Multiphase Flow in Porous Media

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Many natural and technical processes involve multiphase flow processes in porous media. Despite that fact fundamental concepts of twophase flow on macroscopic scales still remain unclear. The predictive power of the most commonly used extended multiphase Darcy theory is at best limited to simple problems where neither hysteresis nor dynamic effects like trapping nor varying residual saturations have a substantial impact on the solutions.

Our Project

It is known that percolating and nonpercolating fluid parts show fundamental different behavior (e.g. Abrams (1975), Avraam et al. (1995), Taber (1969), Wyckoff (1936)). This insight is incorporated into a macroscopic theory which treats percolating(=connected) and nonpercolating (=nonconnected) fluid parts as separate phases. Thereby a two phase system is described by four phases.

The resulting set of partial differential equations is strongly coupled, highly nonlinear and of mixed type. We study these equations analytically and numerically .

Recent results

  • Initial and boundary conditions have been formulated to model experiments with a homogeneous porous column in the gravity field. The resulting 9 PDE have been solved with an adaptive moving grid PDE solver.
  • A limiting case of immobile nonpercolating fluid phases has been formulated. Hyperbolic and parabolic limits of this case have been treated (quasi) analytically.

Current Coworkers


  • The project is part of Nupus (International Research Training Group 'Non-linearities and Upscaling in PoroUS media').
  • Prof. Dr. Paul Zegeling, Department of Mathematics, Faculty of Sciences, Utrecht University
  • Prof. Dr. Majid Hassanizadeh, Department of Earth Sciences, Faculty of Geosciences, Utrecht University