Convergence of a Finite Volume Scheme for Gas Water Flow in a Multi-Dimensional Porous Media
Provides the first convergence proof for finite volume schemes in compressible multiphase flow, addressing a key theoretical gap for reservoir simulation.
The authors prove convergence of a finite volume scheme for compressible, immiscible gas-water flow in 2D/3D porous media, extending previous results limited to incompressible fluids.
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence properties of these schemes are only known for incompressible fluids. This chapter deals with construction and convergence analysis of a finite volume scheme for compressible and immiscible flow in porous media. In comparison with incompressible fluid, compressible fluids requires more powerful techniques. We present a new result of convergence in a two or three dimensional porous medium and under the only modification that the density of gas depends on global pressure.