Unsteady State Heat Transfer in Packed-Bed Elliptic Cylindrical Reactor: Theory, Advanced Modeling and Applications

  • R. M. da Silva
  • Antonio Gilson Barbosa de Lima
  • A. S. Pereira
  • M. C. N. Machado
  • R. S. Santos
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 93)

Abstract

Transport phenomena through porous media has been of continuing interest for scientists, researchers and engineers due to the wide range of industrial applications. This chapter presents information about unsteady-state heat transfer and fluid flow inside of packed-bed reactors. The topics covered are related to fundamentals of porous media, chemical reactors, including mathematical modeling and applications. Emphasis is placed on packed-bed elliptic-cylindrical reactor. Based on the concept of local thermal equilibrium, a general mathematical formulation for a pseudo-homogeneous heat transfer model written in elliptic-cylindrical coordinates along with the numerical solution of the governing equation has been presented. Herein, an overview of currently-used models and the pertinent transient conductive transport processes inside the reactor were explored. A numerical example of heat transfer and fluid flow in a multiphase system (elliptic-cylindrical reactor filled with particles) was performed, and results of the temperature distribution inside the equipment at different instant of process are presented and discussed.

Keywords

Reactor Porous media Packed-bed Elliptic-cylindrical Finite volume Unsteady-state 

Notes

Acknowledgements

The authors thank to FINEP, CAPES and CNPq (Brazilian Research Agencies) for financial support to this research, and also to the researchers for their referenced studies which helped in improving the quality of this work.

References

  1. 1.
    Dullien, F.A.L.: Porous Media—Fluid Transport and Pore Structure, 2nd edn, p. 574. Academic Press Inc, San Diego, USA (1992)Google Scholar
  2. 2.
    Martins, A.A.A.: Transport phenomena in porous media. Single phase flow and mass transport. Ph.D. Thesis, Faculty of Engineering (FEUP), University of Porto, Porto, Portugal (2006) (in Portuguese)Google Scholar
  3. 3.
    McCabe, W.L., Smith, J.C., Harriot, P.: Unit Operations of Chemical Engineering. Chemical Engineering Series, 5th edn, p. 1129. McGraw Hill, USA (1993)Google Scholar
  4. 4.
    Rawlings, J.B., Ekerdt, J.G.: Chemical Reactor Analysis and Design Fundamentals, p. 609. Nob Hill Publishing, Madison, WI, USA (2002)Google Scholar
  5. 5.
    Froment, G.F., Bischoff, K.B., De Wilde, J.: Chemical Reactor Analysis and Design, 3rd edn, p. 859. Wiley, NewYork, USA (2011)Google Scholar
  6. 6.
    Eppinger, T., Seidler, K., Kraume, M.: DEM-CFD simulations of fixed bed reactors with small tube to particle diameter ratios. Chem. Eng. J. 166(01), 324–331 (2011)CrossRefGoogle Scholar
  7. 7.
    Hill Jr., C.G.: An Introduction to Chemical Engineering Kinetics and Reactor Design, p. 594. Wiley, NewYork (1977)Google Scholar
  8. 8.
    Oliveira, L.G.: Heat transfer in packed bed cylindrical-elliptical reactor: thermal, fluiddynamics and geometric aspects. Ph.D Thesis in Process Engineering, Federal University of Campina Grande, Campina Grande, Brazil, (2004) (in Portuguese)Google Scholar
  9. 9.
    Pirkle Jr., J.C., Reyes, S.C., Hagan, P.S., Khesgid, H.: Solution of dynamic distributed parameter model of nonadiabatic fixed—bed reactor. Comput. Chem. Eng. 11(06), 737–747 (1987)CrossRefGoogle Scholar
  10. 10.
    Shafeeyan, M.S., Daud, W.M.A.W., Shamiri, A.: A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption. Chem. Eng. Res. Des. 92(5), 961–988 (2014)CrossRefGoogle Scholar
  11. 11.
    Jee, J.G., Park, H.J., Haam, S.J., Lee, C.H.: Effects of nonisobaric and isobaric steps on O2 pressure swing adsorption for a reactor. Ind. Eng. Chem. Res. 41(17), 4383–4392 (2002)CrossRefGoogle Scholar
  12. 12.
    Kim, M.B., Bae, Y.S., Choi, D.K., Lee, C.H.: Kinetic separation of landfill gas by a two-bed pressure swing adsorption process packed with carbon molecular sieve: non isothermal operation. Ind. Eng. Chem. Res. 45(14), 5050–5058 (2006)CrossRefGoogle Scholar
  13. 13.
    Kim, M.B., Moon, J.H., Lee, C.H., Ahn, H., Cho, W.: Effect of heat transfer on the transient dynamics of temperature swing adsorption process. Korean J. Chem. Eng. 21(3), 703–711 (2004)CrossRefGoogle Scholar
  14. 14.
    Amiri, A., Vafai, K.: Transient analysis of incompressible flow through a packed bed. Int. J. Heat Mass Transf. 41, 4259–4279 (1998)CrossRefGoogle Scholar
  15. 15.
    Ergun, S.: Fluid flow through packed columns. J. Chem. Eng. Prog. 48(2), 89–94 (1952)Google Scholar
  16. 16.
    Benanati, R.F., Brosilow, C.B.: Void fraction distribution in beds of spheres. Am. Inst. Chem. Eng. J. 8(3), 359–361 (1962)CrossRefGoogle Scholar
  17. 17.
    Wakao, N., Kaguei, S.: Heat and Mass Transfer in Packed Beds. Gordon and Breach Science Publishers, New York (1982)Google Scholar
  18. 18.
    Colburn, A.P.: Heat transfer and pressure drop in empty, baffled and packed tubes: I. Heat transfer in packed tubes. Ind. Eng. Chem. Res. 23(8), 910–913 (1931)CrossRefGoogle Scholar
  19. 19.
    de Azevedo, S.F., Romero, M.A.O., Wardle, A.P.: Modeling of tubular fixed-bed catalytic reactor: a brief review. Chem. Eng. Res. Des. 68, 483–502 (1990)Google Scholar
  20. 20.
    Moreira, M.F.P., Ferreira, M.C., Freire, J.T.: Evaluation of pseudo-homogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow. Chem. Eng. Sci. 61(06), 2056–2068 (2006)CrossRefGoogle Scholar
  21. 21.
    Coberly, C.A., Marshall Jr., M.W.R.: Temperature gradients in gas streams flowing through fixed granular beds. Chem. Eng. Prog. 47(3), 141–150 (1951)Google Scholar
  22. 22.
    Dixon, A.G., Paterson, W.R., Cresswell, D.L.: Heat transfer in packed beds of low tube/particle diameter ratio. ACS Symp. Ser. 65, 238–253 (1978)CrossRefGoogle Scholar
  23. 23.
    Borkink, J.G.H., Westerterp, K.R.: Determination of effective heat transport coefficients for wall-cooled packed beds. Chem. Eng. Sci. 47(9–11), 2337–2342 (1992)CrossRefGoogle Scholar
  24. 24.
    Giudici, R.: Modeling of ethylene oxidation reactor: study of thermal parameters and strategy of catalyst dilution. Ph.D. Thesis, Poli/USP, São Paulo, Brazil, p. 183(1990) (in Portuguese)Google Scholar
  25. 25.
    Silva, R.M., Lima, A.G.L., Oliveira, L.G., Araújo, M.V., Santos, R.S.: Transient heat transfer in a packed-bed elliptic cylindrical reactor: a finite-volume approach. Defect and Diffusion Forum 380, 79–85 (2017)CrossRefGoogle Scholar
  26. 26.
    Lima, A.G.B.: Diffusion phenomena in prolate spheroidal solids. Studied case: drying of Banana. Ph.D Thesis in Mechanical Engineering, State University of Campinas, Campinas, Brazil, p. 244 (1999) (in Portuguese)Google Scholar
  27. 27.
    Kreyszig, E.: Advanced engineering Mathematics, vol. 1, 10th edn. Wiley, New York (2011)Google Scholar
  28. 28.
    Maliska, C.R.: Heat transfer and computational fluid mechanics. 2nd edn, LTC—Livros Técnicos e Científicos Editora S.A., Rio de Janeiro, Brazil (2004) (in Portuguese)Google Scholar
  29. 29.
    Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd edn. Springer, Berlin (1966)CrossRefGoogle Scholar
  30. 30.
    Brodkey, R.S.: The Phenomena of Fluid Motions. Addison-Wesley Publishing Company, London (1967)Google Scholar
  31. 31.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Wiley, New York (1970)MATHGoogle Scholar
  32. 32.
    Bergman, T.L., Lavine, A.S., Incropera, F.P., De Witt, D.P.: Fundamentals of Heat and Mass Transfer, 7th edn, LTC—Livros Técnicos e Científicos Editora S.A, Rio de Janeiro, Brazil (2014). (in Portuguese)Google Scholar
  33. 33.
    Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, New York, USA (1980)MATHGoogle Scholar
  34. 34.
    Pakowski, Z., Bartczak, Z., Strumillo, C., Stenström, S.: Evaluation of equations approximating thermodynamic and transport properties of water, steam and air for use in cad of drying processes. Drying Technol. 09(3), 753–773 (1991)CrossRefGoogle Scholar
  35. 35.
    Jumah, R.Y., Mujumdar, A.S., Raghavan, G.S.V.: A Mathematical model for constant and intermittent batch drying of grains in a novel rotating jet spouted bed. Drying Technol. 14(03–04), 765–802 (1996)Google Scholar
  36. 36.
    Taylor, K., Smith, A.G., Ross, S.: The prediction of pressure drop and flow distribution in packed-bed filters. In: Second International Conference on CFD in the Minerals and Process Industries (CSIRO), Melbourne, Australia, 273 (1999)Google Scholar
  37. 37.
    Schwartz, C.E., Smith, J.M.: Flow distribution in packed beds. Ind. Eng. Chem. Res. 45(6), 1209–1218 (1953)CrossRefGoogle Scholar
  38. 38.
    Zotin, F.M.Z.: The wall effect on filling columns, Masters Dissertation in Chemical Engineering, Federal University of São Carlos, São Carlos, Brazil (1985)Google Scholar
  39. 39.
    Kufner, R., Hofmann, H.: Implementation of radial porosity and velocity distribution in a reactor model for heterogeneous catalytic gas phase reactions (TORUS-model). Chem. Eng. Sci. 45(8), 2141–2146 (1990)CrossRefGoogle Scholar
  40. 40.
    Mueller, G.E.: Radial void fraction distributions in randomly packed-fixed beds of uniformly sized spheres in cylindrical containers. Powder Technol. 72(3), 269–275 (1992)CrossRefGoogle Scholar
  41. 41.
    de Klerk, A.: Voidage variation in packed beds at small column to particle diameter ratio. Am. Inst. Chem. Eng. J. 49(8), 2022–2029 (2003)CrossRefGoogle Scholar
  42. 42.
    Dong, Y., Sosna, B., Korup, O., Rosowski, F., Horn, R.: Investigation of radial heat transfer in a fixed-bed reactor: CFD simulations and profile measurements. Chem. Eng. J. 317, 204–214 (2017)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • R. M. da Silva
    • 1
  • Antonio Gilson Barbosa de Lima
    • 2
  • A. S. Pereira
    • 3
  • M. C. N. Machado
    • 4
  • R. S. Santos
    • 5
  1. 1.Federal Institute of Education, Science and Technology of ParaíbaAccess Highway PB 426, Rural area, Princesa IsabelBrazil
  2. 2.Department of Mechanical EngineeringFederal University of Campina GrandeCampina GrandeBrazil
  3. 3.Baiano Federal Institute of EducationScience and TechnologySanta InêsBrazil
  4. 4.Department of ChemicalState University of ParaibaCampina GrandeBrazil
  5. 5.Rural Federal University of the Semi-AridMossoróBrazil

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