Appendix: pinning and cavity equations
References
  1. H. Y. Wang, Y. S. Liu, G. Z. Zhang, et al. Study on variable mass flow laws in π-shaped centripetal radial flow adsorber, CIESC Journal, 70(9)(2019) 3385-3395.
  2. G. E. Mueller., Radial void fraction correlation for annular packed beds, AIChE J., 45 (1999):2458-2460.
  3. C. J. Hsu, S. S. Hsiau, A study of filtration performance in a cross-flow moving granular bed filter: The influence of gas flow uniformity, Powder Technol., 274(2015) 20-27.
  4. O. Nekhamkina, M. Sheintuch, Cross-flow reactor design for Fischer Tropsch synthesis, Chemical Engineering Journal, 372(2019) 277-293.
  5. J. D. McTigue, A. J. White, A comparison of radial-flow and axial-flow packed beds for thermal energy storage, Applied Energy, 227(2018) 533-541.
  6. X. Q. Song, Y. Jin, Z. Q. Yu, Influence of outward radial gas flow on particle movement in an annular moving bed, Powder Technol. 79 (1994) 247-256.
  7. Y. H. Chen, X. D. Zhu, Y. Q. Wu,Z. B. Zhu, The investigation of pressure drop in a moving bed, Chinese J. Process. Eng., (2006) 697-702 (in Chinese).
  8. Y. J. He, F. Z. Xiao, Z. H. Luo, Numerical modeling of the cavity phenomenon and its elimination way in rectangular radial moving bed reactor, Powder Technol., 274 (2015) 28-36.
  9. W. Y. Long, J. Xu, Y. P. Fan, C. X. Lu, Pinning and cavity in two types of cross-flow moving beds, Powder. Technol., 269 (2015) 66-74.
  10. Y. H. Chen, X. D. Zhu, Y. Q. Wu, Y. H. Dong, Z. B. Zhu, Phenomenon of cavity and its size in rectangular moving-bed, J. Chem. Ind. Eng., 57 (2006) 731-737 (in Chinese).
  11. K. A. Pilcher, J. Bridgwater, Pinning in a rectangular moving bed reactor with gas cross-flow, Chem. Eng. Sci., 45 (1990) 2535-2542.
  12. F. J. Doyle, R. Jackson, J. C. Ginestra, The phenomenon of pinning in an annular moving bed reactor with crossflow of gas, Chem. Eng. Sci., 41 (1986) 1485-1495.
  13. J. Tsubaki, C. Tien, Solid velocity in cross-flow moving beds, Powder Technol., 53 (1987) 105-112.
  14. J. C. Ginestra, R. Jackson, Pinning of a bed of particles in a Vertical Channel by a Cross Flow of Gas, Ind. Eng. Chem. Fundam., 24 (1985) 121-128.
  15. F. J. Doyle, R. Jackson, J. C. Ginestra, The phenomenon of pinning in an annular moving bed reactor with crossflow of gas, Chem. Eng. Sci., 41 (1986) 1485-1495.
  16. W. Y. Long, Hydrodynamic characteristics of cross-flow moving beds, China University of Petroleum (Beijing), Beijing, 2014.
  17. R. J. Wang, Y. P. Fan, C. X. Lu., Influences of different operating parameters and gas/solid properties in the rectangular cross-flow moving bed, Powder Technol., 318(2017)135-150.
  18. C. J. Hsu, S. S. Hsiau, A study of filtration performance in a cross-flow moving granular bed filter: The influence of gas flow uniformity, Powder Technol. 274 (2015) 20-27.
  19. P. R. Ponzi, L. A. Kaye, Effects of flow maldistribution on conversion and selectivity in radial flow fixed-bed reactors, AICHE J., 25(1)(1979)100-108.
  20. C. F. Zhang, Z. B. Zhu, M. S. Xu, B. C. Zhu, Design for uniform distribution of stream in radial reactor, J. Che. In., 1(1979)67-90 (in Chinese).
  21. Z. Z. Mu, J. F. Wang, T. F. Wang, Y. J, optimized design of radial flow moving-bed reactors based on a mathematical hydrodynamic model, Che. Eng. Pro.. 42 (2003) 409-417.
  22. C. X. Lu, W. Y. Long, Q. Z. Lin, Numerical simulation of gas-solid flow characteristics in radial moving bed, J. Chem. Eng. Chinese Univ., 29 (2015) 49-57 (in Chinese).
  23. Y. H. Chen, X. D. Zhu, Y. Q. Wu, Z. B. Zhu, Investigation of the effect of a dividing wall in a moving bed, Chem. Eng. Technol., 30(8) (2007) 1028-1035.
  24. C. S. Chou, T. L. Yang, J. C. Chang, Flow patterns and wall stresses in a moving granular filter bed with an asymmetric louvered-wall and obstacles, Chem. Eng. Process., 45 (2006) 79-89.
  25. H. P. Wan, T. Y. Yang, I. L. Chung, H. T. Lee, Hydrodynamic behavior in a moving granular bed filter for modeling on char separation during the biomass fast pyrolysis process, J. Taiwan Inst. Chem. E., 44 (2013) 1016-1021.
  26. J. T. Wu, J. Z. Chen, Y. R. Yang. A modified kinematic model for particle flow in moving beds, Powder Technol., 181 (2008) 74-82.
  27. S. S. Hsiau, J. Smid, Y. P. Chyou, T. C. Liu, T. C. Huang, C. J. Hsu, Impact of flow-corrective insert on flow patterns in two-dimensional moving bed, Chem. Eng. Process., 73 (2013) 7-15.
  28. A.Bombač, Z. Rek, J. Levec, Void fraction distribution in a bisectional bubble column reactor. AIChE J, 65 (2019) 1186-1197.
  29. F. Z. Xiao, Z. H. Luo, A Two-Phase CFD Modeling Approach to Investigate the Flow Characteristics in Radial Flow Moving-Bed Reactors, Int. J. Chem. React. Eng., 12 (2014) 497-512.
  30. R. J. Wang, Y. P. Fan, C. X. Lu, Gas axial dispersion behavior and gas residence time in the radial flow bed, Ind. Eng. Chem. Res., 56 (42)(2017) 12203-12214.
  31. S. S. Hsiau, J. Smid, S. A. Tsai, C. C. Tzeng, Y. J. Yu, Flow of filter granules in moving granular beds with louvers and sublouvers, Chem. Eng. Process., 47 (2008) 2084-2097.
  32. Y. K. Ahn, H. C. Chen, L. T. Fan, C. G. Wan, A modified moving bed grain dryer, I&EC Process design and development, 3(2) (1964) 96-100.
  33. W. A. Beverloo, H. A. Leniger, J. V. Velde, The flow of granular solids through orifices, Chem. Eng. Sci., 15 (1961)260-269.