[1] de Munck, M.J.A., Peters, E.A.J.F., Kuipers, J.A.M. 2023. Fluidized bed gas-solid heat transfer using a CFD-DEM coarse-graining technique. Chemical Engineering Science, 280, 119048. doi: https://doi.org/10.1016/j.ces.2023.119048.
[2] Deen, N.G., Van Sint Annaland, M., Van der Hoef, M.A., Kuipers, J.A.M. 2007. Review of discrete particle modeling of fluidized beds. Chemical Engineering Science, 62, pp. 28–44. doi: https://doi.org/10.1016/j.ces.2006.08.014.
[3] Davidson, J.F., Harrison, D., 1971. Fluidization, Academic Press, London, New York.
[4] Balag, J., Franco, D.A.T., Miral, V.G., Reyes, V., Tongco, L.J., Lopez, E.C.R., 2023. Recent Advances in Particle Fluidization. ASEC 2023, 62. doi: https://doi.org/10.3390/ASEC2023-15321.
[5] Chen, C., 2016. Investigations on Mesoscale Structure in Gas–Solid Fluidization and Heterogeneous Drag Model, in: Springer Berlin Heidelberg, Berlin, Heidelberg, doi: https://doi.org/10.1007/978-3-662-48373-2.
[6] Wang, J., Ren, C., Yang, Y., Hou, L., 2009. Characterization of Particle Fluidization Pattern in a Gas Solid Fluidized Bed Based on Acoustic Emission (AE) Measurement. Ind. Eng. Chem. Res., 48, pp. 8508–8514. doi: https://doi.org/10.1021/ie8018774.
[7] Van Der Hoef, M.A., Ye, M., Van Sint Annaland, M., Andrews, A.T., Sundaresan, S., Kuipers, J.A.M., 2006. Multiscale Modeling of Gas-Fluidized Beds. Advances in Chemical Engineering, 31, pp. 65–149. doi: https://doi.org/10.1016/S0065-2377(06)31002-2.
[8] Di Renzo, A., Scala, F., Heinrich, S., 2021. Recent Advances in Fluidized Bed Hydrodynamics and Transport Phenomena—Progress and Understanding. Processes, 9, (2021)639. doi: https://doi.org/10.3390/pr9040639.
[9] Lettieri, P., Mazzei, L., 2009. Challenges and Issues on the CFD Modeling of Fluidized Beds: A Review. The Journal of Computational Multiphase Flows, 1, pp. 83–131. doi: https://doi.org/10.1260/175748209789563937.
[10] Patterson, E.E., Halow, J., Daw, S., 2010. Innovative Method Using Magnetic Particle Tracking to Measure Solids Circulation in a Spouted Fluidized Bed. Ind. Eng. Chem. Res., 49, pp. 5037–5043. doi: https://doi.org/10.1021/ie9008698.
[11] Grace, J.R., 1997. Circulating fluidized beds, 1st ed., Blackie Academic & Professional, London, New York.
[12] Esin, A., Altun, M., 1984. Correlation of axial mixing of solids in fluidized beds by a dispersion coefficient. Powder Technology, 39, pp. 241–244. doi: https://doi.org/10.1016/0032-5910(84)85041-X.
[13] Geldart, D., 1973. Types of gas fluidization. Powder Technology, 7, (1973)pp. 285–292. doi: https://doi.org/10.1016/0032-5910(73)80037-3.
[14] Shaul, S., Rabinovich, E., Kalman, H., 2014. Typical Fluidization Characteristics for Geldart’s Classification Groups. Particulate Science and Technology, 32, pp. 197–205. doi: https://doi.org/10.1080/02726351.2013.842624.
[15] Cocco, R., Chew, J.W., 2023. 50 years of Geldart classification. Powder Technology, 428 118861. doi: https://doi.org/10.1016/j.powtec.2023.118861.
[16] Drake, J.B., Heindel, T.J., 2012. Comparisons of Annular Hydrodynamic Structures in 3D Fluidized Beds Using X-Ray Computed Tomography Imaging. Journal of Fluids Engineering, 134, 081305. doi: https://doi.org/10.1115/1.4007119.
[17] Sun, J., Yan, Y., 2016. Non-intrusive measurement and hydrodynamics characterization of gas–solid fluidized beds: a review. Meas. Sci. Technol., 27, 112001. doi: https://doi.org/10.1088/0957-0233/27/11/112001.
[18] Errigo, M., Windows-Yule, C., Materazzi, M., Werner, D., Lettieri, P., 2024. Non-invasive and non-intrusive diagnostic techniques for gas-solid fluidized beds – A review. Powder Technology, 431, 119098. doi: https://doi.org/10.1016/j.powtec.2023.119098.
[19] Golshan, S., Sotudeh-Gharebagh, R., Zarghami, R., Mostoufi, N., Blais, B., Kuipers, J.A.M., 2020. Review and implementation of CFD-DEM applied to chemical process systems. Chemical Engineering Science, 221, 115646. doi: https://doi.org/10.1016/j.ces.2020.115646.
[20] Mladenovic, M., Nemoda, S., Paprika, M., Marinkovic, A., 2019. Application of analytical and CFD models of liquid fuels combustion in a fluidized bed. Therm Sci., 23, pp. 1627–1636. doi: https://doi.org/10.2298/TSCI180226317M.
[21] Ma, H., Zhou, L., Liu, Z., M Chen, M., Xia, X., Zhao, Y., 2022. A review of recent development for the CFD-DEM investigations of non-spherical particles. Powder Technology, 412 117972. doi: https://doi.org/10.1016/j.powtec.2022.117972.
[22] Berthiaux, H., Mizonov, V., Zhukov, V., 2005. Application of the theory of Markov chains to model different processes in particle technology. Powder Technology, 157, pp. 128–137. doi: https://doi.org/10.1016/j.powtec.2005.05.019.
[23] Berthiaux, H., Mizonov, V., 2008. Applications of Markov Chains in Particulate Process Engineering: A Review. Can. J. Chem. Eng., 82, pp. 1143–1168. doi: https://doi.org/10.1002/cjce.5450820602.
[24] Dehling, H.G., Hoffmann, A.C., Stuut, H.W., 1999. Stochastic Models for Transport in a Fluidized Bed. SIAM J. Appl. Math., 60, pp. 337–358. doi: https://doi.org/10.1137/S0036139996306316.
[25] Cronin, K., Catak, M., Bour, J., Collins, A., Smee, J., 2011. Stochastic modelling of particle motion along a rotary drum. Powder Technology, 213, pp. 79–91. doi: https://doi.org/10.1016/j.powtec.2011.07.009.
[26] Li, J., Huang, W., 2018. From Multiscale to Mesoscience: Addressing Mesoscales in Mesoregimes of Different Levels. Annu. Rev. Chem. Biomol. Eng., 9, pp. 41–60. doi: https://doi.org/10.1146/annurev-chembioeng-060817-084249.
[27] Di Renzo, A., Napolitano, E., Di Maio, F., 2021. Coarse-Grain DEM Modelling in Fluidized Bed Simulation: A Review. Processes, 9, 279. doi: https://doi.org/10.3390/pr9020279.
[28] Catak, M., Cronin, K., Medina-Tellez, D., 2011. Markov Chain Modeling of Fluidized Bed Granulation Incorporating Simultaneous Aggregation and Breakage. Ind. Eng. Chem. Res., 50, pp. 10811–10823. doi: https://doi.org/10.1021/ie102513v.
[29] Li, J., Kwauk, M., 2001. Multiscale Nature of Complex Fluid−Particle Systems. Ind. Eng. Chem. Res., 40, pp. 4227–4237. doi: https://doi.org/10.1021/ie0011021.
[30] Lu, B., Niu, Y., Chen, F., Ahmad, N., Wang, W., Li, J., 2019. Energy-minimization multiscale based mesoscale modeling and applications in gas-fluidized catalytic reactors. Reviews in Chemical Engineering, 35, pp. 879–915. doi: https://doi.org/10.1515/revce-2017-0023.
[31] Zhuang, Y., Chen, X., Liu, D., 2016. Stochastic bubble developing model combined with Markov process of particles for bubbling fluidized beds. Chemical Engineering Journal, 291, pp. 206–214. doi: https://doi.org/10.1016/j.cej.2016.01.095.
[32] Hernández-Jiménez, F., Sánchez-Delgado, S., Gómez-García, A., Acosta-Iborra, A., 2011. Comparison between two-fluid model simulations and particle image analysis & velocimetry (PIV) results for a two-dimensional gas–solid fluidized bed. Chemical Engineering Science, 66, pp. 3753–3772. doi: https://doi.org/10.1016/j.ces.2011.04.026.
[33] Link, J., Zeilstra, C., Deen, N., Kuipers, H., 2008. Validation of a Discrete Particle Model in a 2D Spout-Fluid Bed Using Non-Intrusive Optical Measuring Techniques. Can. J. Chem. Eng., 82, pp. 30–36. doi: https://doi.org/10.1002/cjce.5450820105.
[34] Ismail, T.M., Abd El-Salam, M., Monteiro, E., Rouboa, A., 2016. Eulerian – Eulerian CFD model on fluidized bed gasifier using coffee husks as fuel. Applied Thermal Engineering, 106, pp. 1391–1402. doi: https://doi.org/10.1016/j.applthermaleng.2016.06.102.
[35] Reddy, P.N., Verma, V., Kumar, A., Awasthi, M.K., 2023. CFD Simulation and Thermal Performance Optimization of Channel Flow with Multiple Baffles. Journal of Heat and Mass Transfer Research, 10, pp. 257–268. doi: https://doi.org/10.22075/jhmtr.2023.31108.1458.
[36] Vahedi, S.M., Parvaz, F., Rafee, R., Khandan Bakavoli, M., 2018. Computational fluid dynamics simulation of the flow patterns and performance of conventional and dual-cone gas-particle cyclones. Journal of Heat and Mass Transfer Research, 5, pp. 27–38. doi: https://doi.org/10.22075/jhmtr.2017.11918.1170.
[37] Zhonghua, W., Mujumdar, A.S., 2008. CFD modeling of the gas–particle flow behavior in spouted beds. Powder Technology, 183, 260-272. doi: https://doi.org/10.1016/j.powtec.2007.07.040.
[38] Feng, Y.Q., Xu, B.H., Zhang, S.J., Yu, A.B., Zulli, P., 2004. Discrete particle simulation of gas fluidization of particle mixtures. AIChE Journal, 50, pp. 1713–1728. doi: https://doi.org/10.1002/aic.10169.
[39] Zhao, Y., Shi, X., Wang, C., Lan, X., Gao, J., 2023. Study on flow characteristics of turbulent fluidized bed with variable gas velocity due to chemical reactions. Powder Technology, 416, 118211. doi: https://doi.org/10.1016/j.powtec.2022.118211.
[40] Liu, F., Li, C., Zeng, X., Chen, J., Guan, J., Yang, L., 2024. Study on the flow and collision characteristics of catalyst particles in FCC reactor. Powder Technology, 438, 119642. doi: https://doi.org/10.1016/j.powtec.2024.119642.
[41] Zhao, Y., Shi, X., Lan, X., Gao, J., Jing, W., Xiong, Q., 2024. Simulation analysis of micro-explosion during emulsification feeding of residue fluidized catalytic cracking. Applied Thermal Engineering, 250, 123514. doi: https://doi.org/10.1016/j.applthermaleng.2024.123514.
[42] Ma, H., Zhao, Y., 2018. CFD-DEM investigation of the fluidization of binary mixtures containing rod-like particles and spherical particles in a fluidized bed. Powder Technology, 336, 533–545. doi: https://doi.org/10.1016/j.powtec.2018.06.034.
[43] He, L., Liu, Z., Zhao, Y., 2022. An extended unresolved CFD-DEM coupling method for simulation of fluid and non-spherical particles. Particuology, 68, 1–12. doi: https://doi.org/10.1016/j.partic.2021.11.001.
[44] Xu, J., Zhao, P., Zhang, Y., Wang, J., Ge, W., 2022. Discrete particle methods for engineering simulation: Reproducing mesoscale structures in multiphase systems. Resources Chemicals and Materials, 1, pp. 69–79. doi: https://doi.org/10.1016/j.recm.2022.01.002.
[45] Liu, X., Zhu, A., Yang, L., Xu, J., Li, H., Ge, W., Ye, M., 2022. Numerical simulation of commercial MTO fluidized bed reactor with a coarse-grained discrete particle method — EMMS–DPM,. Powder Technology, 406, 117576. doi: https://doi.org/10.1016/j.powtec.2022.117576.
[46] Wang, T., Zhang, F., Furtney, J., Damjanac, B., 2022. A review of methods, applications and limitations for incorporating fluid flow in the discrete element method. Journal of Rock Mechanics and Geotechnical Engineering, 14, pp. 1005–1024. doi: https://doi.org/10.1016/j.jrmge.2021.10.015.
[47] Gutsche, R., Hartmann, K., 1995. Application of Markov chains in deriving for predicting the dynamic behaviour of chemical engineering processes. Computers & Chemical Engineering, 19 pp. 729–734. doi: https://doi.org/10.1016/0098-1354(95)87121-7.
[48] Tamir, A., 1998. Applications of Markov chains in chemical processes, in: Elsevier, pp. 498–589. doi: https://doi.org/10.1016/B978-044482356-4/50007-9.
[49] Mitrofanov, A., Mizonov, V., Tannous, K., Ovchinnikov, L., 2018. A Markov chain model to describe fluidization of particles with time-varying properties. Particulate Science and Technology, 36, 244–253. doi: https://doi.org/10.1080/02726351.2016.1243180.
[50] Sánchez-Prieto, J., Hernández-Jiménez, F., Garcia-Gutierrez, L.M., Soria-Verdugo, A., 2017. Experimental study on the characteristic mixing time of solids and its link with the lateral dispersion coefficient in bubbling fluidized beds. Chemical Engineering Journal, 307, pp. 113–121. doi: https://doi.org/10.1016/j.cej.2016.08.075.
[51] Liu, D., Chen, X., 2010. Lateral solids dispersion coefficient in large-scale fluidized beds. Combustion and Flame, 157, pp. 2116–2124. doi: https://doi.org/10.1016/j.combustflame.2010.04.020.
[52] Castilla, G.M.. Larsson, A., Lundberg, L., Johnsson, F., Pallarès, D., 2020. A novel experimental method for determining lateral mixing of solids in fluidized beds – Quantification of the splash-zone contribution. Powder Technology, 370, pp. 96–103. doi: https://doi.org/10.1016/j.powtec.2020.05.036.
[53] Bokkers, G.A., Van Sint Annaland, M., Kuipers, J.A.M., 2004. Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study. Powder Technology, 140, pp. 176–186. doi: https://doi.org/10.1016/j.powtec.2004.01.018.
[54] Sánchez-Prieto, J., Hernández-Jiménez, F., Garcia-Gutierrez, L.M., Soria-Verdugo, A., 2017. Experimental study on the characteristic mixing time of solids and its link with the lateral dispersion coefficient in bubbling fluidized beds. Chemical Engineering Journal, 307, pp. 113–121. doi: https://doi.org/10.1016/j.cej.2016.08.075.
[55] Köhler, A., Rasch, A., Pallarès, D., Johnsson, F., 2017. Experimental characterization of axial fuel mixing in fluidized beds by magnetic particle tracking. Powder Technology, 316, pp. 492–499. doi: https://doi.org/10.1016/j.powtec.2016.12.093.
[56] Rhodes, M.J., Wang, X.S., Nguyen, M., Stewart, P., Liffman, K., 2001. Study of mixing in gas-fluidized beds using a DEM model. Chemical Engineering Science, 56, pp. 2859–2866. doi: https://doi.org/10.1016/S0009-2509(00)00524-8.
[57] Niklasson, F., Thunman, H., Johnsson, F., Leckner, B., 2002. Estimation of Solids Mixing in a Fluidized-Bed Combustor. Ind. Eng. Chem. Res., 41, pp. 4663–4673. doi: https://doi.org/10.1021/ie020173s.
[58] Borodulya, V.A., Epanov, Yu.G., Teplitskii, Yu.S., 1982. Horizontal particle mixing in a free fluidized bed. Journal of Engineering Physics, 42, pp. 528–533. doi: https://doi.org/10.1007/BF00824945.
[59] Mizonov, V., Mitrofanov, A., Ogurtzov, A., Tannous, K., 2014. Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains. Particulate Science and Technology, 32, pp. 171–178. doi: https://doi.org/10.1080/02726351.2013.839016.
[60] Mitrofanov, A.V., Mizonov, V.E., Shpeynova, N.S., Vasilevich, S.V., Kasatkina, N.K., 2021. Experimental and Theoretical Study of the Axial Distribution of Solid Phase Particles in a Fluidized Bed, Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64, pp. 349–362. doi: https://doi.org/10.21122/1029-7448-2021-64-4-349-362.
[61] Mitrofanov, A., Vasilevich, S., Mal’ko, M., Ogurtsov, A., Shpeynova, N., 2023. Design and verification of the model of structure formation and heat transfer in a fluidized bed apparatus with a heat jacket. ChemChemTech., 5, pp. 128–138. doi: https://doi.org/10.6060/ivkkt.20236605.6748.
[62] Li, R., Huang, X., Wu, Y., Dong, L., Belošević, S., Milićević, A., Tomanović, I., Deng, L., Che, D., 2023. Comparative analysis on gas–solid drag models in MFIX-DEM simulations of bubbling fluidized bed. Chinese Journal of Chemical Engineering, 64, pp. 64–75. doi: https://doi.org/10.1016/j.cjche.2023.06.002.
[63] Mikhailov, M.D., Freire, A.P.S., The drag coefficient of a sphere: An approximation using Shanks transform. 2013. Powder Technology, 237, pp. 432–435. doi: https://doi.org/10.1016/j.powtec.2012.12.033.
[64] Khan, A.R., Richardson, J.F., 1987. The resistance to motion of a solid sphere in a fluid. Chemical Engineering Communications, 62, pp. 135–150. doi: https://doi.org/10.1080/00986448708912056.
[65] Mitrofanov, A., Ovchinnikov, L., Ovchinnikov, N., Ogurtsov, A., Lapshina, O., 2022. Computational and experimental study of the thermal process in an individual cylindrical particle. ChemChemTech., 65, pp. 97–104. doi: https://doi.org/10.6060/ivkkt.20226509.6679.
[66] Muir, C.E., Lowry, B.J., Balcom, B.J., 2011. Measuring diffusion using the differential form of Fick’s law and magnetic resonance imaging. New J. Phys., 13, 015005. doi: https://doi.org/10.1088/1367-2630/13/1/015005.
[67] Chanson, H., 2009. Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows, in: 0 ed., CRC Press, p. 464. doi: https://doi.org/10.1201/b11464.
[68] Lin, J.S., Chen, M.M., Chao, B.T., 1985. A novel radioactive particle tracking facility for measurement of solids motion in gas-fluidized beds. AIChE Journal, 31, pp. 465–473. doi: https://doi.org/10.1002/aic.690310314.
[69] Yamazaki, R., Ueda, N., Jimbo, G., 1986. Mechanism of incipient fluidization in fluidized bed at elevated temperature. Journal of Chemical Engineering of Japan, 19, pp. 251–257.
[70] De Chant, L.J., 2005. The venerable 1/7th power law turbulent velocity profile: a classical nonlinear boundary value problem solution and its relationship to stochastic processes. Applied Mathematics and Computation, 161, pp. 463–474. doi: https://doi.org/10.1016/j.amc.2003.12.109.