Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Experimental Study on the Effective Particle Diameter of a Packed Bed with Non-Spherical Particles

Abstract

An experimental study is conducted to determine the characteristics of frictional pressure drops of fluid flow in porous beds packed with non-spherical particles. The objective is to examine the applicability of the Ergun equation to flow resistance assessment for packed beds with non-spherical particles. The experiments are carried out on the POMECOFL facility at KTH. Hollow spheres and cylinders are used to pack the beds. Either water or air is chosen as the working fluid. The experimental data show that the Ergun equation is applicable to all the test beds if the effective particle diameter used in the equation is chosen as the equivalent diameter of the particles, which is the product of Sauter mean diameter and shape factor of the particles in each bed.

This is a preview of subscription content, log in to check access.

Abbreviations

A, B, C :

Constant

A p :

Surface area of particle, m2

A sp :

Surface area of the equivalent-volume sphere, m2

d :

Particle diameter, m

d e :

Effective diameter, m

d eq :

Equivalent diameter of non-spherical particles, m

d p :

Particle diameter, m

d sd :

Sauter mean diameter, m

d vs :

Volume-surface mean diameter, m

d t :

Tube diameter, m

J :

Superficial fluid velocity, m/s

K :

Permeability

L :

Beds length, m

M :

Mass of particles, kg

ΔP :

Pressure drop, kPa

S V :

Specific surface area of particles, m−1

V p :

Volume of particles, m3

V 0 :

Total volume of the porous bed occupied, m3

Ψ:

Wadell’s sphericity

\({\varepsilon}\) :

Porosity of the porous beds

η :

Passability

μ :

Dynamic viscosity of fluid, N S/m2

ρ :

Density, kg/m3

References

  1. Carman P.C.: Fluid flow through packed beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)

  2. Comiti J., Renaud M.: A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles. Chem. Eng. Sci. 44(7), 1539–1545 (1989)

  3. Dolejš V., Machac I.: Pressure drop during the flow of a Newtonian fluid through a fixed bed of particles. Chem. Eng. Process. 34, 1–8 (1995)

  4. Dullien F.A.L.: Single phase flow through porous media and pore structure. Chem. Eng. J. 10, 1–34 (1975)

  5. Ergun S.: Fluid flow through packed columns. Chem. Eng. Prog. 48(2), 89–94 (1952)

  6. Foumeny E.A., Benyahia F., Castro J.A.A. et al.: Correlations of pressure drop in packed beds taking into account the effect of confining wall. Int. J. Heat Mass Transf. 36(2), 536–540 (1993)

  7. Foumeny E.A., Kulkarni A., Roshani S., Vatani A.: Elucidation of pressure drop in packed beds systems. Appl. Therm. Eng. 16, 195–202 (1996)

  8. Handley D., Heggs P.J.: Momentum and heat transfer mechanisms in regular shaped packings. Trans. Inst. Chem. Eng. 46(9), 251–264 (1968)

  9. Hu K., Theofanous T.G.: On the measurement and mechanism of dryout in volumetrically heated coarse particle beds. Int. J. Multiphase Flow 17(4), 519–532 (1991)

  10. Jamialahmadi M., Muller-Steinhagen H., Izadpanah M.R.: Pressure drop, gas hold-up and heat transfer during single and two-phase flow through porous media. Int. J. Heat Fluid Flow 26, 156–172 (2005)

  11. Konovalikhin, M.J.: Investigations on melt spreading and coolability in a LWR severe accident. Ph.D Thesis of Royal Institute of Technology, Stockholm (2001)

  12. Leva M.: Fluidization. McGraw-Hill, New York (1959)

  13. Lindholm, I.: A review of Dryout heat fluxes and coolability of particle beds. SKI Report 02:17(2002)

  14. Lindholm I., Holmström S., Miettinen J. et al.: Dryout heat flux experiments with deep heterogeneous particle bed. Nucl. Eng. Des. 236, 2060–2074 (2006)

  15. Lipinski R.J.: A coolability model for postaccident nuclear reactor debris. Nucl. Technol. 65, 53–66 (1984)

  16. Liu S., Afacan A., Masliyah J.H.: Steady incompressible laminar flow in porous media. Chem. Eng. Sci. 49(21), 3565–3586 (1994)

  17. Macdonald I.F., El-Sayed M.S., Mow K., Dullien F.A.L.: Flow through porous media—the Ergun equation revisited. Ind. Eng. Chem. Fundam. 18(3), 199–208 (1979)

  18. Nemec D., Levec J.: Flow through packed bed reactors: 1. Single-phase flow. Chem. Eng. Sci. 60, 6947–6957 (2005)

  19. Niven R.K.: Physical insight into the Ergun and Wen & Yu equations for fluid flow in packed and fluidized beds. Chem. Eng. Sci. 57, 527–534 (2002)

  20. Ozahi E., Gundogdu M.Y., Carpinlioglu M.Ö.: A modification on Ergun’s correlation for use in cylindrical packed beds with non-spherical particles. Adv. Powder Technol. 19, 369–381 (2008)

  21. Reed, A.W.: The effect of channeling on the dryout of heated particulate beds immersed in a liquid pool. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge (1982)

  22. Richard G.H.: Fundamentals of Particle Technology. Midland Information Technology and Publishing, Leicestershire (2002)

  23. Schulenberg T., Műller U.: An improved model for two-phase flow through beds of course particles. Int. J. Multiphase Flow 13(1), 87–97 (1987)

  24. Standish N., Drinkwater J.B.: The effect of particle shape on flooding rates in packed columns. Chem. Eng. Sci. 25, 1619–1621 (1970)

  25. Tung V.X., Dhir V.K.: A hydrodynamic model for two-phase flow through porous media. Int. J. Multiphase Flow 14(1), 47–65 (1988)

  26. Wadell H.: Volume, shape and roundness of quartz particles. J. Geol. 43, 250–280 (1935)

Download references

Author information

Correspondence to Liangxing Li.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Li, L., Ma, W. Experimental Study on the Effective Particle Diameter of a Packed Bed with Non-Spherical Particles. Transp Porous Med 89, 35–48 (2011). https://doi.org/10.1007/s11242-011-9757-2

Download citation

Keywords

  • Porous media
  • Non-spherical particles
  • Frictional pressure drop
  • Equivalent diameter