Numerical study of compositional compressible degenerate two-phase flow in saturated–unsaturated heterogeneous porous media
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AbstractWe study the convergence of a combined finite volume-nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phases. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentered according to the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of hydrogen production in nuclear waste management. Numerical results are obtained by in-house numerical code. © 2015 Elsevier Ltd.
CitationSaad AS, Saad B, Saad M (2016) Numerical study of compositional compressible degenerate two-phase flow in saturated–unsaturated heterogeneous porous media. Computers & Mathematics with Applications 71: 565–584. Available: http://dx.doi.org/10.1016/j.camwa.2015.12.010.
SponsorsThe authors extend their appreciation to the College of Applied Medical Sciences Research Centre and the Deanship of Scientific Research at King Saud University for its funding for this research.