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.
| Language | English |
|---|---|
| Pages | 707-723 |
| Number of pages | 17 |
| Journal | Journal of Petroleum Science and Engineering |
| Volume | 172 |
| DOIs | |
| Publication status | Published - 1 Jan 2019 |
Cite this
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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 journal › Article › Research › peer-review
TY - JOUR
T1 - An HMM–ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media
AU - Cheng, Hanz Martin
AU - Droniou, Jérôme
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85052839010&partnerID=8YFLogxK
U2 - 10.1016/j.petrol.2018.08.062
DO - 10.1016/j.petrol.2018.08.062
M3 - Article
VL - 172
SP - 707
EP - 723
JO - Journal of Petroleum Science and Engineering
T2 - Journal of Petroleum Science and Engineering
JF - Journal of Petroleum Science and Engineering
SN - 0920-4105
ER -