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

Hanz Martin Cheng, Jérôme Droniou

Research output: Contribution to journalArticleResearchpeer-review

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.

LanguageEnglish
Pages707-723
Number of pages17
JournalJournal of Petroleum Science and Engineering
Volume172
DOIs
Publication statusPublished - 1 Jan 2019

Cite this

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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.",
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An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media. / Cheng, Hanz Martin; Droniou, Jérôme.

In: Journal of Petroleum Science and Engineering, Vol. 172, 01.01.2019, p. 707-723.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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