, 2020, 154: 47-59.
[8]	WANG Tiefeng, WANG Jinfu, JIN Yong. A CFD-PBM coupled model for gas-liquid flows[J]. AIChE Journal, 2006, 52(1): 125-140.
[9]	高一博, 耿琳琳, 王振, 等. 基于欧拉-欧拉方法的气液两相流数值模型发展综述[J]. 力学与实践, 2022, 44(5): 1021-1036.
	GAO Yibo, GENG Linlin, WANG Zhen, et al. A review of numerical models development for gas-liquid two-phase flow based on Eulerian-Eulerian method[J]. Mechanics in Engineering, 2022, 44(5): 1021-1036.
[10]	张华海, 王悦琳, 李邦昊, 等. 湍流中气泡破碎建模与实验研究进展[J]. 化工学报, 2021, 72(12): 5936-5954.
	ZHANG Huahai, WANG Yuelin, LI Banghao, et al. Review of bubble breakup modelling and experimental study in turbulent flow[J]. CIESC Journal, 2021, 72(12): 5936-5954.
[11]	PRINCE Michael J, BLANCH Harvey W. Bubble coalescence and break-up in air-sparged bubble columns[J]. AIChE Journal, 1990, 36(10): 1485-1499.
[12]	LUO Hean, SVENDSEN Hallvard F. Theoretical model for drop and bubble breakup in turbulent dispersions[J]. AIChE Journal, 1996, 42(5): 1225-1233.
[13]	LEHR F, MILLIES M, MEWES D. Bubble-size distributions and flow fields in bubble columns[J]. AIChE Journal, 2002, 48(11): 2426-2443.
[14]	LAAKKONEN Marko, ALOPAEUS Ville, AITTAMAA Juhani. Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel[J]. Chemical Engineering Science, 2006, 61(1): 218-228.
[15]	YAN Peng, JIN Haibo, GAO Xin, et al. Numerical analysis of bubble characteristics in a pressurized bubble column using CFD coupled with a population balance model[J]. Chemical Engineering Science, 2021, 234: 116427.
[16]	XING Chutian, WANG Tiefeng, WANG Jinfu. Experimental study and numerical simulation with a coupled CFD-PBM model of the effect of liquid viscosity in a bubble column[J]. Chemical Engineering Science, 2013, 95: 313-322.
[17]	PRAJAPATI Ravindra, KOHLI Kirtika, MAITY Samir K. Slurry phase hydrocracking of heavy oil and residue to produce lighter fuels: An experimental review[J]. Fuel, 2021, 288: 119686.
[18]	Frank SAUERHÖFER-RODRIGO, Ismael DÍAZ, Manuel RODRÍGUEZ, et al. Modelling of fixed bed and slurry bubble column reactors for Fischer-Tropsch synthesis[J]. Reviews in Chemical Engineering, 2024, 40(2): 151-192.
[19]	CHILEKAR Vinit P, VAN DER SCHAAF John, KUSTER Ben F M, et al. Influence of elevated pressure and particle lyophobicity on hydrodynamics and gas-liquid mass transfer in slurry bubble columns[J]. AIChE Journal, 2010, 56(3): 584-596.
[20]	HASHEMI Shahrzad, MACCHI Arturo, SERVIO Phillip. Gas-liquid mass transfer in a slurry bubble column operated at gas hydrate forming conditions[J]. Chemical Engineering Science, 2009, 64(16): 3709-3716.
[21]	ROLLBUSCH Philipp, BECKER Marc, LUDWIG Martina, et al. Experimental investigation of the influence of column scale, gas density and liquid properties on gas holdup in bubble columns[J]. International Journal of Multiphase Flow, 2015, 75: 88-106.
[22]	LAU R, PENG W, VELAZQUEZ-VARGAS L G, et al. Gas-liquid mass transfer in high-pressure bubble columns[J]. Industrial & Engineering Chemistry Research, 2004, 43(5): 1302-1311.
[23]	URSEANU M I, GUIT R P M, STANKIEWICZ A, et al. Influence of operating pressure on the gas hold-up in bubble columns for high viscous media[J]. Chemical Engineering Science, 2003, 58(3/4/5/6): 697-704.
[24]	JORDAN Uwe, SAXENA Alok K, SCHUMPE Adrian. Dynamic gas disengagement in a high-pressure bubble column[J]. The Canadian Journal of Chemical Engineering, 2003, 81(3/4): 491-498.
[25]	KEMOUN Abdenour, Boon Cheng ONG, GUPTA Puneet, et al. Gas holdup in bubble columns at elevated pressure via computed tomography[J]. International Journal of Multiphase Flow, 2001, 27(5): 929-946.
[26]	DEWES I, SCHUMPE A. Gas density effect on mass transfer in the slurry bubble column[J]. Chemical Engineering Science, 1997, 52(21/22): 4105-4109.
[27]	YANG G Q, FAN L S. Axial liquid mixing in high-pressure bubble columns[J]. AIChE Journal, 2003, 49(8): 1995-2008.
[28]	ZHANG Huahai, WANG Yuelin, SAYYAR Ali, et al. Experimental study on breakup of a single bubble in a stirred tank: Effect of gas density and liquid properties[J]. AIChE Journal, 2023, 69(1): e17511.
[29]	ZHANG Huahai, FU Shaotong, XIANG Xing, et al. Direct numerical simulations of internal flow inside deformed bubble by phase-field-based lattice Boltzmann method[J]. Chemical Engineering Journal, 2024, 495: 153312.
[30]	JIN Haibo, YANG Suohe, ZHANG Wenlong, et al. Numerical simulation of gas-liquid two-phase flow in the N₂-acetic acid system under elevated pressures and temperatures based on CFD-PBM model[J]. Chemical Engineering Research and Design, 2024, 204: 20-31.
[31]	张华海, 王铁峰. CFD-PBM耦合模型模拟气液鼓泡床的通用性研究[J]. 化工学报, 2019, 70(2): 487-495.
	ZHANG Huahai, WANG Tiefeng. Generality of CFD-PBM coupled model for simulations of gas-liquid bubble column[J]. CIESC Journal, 2019, 70(2): 487-495.
[32]	GUAN Xiaoping, YANG Ning. CFD simulation of bubble column hydrodynamics with a novel drag model based on EMMS approach[J]. Chemical Engineering Science, 2021, 243: 116758.
[33]	ZANG Hongyang, HU Shanwei, LIU Xinhua, et al. Applying a CFD-PBM approach to modeling the flow behavior in pressurized bubbling fluidized beds[J]. Powder Technology, 2025, 452: 120541.
[34]	ZHANG Huahai, YANG Guangyao, SAYYAR Ali, et al. An improved bubble breakup model in turbulent flow[J]. Chemical Engineering Journal, 2020, 386: 121484.
[35]	XING Chutian, WANG Tiefeng, GUO Kunyu, et al. A unified theoretical model for breakup of bubbles and droplets in turbulent flows[J]. AIChE Journal, 2015, 61(4): 1391-1403.
[36]	WILKINSON Peter M, DIERENDONCK Laurent L. Pressure and gas density effects on bubble break-up and gas hold-up in bubble columns[J]. Chemical Engineering Science, 1990, 45(8): 2309-2315.
[37]	WILKINSON Peter M, VAN SCHAYK Antoinet, SPRONKEN Josette P M, et al. The influence of gas density and liquid properties on bubble breakup[J]. Chemical Engineering Science, 1993, 48(7): 1213-1226.
[38]	LETZEL Martin H, SCHOUTEN Jaap C, VAN DEN BLEEK Cor M, et al. Effect of gas density on large-bubble holdup in bubble column reactors[J]. AIChE Journal, 1998, 44(10): 2333-2336.
[39]	ZHANG Huahai, SAYYAR Ali, WANG Yuelin, et al. Generality of the CFD-PBM coupled model for bubble column simulation[J]. Chemical Engineering Science, 2020, 219: 115514.
[40]	LAUPSIEN David, LE MEN Claude, COCKX Arnaud, et al. Effects of liquid viscosity and bubble size distribution on bubble plume hydrodynamics[J]. Chemical Engineering Research and Design, 2022, 180: 451-469.
[41]	GAO Deyang, LI Xue, HOU Baolin, et al. Study of bubble behavior in high-viscosity liquid in a pseudo-2D column using high-speed imaging[J]. Chemical Engineering Science, 2022, 252: 117532.
[42]	ZHANG Huahai, WANG Yuelin, SAYYAR Ali, et al. A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media[J]. AIChE Journal, 2023, 69(1): e17473.
[43]	GRUND G, SCHUMPE A, DECKWER W D. Gas-liquid mass transfer in a bubble column with organic liquids[J]. Chemical Engineering Science, 1992, 47(13/14): 3509-3516.
[44]	Manuel GÖTZ, LEFEBVRE Jonathan, Friedemann MÖRS, et al. Hydrodynamics of organic and ionic liquids in a slurry bubble column reactor operated at elevated temperatures[J]. Chemical Engineering Journal, 2016, 286: 348-360.
[45]	VANDU C O, KRISHNA R. Volumetric mass transfer coefficients in slurry bubble columns operating in the churn-turbulent flow regime[J]. Chemical Engineering and Processing: Process Intensification, 2004, 43(8): 987-995.
[46]	LAKHDISSI El Mahdi, SOLEIMANI Iman, Christophe GUY, et al. Simultaneous effect of particle size and solid concentration on the hydrodynamics of slurry bubble column reactors[J]. AIChE Journal, 2020, 66(2): e16813.
[47]	LI H, PRAKASH A, MARGARITIS A, et al. Effects of micron-sized particles on hydrodynamics and local heat transfer in a slurry bubble column[J]. Powder Technology, 2003, 133(1/2/3): 171-184.
[48]	GANDHI B, PRAKASH A, BERGOUGNOU M A. Hydrodynamic behavior of slurry bubble column at high solids concentrations[J]. Powder Technology, 1999, 103(2): 80-94.
[49]	MENA P C, RUZICKA M C, ROCHA F A, et al. Effect of solids on homogeneous-heterogeneous flow regime transition in bubble columns[J]. Chemical Engineering Science, 2005, 60(22): 6013-6026.
[50]	OJIMA Shimpei, SASAKI Shohei, HAYASHI Kosuke, et al. Effects of particle diameter on bubble coalescence in a slurry bubble column[J]. Journal of Chemical Engineering of Japan, 2015, 48(3): 181-189.
[51]	LI Weiling, ZHOU Genfu, SUN Jian, et al. Impacts of particle properties on gas holdup under four flow regimes in three-phase bubble columns[J]. Chemical Engineering & Technology, 2021, 44(12): 2347-2354.
[52]	WANG Haozheng, DUAN Xiaoxia, FENG Xin, et al. Investigation of the gas-liquid-solid stirred tank by using the intrusive image-based method[J]. Industrial & Engineering Chemistry Research, 2023, 62(47): 20436-20448.
[53]	LIAO Yixiang, WANG Qingdong, CALISKAN Utkan, et al. Investigation of particle effects on bubble coalescence in slurry with a chimera MP-PIC and VOF coupled method[J]. Chemical Engineering Science, 2023, 265: 118174.
[54]	CHEN Yekui, LI Chaojie, YU Zhixin, et al. Effect of solid loading and particle size on bubble behavior and flow field structure in slurry bubble column[J]. Physics of Fluids, 2024, 36(11): 113344.
[55]	OJIMA Shimpei, HAYASHI Kosuke, TOMIYAMA Akio. Effects of hydrophilic particles on bubbly flow in slurry bubble column[J]. International Journal of Multiphase Flow, 2014, 58: 154-167.
[56]	WANG Peipei, CILLIERS Jan J, NEETHLING Stephen J, et al. The behavior of rising bubbles covered by particles[J]. Chemical Engineering Journal, 2019, 365: 111-120.
[57]	LI Weiling, ZHONG Wenqi. CFD simulation of hydrodynamics of gas-liquid-solid three-phase bubble column[J]. Powder Technology, 2015, 286: 766-788.
[58]	SCHNEIDERS Lennart, MEINKE Matthias, Wolfgang SCHRÖDER. Direct particle-fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence[J]. Journal of Fluid Mechanics, 2017, 819: 188-227.
[59]	SCHNEIDERS Lennart, Konstantin FRÖHLICH, MEINKE Matthias, et al. The decay of isotropic turbulence carrying non-spherical finite-size particles[J]. Journal of Fluid Mechanics, 2019, 875: 520-542.
[60]	SU Wu, SHI Xiaogang, WU Yingya, et al. Population balance model simulation of the particle effect on flow hydrodynamics in slurry beds[J]. Chemical Engineering & Technology, 2019, 42(4): 761-768.
[61]	AN Min, GUAN Xiaoping, YANG Ning. Modeling the effects of solid particles in CFD-PBM simulation of slurry bubble columns[J]. Chemical Engineering Science, 2020, 223: 115743.
[62]	ZHANG Huahai, GUO Zhongshan, WANG Yuelin, et al. Effect of particles on hydrodynamics and mass transfer in a slurry bubble column: Correlation of experimental data[J]. AIChE Journal, 2023, 69(3): e17843.
[63]	SHEN Xiankun, ZHANG Huahai, JIA Zhiyong, et al. Numerical simulations of particle concentration and size effects in a slurry bubble column with a CFD-PBM coupled model[J]. AIChE Journal, 2024, 70(11): e18518.