Conforming finite element methods for modeling convection in an incompressible rock matrix

Gross, Lutz, Poulet, Thomas and Sheldon, Heather A. (2013) Conforming finite element methods for modeling convection in an incompressible rock matrix. Transport in Porous Media, 100 2: 225-246. doi:10.1007/s11242-013-0213-3

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Author Gross, Lutz
Poulet, Thomas
Sheldon, Heather A.
Title Conforming finite element methods for modeling convection in an incompressible rock matrix
Journal name Transport in Porous Media   Check publisher's open access policy
ISSN 0169-3913
Publication date 2013-08-01
Year available 2013
Sub-type Article (original research)
DOI 10.1007/s11242-013-0213-3
Volume 100
Issue 2
Start page 225
End page 246
Total pages 22
Place of publication Dordrecht, Netherlands
Publisher Springer
Language eng
Subject 290704 Geomechanics
260204 Petrophysics
280404 Numerical Analysis
Abstract Coupled heat transport and fluid flowin porous rocks play a role in many geological phenomena, including the formation of hydrothermal mineral deposits, the productivity of geothermal reservoirs and the reliability of geo-sequestration. Due to the low compressibility of the fluid and rock matrix and the long-time scales the fluid can be treated as incompressible. The solution of the incompressible Darcy flux problem and the advection-dominated heat transport both provide numerically challenging problems typically addressed using methods specialized for the individual equations. In order to avoid the usage of two different meshes and solution approximations for pressure, flux, and temperature we propose to use standard conforming finite-element methods on the same mesh for both problems. The heat transport equation is solved using a linearized finite-element flux corrected transport scheme which introduces minimum artificial diffusion based on the discretized transport problem.The Darcy flux calculation from pressure uses a global post-processing strategy which at the cost of an extra partial differential equation leads to highly accurate flux approximation. In the limit of zero element size the flux is in fact incompressible.We investigate the numerical performance of our proposed method on a test problem using the parallelized modeling environment escript. We also test the approach to simulate convection in geologically relevant scenarios.
Keyword Finite-element method
Incompressible porous media
Darcy flow
Advective transport
Flux corrected transport
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online 13 August 2013. Article in press

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2014 Collection
School of Earth Sciences Papers
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Created: Fri, 14 Dec 2012, 20:01:28 EST by Lutz Gross on behalf of School of Earth Sciences