Transport in Porous Media

, Volume 109, Issue 1, pp 43–60 | Cite as

Coupled LBM–DEM Micro-scale Simulations of Cohesive Particle Erosion Due to Shear Flows

  • Paul E. Brumby
  • Toru Sato
  • Jiro Nagao
  • Norio Tenma
  • Hideo Narita


In this paper, the erodibility of cohesive micro-scale particles is investigated for a range of surface shear stresses. Compacted layers of particles, formed by compressing 100 cohesive spheres together, are subjected to shear flow conditions. Fluid–particle interactions are solved using the lattice Boltzmann method (LBM), while the particle–particle interactions are treated by coupling with the distinct element method (DEM). Results reveal a clearly defined critical surface shear stress, beyond which erosion occurs, and a linear relation between the rate of erosion and excess surface shear stress. Further to this, an interesting mechanism by which detached particles gain upward movement is observed. This work also serves to highlight the potential of the coupled LBM–DEM approach for modelling dynamic erosion processes in three dimensions.


LBM DEM 3D Simulation Erosion 



The authors would like to thank the editor and anonymous reviewers for excellent insight, advice, and corrections, which have markedly improved this paper. This research was entrusted by the Ministry of Economy, Trade, and Industry, Japan and the MH21 Research Consortium, as a part of the research group for production method and modelling of methane hydrate.

Supplementary material

11242_2015_500_MOESM1_ESM.doc (108 kb)
Supplementary material 1 (doc 108 KB)


  1. Abdelhamid, Y., El Shamy, U.: Pore-scale modeling of surface erosion in a particle bed. Int. J. Numer. Anal. Methods 38(2), 142–166 (2014)CrossRefGoogle Scholar
  2. Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511–525 (1954)CrossRefGoogle Scholar
  3. Black, K., Tolhurst, T., Paterson, D., Hagerthey, S.: Working with natural cohesive sediments. J. Hydraul. Eng. 128(1), 2–8 (2002)CrossRefGoogle Scholar
  4. Bonelli, S., Marot, D.: Micromechanical modeling of internal erosion. Eur. J. Environ. Civ. Eng. 15(8), 1207–1224 (2011)CrossRefGoogle Scholar
  5. Boutt, D., Cook, B., McPherson, B., Williams, J.: Direct simulation of fluid–solid mechanics in porous media using the discrete element and lattice-Boltzmann methods. J. Geophys. Res. 112(B10), 1–13 (2007)Google Scholar
  6. Boutt, D.F., Cook, B.K., Williams, J.R.: A coupled fluid–solid model for problems in geomechanics: application to sand production. Int. J. Numer. Anal. Methods Geomech. 35(9), 997–1018 (2011)CrossRefGoogle Scholar
  7. Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., Pöschel, T.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382–5392 (1996)CrossRefGoogle Scholar
  8. Broday, D., Fichman, M., Shapiro, M., Gutfinger, C.: Motion of spheroidal particles in vertical shear flows. Phys. Fluids 10(1), 86–100 (1998)CrossRefGoogle Scholar
  9. Cavin, A.: Relations between textural characteristics and physical properties of sediments in northwestern Cascadia Basin. Proc. Ocean Drill. Prog. Sci. Res. 168, 67 (2000)Google Scholar
  10. Cook, B., Noble, D., Preece, D., Williams, J.: Direct simulation of particle-laden fluids. In: Girard, L., Breeds, D. (eds.) Pacific Rocks, pp. 279–286. Balkema, Rotterdam (2000)Google Scholar
  11. Cui, X., Li, J., Chan, A., Chapman, D.: A 2D DEM–LBM study on soil behaviour due to locally injected fluid. Particuology 10(2), 242–252 (2012)CrossRefGoogle Scholar
  12. Cui, X., Li, J., Chan, A., Chapman, D.: Coupled DEM–LBM simulation of internal fluidisation induced by a leaking pipe. Powder Technol. 254, 299–306 (2014)CrossRefGoogle Scholar
  13. Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  14. Debnath, K., Nikora, V., Aberle, J., Westrich, B., Muste, M.: Erosion of cohesive sediments: resuspension, bed load, and erosion patterns from field experiments. J. Hydraul. Eng. 133(5), 508–520 (2007)CrossRefGoogle Scholar
  15. Di Renzo, A., Di Maio, F.P.: Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem. Eng. Sci. 59(3), 525–541 (2004)CrossRefGoogle Scholar
  16. Dijkstra, M.: Capillary freezing or complete wetting of hard spheres in a planar hard slit? Phys. Rev. Lett. 93(10), 108303 (2004)CrossRefGoogle Scholar
  17. Feng, Y.T., Han, K., Owen, D.R.J.: Combined three-dimensional lattice Boltzmann method and discrete element method for modelling fluid–particle interactions with experimental assessment. Int. J. Numer. Methods Eng. 81(2), 229–245 (2010)Google Scholar
  18. Fortini, A., Dijkstra, M.: Phase behaviour of hard spheres confined between parallel hard plates: manipulation of colloidal crystal structures by confinement. J. Phys. Condens. Matter 18(28), L371 (2006)CrossRefGoogle Scholar
  19. Galindo-Torres, S., Scheuermann, A., Mühlhaus, H., Williams, D.: A micro-mechanical approach for the study of contact erosion. Acta Geotech. 1–12 (2013). doi: 10.1007/s11440-013-0282-z
  20. Gallier, S., Lemaire, E., Lobry, L., Peters, F.: A fictitious domain approach for the simulation of dense suspensions. J. Comput. Phys. 256, 367–387 (2014)CrossRefGoogle Scholar
  21. Golay, F., Bonelli, S.: Numerical modeling of suffusion as an interfacial erosion process. Eur. J. Environ. Civ. Eng. 15(8), 1225–1241 (2011)CrossRefGoogle Scholar
  22. Grabowski, R.C., Droppo, I.G., Wharton, G.: Erodibility of cohesive sediment: the importance of sediment properties. Earth Sci. Rev. 105(3–4), 101–120 (2011)CrossRefGoogle Scholar
  23. Han, Y., Cundall, P.A.: Lattice Boltzmann modeling of pore-scale fluid flow through idealized porous media. Int. J. Numer. Methods Fluids 67(11), 1720–1734 (2011a)CrossRefGoogle Scholar
  24. Han, Y., Cundall, P.A.: Resolution sensitivity of momentum-exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method. Int. J. Numer. Methods Fluids 67(3), 314–327 (2011b)CrossRefGoogle Scholar
  25. Han, Y., Cundall, P.A.: Lbm-dem modeling of fluid–solid interaction in porous media. Int. J. Numer. Anal. Methods Geomech. 37(10), 1391–1407 (2013)CrossRefGoogle Scholar
  26. He, X., Luo, L.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56(6), 6811–6817 (1997)CrossRefGoogle Scholar
  27. He, X., Zou, Q., Luo, L., Dembo, M.: Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model. J. Stat. Phys. 87(1–2), 115–136 (1997)CrossRefGoogle Scholar
  28. Holdych, D.: Lattice Boltzmann methods for diffuse and mobile interfaces. PhD thesis, University of Illinois at Urbana, Champaign (2003)Google Scholar
  29. Israelachvili, J.N.: Intermolecular and Surface Forces: Revised, 3rd edn. Academic Press, London (2011)Google Scholar
  30. Kloss, C., Goniva, C.: Liggghts—a new open source discrete element simulation software. In: Proceedings of the 5th International Conference on Discrete Element Methods, London, UK, 25–26 Aug. ISBN: 978-0-9551179-8-5 (2010)Google Scholar
  31. Kloss, C., Goniva, C.: Liggghts an open source discrete element simulations of granular materials based on lammps. In: Proceedings of the TMS Annual Meeting, pp. 781–788. San Diego (2011)Google Scholar
  32. Kloss, C., Goniva, C., Hager, A., Amberger, S., Pirker, S.: Models, algorithms and validation for opensource DEM and CFD–DEM. Prog. Comput. Fluid Dyn. 12(2/3), 140–152 (2012)CrossRefGoogle Scholar
  33. Krone, R.B.: Effects of bed structure on erosion of cohesive sediments. J. Hydraul. Eng. 125(12), 1297–1301 (1999)CrossRefGoogle Scholar
  34. Ladd, A.J.C.: Numerical simulations of particulate suspensions via a discretized boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309 (1994)CrossRefGoogle Scholar
  35. Lick, W., McNeil, J.: Effects of sediment bulk properties on erosion rates. Sci. Total Environ. 266(1–3), 41–48 (2001)CrossRefGoogle Scholar
  36. Lominè, F., Scholtès, L., Sibille, L., Poullain, P.: Modeling of fluid–solid interaction in granular media with coupled lattice Boltzmann/discrete element methods: application to piping erosion. Int. J. Numer. Anal. Methods Geomech. 37(6), 577–596 (2013)CrossRefGoogle Scholar
  37. Lundkvist, M., Grue, M., Friend, P., Flindt, M.: The relative contributions of physical and microbiological factors to cohesive sediment stability. Cont. Shelf Res. 27(8), 1143–1152 (2007)CrossRefGoogle Scholar
  38. Mansouri, M., Delenne, J., El Youssoufi, M., Seridi, A.: A 3D DEM–LBM approach for the assessment of the quick condition for sands. C. R. Méc. 337(9–10), 675–681 (2009)CrossRefGoogle Scholar
  39. McAnally, W. H., Mehta, A. J.: Coastal and estuarine fine sediment processes. In: Proceedings of Marine Science, vol. 3, p. 540. Elsevier Science, Amsterdam (2001)Google Scholar
  40. Mitchener, H., Torfs, H.: Erosion of mud/sand mixtures. Coast. Eng. 29(1–2), 1–25 (1996)CrossRefGoogle Scholar
  41. Noble, D.R., Torczynski, J.R.: A lattice-Boltzmann method for partially saturated computational cells. Int. J. Mod. Phys. C 9(8), 1189–1201 (1998)CrossRefGoogle Scholar
  42. Owen, D.R.J., Leonardi, C.R., Feng, Y.T.: An efficient framework for fluid–structure interaction using the lattice Boltzmann method and immersed moving boundaries. Int. J. Numer. Methods Eng. 87(1–5), 66–95 (2010)Google Scholar
  43. Qian, Y.H., D’Humières, D., Lallemand, P.: Lattice BGK models for the Navier–Stokes equation. Europhys. Lett. 17, 479–484 (1992)CrossRefGoogle Scholar
  44. Silbert, L.E.E.D., Grest, G.S., Halsey, T.C., Levine, D., Plimpton, S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64(5), 051302 (2001)CrossRefGoogle Scholar
  45. Sterpi, D.: Effects of the erosion and transport of fine particles due to seepage flow. Int. J. Geomech. 3(1), 111–122 (2003)CrossRefGoogle Scholar
  46. Tchistiakov, A.: Physico-chemical aspects of clay migration and injectivity decrease of geothermal classic reservoirs. In: Proceedings of World Geothermal Congress, pp. 3087–3095. Kyushu-Tohoku, Kyushu-Tohoku, Japan (2000)Google Scholar
  47. Tolhurst, T., Black, K., Paterson, D., Mitchener, H., Termaat, G., Shayler, S.: A comparison and measurement standardisation of four in situ devices for determining the erosion shear stress of intertidal sediments. Cont. Shelf Res. 20(10–11), 1397–1418 (2000)CrossRefGoogle Scholar
  48. Yamamoto, K.: Methane hydrate bearing sediments: a new subject of geomechanics. In: International Association for Computer Methods and Advances in Geomechanics (IACMAG).Goa, India (2008)Google Scholar
  49. Zhang, H., Tan, Y., Shu, S., Niu, X., Trias, F.X., Yang, D., Li, H., Sheng, Y.: Numerical investigation on the role of discrete element method in combined LBM–IBM–DEM modeling. Comput. Fluids 94, 37–48 (2014)CrossRefGoogle Scholar
  50. Zhu, H., Zhou, Z., Yang, R., Yu, A.: Discrete particle simulation of particulate systems: theoretical developments. Chem. Eng. Sci. 62, 3378–3396 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Paul E. Brumby
    • 1
  • Toru Sato
    • 1
  • Jiro Nagao
    • 2
  • Norio Tenma
    • 3
  • Hideo Narita
    • 2
  1. 1.Department of Ocean Technology, Policy, and EnvironmentThe University of TokyoKashiwaJapan
  2. 2.Methane Hydrate Research CenterNational Institute of Advanced Industrial Science and TechnologySapporoJapan
  3. 3.Methane Hydrate Research CentreNational Institute of Advanced Industrial Science and TechnologyTsukubaJapan

Personalised recommendations