An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

Hanz Martin Cheng, Jérôme Droniou

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Abstract

We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method, and the diffusive parts by a finite volume method. The scheme is applicable on generic (possibly non-conforming) meshes as encountered in applications. The main features of our work are the reconstruction of a Darcy velocity, from the discrete pressure fluxes, that enjoys a local consistency property, an analysis of implementation issues faced when tracking, via the characteristic method, distorted cells, and a new treatment of cells near the injection well that accounts better for the conservativity of the injected fluid.

Original languageEnglish
Pages (from-to)707-723
Number of pages17
JournalJournal of Petroleum Science and Engineering
Volume172
DOIs
Publication statusPublished - 1 Jan 2019

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