气固流化床化学反应数值模拟中颗粒尺度模型研究进展

doi:10.16085/j.issn.1000-6613.2022-2138

摘要/Abstract

摘要：

气固流化床由于其优良的气固接触效率和传热传质效率，已经被广泛应用于能源、矿冶、化工、制药等工业领域。本文针对颗粒流态化-反应系统数值模拟研究进行了综述，阐述了数值模拟的三个尺度：化学反应工程模型、双流体模型以及颗粒尺度模型。然后聚焦于基于CFD-DEM方法的变粒径颗粒流态化-化学反应过程模拟，梳理分析了6种颗粒反应模型，即均匀转化模型、缩粒反应模型、缩核反应模型、联合收缩模型、细颗粒反应模型和随机孔隙模型，并从颗粒性质变化、化学反应模型、不同尺度耦合三个角度探讨了不同的颗粒反应模型的优点和应用中的局限性，分析了跨尺度颗粒系统模拟方法的发展近况，最后讨论了CFD-DEM方法在气固流化床化学反应过程模拟的应用上未来可能的发展方向，包括颗粒尺度大规模高效计算算法、颗粒反应模型的精确化以及颗粒-气体信息传递的精细化描述方面。有助于气固流化床化学反应模拟领域的梳理和发展，尤其是可供颗粒尺度模拟领域的研究人员参考和借鉴。

关键词: 气固流化床化学反应, 多尺度模拟方法, 计算流体力学-离散单元法, 颗粒尺度反应模型

Abstract:

Gas-solid fluidized bed has been widely used in energy, mining, chemical, pharmaceutical, and other industrial fields because of its excellent gas-solid contact and heat and mass transfer efficiency. In this paper, the research on the numerical simulation of particle fluidization reaction system is reviewed, and three scales of numerical simulation: chemical reaction engineering model, two-fluid model, and CFD-DEM model in particle scale are compared. This review focuses on the fluidization chemical reaction process with variable particle sizes based on the CFD-DEM method. Six particle reaction models were analyzed: uniform reaction model, shrinking particle model, shrinking core model, hybrid shrinking core & particle model, grain reaction model, and random pore model. The advantages and limitations of different particle reaction models were discussed. The recent development of simulation methods for cross-scale particle systems was analyzed. Finally, the CFD-DEM method's future development in chemical reaction processes simulation was discussed, including large-scale and efficient simulation algorithms, the precision of the particle reaction model, and the accurate description of gas-particle information transfer. This review can provide some guidance for researchers in the field of gas-solid fluidization reaction progress simulation, especially at the particle scale.

Key words: gas-solid fluidized bed chemical reaction, multiscale simulation, computational fluid dynamics-discrete element method (CFD-DEM), particle-scale reaction model

中图分类号:

邱沫凡, 蒋琳, 刘荣正, 刘兵, 唐亚平, 刘马林. 气固流化床化学反应数值模拟中颗粒尺度模型研究进展[J]. 化工进展, 2023, 42(10): 5047-5058.

QIU Mofan, JIANG Lin, LIU Rongzheng, LIU Bing, TANG Yaping, LIU Malin. Research progress of particle-scale model in chemical reaction numerical simulation of gas-solid fluidized bed[J]. Chemical Industry and Engineering Progress, 2023, 42(10): 5047-5058.

图/表 10

参考文献 91

1	MATHUR K B, GISHLER P E. A technique for contacting gases with coarse solid particles[J]. AIChE Journal, 1955, 1(2): 157-164.
2	TAGHIPOUR F, ELLIS N, WONG C. Experimental and computational study of gas-solid fluidized bed hydrodynamics[J]. Chemical Engineering Science, 2005, 60(24): 6857-6867.
3	WANG S, SHEN Y S. Particle-scale study of heat and mass transfer in a bubbling fluidised bed[J]. Chemical Engineering Science, 2021, 240: 116655.
4	WURZEL T, MALCUS S, MLECZKO L. Reaction engineering investigations of CO₂ reforming in a fluidized-bed reactor[J]. Chemical Engineering Science, 2000, 55(18): 3955-3966.
5	DEEN N G, PETERS E, PADDING J T, et al. Review of direct numerical simulation of fluid-particle mass, momentum and heat transfer in dense gas-solid flows[J]. Chemical Engineering Science, 2014, 116: 710-724.
6	LINDBORG H, LYSBERG M, JAKOBSEN H A. Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds[J]. Chemical Engineering Science, 2007, 62(21): 5854-5869.
7	ZHOU Z Y, KUANG S B, CHU K W, et al. Discrete particle simulation of particle-fluid flow: Model formulations and their applicability[J]. Journal of Fluid Mechanics, 2010, 661: 482-510.
8	LIU D Y, CHEN X P, ZHOU W, et al. Simulation of char and propane combustion in a fluidized bed by extending DEM-CFD approach[J]. Proceedings of the Combustion Institute, 2011, 33(2): 2701-2708.
9	XIE J, ZHONG W Q, SHAO Y J. Study on the char combustion in a fluidized bed by CFD-DEM simulations: Influences of fuel properties[J]. Powder Technology, 2021, 394: 20-34.
10	KU X K, LI T, LØVÅS T. CFD-DEM simulation of biomass gasification with steam in a fluidized bed reactor[J]. Chemical Engineering Science, 2015, 122: 270-283.
11	ZHAO L X, LU Y J. Hydrogen production by biomass gasification in a supercritical water fluidized bed reactor: A CFD-DEM study[J]. The Journal of Supercritical Fluids, 2018, 131: 26-36.
12	CHEN M, CHEN Z, TANG Y P, et al. CFD-DEM simulation of particle coating process coupled with chemical reaction flow model[J]. International Journal of Chemical Reactor Engineering, 2021, 19(4): 393-413.
13	ZHUANG Y Q, CHEN X M, LUO Z H, et al. CFD-DEM modeling of gas-solid flow and catalytic MTO reaction in a fluidized bed reactor[J]. Computers & Chemical Engineering, 2014, 60: 1-16.
14	ZHANG Z L, LIU D Y, ZHUANG Y M, et al. CFD-DEM modeling of CO₂ capture using alkali metal-based sorbents in a bubbling fluidized bed[J]. International Journal of Chemical Reactor Engineering, 2014, 12(1): 441-449.
15	DIANYU E. Validation of CFD-DEM model for iron ore reduction at particle level and parametric study[J]. Particuology, 2020, 51: 163-172.
16	刘马林. 化工流化床技术在铀燃料循环工业中的应用[J]. 化工进展, 2013, 32(3): 508-514, 548.
	LIU Malin. Review on application of fluidized bed technology in industry of uranium fuel cycle[J]. Chemical Industry and Engineering Progress, 2013, 32(3): 508-514, 548.
17	GUPTA C K， SATHIYAMOORTHY D. Fluid technology in materials processing chapter 3: Fluidization in nuclear engineering[M]. Boca Raton: CRC Press，1998.
18	ABELSON P H, ROSEN N, HOOVER J I. Liquid thermal diffusion[M]. Oak Ridge: U.S. Atomic Energy Commission, Technical Information Service Extension, 1958.
19	LABATON V Y. The fluorides of uranium-‍Ⅳ Kinetic studies of the fluorination of uranium tetrafluoride by chlorine trifluoride[J]. Journal of Inorganic and Nuclear Chemistry, 1959, 10(1/2): 86-93.
20	LABATON V Y, JOHNSON K D B. The fluorides of uranium-‍Ⅲ Kinetic studies of the fluorination of uranium tetrafluoride by flourine[J]. Journal of Inorganic and Nuclear Chemistry, 1959, 10(1/2): 74-85.
21	VOGEL C, MECHAM W. Fluid-bed conversion of uranium tetrafluoride to uranium hexafluoride[R]. Lemont: Argonne National Lab., 1959.
22	CORELLA J. A Kinetics of non-catalytic gas-solid reactions in semicontinuous integral fluidized-bed reactors. Apllication to the determination of the kinetics of the fluorination of uranium tetrafluoride[J]. Chemical Engineering Science, 1980, 35(1/2): 25-32.
23	NIKOLOPOULOS A, STROH A, ZENELI M, et al. Numerical investigation and comparison of coarse grain CFD-DEM and TFM in the case of a 1MW_th fluidized bed carbonator simulation[J]. Chemical Engineering Science, 2017, 163: 189-205.
24	OSTERMEIER P, DEYOUNG S, VANDERSICKEL A, et al. Comprehensive investigation and comparison of TFM, DenseDPM and CFD-DEM for dense fluidized beds[J]. Chemical Engineering Science, 2019, 196: 291-309.
25	尹炜迪, 王庆功, 吕俊复, 等. 选煤流化床内气固流动和颗粒分层的数值模拟[J]. 中国矿业大学学报, 2019, 48(2): 430-436.
	YIN Weidi, WANG Qinggong, Junfu LYU, et al. Modelling of the gas-solid flow and particle segregation behavior in coal beneficiation fluidized beds[J]. Journal of China University of Mining & Technology, 2019, 48(2): 430-436.
26	KLOSS C, GONIVA C, HAGER A, et al. Models, algorithms and validation for opensource DEM and CFD-DEM[J]. Progress in Computational Fluid Dynamics, an International Journal, 2012, 12(2/3): 140.
27	NOROUZI H R, ZARGHAMI R, SOTUDEH-GHAREBAGH R, et al. Coupled CFD-DEM modeling: Formulation, implementation and applications to multiphase flows[M]. Chichester, West Sussex, US: Wiley, 2016.
28	TSUJI Y, KAWAGUCHI T, TANAKA T. Discrete particle simulation of two-dimensional fluidized bed[J]. Powder Technology, 1993, 77(1): 79-87.
29	BERROUK A S, HUANG A, BALE S, et al. Numerical simulation of a commercial FCC regenerator using multiphase particle-in-cell methodology (MP-PIC)[J]. Advanced Powder Technology, 2017, 28(11): 2947-2960.
30	LI F, SONG F, BENYAHIA S, et al. MP-PIC simulation of CFB riser with EMMS-based drag model[J]. Chemical Engineering Science, 2012, 82: 104-113.
31	吴诗鸣, 陈皓宁, 宗原, 等. 基于MP-PIC方法的冶金硅氢氯化流化床反应器模拟[J]. 化工学报, 2022, 73(10): 4419-4428
	WU Shiming, CHEN Haoning, ZONG Yuan, et al. Fluidized bed reactor simulation for hydrochlorination of metallurgical silicon based on MP-PIC method[J]. CIESC Journal, 2022, 73(10): 4419-4428.
32	CHILAMKURTI Y N, GOULD R D. CFD-DEM and PR-DNS studies of low-temperature densely packed beds[J]. International Journal of Heat and Mass Transfer, 2020, 159: 120056.
33	TENNETI S, SUBRAMANIAM S. Particle-resolved direct numerical simulation for gas-solid flow model development[J]. Annual Review of Fluid Mechanics, 2014, 46: 199-230.
34	HU C S, LUO K, ZHOU M M, et al. Influences of secondary gas injection pattern on fluidized bed combustion process: A CFD-DEM study[J]. Fuel, 2020, 268: 117314.
35	HWANG I S, SOHN J, LEE U D, et al. CFD-DEM simulation of air-blown gasification of biomass in a bubbling fluidized bed gasifier: Effects of equivalence ratio and fluidization number[J]. Energy, 2021, 219: 119533.
36	WANG S, SHEN Y S. CFD-DEM modelling of raceway dynamics and coke combustion in an ironmaking blast furnace[J]. Fuel, 2021, 302: 121167.
37	LAN X Y, YAN W C, XU C M, et al. Hydrodynamics of gas-solid turbulent fluidized bed of polydisperse binary particles[J]. Powder Technology, 2014, 262: 106-123.
38	LICHTENEGGER T, PIRKER S. CFD-DEM modeling of strongly polydisperse particulate systems[J]. Powder Technology, 2018, 325: 698-711.
39	陈涛, 谢诞梅, 岳亚楠, 等. 生物质流化床热解焦油演化的CFD-DEM数值模拟研究[J]. 力学与实践, 2022, 44(4): 827-833.
	CHEN Tao, XIE Danmei, YUE Yanan, et al. Modeling tar evolution during biomass pyrolysis in a fluidized bed reactor by using a CFD-DEM method[J]. Mechanics in Engineering, 2022, 44(4): 827-833.
40	孔大力, 王帅, 罗坤, 等. 流化床生物质气化过程的CFD-DEM模拟研究[J]. 力学与实践, 2022, 44(4): 834-843.
	KONG Dali, WANG Shuai, LUO Kun, et al. CFD-DEM simulation of biomass gasificaiton in fluidized bed[J]. Mechanics in Engineering, 2022, 44(4): 834-843.
41	李振山, 蔡宁生. 气固反应动力学速率方程理论[J]. 清华大学学报(自然科学版), 2022, 62(4): 704-721.
	LI Zhenshan, CAI Nningsheng. Rate equation theory for gas-solid reaction kinetics[J]. Journal of Tsinghua University (Science and Technology), 2022, 62(4): 704-721.
42	SINGH R I, BRINK A, HUPA M. CFD modeling to study fluidized bed combustion and gasification[J]. Applied Thermal Engineering, 2013, 52(2): 585-614.
43	ZHONG W Q, YU A B, ZHOU G W, et al. CFD simulation of dense particulate reaction system: Approaches, recent advances and applications[J]. Chemical Engineering Science, 2016, 140: 16-43.
44	RAMOS A, MONTEIRO E, ROUBOA A. Numerical approaches and comprehensive models for gasification process: A review[J]. Renewable and Sustainable Energy Reviews, 2019, 110: 188-206.
45	GOLSHAN S, SOTUDEH-GHAREBAGH R, ZARGHAMI R, et al. Review and implementation of CFD-DEM applied to chemical process systems[J]. Chemical Engineering Science, 2020, 221: 115646.
46	RONG D, HORIO M. DEM simulation of char combustion in a fluidized bed[C]. proceedings of the Second International Conference on CFD in the Minerals and Process Industries CSIRO. Melbourne: 1999.
47	KRUGGEL-EMDEN H, RICKELT S, WIRTZ S, et al. A study on the validity of the multi-sphere discrete element method[J]. Powder Technology, 2008, 188(2): 153-165.
48	HÖHNER D, WIRTZ S, KRUGGEL-EMDEN H, et al. Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts[J]. Powder Technology, 2011, 208(3): 643-656.
49	ZHONG W Q, YU A B, LIU X J, et al. DEM/CFD-DEM modelling of non-spherical particulate systems: Theoretical developments and applications[J]. Powder Technology, 2016, 302: 108-152.
50	LIU Z H, MA H Q, ZHAO Y Z. CFD-DEM simulation of fluidization of polyhedral particles in a fluidized bed[J]. Energies, 2021, 14(16): 4939.
51	HE L P, LIU Z X, ZHAO Y Z. An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles[J]. Particuology, 2022, 68: 1-12.
52	SHEN Z H, WANG G, HUANG D R, et al. A resolved CFD-DEM coupling model for modeling two-phase fluids interaction with irregularly shaped particles[J]. Journal of Computational Physics, 2022, 448: 110695.
53	OCTAVE L. Chemical Reaction Engineering[M]. New York: John Wiley & Sons, 1998.
54	DI R A, DI M F P, GIRIMONTE Rossella, et al. DEM simulation of the mixing equilibrium in fluidized beds of two solids differing in density[J]. Powder Technology, 2008, 184(2): 214-223.
55	OLAOFE O O, BUIST K A, DEEN N G, et al. Segregation dynamics in dense polydisperse gas-fluidized beds[J]. Powder Technology, 2013, 246: 695-706.
56	GENG Y M, CHE D F. An extended DEM-CFD model for char combustion in a bubbling fluidized bed combustor of inert sand[J]. Chemical Engineering Science, 2011, 66(2): 207-219.
57	XIE J, ZHONG W Q, SHAO Y J, et al. Coupling of CFD-DEM and reaction model for 3D fluidized beds[J]. Powder Technology, 2019, 353: 72-83.
58	YAGI S, KUNII D. Fluidized-solids reactors with continuous solids feed-I: Residence time of particles in fluidized beds[J]. Chemical Engineering Science, 1961, 16(3/4): 364-371.
59	MEARS D E. Tests for transport limitations in experimental catalytic reactors[J]. Industrial & Engineering Chemistry Process Design and Development, 1971, 10(4): 541-547.
60	FOGLER H S. Elements of chemical reaction engineering[M]. 3rd ed. Upper Saddle Rive: Prentice Hall PTR, 1999.
61	WEN C Y. Noncatalytic heterogeneous solid-fluid reaction models[J]. Industrial & Engineering Chemistry, 1968, 60(9): 34-54.
62	ISHIDA M, WEN C Y, SHIRAI T. Comparison of zone-reaction model and unreacted-core shrinking model in solid-gas reactions-‍Ⅱ non-isothermal analysis[J]. Chemical Engineering Science, 1971, 26(7): 1043-1048.
63	WEN C Y, WANG S C. Thermal and diffusional effects in noncatalytic solid gas reactions[J]. Industrial & Engineering Chemistry, 1970, 62(8): 30-51.
64	REHMAT A, SAXENA S C, LAND R, et al. Noncatalytic gas-solid reaction with changing particle size: Unsteady state heat transfer[J]. The Canadian Journal of Chemical Engineering, 1978, 56(3): 316-322.
65	BRAUN A, BÄRTSCH M, SCHNYDER B, et al. A model for the film growth in samples with two moving reaction frontiers—An application and extension of the unreacted-core model[J]. Chemical Engineering Science, 2000, 55(22): 5273-5282.
66	OGATA S, HOMMA S, SASAHIRA A, et al. Fluorination reaction of uranium dioxide by fluorine[J]. Journal of Nuclear Science and Technology, 2004, 41(2): 135-141.
67	HOMMA S, OGATA S, KOGA J, et al. Gas-solid reaction model for a shrinking spherical particle with unreacted shrinking core[J]. Chemical Engineering Science, 2005, 60(18): 4971-4980.
68	PEDNEKAR P, BHATTACHARYYA D, KASULE J S, et al. Development of a hybrid shrinking-core shrinking-particle model for entrained-flow gasifiers[J]. AIChE Journal, 2016, 62(3): 659-669.
69	ZHANG X S, ZHU Z M, WEN G C, et al. Study on gas desorption and diffusion kinetic behavior in coal matrix using a modified shrinking core model[J]. Journal of Petroleum Science and Engineering, 2021, 204: 108701.
70	GARCÍA-LABIANO F, ABAD A, DE D L F, et al. Calcination of calcium-based sorbents at pressure in a broad range of CO₂ concentrations[J]. Chemical Engineering Science, 2002, 57(13): 2381-2393.
71	FU D, TANG G W, ZHAO Y F, et al. Modeling of iron ore reactions in blast furnace[J]. International Journal of Heat and Mass Transfer, 2016, 103: 77-86.
72	BHATIA S K, PERLMUTTER D D. The effect of pore structure on fluid-solid reactions: Application to the SO₂-lime reaction[J]. AIChE Journal, 1981, 27(2): 226-234.
73	BHATIA S K, PERLMUTTER D D. A random pore model for fluid-solid reactions: Ⅰ‍. Isothermal, kinetic control[J]. AIChE Journal, 1980, 26(3): 379-386.
74	HASELI Y, DINCER I, NATERER G F. Hydrodynamic gas-solid model of cupric chloride particles reacting with superheated steam for thermochemical hydrogen production[J]. Chemical Engineering Science, 2008, 63(18): 4596-4604.
75	AZMIR J, HOU Q F, YU A B. CFD-DEM simulation of drying of food grains with particle shrinkage[J]. Powder Technology, 2019, 343: 792-802.
76	ZHOU H S, FLAMANT G, GAUTHIER D. DEM-LES simulation of coal combustion in a bubbling fluidized bed Part Ⅱ: Coal combustion at the particle level[J]. Chemical Engineering Science, 2004, 59(20): 4205-4215.
77	AMIRI A, INGRAM G D, MAYNARD N E, et al. An unreacted shrinking core model for calcination and similar solid-to-gas reactions[J]. Chemical Engineering Communications, 2015, 202(9): 1161-1175.
78	WANG W W, LU Y C, XU K W, et al. Experimental and simulated study on fluidization characteristics of particle shrinkage in a multi-chamber fluidized bed for biomass fast pyrolysis[J]. Fuel Processing Technology, 2021, 216: 106799.
79	ZOU Z, ZHU J Y, YAN D, et al. CFD simulation of fluidized magnetic roasting coupled with random nucleation model[J]. Chemical Engineering Science, 2021, 229: 116148.
80	QIU M F, CHEN Z, JIANG L, et al. Numerical simulation of uranium tetrafluoride fluorination in a multistage spouted bed using the improved CFD-DEM chemical reaction model[J]. Particuology, 2023, 75: 119-136.
81	ABAD A, ADÁNEZ J, CUADRAT A, et al. Kinetics of redox reactions of ilmenite for chemical-looping combustion[J]. Chemical Engineering Science, 2011, 66(4): 689-702.
82	JEONG H J, SEO D K, HWANG J. CFD modeling for coal size effect on coal gasification in a two-stage commercial entrained-bed gasifier with an improved char gasification model[J]. Applied Energy, 2014, 123: 29-36.
83	李向阳, 王浩亮, 冯鑫, 等. 多相反应器的非均相特性测量技术进展[J]. 化工进展, 2019, 38(1): 45-71.
	LI Xiangyang, WANG Haoliang, FENG Xin, et al. Progresses in measurement technologies of heterogeneous characteristics in multiphase reactors[J]. Chemical Industry and Engineering Progress, 2019, 38(1): 45-71.
84	MERZKIRCH W, GUI L, HILGERS S, et al. PIV in multiphase flow[C]. proceedings of the second international workshop on PIV, 1997.
85	HE Y R, PENG W G, WANG T Y, et al. DEM study of wet cohesive particles in the presence of liquid bridges in a gas fluidized bed[J]. Mathematical Problems in Engineering, 2014, 2014: 1-14.
86	LIU G Q, LI S Q, ZHAO X L, et al. Experimental studies of particle flow dynamics in a two-dimensional spouted bed[J]. Chemical Engineering Science, 2008, 63(4): 1131-1141.
87	ZHU R R, ZHU W B, XING L C, et al. DEM simulation on particle mixing in dry and wet particles spouted bed[J]. Powder Technology, 2011, 210(1): 73-81.
88	HAYHURST A N, PARMAR M S. Does solid carbon burn in oxygen to give the gaseous intermediate CO or produce CO₂directly? Some experiments in a hot bed of sand fluidized by air[J]. Chemical Engineering Science, 1998, 53(3): 427-438.
89	HAYHURST A N, PARMAR M S. Measurement of the mass transfer coefficient and Sherwood number for carbon spheres burning in a bubbling fluidized bed[J]. Combustion and Flame, 2002, 130(4): 361-375.
90	SONG T, WU J H, SHEN L H, et al. Experimental investigation on hydrogen production from biomass gasification in interconnected fluidized beds[J]. Biomass and Bioenergy, 2012, 36: 258-267.
91	QIU M F, JIANG L, LIU R Z, et al. CFD-DEM simulation of fluorination reactions in fluidized beds with local grid and time refinement method[J]. Particuology, 2023: doi.org/10.1016/j.partic. 2023.03.016.

颗粒反应模型	研究对象	颗粒反应模型特点	作者	发表年份
均匀转化模型	氯化铜与过热蒸汽反应	颗粒内部反应速率均匀	Haseli等^[74]	2008
缩粒反应模型	煤焦燃烧	考虑惰性颗粒对反应的抑制效应	Geng等^[56]	2011
缩粒反应模型	谷物干燥	根据经验公式计算颗粒收缩率	Azmir等^[75]	2019
缩核反应模型	煤焦燃烧	颗粒粒径不发生改变	Zhou等^[76]	2004
	煤焦和丙烷燃烧	颗粒粒径不发生改变	Liu等^[8]	2011
	矿石煅烧	考虑气体产物对反应的抑制效应	Amiri等^[77]	2015
	煤热解和煤焦燃烧	中间产物层在碰撞过程中脱离颗粒	Xie等^[57]	2019
	生物质热解液化	气体产物在颗粒内部的扩散被忽略	Wang等^[78]	2021
	赤铁矿磁化焙烧	反应过程中引入随机成核模型	Zou等^[79]	2021
联合收缩模型	二氧化铀氟化	缩粒反应模型与缩核反应模型相结合	Ogata等^[66]	2004
	二氧化铀氟化	缩粒反应模型与缩核反应模型相结合	Homma等^[67]	2005
	煤焦气化	考虑颗粒表面液滴形成与脱离过程	Pednekar等^[68]	2016
	煤基质中气体的解吸与扩散	考虑中间产物层中气体扩散率变化	Zhang等^[69]	2021
	四氟化铀氟化	修正非均匀的空间浓度场引入误差	Qiu等^[80]	2023
细颗粒反应模型	石灰石煅烧	考虑气体产物对反应的抑制效应	García-Labiano等^[70]	2002
	钛铁矿氧化和还原	建立反应动力学参数	Abad等^[81]	2011
	铁矿石还原	考虑径向晶粒反应速率差异	Fu等^[71]	2016
随机孔隙模型	煤焦气化	考虑颗粒内部和外部的气体扩散	Jeong等^[82]	2014

颗粒反应模型	研究对象	颗粒反应模型特点	作者	发表年份
均匀转化模型	氯化铜与过热蒸汽反应	颗粒内部反应速率均匀	Haseli等^[74]	2008
缩粒反应模型	煤焦燃烧	考虑惰性颗粒对反应的抑制效应	Geng等^[56]	2011
缩粒反应模型	谷物干燥	根据经验公式计算颗粒收缩率	Azmir等^[75]	2019
缩核反应模型	煤焦燃烧	颗粒粒径不发生改变	Zhou等^[76]	2004
	煤焦和丙烷燃烧	颗粒粒径不发生改变	Liu等^[8]	2011
	矿石煅烧	考虑气体产物对反应的抑制效应	Amiri等^[77]	2015
	煤热解和煤焦燃烧	中间产物层在碰撞过程中脱离颗粒	Xie等^[57]	2019
	生物质热解液化	气体产物在颗粒内部的扩散被忽略	Wang等^[78]	2021
	赤铁矿磁化焙烧	反应过程中引入随机成核模型	Zou等^[79]	2021
联合收缩模型	二氧化铀氟化	缩粒反应模型与缩核反应模型相结合	Ogata等^[66]	2004
	二氧化铀氟化	缩粒反应模型与缩核反应模型相结合	Homma等^[67]	2005
	煤焦气化	考虑颗粒表面液滴形成与脱离过程	Pednekar等^[68]	2016
	煤基质中气体的解吸与扩散	考虑中间产物层中气体扩散率变化	Zhang等^[69]	2021
	四氟化铀氟化	修正非均匀的空间浓度场引入误差	Qiu等^[80]	2023
细颗粒反应模型	石灰石煅烧	考虑气体产物对反应的抑制效应	García-Labiano等^[70]	2002
	钛铁矿氧化和还原	建立反应动力学参数	Abad等^[81]	2011
	铁矿石还原	考虑径向晶粒反应速率差异	Fu等^[71]	2016
随机孔隙模型	煤焦气化	考虑颗粒内部和外部的气体扩散	Jeong等^[82]	2014

[1]	王戈, 孙志伟, 谭蔚, 邱威, 朱国瑞. 异形纤维阵列过滤特性的数值模拟[J]. 化工进展, 2022, 41(1): 30-39.
[2]	刘洪斌,张进,肖慧娜,谢超. 固相颗粒在旋流场形成过程中的运动分析[J]. 化工进展, 2019, 38(03): 1236-1243.
[3]	任立波, 赵新强, 张少峰. 水平窄矩形通道内液固两相的流动特性[J]. 化工进展, 2018, 37(06): 2092-2100.