Review of numerical study on liquid-solids two-phase mass transfer process in fluidized bed

doi:10.11949/0438-1157.20210680

Abstract

Abstract:

The liquid-solid two-phase fluidized bed has the advantages of high liquid-solid contact efficiency, good mass and heat transfer performance, uniform particle distribution, etc., and has been widely used in many industrial processes. However, due to the complex nonlinear characteristics and turbulent characteristics of the particle fluidization coupled with the mass transfer process in the fluidized bed, it is very difficult to study the characteristics of the mass transfer process. Moreover, it is difficult to reveal the interaction law of multiphase flow and impossible to obtain a comprehensive and detailed distribution of velocity field and concentration field only by relying on experimental observations and theoretical predictions. In recent years, the rapid development of numerical simulation has provided an important way for in-depth exploration of the liquid-solids two-phase flow behavior and its coupling with the mass transfer process in a fluidized bed. In this paper, the simulation methods of fluidized bed liquid-solids two-phase flow and mass transfer process are reviewed, and its future research trends is prospected. With the help of computational mass transfer (CMT) theory, the local concentration distribution can be predicted more accurately, and the mass transfer characteristics in the liquid-solids two-phase fluidized bed can be analyzed in depth, which provides the design and optimization of the liquid-solids two-phase fluidized bed a solid foundation.

Key words: fluidized-bed, two-phase flow, mass transfer process, numerical simulation, computational mass transfer, turbulent mass diffusion

摘要：

液固两相流化床具有液固相接触效率高、传质和传热性能好、颗粒分布均匀等优点，已被广泛应用于众多工业过程中。然而，流化床中与传质过程耦合的颗粒流化的复杂非线性特征及其湍动特性，使得对传质过程特性的研究十分困难。且仅依靠实验观测和理论预测难以揭示多相流相互作用规律，无法获得全面和详细的速度场和浓度场分布情况。近年来，数值模拟的快速发展为深入探索流化床中液固两相流动行为及其与传质过程耦合问题提供了重要的途径。本文对流化床液固两相流动与传质过程模拟方法进行了综述，并对其未来研究趋势进行了展望。借助于计算传质学理论可以更精确地预测局部浓度的分布情况，进而可以深入分析液固两相流化床中的传质过程规律与传质特性，为液固两相流化床的设计和优化提供理论基础。

关键词: 流化床, 两相流动, 传质过程, 数值模拟, 计算传质学, 湍流传质扩散

CLC Number:

TQ 021.4

Panfeng REN, Runze HAI, Qi LI, Wenbin LI, Guocong YU. Review of numerical study on liquid-solids two-phase mass transfer process in fluidized bed[J]. CIESC Journal, 2022, 73(1): 1-17.

任盼锋, 海润泽, 李奇, 李文彬, 余国琮. 流化床液固两相传质过程的模拟研究进展[J]. 化工学报, 2022, 73(1): 1-17.

Figures/Tables 9

Fig.1 Schematic diagram of liquid-solids two-phase fluidized bed devices

Fig.2 Schematic diagram of core-annular flow structure model for LSCFB[27]

Fig.3 Numerical simulation of transfer process

Fig.4 Different simulation methods of liquid-solids two-phase flow

Fig.5 Anisotropic turbulent mass transfer model in gas-solid bubble column[40]

Table 1 Correlations and main parameters of liquid-solids mass transfer coefficients in fluidized beds

文献	颗粒直径/m	几何参数			颗粒Reynolds数(Re_p)	Schmidt数(Sc)	关联式
文献	颗粒直径/m	塔径/m	塔高/m	液含率	颗粒Reynolds数(Re_p)	Schmidt数(Sc)	关联式
[64]	0.0007~0.0024	0.051	0.6096	0.65~0.90	5~130	1020~1540	$j D = 1.340 R e p' 1 - ε l - 0.468 S h = 2 + 1.031 1 - ε l ? R e p' 0.5 S c 0.333$
[65]	0.0381	—	—	0.26~0.47	200~1230	1310~1670	$S h = 2 1 - 1 - ε l 0.333 + 0.7 ε l S c 0.333 R e p n 2 - 3 n 3 n - 1 = 4.65 R e - 0.28$
[66]	0.00027~0.00055	0.035	0.2	0.5~0.92	0.22~6.4	0.052	$S h ε l = 0.7 R e S c 0.33 ?$
[67]	0.00305~0.00635	—	—	0.49~0.94	7~7000	1~2000	$j D = 17 6 G a μ l - 1 1 - ε l 0.2, ? R e p ″ < 10 1.46 6 G a μ l - 0.41 1 - ε l 0.2, ? R e p ″ > 10$
[68]	0.0005~0.002	0.054	0.5	0.47~0.91	1~100	991~1130	$j D 1 - ε l d p 2.6 f' ? = K G d p 0.27 - 1 K = 1.15 × 10 - 10 ρ l ρ s - ρ l μ 1.33 S c 23$
[69]	0.012~0.009	0.045	—	0.50~0.90	0.0405~11610	572~1350	$j D = 1.622 ? R e p ″ - 0.444, ? R e p ″ < 20 3.815 ? R e p ″ - 0.731, ? R e p ″ > 20$
[70]	0.0046~0.0082	—	—	0.40~0.95	16~1320	305~1595	$S h = 0.254 G a 0.323 ? M v 0.3 S c 0.4$
[71]	—	0.05	1	0.80~1.0	—	—	$S h = 0.254 Φ 1.35 G a 0.323 ? M v 0.3 S c 0.4$
[72]	0.0046~0.0381	—	—	0.40~0.95	1~1320	305~1670	$S h = 1.2 0.33 d p Φ U t ρ l μ l 0.333 S c 13, ? R e t < 500 0.5 0.33 d p Φ U t ρ l μ l 0.667 S c 13, ? R e t > 500$
[73]	0.0004~0.0009	0.0508	—	0.61~0.81	0.25~22.2	368~2896	$S h = 0.65 R e t 0.468 S c 0.333$
[74]	0.0000236~0.127	—	—	0.40~0.95	0.01~1000	0.3~1755	$ε l j D = 1.1068 R e - 0.72, ? R e p < 10 0.455 R e - 0.407, ? R e p > 10$
[75]	0.0004~0.001	0.051	—	0.55~0.85	2~25	336~451	$S h = 0.86 ε l R e p 0.5 S c 0.333$
[76]	0.0003~0.0008	—	—	0.54~0.65	0.644~7.312	998~1316	$j D = 1.489 ? R e p' - 0.4506 k s l = 3.22 × 10 - 5 U l 0.272 d p - 0.04$
[77]	0.000614	0.039	0.6	0.7~0.9	5~8	470	$S h = 7.55 ε l - 1 R e m - 0.6 S c 0.33$
[78]	0.021	0.04	—	0.41~0.46		969	$ε l j D = 0.64 R e - 0.6 1 - ε l 0.4$
[79]	0.0049~0.0061	0.192	0.6	0.50~0.70	112~288	970	$S h = 5.4 × 10 - 2 ε l 2 R e S c 0.33$
[80]	0.0064~0.0082	0.094	2	0.70~0.95	590~2120	1~1.06	$S h = 0.763 ε l - 1.20 R e 0.556 S c 0.333, ? ε l < 0.815 0.268 ε l - 2.40 R e 0.669 S c 0.333, ? ε l > 0.815$
[81]	—	—	—	0.53~0.96	180~1320	300~2000	$S h = 0.215 R e 0.011 G a 0.309 M v 0.303 S c 0.436, ? ε l < 0.815 0.115 R e - 0.076 G a 0.390 M v 0.503 S c 0.436, ? ε l > 0.815$

Table 1 Correlations and main parameters of liquid-solids mass transfer coefficients in fluidized beds

文献	颗粒直径/m	几何参数			颗粒Reynolds数(Re_p)	Schmidt数(Sc)	关联式
文献	颗粒直径/m	塔径/m	塔高/m	液含率	颗粒Reynolds数(Re_p)	Schmidt数(Sc)	关联式
[64]	0.0007~0.0024	0.051	0.6096	0.65~0.90	5~130	1020~1540	$j D = 1.340 R e p' 1 - ε l - 0.468 S h = 2 + 1.031 1 - ε l ? R e p' 0.5 S c 0.333$
[65]	0.0381	—	—	0.26~0.47	200~1230	1310~1670	$S h = 2 1 - 1 - ε l 0.333 + 0.7 ε l S c 0.333 R e p n 2 - 3 n 3 n - 1 = 4.65 R e - 0.28$
[66]	0.00027~0.00055	0.035	0.2	0.5~0.92	0.22~6.4	0.052	$S h ε l = 0.7 R e S c 0.33 ?$
[67]	0.00305~0.00635	—	—	0.49~0.94	7~7000	1~2000	$j D = 17 6 G a μ l - 1 1 - ε l 0.2, ? R e p ″ < 10 1.46 6 G a μ l - 0.41 1 - ε l 0.2, ? R e p ″ > 10$
[68]	0.0005~0.002	0.054	0.5	0.47~0.91	1~100	991~1130	$j D 1 - ε l d p 2.6 f' ? = K G d p 0.27 - 1 K = 1.15 × 10 - 10 ρ l ρ s - ρ l μ 1.33 S c 23$
[69]	0.012~0.009	0.045	—	0.50~0.90	0.0405~11610	572~1350	$j D = 1.622 ? R e p ″ - 0.444, ? R e p ″ < 20 3.815 ? R e p ″ - 0.731, ? R e p ″ > 20$
[70]	0.0046~0.0082	—	—	0.40~0.95	16~1320	305~1595	$S h = 0.254 G a 0.323 ? M v 0.3 S c 0.4$
[71]	—	0.05	1	0.80~1.0	—	—	$S h = 0.254 Φ 1.35 G a 0.323 ? M v 0.3 S c 0.4$
[72]	0.0046~0.0381	—	—	0.40~0.95	1~1320	305~1670	$S h = 1.2 0.33 d p Φ U t ρ l μ l 0.333 S c 13, ? R e t < 500 0.5 0.33 d p Φ U t ρ l μ l 0.667 S c 13, ? R e t > 500$
[73]	0.0004~0.0009	0.0508	—	0.61~0.81	0.25~22.2	368~2896	$S h = 0.65 R e t 0.468 S c 0.333$
[74]	0.0000236~0.127	—	—	0.40~0.95	0.01~1000	0.3~1755	$ε l j D = 1.1068 R e - 0.72, ? R e p < 10 0.455 R e - 0.407, ? R e p > 10$
[75]	0.0004~0.001	0.051	—	0.55~0.85	2~25	336~451	$S h = 0.86 ε l R e p 0.5 S c 0.333$
[76]	0.0003~0.0008	—	—	0.54~0.65	0.644~7.312	998~1316	$j D = 1.489 ? R e p' - 0.4506 k s l = 3.22 × 10 - 5 U l 0.272 d p - 0.04$
[77]	0.000614	0.039	0.6	0.7~0.9	5~8	470	$S h = 7.55 ε l - 1 R e m - 0.6 S c 0.33$
[78]	0.021	0.04	—	0.41~0.46		969	$ε l j D = 0.64 R e - 0.6 1 - ε l 0.4$
[79]	0.0049~0.0061	0.192	0.6	0.50~0.70	112~288	970	$S h = 5.4 × 10 - 2 ε l 2 R e S c 0.33$
[80]	0.0064~0.0082	0.094	2	0.70~0.95	590~2120	1~1.06	$S h = 0.763 ε l - 1.20 R e 0.556 S c 0.333, ? ε l < 0.815 0.268 ε l - 2.40 R e 0.669 S c 0.333, ? ε l > 0.815$
[81]	—	—	—	0.53~0.96	180~1320	300~2000	$S h = 0.215 R e 0.011 G a 0.309 M v 0.303 S c 0.436, ? ε l < 0.815 0.115 R e - 0.076 G a 0.390 M v 0.503 S c 0.436, ? ε l > 0.815$

Table 2 Simulation of liquid-solids two-phase flow in fluidized beds

文献	颗粒密度/ (kg/m³)	颗粒直径/mm	模拟对象				表观液速/(m/s)	曳力模型	多相流模型
文献	颗粒密度/ (kg/m³)	颗粒直径/mm	装置	塔径/m	塔高/m	液含率	表观液速/(m/s)	曳力模型	多相流模型
[82]	2490	0.508	LSCFB riser	0.076	3.0	0.94~1	0.12~0.35	Wen-Yu	E-E
[83]	2540	1.13	LSFB	0.127	1.1	0.6~1	0.0085~0.110	Wen-Yu, Gidaspow	E-E
[84]	1075~2803	0.8~3.0	LSFB	0.1	1.2	0.7~1	0.003~0.0012	Pandit-Joshi	E-E
[85]	3000	25	LSFB	0.1	0.5	0.44~1	0.03~0.14	Syamlal O’Brien	E-E
[86]	2500	0.3	LSFB	0.14	1.5	0.37~1	0.025	Beetstra et al., Wen-Yu, Gidaspow	E-E
[87]	2173	0.75~0.93	LSFB	0.1	1.8	0.7~1	0.031~0.093	Wen-Yu, Gidaspow, Ergun, Gibilaro, Swamee-Ohja, Haider-Levenspiel, Schiller-Naumann, Syamlal O’Brien	E-E
[88]	2500	3	LSFB	0.14	0.5	0.5~1	0.07~0.13	Gidaspow	E-L
[89]	2540	1.13	LSFB	0.14	0.5	0.5~1	0.0085~0.110	Gibilaro	E-E
[90]	2500	0.508	LSCFB riser	0.0762	3	0.8~1	0.0075	EMMS	E-E
[91]	8710	6~8	LSFB	0.05	1.5	0.4~1	0.06~0.22	—	E-E, E-L
[92]	897	2	inverse LSFB	0.5	1.5	0.45~1	0.009~0.025	Gidaspow	E-E
[93]	1080	0.32	LSCFB downer	0.06	3	0.6~1	0.0055	Wen-Yu	E-E
[94]	2540~7780	2.06~6	LSFB	0.512	2.04	0.45~1	0.04~0.1	Huilin-Gidaspow	E-L
[95]	1050~8000, 25~950	0.8~3	UCFB, DCFB	0.076, 0.2	5.4	0.89~1	0.12~0.53	Syamlal O’Brien	E-E
[96]	2460	0.9~1	cuboid LSFB	0.3×0.025	1	0.5~1	0.025~0.054	Wen-Yu, Dallavalle, TGS, Gidaspow, Syamlal O’Brien	E-E
[53]	1080	0.32	LSCFB riser	0.038	3	0.98~1	0.0113~0.0187	Gidaspow	E-E
[51]	1200~1800	0.135~0.2	LSFB	0.05	1	0.8~1	0.0003~0.0014	Wen-Yu, Syamlal O’Brien, Gibilaro, Gidaspow	E-E
[52]	2490	0.508	LSCFB riser	0.076	3	0.98~1	0.15	Gidaspow	E-E

Fig.6 Simulation results of tracer diffusion process[53]

Fig.7 CFD simulation results of flow behavior coupling mass transfer process[51]

References 103

1	Dong K J, Guo B Y, Chu K W, et al. Simulation of liquid-solid flow in a coal distributor[J]. Minerals Engineering, 2008, 21(11): 789-796.
2	Zheng Y, Zhu J X, Marwaha N S, et al. Radial solids flow structure in a liquid-solids circulating fluidized bed[J]. Chemical Engineering Journal, 2002, 88(1/2/3): 141-150.
3	Wang J Y, Shao Y Y, Yan X L, et al. Review of (gas)-liquid-solid circulating fluidized beds as biochemical and environmental reactors[J]. Chemical Engineering Journal, 2020, 386: 121951.
4	Sur D H, Mukhopadhyay M. Process aspects of three-phase inverse fluidized bed bioreactor: a review[J]. Journal of Environmental Chemical Engineering, 2017, 5(4): 3518-3528.
5	Lan Q D, Bassi A S, Zhu J X, et al. Continuous protein recovery with a liquid–solid circulating fluidized-bed ion exchanger[J]. AIChE Journal, 2002, 48(2): 252-261.
6	Patel A, Zhu J, Nakhla G. Simultaneous carbon, nitrogen and phosphorous removal from municipal wastewater in a circulating fluidized bed bioreactor[J]. Chemosphere, 2006, 65(7): 1103-1112.
7	Nelson M J, Nakhla G, Zhu J. Fluidized-bed bioreactor applications for biological wastewater treatment: a review of research and developments[J]. Engineering, 2017, 3(3): 330-342.
8	Bello M M, Abdul Raman A A, Purushothaman M. Applications of fluidized bed reactors in wastewater treatment—a review of the major design and operational parameters[J]. Journal of Cleaner Production, 2017, 141: 1492-1514.
9	Liang W G, Yu Z Q, Jin Y, et al. Synthesis of linear alkylbenzene in a liquid-solid circulating fluidized bed reactor[J]. Journal of Chemical Technology & Biotechnology, 1995, 62(1): 98-102.
10	Chen J H, Lu X F. Progress of petroleum coke combusting in circulating fluidized bed boilers—a review and future perspectives[J]. Resources, Conservation and Recycling, 2007, 49(3): 203-216.
11	Mertes T S, Rhodes H B. Liquid-particle behavior (I)[J]. Chemical Engineering Progress, 1995, 51: 517-522.
12	Reh L. New and efficient high-temperature processes with circulating fluid bed reactors[J]. Chemical Engineering & Technology, 1995, 18(2): 75-89.
13	金涌, 程易, 颜彬航. 化学反应工程的前世、今生与未来[J]. 化工学报, 2013, 64(1): 34-43.
	Jin Y, Cheng Y, Yan B H. Past, present and future of chemical reaction engineering[J]. CIESC Journal, 2013, 64(1): 34-43.
14	刘伯潭. 流体力学传质计算新模型的研究和在塔板上的应用[D]. 天津:天津大学, 2003.
	Liu B T. Study of a new mass transfer model of CFD and its application on distillation tray[D]. Tianjin: Tianjin University, 2003.
15	孙志民. 化工计算传质学的研究[D]. 天津: 天津大学, 2005.
	Sun Z M. Study on computational mass transfer in chemical engineering[D]. Tianjin: Tianjin University, 2005.
16	Fan L S, Yamashita T, Jean R H. Solids mixing and segregation in a gas-liquid-solid fluidized bed[J]. Chemical Engineering Science, 1987, 42(1): 17-25.
17	Briens L A, Briens C L, Margaritis A, et al. Minimum liquid fluidization velocity in gas-liquid-solid fluidized beds of low-density particles[J]. Chemical Engineering Science, 1997, 52(21/22): 4231-4238.
18	Wen C Y, Yu Y H. A generalized method for predicting the minimum fluidization velocity[J]. AIChE Journal, 1966, 12(3): 610-612.
19	Narsimhan G. On a generalized expression for prediction of minimum fluidization velocity[J]. AIChE Journal, 1965, 11(3): 550-554.
20	Eldyasti A, Chowdhury N, Nakhla G, et al. Biological nutrient removal from leachate using a pilot liquid-solid circulating fluidized bed bioreactor (LSCFB)[J]. Journal of Hazardous Materials, 2010, 181(1/2/3): 289-297.
21	Hamidipour M, Chen J W, Larachi F. CFD study on hydrodynamics in three-phase fluidized beds—application of turbulence models and experimental validation[J]. Chemical Engineering Science, 2012, 78: 167-180.
22	Pan H, Chen X Z, Liang X F, et al. CFD simulations of gas-liquid-solid flow in fluidized bed reactors—a review[J]. Powder Technology, 2016, 299: 235-258.
23	Zhou X H, Ma Y L, Liu M Y, et al. CFD-PBM simulations on hydrodynamics and gas-liquid mass transfer in a gas-liquid-solid circulating fluidized bed[J]. Powder Technology, 2020, 362: 57-74.
24	刘星. 液固流化床中流体动力特性的研究[D]. 哈尔滨: 哈尔滨工业大学, 2009.
	Liu X. Study on hydrodynamics characteristics of the flow in a liquid-solid fluidized bed[D]. Harbin: Harbin Institute of Technology, 2009.
25	金涌. 流态化工程原理[M]. 北京: 清华大学出版社, 2001.
	Jin Y. Fluidization Engineering Principles[M]. Beijing: Tsinghua University Press, 2001.
26	Richardson J F, Zaki W N. The sedimentation of a suspension of uniform spheres under conditions of viscous flow[J]. Chemical Engineering Science, 1954, 3(2): 65-73.
27	Liang W G, Zhu J X. A core-annulus model for the radial flow structure in a liquid-solid circulating fluidized bed (LSCFB)[J]. Chemical Engineering Journal, 1997, 68(1): 51-62.
28	Lan Q D, Zhu J X, Bassi A S, et al. Continuous protein recovery using a liquid-solid circulating fluidized bed ion exchange system: modelling and experimental studies[J]. The Canadian Journal of Chemical Engineering, 2000, 78(5): 858-866.
29	Zheng Y, Zhu J X, Wen J Z, et al. The axial hydrodynamic behavior in a liquid-solid circulating fluidized bed[J]. The Canadian Journal of Chemical Engineering, 1999, 77(2): 284-290.
30	Razzak S A. Study of phase distribution of a liquid-solid circulating fluidized bed reactor using abductive network modeling approach[J]. Chemical Product and Process Modeling, 2013, 8(2): 77-91.
31	Cussler E L. 扩散: 流体系统中的传质[M]. 王宇新, 姜忠义,译. 2版. 北京: 化学工业出版社, 2002.
	Cussler E L. Diffusion: Mass Transfer in Fluid Systems [M]. Wang Y X, Jiang Z Y,trans. 2nd ed. Beijing: Chemical Industry Press, 2002.
32	刘国标. 计算传递学及其在填料床传质与反应过程中的应用[D]. 天津: 天津大学, 2007.
	Liu G B. Computational transport and its application to mass transfer and reaction processes in packed-beds[D]. Tianjin: Tianjin University, 2007.
33	Liu G B, Yu K T, Yuan X G, et al. Simulations of chemical absorption in pilot-scale and industrial-scale packed columns by computational mass transfer[J]. Chemical Engineering Science, 2006, 61(19): 6511-6529.
34	Li W B, Liu B T, Yu K T, et al. Rigorous model for the simulation of gas adsorption and its verification[J]. Industrial & Engineering Chemistry Research, 2011, 50(13): 8361-8370.
35	Sun Z M, Liu B T, Yuan X G, et al. New turbulent model for computational mass transfer and its application to a commercial-scale distillation column[J]. Industrial & Engineering Chemistry Research, 2005, 44(12): 4427-4434.
36	Liu G B, Yu K T, Yuan X G, et al. New model for turbulent mass transfer and its application to the simulations of a pilot-scale randomly packed column for CO₂-NaOH chemical absorption[J]. Industrial & Engineering Chemistry Research, 2006, 45(9): 3220-3229.
37	Liu G B, Yu K T, Yuan X G, et al. A computational transport model for wall-cooled catalytic reactor[J]. Industrial & Engineering Chemistry Research, 2008, 47(8): 2656-2665.
38	Li W B, Zhang Y W, Shao Y Y, et al. A rigorous model for the simulation of chemical reaction in gas-particle bubbling fluidized bed (I): Modeling and validation[J]. Powder Technology, 2018, 327: 399-407.
39	Zhang Y W, Li W B, Shao Y Y, et al. A rigorous model for the simulation of chemical reaction in gas-particle bubbling fluidized bed (‍Ⅱ): Application to gas combustion case[J]. Powder Technology, 2018, 327: 392-398.
40	Li W B, Shao Y Y, Zhu J. Anisotropic turbulent mass transfer model and its application to a gas-particle bubbling fluidized bed[J]. Industrial & Engineering Chemistry Research, 2018, 57(5): 1671-1678.
41	Li W B, Zhao X J, Liu B T, et al. Mass transfer coefficients for CO₂ absorption into aqueous ammonia using structured packing[J]. Industrial & Engineering Chemistry Research, 2014, 53(14): 6185-6196.
42	Li W B, Yu K, Yuan X G, et al. An anisotropic turbulent mass transfer model for simulation of pilot-scale and industrial-scale packed columns for chemical absorption[J]. International Journal of Heat and Mass Transfer, 2015, 88: 775-789.
43	Li W B, Yu K, Yuan X G, et al. A Reynolds mass flux model for gas separation process simulation(‍Ⅰ): Modeling and validation[J]. Chinese Journal of Chemical Engineering, 2015, 23(7): 1085-1094.
44	Li W B, Yu K, Yuan X G, et al. A Reynolds mass flux model for gas separation process simulation(‍Ⅱ): Application to adsorption on activated carbon in a packed column[J]. Chinese Journal of Chemical Engineering, 2015, 23(8): 1245-1255.
45	Li W B, Liu B T. A Reynolds mass flux model for the simulation of chemical absorption of CO₂ into 2-amino-2-methyl-1-propanol in a packed column[J]. Industrial & Engineering Chemistry Research, 2015, 54(4): 1385-1396.
46	李文彬, 刘伯潭, 余国琮, 等. 雷诺质流模型在填料床反应过程中的应用(Ⅰ): MEA吸收CO₂过程的模拟[J]. 天津大学学报(自然科学与工程技术版), 2015, 48(5): 379-387.
	Li W B, Liu B T, Yu G C, et al. Reynolds mass flux model and its application to reaction processes in packed bed(Ⅰ): Simulation of MEA-CO₂ absorption process[J]. Journal of Tianjin University (Science and Technology), 2015, 48(5): 379-387.
47	李文彬, 刘伯潭, 余国琮, 等. 雷诺质流模型在填料床反应过程中的应用(Ⅱ):合成醋酸乙烯过程的模拟[J]. 天津大学学报(自然科学与工程技术版), 2015, 48(9): 771-778.
	Li W B, Liu B T, Yu G C, et al. Reynolds mass flux model and its application to reaction processes in packed bed(Ⅱ): Simulation of vinyl acetate synthesis process[J]. Journal of Tianjin University (Science and Technology), 2015, 48(9): 771-778.
48	Li W B, Yu K, Yuan X G, et al. An anisotropic Reynolds mass flux model for the simulation of chemical reaction in gas-particle CFB risers[J]. Chemical Engineering Science, 2015, 135: 117-127.
49	Li W B, Yu K, Liu B T, et al. Computational fluid dynamics simulation of hydrodynamics and chemical reaction in a CFB downer[J]. Powder Technology, 2015, 269: 425-436.
50	Li W B, Yu K, Yuan X G, et al. Simulation of chemical reaction process in gas-particle CFB downers by anisotropic turbulent mass transfer model[J]. Chemical Engineering Research and Design, 2018, 132: 452-459.
51	Ren P F, Li W B, Yu K. Computational fluid dynamics simulation of adsorption process in a liquid-solids fluidized bed[J]. Journal of Environmental Chemical Engineering, 2021, 9(4): 105428.
52	Ren P F, Zhang Y W, Li W B, et al. Turbulent mass transfer model for simulating protein desorption in liquid-solid circulating fluidized bed risers[J]. Particuology, 2021, 57: 167-175.
53	Zhang Y W, Ren P F, Li W B, et al. Turbulent mass transfer model for the simulation of liquid-solid CFB risers and its verification[J]. Powder Technology, 2021, 377: 847-856.
54	Durst F, Miloievic D, Schönung B. Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study[J]. Applied Mathematical Modelling, 1984, 8(2): 101-115.
55	Li X K. Multiphase flow and fluidization, continuum and kinetic theory descriptions : Dimitri Gidaspow; Academic Press, New York, 1993, 467 pp. Price $60.00. ISBN 0-12-282770-9[J]. Journal of Non Newtonian Fluid Mechanics, 1994, 55(2): 207-208.
56	蒋新, 陈甘棠, 李希. 湍流中粒子-流体间的传质[J]. 高校化学工程学报, 1996, 10(3): 37-42.
	Jiang X, Chen G T, Li X. Particle/fluid mass transfer in turbulence[J]. Journal of Chemical Engineering of Chinese Universities, 1996, 10(3): 37-42.
57	修伍德, 皮克福特, 威尔基. 传质学[M]. 时钧,李盘生,译.北京: 化学工业出版社, 1988.
	Sherwood T K, Pigford R L, Wilke C R. Mass Transfer[M]. Shi J, Li P S, trans. Beijing: Chemical Industry Press, 1988.
58	van der Meer A P, Blanchard C M R J P, Wesselingh J A. Mixing of particles in liquid fluidized beds[J]. Chemical Engineering Research and Design, 1984, 62(4): 214-222.
59	Lemoine F, Antoine Y, Wolff M, et al. Some experimental investigations on the concentration variance and its dissipation rate in a grid generated turbulent flow[J]. International Journal of Heat and Mass Transfer, 2000, 43(7): 1187-1199.
60	余国琮, 袁希钢. 化工计算传质学导论[M]. 天津: 天津大学出版社, 2011.
	Yu G C, Yuan X G. Introduction to Computational Mass Transfer [M]. Tianjin: Tianjin University Press, 2011.
61	Gunn D J. Proceedings of the symposium on the interaction between fluids and particles, The Institution of Chemical Engineers, London (1962), 351 pp., £6[J]. Chemical Engineering Science, 1964, 19(4): 324.
62	Hsu C T, Molstad M C. Process design data—rate of mass transfer from gas stream to porous solid in fluidized beds[J]. Industrial & Engineering Chemistry, 1955, 47(8): 1550-1559.
63	Richardson J F, Szekely J. Mass transfer in a fluidized bed[J]. Trans. Inst. Chem. Eng., 1961, 39: 212-222.
64	Fan L T, Yang Y C, Wen C Y. Mass transfer in semifluidized beds for solid-liquid system[J]. AIChE Journal, 1960, 6(3): 482-487.
65	Rowe P N, Partridge B A, Cheney A G, et al. Heat and mass transfer from a single sphere to a fluidflowing through an array[J]. Transactions of the Institution of Chemical Engineers, 1965, 43: 271-286
66	Tournie P, Laguerie C, Couderc J P. Mass transfer in a liquid fluidized bed at low Reynolds numbers[J]. Chemical Engineering Science, 1977, 32(10): 1259-1261.
67	Gamson B. Heat and mass transfer fluid solid systems[J]. Chemical Engineering Progress, 1951, 47: 19-28.
68	Evans G C, Gerald C F. Mass transfer from benzoic acid granules to water in fixed and fluidized beds at low Reynolds numbers[J]. Chemical Engineering Progress, 1953, 49(3): 135-139.
69	Upadhyay S N, Tripathi G. Liquid-phase mass transfer in fixed and fluidized beds of large particles[J]. Journal of Chemical & Engineering Data, 1975, 20(1): 20-26.
70	Tournié P, Laguerie C, Couderc J P. Correlations for mass transfer between fluidized spheres and a liquid[J]. Chemical Engineering Science, 1979, 34(10): 1247-1255.
71	Ballesteros R L, Riba J P, Couderc J P. Dissolution of non spherical particles in solid-liquid fluidization[J]. Chemical Engineering Science, 1982, 37(11): 1639-1644.
72	Joshi J B. Solid-liquid fluidised beds: some design aspects[J]. Chemical Engineering Research & Design, 1983, 61(3): 143-161.
73	Livingston A G, Noble J B. Mass transfer in liquid-solid fluidized beds of ion exchange resins at low Reynolds numbers[J]. Chemical Engineering Science, 1993, 48(6): 1174-1178.
74	Dwivedi P N, Upadhyay S N. Particle-fluid mass transfer in fixed and fluidized beds[J]. Industrial & Engineering Chemistry Process Design and Development, 1977, 16(2): 157-165.
75	Rahmant K, Streat M. Mass transfer in liquid fluidized beds of ion exchange particles[J]. Chemical Engineering Science, 1981, 36(2): 293-300.
76	Shen G C, Geankoplis C J, Brodkey R S. A note on particle-liquid mass transfer in a fluidized bed of small irregular-shaped benzoic acid particles[J]. Chemical Engineering Science, 1985, 40(9): 1797-1802.
77	Yang J, Renken A. Intensification of mass transfer in liquid fluidized beds with inert particles[J]. Chemical Engineering and Processing: Process Intensification, 1998, 37(6): 537-544.
78	Boskovic-Vragolovic N, Brzic D V, Grbavcic Z. Mass transfer between a fluid and an immersed object in liquid-solid packed and fluidized beds[J]. Journal of the Serbian Chemical Society, 2005, 70(11): 1373-1379.
79	Couderc J P, Gibert H, Angelino H. Transfert de matière par diffusion en fluidisation liquide[J]. Chemical Engineering Science, 1972, 27(1): 11-20.
80	Damronglerd S, Couderc J, Angelino H. Mass transfer in particulate fluidisation[J]. Transactions of the Institution of Chemical Engineers, 1975, 53: 175-180.
81	Vanadurongwan V, Laguerie C, Couderc J P. Influence des propriétés physiques sur le transfert de matiére en fluidisation liquide[J]. The Chemical Engineering Journal, 1976, 12(1): 29-31.
82	Cheng Y, Zhu J X. CFD modelling and simulation of hydrodynamics in liquid-solid circulating fluidized beds[J]. The Canadian Journal of Chemical Engineering, 2005, 83(2): 177-185.
83	Cornelissen J T, Taghipour F, Escudié R, et al. CFD modelling of a liquid-solid fluidized bed[J]. Chemical Engineering Science, 2007, 62(22): 6334-6348.
84	Reddy R K, Joshi J B. CFD modeling of solid-liquid fluidized beds of mono and binary particle mixtures[J]. Chemical Engineering Science, 2009, 64(16): 3641-3658.
85	姚秀颖, 吴桂英, 关彦军, 等. 液固流化床内固含率时空分布特性的CFD模拟[J]. 化工学报, 2010, 61(9): 2287-2295.
	Yao X Y, Wu G Y, Guan Y J, et al. CFD simulation for spatio-temporal distribution of solid holdup in liquid-fluidized beds[J]. CIESC Journal, 2010, 61(9): 2287-2295.
86	Huang X Y. CFD modeling of liquid-solid fluidization: effect of drag correlation and added mass force[J]. Particuology, 2011, 9(4): 441-445.
87	Visuri O, Wierink G A, Alopaeus V. Investigation of drag models in CFD modeling and comparison to experiments of liquid-solid fluidized systems[J]. International Journal of Mineral Processing, 2012, 104/105: 58-70.
88	Wang S Y, Guo S, Gao J S, et al. Simulation of flow behavior of liquid and particles in a liquid-solid fluidized bed[J]. Powder Technology, 2012, 224: 365-373.
89	Zhang K, Wu G Y, Brandani S, et al. CFD simulation of dynamic characteristics in liquid-solid fluidized beds[J]. Powder Technology, 2012, 227: 104-110.
90	Liu G D, Wang P, Wang S, et al. Numerical simulation of flow behavior of liquid and particles in liquid-solid risers with multi scale interfacial drag method[J]. Advanced Powder Technology, 2013, 24(2): 537-548.
91	Ghatage S V, Peng Z B, Sathe M J, et al. Stability analysis in solid-liquid fluidized beds: experimental and computational[J]. Chemical Engineering Journal, 2014, 256: 169-186.
92	Wang S Y, Sun J, Yang Q, et al. Numerical simulation of flow behavior of particles in an inverse liquid-solid fluidized bed[J]. Powder Technology, 2014, 261: 14-21.
93	Dadashi A, Zhang C, Zhu J X. Numerical simulation of counter-current flow field in the downcomer of a liquid-solid circulating fluidized bed[J]. Particuology, 2015, 21: 48-54.
94	Liu G D, Yu F, Lu H L, et al. CFD-DEM simulation of liquid-solid fluidized bed with dynamic restitution coefficient[J]. Powder Technology, 2016, 304: 186-197.
95	Song Y F, Zhu J, Zhang C, et al. Comparison of liquid-solid flow characteristics in upward and downward circulating fluidized beds by CFD approach[J]. Chemical Engineering Science, 2019, 196: 501-513.
96	张仪, 李兵, 白玉龙, 等. 液固流态化动态过程中相间作用力的数值模拟及实验验证[J]. 化工学报, 2020, 71(11): 5129-5139.
	Zhang Y, Li B, Bai Y L, et al. Numerical simulation and experimental validation of inter-phase forces in dynamic process of liquid-solid fluidization[J]. CIESC Journal, 2020, 71(11): 5129-5139.
97	Dadashi A, Zhu J X, Zhang C. A computational fluid dynamics study on the flow field in a liquid-solid circulating fluidized bed riser[J]. Powder Technology, 2014, 260: 52-58.
98	Yang N, Wang W, Ge W, et al. Simulation of heterogeneous structure in a circulating fluidized-bed riser by combining the two-fluid model with the EMMS approach[J]. Industrial & Engineering Chemistry Research, 2004, 43(18): 5548-5561.
99	Karimipour S, Mostoufi N, Sotudeh-Gharebagh R. Modeling the hydrodynamics of downers by cluster-based approach[J]. Industrial & Engineering Chemistry Research, 2006, 45(21): 7204-7209.
100	Mazumder J, Zhu J X, Bassi A S, et al. Modeling and simulation of liquid-solid circulating fluidized bed ion exchange system for continuous protein recovery[J]. Biotechnology and Bioengineering, 2009, 104(1): 111-126.
101	Kalaga D V, Reddy R K, Joshi J B, et al. Liquid phase axial mixing in solid-liquid circulating multistage fluidized bed: CFD modeling and RTD measurements[J]. Chemical Engineering Journal, 2012, 191: 475-490.
102	Dadashi A, Zhu J X, Zhang C. CFD modelling of continuous protein extraction process using liquid-solid circulating fluidized beds[J]. The Canadian Journal of Chemical Engineering, 2014, 92(11): 1911-1919.
103	Derksen J J. Simulations of solid-liquid mass transfer in fixed and fluidized beds[J]. Chemical Engineering Journal, 2014, 255: 233-244.

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