Transport in Porous Media

, Volume 84, Issue 1, pp 133–152 | Cite as

Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure

  • Brahim AmazianeEmail author
  • Mladen Jurak
  • Ana Žgaljić Keko


A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986).


Immiscible compressible two-phase flow Global pressure Porous media Water hydrogen 

Mathematics Subject Classification (2000)

76S05 35Q35 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Brahim Amaziane
    • 1
    Email author
  • Mladen Jurak
    • 2
  • Ana Žgaljić Keko
    • 3
  1. 1.Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142Université de PauPauFrance
  2. 2.Department of MathematicsUniversity of ZagrebZagrebCroatia
  3. 3.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia

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