Computational Geosciences

, Volume 14, Issue 2, pp 273–287 | Cite as

Numerical modeling of two-phase hysteresis combined with an interface condition for heterogeneous porous media

  • Alexandros Papafotiou
  • Hussam Sheta
  • Rainer Helmig
Original paper
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Abstract

This paper presents a numerical implementation of two-phase capillary hysteresis and its combination with a capillary interface condition for the treatment of heterogeneities. The hysteresis concepts chosen in this work are first implemented in a node-centered FV discretization scheme and subsequently combined with the interface condition that predicts sharp saturation discontinuities at material interfaces, based on a pressure equilibrium concept. This approach allows for the approximation of history-dependent, and at the same time discontinuous, saturations at material interfaces. The resulting model provides a well-defined evolution of the hysteretic capillary pressure–saturation relationships at material interfaces that is independent of the grid spacing. As demonstrated with a simple 1-D example, this concept therefore offers the advantage that the solution of a two-phase flow problem involving hysteresis does not relate to the grid resolution at the material interfaces.

Keywords

Hysteresis Numerical modeling Heterogeneous Interface condition Two-phase flow 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Alexandros Papafotiou
    • 1
  • Hussam Sheta
    • 2
  • Rainer Helmig
    • 3
  1. 1.Institute of Fluid Mechanics and Environmental Physics in Civil EngineeringLeibniz Universität HannoverHannoverGermany
  2. 2.Exploration and GeosurveyDMT GmbH & Co. KGEssenGermany
  3. 3.Institute of Hydraulic EngineeringUniversität StuttgartStuttgartGermany

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