Numerical methods for flow in a porous medium with internal boundaries |
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| Authors: | Brit Gunn Ersland Magne S Espedal Roger Nybø |
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| Institution: | (1) Statoil, N-5020 Bergen, Norway;(2) Department of Mathematics, University of Bergen, N-5008 Bergen, Norway;(3) Norsk Hydro, N-5020 Bergen, Norway |
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| Abstract: | Flow of fluids and transport of solutes in porous media are subjects of wide interest in several fields of applications: reservoir
engineering, subsurface hydrology, chemical engineering, etc. In this paper we will study two-phase flow in a model consisting
of two different types of sediments. Here, the absolute permeability, the relative permeabilities and the capillary pressure
are discontinuous functions in space. This leads to interior boundary value problems at the interface between the sediments.
The saturation Sw will be discontinuous or experience large gradients at the interface. A new solution procedure for such problems will be
presented. The method combines the modified method of characteristics with a weak formulation where the basis functions are
discontinuous at the interior boundary. The modified method of characteristics will provide a good first approximation for
the jump in the discontinuous basis functions, which leads to a fast converging iterative solution scheme for the complete
problem.
The method has been implemented in a two-dimensional simulator, and results from numerical experiments will be presented.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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| Keywords: | two-phase fluid flow discontinuous parameters discontinuous finite elements characteristic methods |
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