Bed expansion and fluidized states change of Geldart-B particle gas-solid fluidized bed

doi:10.11949/0438-1157.20190013

Abstract

Abstract:

Based on the combination of theoretical derivation and empirical formula, the general formula of the bed expansion ratio of fluidized process of Geldart-B particles in fluidized bed is established, and the convergence iteration formula of bed expansion ratio is constructed in the whole value range. The formula has divergence when the initial bed height is small or the gas velocity is large and is not always available. Bed expansion ratio iteration formulas that converge across the full range of values are constructed by introducing power series and numerical processing. The calculation results are closed to the experimental data of silica, Diakon and a small Geldart-B particles. The relationship between bed expansion ratio and bubbling fluidized flow regimes is further discussed. At the critical point of the flow regime transitions, the critical expansion ratio can be obtained from particle properties and bed structure parameters. The main factors affecting bed expansion ratio can be divided into three aspects: operating conditions, particle properties and bed structure. It is difficult for the bed to expand when the Archimedes number of particles is large, the initial bed height is high and the bed diameter is small.

Key words: fluidized-bed, two-phase flow, fluidization, Geldart-B particles, bed expansion, fluidized states change

摘要：

采用理论推导和经验公式相结合方法，建立了Geldart-B类颗粒在流化床中流化过程的床层膨胀比(R)的通式，并在全取值范围内构建了床层膨胀比的收敛迭代公式。采用不同颗粒的流化实验数据对上述通式(模型)进行了验证，结果表明该模型很好地预测了床层膨胀比。进一步讨论了床层膨胀比与鼓泡流化流型变化之间的关系，给出了临界膨胀比的取值规律。有关床层膨胀比的研究结果一定程度上可有效改善流化床的监控，优化操作条件选取。

关键词: 流化床, 两相流, 流态化, Geldart-B类颗粒, 床层膨胀, 流型转变

CLC Number:

O 359

Wangyu MA, Zhenghong LUO. Bed expansion and fluidized states change of Geldart-B particle gas-solid fluidized bed[J]. CIESC Journal, 2019, 70(7): 2472-2479.

马旺宇, 罗正鸿. Geldart-B类颗粒在气固流化床中的床层膨胀与流型转变[J]. 化工学报, 2019, 70(7): 2472-2479.

Figures/Tables 10

Fig.1 Expansion of fluidized bed

Table 1 Non-integral simplifications for calculating expansion ratio and iterative formula for convergence

Rα_mf取值	非整次项化简 / 迭代公式
$R α m f ≤ 2.20 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ 2.323 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$R α m f ≤ 2.20 ε 0 0.5$	$R = φ ε 0 0.2 φ ε 0 0.2 - 0.820 Y U - U m f / g D 0.8$
$2.20 ε 0 0.5 < R α m f ≤ 6.52 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ 0.131 ε 0 - 0.3 R α m f 2 + 2.323 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$2.20 ε 0 0.5 < R α m f ≤ 6.52 ε 0 0.5$	$R = 14.536 Y φ - 1 ε 0 0.3 U - U m f / g D 0.8 + α m f - 17.725 ε 0 0.5 R α m f + 17.725 ε 0 0.5 α m f$
$6.52 ε 0 0.5 < R α m f ≤ 26.01 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 - 0.01783 ε 0 - 0.3 R α m f 2 + 0.9219 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$6.52 ε 0 0.5 < R α m f ≤ 26.01 ε 0 0.5$	$R = φ R α m f 0.4 - 0.018 ε 0 - 0.3 R α m f + 0.922 ε 0 0.2 φ R α m f 0.4 - 0.018 ε 0 - 0.3 R α m f + 0.922 ε 0 0.2 - 1.905 Y U - U m f / g D 0.8$
$26.01 ε 0 0.5 < R α m f ≤ 79.72 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 + 0.3914 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$26.01 ε 0 0.5 < R α m f ≤ 79.72 ε 0 0.5$	$R = α m f - 0.286 0.391 ε 0 0.2 - 1.905 Y φ - 1 U - U m f / g D 0.8 R + R α m f 0.4 + 0.391 ε 0 0.2 0.714$
$R α m f > 79.72 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 + 5.8806 ε 0 0.7$
$R α m f > 79.72 ε 0 0.5$	$R = 1.905 Y R 0.6 α m f - 0.4 φ - 1 U - U m f / g D 0.8 + 1$

Table 1 Non-integral simplifications for calculating expansion ratio and iterative formula for convergence

Rα_mf取值	非整次项化简 / 迭代公式
$R α m f ≤ 2.20 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ 2.323 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$R α m f ≤ 2.20 ε 0 0.5$	$R = φ ε 0 0.2 φ ε 0 0.2 - 0.820 Y U - U m f / g D 0.8$
$2.20 ε 0 0.5 < R α m f ≤ 6.52 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ 0.131 ε 0 - 0.3 R α m f 2 + 2.323 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$2.20 ε 0 0.5 < R α m f ≤ 6.52 ε 0 0.5$	$R = 14.536 Y φ - 1 ε 0 0.3 U - U m f / g D 0.8 + α m f - 17.725 ε 0 0.5 R α m f + 17.725 ε 0 0.5 α m f$
$6.52 ε 0 0.5 < R α m f ≤ 26.01 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 - 0.01783 ε 0 - 0.3 R α m f 2 + 0.9219 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$6.52 ε 0 0.5 < R α m f ≤ 26.01 ε 0 0.5$	$R = φ R α m f 0.4 - 0.018 ε 0 - 0.3 R α m f + 0.922 ε 0 0.2 φ R α m f 0.4 - 0.018 ε 0 - 0.3 R α m f + 0.922 ε 0 0.2 - 1.905 Y U - U m f / g D 0.8$
$26.01 ε 0 0.5 < R α m f ≤ 79.72 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 + 0.3914 ε 0 0.2 R α m f + 5.8806 ε 0 0.7$
$26.01 ε 0 0.5 < R α m f ≤ 79.72 ε 0 0.5$	$R = α m f - 0.286 0.391 ε 0 0.2 - 1.905 Y φ - 1 U - U m f / g D 0.8 R + R α m f 0.4 + 0.391 ε 0 0.2 0.714$
$R α m f > 79.72 ε 0 0.5$	$R α m f + 3.545 ε 0 0.5 1.4 ≈ R α m f 1.4 + 5.8806 ε 0 0.7$
$R α m f > 79.72 ε 0 0.5$	$R = 1.905 Y R 0.6 α m f - 0.4 φ - 1 U - U m f / g D 0.8 + 1$

Fig.2 Verification results of silica sand

Fig.3 Verification results of Diakon particles

Fig.4 Verification results of particles in Experiment 3

Fig.5 Comparison with other simulation results

Fig.6 Critical expansion ratio Rtr from bubbling fluidization to turbulent fluidization

Fig.7 Critical expansion ratio Rtr from turbulent fluidization to fast fluidization

Fig.8 Effect of αmf on R

Fig.9 Effect of Ar on R

References 37

1	郑晓野, 蒲文灏, 岳晨, 等. 采用改进的曳力模型模拟 2D 鼓泡流化床的流化特性[J]. 过程工程学报, 2015, 15(5): 737-743.
	ZhengX Y, PuW H, YueC, et al. A modified drag model used for CFD simulation on the fluidization characteristics of 2D bubbling fluidized bed[J]. The Chinese Journal of Process Engineering, 2015, 15(5): 737-743.
2	曾涛, 柳忠彬, 黄卫星, 等. 方形气固流化床从鼓泡到湍动流态化转变速度预测模型[J]. 过程工程学报, 2011, 11(3): 376-379.
	ZengT, LiuZ B, HuangW X, et al. Prediction model of transition velocity from bubbling to turbulent fluidization in a square gas-solid fluidized bed[J]. The Chinese Journal of Process Engineering, 2011, 11(3): 376-379.
3	王维, 王璐瑶, 许英梅, 等. 流化床氛围下多孔物料干燥传热传质的数值模拟[J]. 化工学报, 2012, 63(4): 1044-1049.
	WangW, WangL Y, XuY M, et al. Numerical simulation on porous material drying with fluidized bed[J]. CIESC Journal, 2012, 63(4): 1044-1049.
4	杨秀娟, 阎维平. 烟气流态化褐煤干燥与非稳态传热传质过程研究[J]. 热力发电, 2018, (4): 1-8.
	YangX J, YanW P. Study on the process of the flue gas fluidized lignite drying and unsteady heat and mass transfer[J]. Thermal Power Generation, 2018, (4): 1-8.
5	张健平, 赵周能. 油菜籽流化床恒速干燥传热传质特性及模型研究[J]. 农业工程学报, 2017, 33(13): 287-295.
	ZhangJ P, ZhaoZ N. Heat and mass transfer characteristics and model of rapeseed (Bassica rapus) fluidized-bed drying with constant drying rate [J]. Transactions of the Chinese Society of Agricultural Engineering, 2017, 33(13): 287-295.
6	陈程, 祁海鹰. EMMS曳力模型及其颗粒团模型的构建和检验[J]. 化工学报, 2014, 65(6): 2003-2012.
	ChenC, QiH Y. Development and validation of cluster and EMMS drag model[J]. CIESC Journal, 2014, 65(6): 2003-2012.
7	王会宁, 丁建亮. 流化床烟气脱硫反应器内气固流场数值模拟与分析[J]. 节能技术, 2014, 32(4): 324-326.
	WangH N, DingJ L. Analyses and simulation of hydrodynamics of gas and particles in fluidized bed flue gas desulphurization towers[J]. Energy Conservation Technology, 2014, 32(4): 324-326.
8	吕小林. 基于气泡和聚团的结构模型及其应用[J]. 化工进展, 2017, 36(11): 64-72.
	LyuX L. Structural model based on bubbles and clusters and its applications[J]. Chemical Industry and Engineering Progress, 2017, 36(11): 64-72.
9	周勇, 高凯歌, 李海念, 等. 超细颗粒流化聚团尺寸的预测模型[J]. 中国粉体技术, 2017, (5): 7-12.
	ZhouY, GaoK G, LiH N, et al. Models for estimating agglomerate size of ultrafine particles in fluidized beds[J]. China Powder Science and Technology, 2017, (5): 7-12.
10	朱育丹, 陆小华, 郭晓静, 等. 材料化学工程科学内涵及方法初探: 从介观尺度界面流体行为出发认知材料[J]. 化工学报, 2013, 64(1): 148-154.
	ZhuY D, LuX H, GuoX J, et al. Preliminary discussion on scientific connotation and research method of aterial-oriented chemical engineering: understanding materials based on confined interfacial fluid behavior on mesoscale[J]. CIESC Journal, 2013, 64(1): 148-154.
11	金余其, 王彬全, 万嘉瑜, 等. 基于介观尺度模拟的污泥絮凝形态及机理[J]. 化工学报, 2010, 61(3): 725-731.
	JinY Q, WangB Q, WanJ Y, et al. Morphology and mechanism of sludge flocculation based on mesoscopic simulation[J]. CIESC Journal, 2010, 61(3): 725-731.
12	高智雪, 郝振华. 加压二维鼓泡床气固流动特性的数值模拟[J]. 煤炭转化, 2018, (2): 44-50.
	GaoZ X, HaoZ H. Numerical simulation on gas-solid flow characteristics of a 2D pressurized bubbling fluidized bed[J]. Coal Conversion, 2018, (2): 44-50.
13	张长练, 曾涛, 刘少北, 等. 循环湍动流化床的提升管内FCC颗粒流动特性的数值模拟[J]. 科技通报, 2018, 34(4): 109-117.
	ZhangC L, ZengT, LiuS B, et al. Numerical simulation of the flow characteristics of FCC particles in the circulation turbulent fluidized bed[J]. Bulletin of Science and Technology, 2018, 34(4): 109-117.
14	杨新, 闫俊伏, 麻哲瑞, 等. 双循环流化床石英砂颗粒流动特性研究[J]. 华北电力大学学报(自然科学版), 2018, (3): 81-87.
	YangX, YanJ F, MaZ R, et al. Study on flow characteristics of quartz sand particles in dual circulating fluidized bed[J]. Journal of North China Electric Power University(Natural Science Edition), 2018, (3): 81-87.
15	黄克松, 赵晓军, 杨敬一, 等. 加压条件下气固流化床流动特性的CFD模拟研究[J]. 计算机与应用化学, 2014, 31(2): 181-184.
	HuangK S, ZhaoX J, YangJ Y, et al. The CFD simulation study of flow characteristics of three dimension flow in a fluidized bed reactor at elevated pressure[J]. Computers and Applied Chemistry, 2014, 31(2): 181-184.
16	黄克松, 赵晓军, 杨敬一, 等. 加压条件下气固流化床计算流体力学模型的建立[J]. 计算机与应用化学, 2013, (12): 1417-1421.
	HuangK S, ZhaoX J, YangJ Y, et al. The establish of computational fluid dynamics model for three dimension flow in a gas solid fluidized-bed reactor at elevated pressure[J]. Computers and Applied Chemistry, 2013, (12): 1417-1421.
17	李占勇, 王少铁, 王娟, 等. 狭缝型分布板流化床提高核桃壳颗粒的流化效果[J]. 农业工程学报, 2016, 32(9): 225-232.
	LiZ Y, WangS T, WangJ, et al. Fluidization effect of walnut shell particles in fluidized bed with slotted gas distributor [J]. Transactions of the Chinese Society of Agricultural Engineering, 2016, 32(9): 225-232.
18	李占勇, 王少铁, 刘品达, 等. Geldart D类颗粒在狭缝型分布板流化床的流化特性研究[J]. 天津科技大学学报, 2016, 31(4): 56-59.
	LiZ Y, WangS T, LiuP D, et al. Fluidization characteristics of Geldart D type particles in a fluidizing bed with a slotted gas distributor[J]. Journal of Tianjin University of Science & Technology, 2016, 31(4): 56-59.
19	WangZ J, TangJ, LuC X. Fluidization characteristics of different sizes of quartz particles in the fluidized bed[J]. Petroleum Science, 2016, 13(3): 584-591.
20	吕鹏, 赵跃民. 空气重介质流化床高对流化特性影响[J]. 煤炭技术, 2016, 35(7): 296-299.
	LyuP, ZhaoY M. Effect of bed height on fluidization characteristics of air dense medium fluidized bed[J]. Coal Technology, 2016, 35(7): 296-299.
21	谭明兵, 贺靖峰, 邵换男, 等. 次生布风条件下气固重介质流化床褐煤分选提质研究[J]. 中国矿业大学学报, 2017, 46(2): 404-409.
	TanM B, HaoJ F, ShaoH N, et al. Lignite separation using a gas-solid dense medium fluidized bed with a secondary air distribution layer[J]. Journal of China University of Mining & Technology, 2017, 46(2): 404-409.
22	GeldartD. Expansion of gas fluidized beds[J]. Ins. Eng. Chem. Res., 2004, 43(18): 5802-5809.
23	PetersM H, FanL S, SweeneyT L. Reactant dynamics in catalytic fluidized bed reactors with flow reversal of gas in the emulsion phase [J]. Chemical Engineering Science, 1982, 37(4): 553-565.
24	WertherJ. Fluidization Ⅳ [M]. Kunii D, Toei R, Eds. New York: Engineering Foundation, 1983: 93.
25	DartonR C, LaNauzeR D, DavidsonJ F, et al. Bubble growth due to coalescence in fluidized beds[J]. Trans. Ins. Chem. Eng., 1977, 55(4): 274-280.
26	BaeyensJ, GeldartD. Gas Fluidization Technology[M]. Chichester: John Wiley & Sons, 1986: 105.
27	WertherJ. Effect of gas distributor on the hydrodynamics of gas fluidized beds[J]. German Chemical Engineering, 1978, 1: 166-174.
28	KuniiD, LevenspielO. Fluidization Engineering [M].Oxford: Butterworth-Heinemann Limited Press, 1991.
29	付芝杰. 气固分选流化床两相分布及密度调控机制研究[D]. 北京: 中国矿业大学, 2017.
	FuZ J. Research on the mechanism of two-phase distribution and density regulation of separating gas-solid fluidized bed[D]. Beijing: China University of Mining and Technology, 2017.
30	DubrawskiK, TebianianS, BiH T, et al. Traveling column for comparison of invasive and non-invasive fluidization voidage measurement techniques[J]. Powder Technology, 2013, 235(2): 203-220.
31	FengR, LiJ, ChengZ, et al. Influence of particle size distribution on minimum fluidization velocity and bed expansion at elevated pressure[J]. Powder Technology, 2017, 320: 27-36.
32	BabuS P, ShahB, TalwalkarA. Fluidization correlations for coal gasification materials—minimum fluidization velocity and fluidized bed expansion ratio[J]. AIChE Symp. Ser., 1978, 74(176): 176.
33	GunnD J, HilalN. The expansion of gas-fluidised beds in bubbling fluidisation[J]. Chemical Engineering Science, 1997, 52(16): 2811-2822.
34	ZhuL T, TahaA B R, LuoZ H. Comprehensive validation analysis of sub-grid drag and wall corrections for coarse-grid two-fluid modeling[J]. Chemical Engineering Science, 2019, 196: 478-492.
35	ZhuL T, LiuY X, LuoZ H. An effective three-marker drag model via sub-grid modeling for turbulent fluidization[J]. Chemical Engineering Science, 2018, 192: 759-773.
36	BiH T, FanL S. Regime transition in gas-solid circulating fluidized bed[C]//AIChE Annual Meeting. LA, 1991: 17-22.
37	BaiD, JinY, YuZ. Flow regimes in circulating fluidized beds[J]. Chemical Engineering and Technology, 1993, 16(5): 307-313.

[1]	Shaohua ZHOU, Feilong ZHAN, Guoliang DING, Hao ZHANG, Yanpo SHAO, Yantao LIU, Zheming GAO. Experimental study of flow noise in short tube throttle valve and noise reduction measures [J]. CIESC Journal, 2023, 74(S1): 113-121.
[2]	Mingkun XIAO, Guang YANG, Yonghua HUANG, Jingyi WU. Numerical study on bubble dynamics of liquid oxygen at a submerged orifice [J]. CIESC Journal, 2023, 74(S1): 87-95.
[3]	Kaijie WEN, Li GUO, Zhaojie XIA, Jianhua CHEN. A rapid simulation method of gas-solid flow by coupling CFD and deep learning [J]. CIESC Journal, 2023, 74(9): 3775-3785.
[4]	Yubing WANG, Jie LI, Hongbo ZHAN, Guangya ZHU, Dalin ZHANG. Experimental study on flow boiling heat transfer of R134a in mini channel with diamond pin fin array [J]. CIESC Journal, 2023, 74(9): 3797-3806.
[5]	Song HE, Qiaomai LIU, Guangshuo XIE, Simin WANG, Juan XIAO. Two-phase flow simulation and surrogate-assisted optimization of gas film drag reduction in high-concentration coal-water slurry pipeline [J]. CIESC Journal, 2023, 74(9): 3766-3774.
[6]	Yuying GUO, Jiaqiang JING, Wanni HUANG, Ping ZHANG, Jie SUN, Yu ZHU, Junxuan FENG, Hongjiang LU. Water-lubricated drag reduction and pressure drop model modification for heavy oil pipeline [J]. CIESC Journal, 2023, 74(7): 2898-2907.
[7]	Xuanzhi HE, Yongqing HE, Guiye WEN, Feng JIAO. Ferrofluid droplet neck self-similar breakup behavior [J]. CIESC Journal, 2023, 74(7): 2889-2897.
[8]	Chao NIU, Shengqiang SHEN, Yan YANG, Bonian PAN, Yiqiao LI. Flow process calculation and performance analysis of methane BOG ejector [J]. CIESC Journal, 2023, 74(7): 2858-2868.
[9]	Qichao LIU, Yunlong ZHOU, Cong CHEN. Analysis and calculation of void fraction of gas-liquid two-phase flow in vertical riser under fluctuating vibration [J]. CIESC Journal, 2023, 74(6): 2391-2403.
[10]	Zihan YUAN, Shuyan WANG, Baoli SHAO, Lei XIE, Xi CHEN, Yimei MA. Investigation on flow characteristics of wet particles with power-law liquid-solid drag models in fluidized bed [J]. CIESC Journal, 2023, 74(5): 2000-2012.
[11]	Jinsheng REN, Kerun LIU, Zhiwei JIAO, Jiaxiang LIU, Yuan YU. Research on the mechanism of disaggregation of particle aggregates near the guide vanes of turbo air classifier [J]. CIESC Journal, 2023, 74(4): 1528-1538.
[12]	Shumin ZHENG, Pengcheng GUO, Jianguo YAN, Shuai WANG, Wenbo LI, Qi ZHOU. Experimental and predictive study on pressure drop of subcooled flow boiling in a mini-channel [J]. CIESC Journal, 2023, 74(4): 1549-1560.
[13]	Xingyu YANG, You MA, Chunying ZHU, Taotao FU, Youguang MA. Study on liquid-liquid distribution in comb parallel microchannels [J]. CIESC Journal, 2023, 74(2): 698-706.
[14]	Wanyuan HE, Yiyu CHEN, Chunying ZHU, Taotao FU, Xiqun GAO, Youguang MA. Study on gas-liquid mass transfer characteristics in microchannel with array bulges [J]. CIESC Journal, 2023, 74(2): 690-697.
[15]	Qiaoling SU, Junfeng WANG, Wei ZHANG, Shuiqing ZHAN, Tianyi WU. Experimental study on polarization motion characteristics of bubbles in a low conductivity working medium [J]. CIESC Journal, 2022, 73(9): 3861-3869.