Analysis of criteria for ideal flow patterns in gas-solid micro fluidized bed reaction analyzer

doi:10.11949/0438-1157.20231386

Abstract

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

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

CLC Number:

TQ 021.1

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.

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.

Figures/Tables 18

Fig.1 The schematic diagram of micro fluidized beds

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

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

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	$E (θ) = \bar{t} E (t)$

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	$E (θ) = \bar{t} E (t)$

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)

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)

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

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)

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

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

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

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

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

Fig.8 The solid concentration distribution at different bed diameters

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

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

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

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

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

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

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

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