Transport in Porous Media

, Volume 89, Issue 3, pp 441–457 | Cite as

Fluid Flow Induced Internal Erosion within Porous Media: Modelling of the No Erosion Filter Test Experiment

  • V. FrishfeldsEmail author
  • J. G. I. Hellström
  • T. S. Lundström
  • H. Mattsson


An investigation of the potential to numerically model the no erosion filter test is performed here, where the flow through a large ensemble of particles is considered by applying minimisation of dissipation rate of energy on the ensemble that is discretised with modified Voronoi diagrams and Delaunay triangulation. Low-Reynolds number simulations are applied to each part of the Voronoi diagram using computational fluid dynamics. The mechanical friction between particles is modelled by increasing the effective viscosity for closely spaced particles. Microscopic mechanisms for successful and unsuccessful sealing of filters are obtained. The numerical results agree with previously presented experimental observations by Sherard and Dunnigan. A conformity is that the sealing starts from the end of the channel and continues outwards in the radial direction. The sealing implies that the permeability can be reduced several orders of magnitude during a test.


Internal erosion Filtration Flow-induced deformation No erosion filter test Minimisation of dissipation rate of energy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams K.L., Russel W.B., Rebenfeld L.: Radial penetration of a viscous liquid into a planar anisotropic porous media. Int. J. Multiph. Flow. 14, 203–215 (1988)CrossRefGoogle Scholar
  2. Bear J.: Dynamics of Fluids in Porous Media. Dover Publications Inc., New York (1972)Google Scholar
  3. Chen X., Papathanasiou D.: The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing. Transp. Porous Media 71, 233–251 (2008)CrossRefGoogle Scholar
  4. Day R.A., Hight D.W., Potts D.M.: Finite element analysis of construction stability of Thika Dam. Comput. Geotech. 23, 205–219 (1998)CrossRefGoogle Scholar
  5. Dullien F.A.L.: Porous Media: Fluid Transport and Pore Structure. Academic press, San Diego (1992)Google Scholar
  6. ERCOFTAC (European Research Community On Flow, Turbulence And Combustion): Special Interest Group on Quality and Trust in Industrial CFD: Best Practice Guidelines, Version 1.0, Edited by Casey, M. and Wintergerste, T (2000)Google Scholar
  7. Fell R., MacGregor P., Stapledon D., Bell G.: Geotechnical Engineering of Dams. Balkema, Leiden (2005)Google Scholar
  8. Foster M., Fell R., Spannagle M.: The statistics of embankment dam failures and accidents. Can. Geotech. J. 37, 1000–1024 (2000)CrossRefGoogle Scholar
  9. Foster M., Fell R., Spannagle M.: A method for assessing the relative likelihood of failure of embankment dams by piping. Can. Geotech. J. 37, 1025–1061 (2000)CrossRefGoogle Scholar
  10. Foster M., Fell R.: Assessing embankment dam filters that do not satisfy design criteria. J. Geotech. Geoenviron. Eng. 127(4), 398–407 (2001)CrossRefGoogle Scholar
  11. Frishfelds V., Lundström T.S., Jacovics A.: Permeability of clustered fibre networks: modelling of unit cell. Mech. Compos. Mater. 39, 265–272 (2003)CrossRefGoogle Scholar
  12. Frishfelds V., Lundström T.S., Jakovics A.: Lattice gas analysis of liquid front in non-crimp fabrics. Transp. Porous Media 84, 75–93 (2010)CrossRefGoogle Scholar
  13. Gebart B.R.: Permeability of unidirectional reinforcements for RTM. J. Compos. Mater. 26, 1100–1133 (1992)CrossRefGoogle Scholar
  14. Gebart B.R., Lidström P.: Measurement of in-plane permeability of anisotropic fiber reinforcements. Polym. Compos. 17, 43–51 (1996)CrossRefGoogle Scholar
  15. Ghidaglia C., Arcangelis L., Hinch J., Guazzelli E.: Hydrodynamic interactions in deep bed filtration. Phys. Fluids 8, 6–14 (1996)CrossRefGoogle Scholar
  16. Gray W.G.: General conservation equations for multi-phase systems: 4. Constitutive theory including phase change. Adv. Water Resour. 6, 130–140 (1983)CrossRefGoogle Scholar
  17. Hassanizadeh M., Gray W.G.: General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. Adv. Water Resour. 3, 25 (1980)CrossRefGoogle Scholar
  18. Hellström J.G.I., Marjavaara B.D., Lundström T.S.: Parallel CFD simulations of an original and redesigned hydraulic turbine draft tube. Adv. Eng. Softw. 38, 338–344 (2007)CrossRefGoogle Scholar
  19. Hellström J.G.I., Frishfelds V., Lundström T.S.: Mechanisms of flow-induced deformation of porous media. J. Fluid Mech. 664, 220–237 (2010)CrossRefGoogle Scholar
  20. Hellström J.G.I., Jonsson P.J.P., Lundström T.S.: Laminar and turbulent flow through an array of cylinders. J. Porous Media 13, 1073–1085 (2010)CrossRefGoogle Scholar
  21. Huang T.K.: Stability analysis of an earth dam under steady state seepage. Comput. Struct. 58, 1075–1082 (1996)CrossRefGoogle Scholar
  22. Kershaw T.N.: The three dimensions of water flow in press felts. Tappi J. 55, 880–887 (1972)Google Scholar
  23. Lekakou C., Johari M.A.K., Norman D., Bader M.G.: Measurement techniques and effects on in-plane permeability of woven cloths in resin transfer moulding. Composites A 27, 401–408 (1996)CrossRefGoogle Scholar
  24. Lundström T.S., Gebart B.R.: Effect of perturbation of fibre architecture on permeability inside fibre tows. J. Compos. Mater. 29, 424–443 (1995)CrossRefGoogle Scholar
  25. Lundström T.S., Gebart B.R., Sandlund E.: In-plane permeability measurements on fibre reinforcements by the multi-cavity parallel flow technique. Polym. Compos. 20, 146–154 (1999)CrossRefGoogle Scholar
  26. Lundström T.S., Stenberg R.S., Bergström R., Partanen H., Birkeland P-A.: In-plane permeability measurements: a nordic round-robin study. Composites A 31, 29–43 (2000)CrossRefGoogle Scholar
  27. Lundström T.S., Toll S., Håkanson J.M.: Measurements of the permeability tensor of compressed fibre beds. Transp. Porous Media 47, 363–380 (2002)CrossRefGoogle Scholar
  28. Lundström T.S., Frishfelds V., Jakovics A.: A statistical approach to permeability of clustered fibre reinforcements. J. Compos. Mater. 38, 1137–1149 (2004)CrossRefGoogle Scholar
  29. Lundström T.S., Sundlöf H., Holmberg J.A.: Modelling of power-law fluid flow through fibre bed. J. Compos. Mater. 40, 283–296 (2006)CrossRefGoogle Scholar
  30. Mattsson, H., Hellström, J.G.I., Lundström, T.S., Knutsson, S.: On numerical modelling of internal erosion in embankment dams. In: Proceedings of the 1st International Symposium on Rockfill Dams, 18–21 October, Chengdu, China (2009)Google Scholar
  31. Mellah R., Auvinet G., Masrouri F.: Stochastic finite element method applied to non-linear analysis of embankments. Probab. Eng. Mech. 15, 251–259 (2000)CrossRefGoogle Scholar
  32. Ng A.K.L., Small J.C.: A case study of hydraulic fracturing using finite element methods. Can. Geotech. J. 36, 861–875 (1999)CrossRefGoogle Scholar
  33. Parnas R.S., Salem A.J.: A comparison of the unidirectional and radial in-plane flow of fluids through woven composite reinforcements. Polym. Compos. 14, 383–394 (1993)CrossRefGoogle Scholar
  34. Parnas R.S., Howard J.G., Luce T.L., Advani S.G.: Permeability characterization. Part 1: a proposed standard reference fabric for permeability. Polym. Compos. 16, 429–445 (1995)CrossRefGoogle Scholar
  35. Pikulik I.I., Gilbert D., McDonald J.D., Henderson J.R.: A new instrument for measuring the permeability of paper-machine clothing. Tappi J. 74, 169–176 (1991)Google Scholar
  36. Scheidegger A.E.: The Physics of Flow Through Porous Media. University of Toronto Press, Toronto (1972)Google Scholar
  37. Sharif N.H., Wiberg N.E., Levenstam M.: Free surface flow through rock-fill dams analyzed by FEM with level set approach. Comput. Mech. 27, 233–243 (2001)CrossRefGoogle Scholar
  38. Sheng-Hong C.: Adaptive FEM analysis for two-dimensional unconfined seepage problems. J. Hydrodyn. 8, 60–66 (1996)Google Scholar
  39. Sherard J.L.: Hydraulic fracturing in embankment dams. J. Geotech. Eng. 112, 905–927 (1986)CrossRefGoogle Scholar
  40. Sherard J.L., Dunningan L.P., Talbot J.R.: Filters for silts and clays. J. Geotech. Eng. 110, 701–718 (1984)CrossRefGoogle Scholar
  41. Sherard J.L., Dunnigan L.P.: Critical filters for impervious soils. J. Geotech. Eng. 115, 927–947 (1989)CrossRefGoogle Scholar
  42. Tucker C.L. III, Dessenberger R.B.: Governing equations for flow and heat transfer in stationary fiber beds. In: Advani, S.G. (eds) Flow and Rheology in Polymer Composites, Elsevier Science B.V., Amsterdam (1994)Google Scholar
  43. Weitzenböck J.R., Shenoi R.A., Wilson P.A.: Measurement of three-dimensional permeability. Composites A 29, 159–169 (1998)CrossRefGoogle Scholar
  44. Wörman A., Xu S.: Stochastic analysis of internal erosion in soil structures – implications for risk assessments. J. Hydraul. Eng. 127, 419–428 (2001)CrossRefGoogle Scholar
  45. Young W.B., Wu S.F.: Permeability measurement of bidirectional woven glass fibers. J. Reinf. Plast. Compos. 14, 1108–1119 (1995)Google Scholar
  46. Zhang L., Du J.: Effects of abutment slopes on the performance of high rockfill dams. Can. Geotech. J. 34, 489–497 (1997)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • V. Frishfelds
    • 1
    Email author
  • J. G. I. Hellström
    • 1
  • T. S. Lundström
    • 1
  • H. Mattsson
    • 2
  1. 1.Division of Fluid MechanicsLuleå University of TechnologyLuleåSweden
  2. 2.Division of Mining and Geotechnical EngineeringLuleå University of TechnologyLuleåSweden

Personalised recommendations