气固微型流化床反应分析仪的理想流型判据分析

doi:10.11949/0438-1157.20231386

摘要/Abstract

摘要：

微型流化床因具有气体返混小和可操作性强等优点，在反应动力学测量等领域备受关注。获得流型随操作参数的变化规律，才能实现微型流化床理想流型的有效调控。采用双流体模型耦合考虑结构的相间曳力（又称多尺度CFD）模拟了一系列A类和B类颗粒在不同操作条件下的流化行为，结合颗粒浓度和气体停留时间分布（RTD）特征考察气速、床径和初始床高对气体返混行为的影响。研究表明，当微型流化床在初始鼓泡到湍动流态化之间操作时，才逼近颗粒全混流和气体近似平推流的运动状态。进一步分析气体RTD曲线形状特征（如拖尾、多峰等），提出采用斜度S<0.6作为微型流化床平推流判据，弥补了原判据[满足方差σ_t²<0.25且峰高E(t)_h>1] 的不足，为微型反应分析仪的流型调控奠定了基础。

关键词: 气固微型流化床, 平推流, 停留时间分布, 气体返混, 多尺度, 数值模拟

Abstract:

Micro fluidized bed (MFB) has received much attention in the reaction kinetics measurement due to its unique features like small gas back-mixing and good operability. Only by obtaining the change pattern of flow pattern with operating parameters we can achieve effective control of the ideal flow pattern of the micro fluidized bed. In this study, the combination of two-fluid model (TFM) and the structure-dependent drag model (namely multiscale CFD) is used to simulate a series of fluidization behaviors of Class A particles and Class B particles in MFBs. Then the effects of gas velocity U_g, bed diameter D_t and initial bed height H_s on the gas back-mixing behaviors are investigated by analyzing the characteristics of the solid concentration distribution and the gas residence time distribution (RTD). It is shown that the ideal flow pattern only appears when the MFB is operated between incipient bubbling fluidization and incipient turbulent fluidization. The RTD curves are further analyzed and a new criterion, that is, the skewness S< 0.6, which takes into account the features of RTD curve (e.g., trailing, multiple peaks), is proposed, thus avoiding the misjudgment by using the original criterion [the variance σ_t²<0.25 and peak height E(t)_h>1]. In the future, the effects of material properties and extreme operating conditions will be further investigated to establish an operating standard for MFB used in reaction kinetics measurement.

Key words: gas-solid micro fluidized bed, plug flow, residence time distribution, gas back-mixing, multiscale, numerical simulation

中图分类号:

TQ 021.1

卢飞, 鲁波娜, 许光文. 气固微型流化床反应分析仪的理想流型判据分析[J]. 化工学报, 2024, 75(6): 2201-2213.

Fei LU, Bona LU, Guangwen XU. Analysis of criteria for ideal flow patterns in gas-solid micro fluidized bed reaction analyzer[J]. CIESC Journal, 2024, 75(6): 2201-2213.

图/表 18

图1 微型流化床的示意图

Fig.1 The schematic diagram of micro fluidized beds

表1 模拟验证采用的物性及操作参数

Table 1 Physical properties and operating parameters used for simulation validation

Parameter	Value
particle diameter d_p/µm	53
particle density ρ_p/(kg·m^-3)	1400
gas density ρ_g/(kg·m^-3)	1.225
gas viscosity µ_g/(Pa·s)	1.7894×10^-5
minimum fluidization velocity U_mf/(mm·s^-1)	4.9
operating gas velocity U_g/(mm·s^-1)	4—40

表2 用于流型分析的各参数变化范围

Table 2 The range of variation of various parameters used for flow pattern analysis

Type of particles	U_g/U_mf	D_t/mm	H_s/mm
Geldart A(d_p=92 μm, ρ_p=1200 kg·m^-3, Ar=35.0341)	2,3,4,5,6,7	5,10,15,20,30	10,15,20,25,30,35,40
Geldart B(d_p=240 μm, ρ_p=2644 kg·m^-3, Ar=1371.1474)	1,2,3,4,5,6	5,10,15,20,30	10,15,20,25,30,35,40

表3 停留时间分布（RTD）函数的相关公式

Table 3 The relevant formulas for the residence time distribution （RTD） function

项目	公式
E(t)函数	$E (t) = \frac{C (t)}{\int_{0}^{\infty} C (t) d t}$
平均停留时间 $\bar{t}$	$\bar{t} = \frac{\int_{0}^{\infty} t E (t) d t}{\int_{0}^{\infty} E (t) d t}$
方差 $σ_{t}^{2}$	$σ_{t}^{2} = \frac{\int_{0}^{\infty} t^{2} E (t) d t}{\int_{0}^{\infty} E (t) d t} - {\bar{t}}^{2}$
无量纲方差 $σ_{θ}^{2}$	$σ_{θ}^{2} = \frac{σ_{t}^{2}}{{\bar{t}}^{2}}$
斜度S	$S = (\int_{0}^{\infty} t^{3} E (t) d t + 2 {\bar{t}}^{3} - 3 \bar{t} \int_{0}^{\infty} t^{2} E (t) d t) / σ_{t}^{3}$
E( $θ$ ) 函数	$E (θ) = \bar{t} E (t)$

表3 停留时间分布（RTD）函数的相关公式

Table 3 The relevant formulas for the residence time distribution （RTD） function

项目	公式
E(t)函数	$E (t) = \frac{C (t)}{\int_{0}^{\infty} C (t) d t}$
平均停留时间 $\bar{t}$	$\bar{t} = \frac{\int_{0}^{\infty} t E (t) d t}{\int_{0}^{\infty} E (t) d t}$
方差 $σ_{t}^{2}$	$σ_{t}^{2} = \frac{\int_{0}^{\infty} t^{2} E (t) d t}{\int_{0}^{\infty} E (t) d t} - {\bar{t}}^{2}$
无量纲方差 $σ_{θ}^{2}$	$σ_{θ}^{2} = \frac{σ_{t}^{2}}{{\bar{t}}^{2}}$
斜度S	$S = (\int_{0}^{\infty} t^{3} E (t) d t + 2 {\bar{t}}^{3} - 3 \bar{t} \int_{0}^{\infty} t^{2} E (t) d t) / σ_{t}^{3}$
E( $θ$ ) 函数	$E (θ) = \bar{t} E (t)$

图2 时均颗粒浓度的轴向分布（dp = 53 µm，ρp = 1400 kg·m-3，ρg = 1.225 kg·m-3，μg = 1.7894×10-5 Pa·s，Ug = 15 mm·s-1）

Fig.2 The axial profiles of time-average solid concentration (dp = 53 µm, ρp = 1400 kg·m-3, ρg = 1.225 kg·m-3, μg = 1.7894×10-5 Pa·s, Ug = 15 mm·s-1)

图3 起始鼓泡速度Umb随网格尺寸的变化（dp = 53 µm，ρp = 1400 kg·m-3，ρg = 1.225 kg·m-3，μg = 1.7894×10-5 Pa·s）

Fig.3 The variation of incipient bubbling fluidization velocity Umb with grid size (dp = 53 µm, ρp = 1400 kg·m-3, ρg = 1.225 kg·m-3, μg = 1.7894×10-5 Pa·s)

图4 颗粒浓度分布随Ug的变化

Fig.4 The variation of solid concentration distribution with gas velocity

图5 不同操作气速时的床层空隙率模拟值与实验值的对比（dp = 53 µm，ρp = 1400 kg·m-3，ρg = 1.225 kg·m-3，μg = 1.7894×10-5 Pa·s，Umf = 4.9 mm·s-1）

Fig.5 Comparison between simulated and experimental values of bed porosity at different gas velocities (dp = 53 µm, ρp = 1400 kg·m-3, ρg = 1.225 kg·m-3, μg = 1.7894×10-5 Pa·s, Umf = 4.9 mm·s-1)

表4 采用不同曳力模型时的床层空隙率模拟值与实验值的相对误差

Table 4 The relative error between simulated bed porosity and experiment using different drag models

U_g/mm·s^-1	ε_ο(Exp.)	Gidaspow		EMMS-bubbling
U_g/mm·s^-1	ε_ο(Exp.)	ε_ο	Relative error/%	ε_ο	Relative error/%
10	0.4728	0.5912	25.03	0.4938	4.43
15	0.5168	0.6237	20.69	0.5230	2.55
25	0.5811	0.6747	16.11	0.5948	2.35
30	0.5970	0.6910	15.74	0.6181	3.53

图6 鼓泡阶段随Ug变化的颗粒浓度分布情况

Fig.6 The variation of solid concentration distribution with gas velocity during the bubbling fluidization stage

图7 不同气速时的气体停留时间分布曲线E(t)

Fig.7 The gas residence time distribution curve E(t) at different gas velocities

表5 不同Ug时的微型流化床内气体RTD特征参数（Dt = 10 mm， Hs = 20 mm）

Table 5 The gas RTD characteristic parameters in micro fluidized beds at different operating gas velocities （Dt = 10 mm， Hs = 20 mm）

Type of particles	U_g/U_mf	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3,U_mf=0.0091 m·s^-1, D_t/d_p=109)	2	3.9100	0.7209	0.8944	0.4498	0.0585	1.7587
	3	2.5921	0.6298	0.3261	0.7338	0.0485	1.9021
	4	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	5	1.5519	0.5924	0.1166	1.2138	0.0484	1.8837
	6	1.3086	0.5735	0.0840	1.4261	0.0491	1.8662
	7	1.1244	0.5515	0.0628	1.6330	0.0497	1.8361
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_mf=0.1032 m·s^-1, D_t/d_p=42)	1	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	2	0.3793	0.5826	0.0083	4.2471	0.0576	1.6109
	3	0.2498	0.6218	0.0047	5.6837	0.0753	1.4198
	4	0.1881	0.5986	0.0035	6.3570	0.0992	1.1958
	5	0.1558	1.0118	0.0026	10.2803	0.1087	1.6017
	6	0.1296	0.8004	0.0011	12.8732	0.0662	1.6684

表5 不同Ug时的微型流化床内气体RTD特征参数（Dt = 10 mm， Hs = 20 mm）

Table 5 The gas RTD characteristic parameters in micro fluidized beds at different operating gas velocities （Dt = 10 mm， Hs = 20 mm）

Type of particles	U_g/U_mf	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3,U_mf=0.0091 m·s^-1, D_t/d_p=109)	2	3.9100	0.7209	0.8944	0.4498	0.0585	1.7587
	3	2.5921	0.6298	0.3261	0.7338	0.0485	1.9021
	4	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	5	1.5519	0.5924	0.1166	1.2138	0.0484	1.8837
	6	1.3086	0.5735	0.0840	1.4261	0.0491	1.8662
	7	1.1244	0.5515	0.0628	1.6330	0.0497	1.8361
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_mf=0.1032 m·s^-1, D_t/d_p=42)	1	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	2	0.3793	0.5826	0.0083	4.2471	0.0576	1.6109
	3	0.2498	0.6218	0.0047	5.6837	0.0753	1.4198
	4	0.1881	0.5986	0.0035	6.3570	0.0992	1.1958
	5	0.1558	1.0118	0.0026	10.2803	0.1087	1.6017
	6	0.1296	0.8004	0.0011	12.8732	0.0662	1.6684

图8 不同Dt时的颗粒浓度分布

Fig.8 The solid concentration distribution at different bed diameters

图9 不同Dt时的气体停留时间分布曲线E(t)

Fig.9 The gas residence time distribution curve E(t) at different bed diameters

表6 不同Dt时的微型流化床内气体RTD特征参数（Hs = 20 mm）

Table 6 The gas RTD characteristic parameters in micro fluidized beds at different bed diameters （Hs = 20 mm）

Type of particles	D_t/mm	D_t/d_p	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3, U_g= 4U_mf, H_s=20 mm)	5	54	0.5778	0.6614	0.0129	3.7417	0.0387	2.1620
	10	109	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	15	163	2.8654	0.6841	0.4930	0.6024	0.0601	1.7262
	20	217	3.4392	0.7599	0.8653	0.4592	0.0732	1.5793
	30	326	4.1145	0.9198	1.6549	0.3429	0.0978	1.4109
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_g= 1U_mf, H_s=20 mm)	5	21	0.1858	0.4273	0.0015	10.3461	0.0428	1.9223
	10	42	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	15	63	1.0042	0.6624	0.0636	1.5990	0.0630	1.6057
	20	83	1.1938	0.7697	0.1053	1.2529	0.0739	1.4957
	30	125	1.4222	0.9441	0.1785	1.1184	0.0883	1.5906

表6 不同Dt时的微型流化床内气体RTD特征参数（Hs = 20 mm）

Table 6 The gas RTD characteristic parameters in micro fluidized beds at different bed diameters （Hs = 20 mm）

Type of particles	D_t/mm	D_t/d_p	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3, U_g= 4U_mf, H_s=20 mm)	5	54	0.5778	0.6614	0.0129	3.7417	0.0387	2.1620
	10	109	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	15	163	2.8654	0.6841	0.4930	0.6024	0.0601	1.7262
	20	217	3.4392	0.7599	0.8653	0.4592	0.0732	1.5793
	30	326	4.1145	0.9198	1.6549	0.3429	0.0978	1.4109
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_g= 1U_mf, H_s=20 mm)	5	21	0.1858	0.4273	0.0015	10.3461	0.0428	1.9223
	10	42	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	15	63	1.0042	0.6624	0.0636	1.5990	0.0630	1.6057
	20	83	1.1938	0.7697	0.1053	1.2529	0.0739	1.4957
	30	125	1.4222	0.9441	0.1785	1.1184	0.0883	1.5906

图10 不同Hs时的颗粒浓度分布

Fig.10 The particle concentration distribution at different static bed heights

图11 不同Hs时的气体停留时间分布曲线E(t)

Fig.11 The gas residence time distribution curve E(t) at different static bed heights

表7 不同Hs时的微型流化床内气体RTD特征参数（Dt = 10 mm）

Table 7 The gas RTD characteristic parameters in micro fluidized beds at different static bed heights （Dt = 10 mm）

Type of particles	H_s/mm	H_s/d_p	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3,U_g= 4U_mf, D_t=10 mm)	10	109	2.4550	0.5731	0.2589	0.8171	0.0430	2.0060
	15	163	2.1465	0.5754	0.2035	0.9209	0.0442	1.9767
	20	217	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	25	272	1.7770	0.6331	0.1646	1.0288	0.0521	1.8282
	30	326	1.6204	0.6505	0.1605	1.0419	0.0611	1.6883
	35	380	1.5353	0.7716	0.1574	1.0896	0.0668	1.6729
	40	435	1.4118	0.8737	0.1493	1.1430	0.0749	1.6137
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_g= 1U_mf, D_t=10 mm)	10	42	0.9550	0.5111	0.0405	2.0146	0.0444	1.9239
	15	63	0.8087	0.5265	0.0299	2.3322	0.0457	1.8861
	20	83	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	25	104	0.6222	0.5502	0.0188	2.9247	0.0487	1.8197
	30	125	0.5472	0.5480	0.0148	3.2993	0.0493	1.8054
	35	146	0.4666	0.4142	0.0129	3.6054	0.0593	1.6823
	40	167	0.4140	0.5820	0.0092	4.3143	0.0535	1.7861

表7 不同Hs时的微型流化床内气体RTD特征参数（Dt = 10 mm）

Table 7 The gas RTD characteristic parameters in micro fluidized beds at different static bed heights （Dt = 10 mm）

Type of particles	H_s/mm	H_s/d_p	$\bar{t} / s$	S	$σ_{t}^{2} / s^{2}$	$E {(t)}_{h} / s^{- 1}$	$σ_{θ}^{2}$	$E_{θ, m a x}$
Geldart A (d_p=92 μm, ρ_p=1200 kg·m^-3,U_g= 4U_mf, D_t=10 mm)	10	109	2.4550	0.5731	0.2589	0.8171	0.0430	2.0060
	15	163	2.1465	0.5754	0.2035	0.9209	0.0442	1.9767
	20	217	1.9510	0.6338	0.1820	0.9837	0.0478	1.9192
	25	272	1.7770	0.6331	0.1646	1.0288	0.0521	1.8282
	30	326	1.6204	0.6505	0.1605	1.0419	0.0611	1.6883
	35	380	1.5353	0.7716	0.1574	1.0896	0.0668	1.6729
	40	435	1.4118	0.8737	0.1493	1.1430	0.0749	1.6137
Geldart B (d_p=240 μm, ρ_p=2644 kg·m^-3, U_g= 1U_mf, D_t=10 mm)	10	42	0.9550	0.5111	0.0405	2.0146	0.0444	1.9239
	15	63	0.8087	0.5265	0.0299	2.3322	0.0457	1.8861
	20	83	0.7061	0.5523	0.0233	2.6343	0.0468	1.8601
	25	104	0.6222	0.5502	0.0188	2.9247	0.0487	1.8197
	30	125	0.5472	0.5480	0.0148	3.2993	0.0493	1.8054
	35	146	0.4666	0.4142	0.0129	3.6054	0.0593	1.6823
	40	167	0.4140	0.5820	0.0092	4.3143	0.0535	1.7861

参考文献 42

1	Di Renzo A, Scala F, Heinrich S. Recent advances in fluidized bed hydrodynamics and transport phenomena-progress and understanding[J]. Processes, 2021, 9(4): 639-642.
2	王荘, 吕潇, 邵媛媛, 等. 流态化的往昔寻觅及未来启示[J]. 化工学报, 2021, 72(12): 5904-5927.
	Wang Z, Lyu X, Shao Y Y, et al. Early exploration of fluidization theory and its inspiration to the future[J]. CIESC Journal, 2021, 72(12): 5904-5927.
3	Han Z N, Yue J R, Geng S L, et al. State-of-the-art hydrodynamics of gas-solid micro fluidized beds[J]. Chemical Engineering Science, 2020, 232: 116345.
4	Qie Z P, Alhassawi H, Sun F, et al. Characteristics and applications of micro fluidized beds (MFBs)[J]. Chemical Engineering Journal, 2021, 428(2): 131330.
5	Potic B, Kersten S, Ye M, et al. Fluidization with hot compressed water in micro-reactors[J]. Chemical Engineering Science, 2005, 60(22): 5982-5990.
6	Scott D S, Piskorz J. Low rate entrainment feeder for fine solids[J]. Industrial & Engineering Chemistry Fundamentals, 1982, 21(3): 319-322.
7	Liu X J, Hao W Q, Wang K X, et al. Acquiring real kinetics of reactions in the inhibitory atmosphere containing product gases using micro fluidized bed[J]. AIChE Journal, 2021, 67(9): e17325.
8	Yu J, Yao C B, Zeng X, et al. Biomass pyrolysis in a micro-fluidized bed reactor: characterization and kinetics[J]. Chemical Engineering Journal, 2011, 168(2): 839-847.
9	Saadatkhah N, Carillo Garcia A, Ackermann S, et al. Experimental methods in chemical engineering: thermogravimetric analysis—TGA[J]. The Canadian Journal of Chemical Engineering, 2020, 98(1): 34-43.
10	McDonough J, Law R, Reay D, et al. Fluidization in small-scale gas-solid 3D-printed fluidized beds[J]. Chemical Engineering Science, 2019, 200: 294-309.
11	Liu X H, Xu G W, Gao S Q. Micro fluidized beds: wall effect and operability[J]. Chemical Engineering Journal, 2008, 137(2): 302-307.
12	Wang F, Fan L S. Gas-solid fluidization in mini- and micro-channels[J]. Industrial & Engineering Chemistry Research, 2011, 50(8): 4741-4751.
13	Vanni F, Caussat B, Ablitzer C, et al. Effects of reducing the reactor diameter on the fluidization of a very dense powder[J]. Powder Technology, 2015, 277: 268-274.
14	Guo Q J, Xu Y, Yue X. Fluidization characteristics in micro-fluidized beds of various inner diameters[J]. Chemical Engineering & Technology, 2009, 32(12): 1992-1999.
15	Rao A, Curtis J S, Hancock B C, et al. The effect of column diameter and bed height on minimum fluidization velocity[J]. AIChE Journal, 2010, 56(9): 2304-2311.
16	Trachsel F, Günther A, Khan S, et al. Measurement of residence time distribution in microfluidic systems[J]. Chemical Engineering Science, 2005, 60(21): 5729-5737.
17	胡丹丹, 耿素龙, 曾玺, 等. 返混对气-固反应特性测试和活化能表征的影响[J]. 化工学报, 2021, 72(3): 1354-1363.
	Hu D D, Geng S L, Zeng X, et al. Gas back-mixing characteristics and the effects on gas-solid reaction behavior and activation energy characterization[J]. CIESC Journal, 2021, 72(3): 1354-1363.
18	Geng S L, Han Z N, Yue J R, et al. Conditioning micro fluidized bed for maximal approach of gas plug flow[J]. Chemical Engineering Journal, 2018, 351: 110-118.
19	Wang C, Han Z N, Bai H L, et al. Further analysis of the near-plug gas flow conditions in micro gas-solid fluidized beds[J]. Powder Technology, 2022, 404: 117508.
20	李铁男, 赵碧丹, 赵鹏, 等. 气固流化床启动阶段挡板内构件受力特性的CFD-DEM模拟[J]. 化工学报, 2022, 73(6): 2649-2661.
	Li T N, Zhao B D, Zhao P, et al. CFD-DEM simulation of the force acting on immersed baffles during the start-up stage of a gas-solid fluidized bed[J]. CIESC Journal, 2022, 73(6): 2649-2661.
21	Moliner C, Marchelli F, Spanachi N, et al. CFD simulation of a spouted bed: comparison between the discrete element method (DEM) and the two fluid model (TFM)[J]. Chemical Engineering Journal, 2019, 377: 120466.
22	林俊杰, 罗坤, 王帅, 等. Coarse-grained CFD-DEM方法在不同流态流化床中的模拟验证[J]. 化工学报, 2019, 70(5): 1702-1712.
	Lin J J, Luo K, Wang S, et al. Verification of coarse-grained CFD-DEM method in multiple flow regimes[J]. CIESC Journal, 2019, 70(5): 1702-1712.
23	Wang J W, van der Hoef M A, Kuipers J A M. Why the two-fluid model fails to predict the bed expansion characteristics of Geldart A particles in gas-fluidized beds: a tentative answer[J]. Chemical Engineering Science, 2009, 64(3): 622-625.
24	Liu X X, Zhu C Q, Geng S J, et al. Two-fluid modeling of Geldart A particles in gas-solid micro-fluidized beds[J]. Particuology, 2015, 21(4): 118-127.
25	Fullmer W D, Hrenya C M. Quantitative assessment of fine-grid kinetic-theory-based predictions of mean-slip in unbounded fluidization[J]. AIChE Journal, 2016, 62(1): 11-17.
26	Radl S, Sundaresan S. A drag model for filtered Euler-Lagrange simulations of clustered gas-particle suspensions[J]. Chemical Engineering Science, 2014, 117: 416-425.
27	Li S J, Zhao P, Xu J, et al. Direct comparison of CFD-DEM simulation and experimental measurement of Geldart A particles in a micro-fluidized bed[J]. Chemical Engineering Science, 2021, 242: 116725.
28	Li S J, Zhao P, Xu J, et al. CFD-DEM simulation of polydisperse gas-solid flow of Geldart A particles in bubbling micro-fluidized beds[J]. Chemical Engineering Science, 2022, 253: 117551.
29	Geldart D. Types of gas fluidization[J]. Powder Technology, 1973, 7(5): 285-292.
30	Syamlal M, Rogers W, Obrien T J. MFIX documentation theory guide[R]. USDOE Morgantown Energy Technology Center (METC), WV (United States), 1993.
31	Ahmadi G, Ma D. A thermodynamical formulation for dispersed multiphase turbulent flow(1): Basic theory[J]. International Journal of Multiphase Flow, 1990, 16(2): 323-340.
32	Ma D, Ahmadi G. A thermodynamical formulation for dispersed multiphase turbulent flow(2): Simple shear flows for dense mixtures[J]. International Journal of Multiphase Flow, 1990, 16(2): 341-351.
33	Gidaspow D, Bezburuah R, Ding J. Hydrodynamics of circulating fluidized beds: kinetic theory approach[R]. Illinois Inst. Tech.of, Chicago, (United States)IL. Dept. of Chemical Engineering, 1991.
34	Schaeffer D G. Instability in the evolution equations describing incompressible granular flow[J]. Journal of Differential Equations, 1987, 66(1): 19-50.
35	Yang Z, Lu B N, Wang W. Coupling artificial neural network with EMMS drag for simulation of dense fluidized beds[J]. Chemical Engineering Science, 2021, 246: 117003.
36	Hong K, Shi Z S, Ullah A, et al. Extending the bubble-based EMMS model to CFB riser simulations[J]. Powder Technology, 2014, 266: 424-432.
37	Patil D J, van Sint Annaland M, Kuipers J A M. Critical comparison of hydrodynamic models for gas-solid fluidized beds(part Ⅱ): Freely bubbling gas-solid fluidized beds[J]. Chemical Engineering Science, 2005, 60(1): 73-84.
38	Hulme I, Clavelle E, van der Lee L, et al. CFD modeling and validation of bubble properties for a bubbling fluidized bed[J]. Industrial & Engineering Chemistry Research, 2005, 44(12): 4254-4266.
39	Cao J T, Cheng Z H, Fang Y T, et al. Simulation and experimental studies on fluidization properties in a pressurized jetting fluidized bed[J]. Powder Technology, 2008, 183(1): 127-132.
40	Levenspiel O. Tracer Technology: Modeling the Flow of Fluids[M]. Berlin: Springer Science & Business Media, 2011: 5-26.
41	Guío-Pérez D C, Pröll T, Hofbauer H. Solids residence time distribution in the secondary reactor of a dual circulating fluidized bed system[J]. Chemical Engineering Science, 2013, 104: 269-284.
42	Ham J H, Platzer B. Semi-empirical equations for the residence time distributions in disperse systems(part 1): Continuous phase[J]. Chemical Engineering & Technology, 2004, 27(11): 1172-1178.

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