Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements |
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| Authors: | D Nayagum G Schäfer R Mosé |
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| Institution: | (1) Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000 Strasbourg, France;(2) Institut Franco-Allemand de Recherche sur l'Environnement (IFARE), 23 rue du Loess, B.P 20, 67037 Strasbourg Cedex, France;(3) Ecole Nationale du Génie de l'Eau et de l'Environnement, 1 quai Koch, 67000 Strasbourg, France |
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| Abstract: | In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. |
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| Keywords: | fractional flow formulation mixed hybrid and discontinuous finite elements porous media two-phase flow |
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