Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

Saad, Bilal Mohammed; Saad, Mazen

Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

Type

Conference Paper

Authors

Saad, Bilal Mohammed

Saad, Mazen

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date

2014-05-16

Print Publication Date

2014

Date

2014-05-16

Abstract

We 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 phase. 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 decentred according 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 CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.

Citation

Saad B, Saad M (2014) Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. Springer Proceedings in Mathematics & Statistics: 713–721. Available: http://dx.doi.org/10.1007/978-3-319-05591-6_71.