Percolation as a basic concept for macroscopic capillarity

R. Hilfer*, F. Doster

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


The concepts of relative permeability and capillary pressure are crucial for the accepted traditional theory of two phase flow in porous media. Recently, a theoretical approach was introduced that does not require these concepts as input (Hilfer, Physica A, 359:119-128, 2006a; Phys. Rev. E, 73:016307, 2006b). Instead it was based on the concept of hydraulic percolation of fluid phases. This paper presents the first numerical solutions of the coupled nonlinear partial differential equations introduced in Hilfer (Phys. Rev. E, 73:016307, 2006b). Approximate numerical results for saturation profiles in one spatial dimension have been calculated. Long time limits of dynamic time-dependent profiles are compared to stationary solutions of the traditional theory. The initial and boundary conditions are chosen to model the displacement processes that occur when a closed porous column containing two immiscible fluids of different density is raised from a horizontal to a vertical position in a gravitational field. The nature of the displacement process may change locally in space and time between drainage and imbibition. The theory gives local saturations for nonpercolating trapped fluids near the endpoint of the displacement.

Original languageEnglish
Pages (from-to)507-519
Number of pages13
JournalTransport in Porous Media
Issue number3
Publication statusPublished - Apr 2010


  • Capillarity
  • Hysteresis
  • Immiscible displacement
  • Multiphase flow
  • Porous media
  • Residual saturation

ASJC Scopus subject areas

  • General Chemical Engineering
  • Catalysis


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