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A simple embedded discrete fracture-matrix model for a coupled flow and transport problem in porous media
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 343, p. 572-601Article in journal (Refereed) Published
Abstract [en]

Accurate simulation of fluid flow and transport in fractured porous media is a key challenge in subsurface reservoir engineering. Due to the high ratio between its length and width, fractures can be modeled as lower dimensional interfaces embedded in the porous rock. We apply a recently developed embedded finite element method (EFEM) for the Darcy problem. This method allows for general fracture geometry, and the fractures may cut the finite element mesh arbitrarily. We present here a velocity model for EFEM and couple the Darcy problem to a transport problem for a passive solute. The main novelties of this work are a locally conservative velocity approximation derived from the EFEM solution, and the development of a lowest order upwind finite volume method for the transport problem. This numerical model is compatible with EFEM in the sense that the same computational mesh may be applied, so that we retain the same flexibility with respect to fracture geometry and meshing. Hence, our coupled solution strategy represents a simple approach in terms of formulation, implementation and meshing. We demonstrate our model by some numerical examples on both synthetic and realistic problems, including a benchmark study for single-phase flow. Despite the simplicity of the method, the results are promising.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 343, p. 572-601
Keywords [en]
Discrete fracture-matrix model, Embedded interface, Finite element method, Finite volume method, Porous media flow
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-153110DOI: 10.1016/j.cma.2018.09.003ISI: 000447411100026OAI: oai:DiVA.org:umu-153110DiVA, id: diva2:1262695
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved

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Larson, Mats G.

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CiteExportLink to record
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  • apa
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  • de-DE
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  • fi-FI
  • nn-NO
  • nn-NB
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  • html
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