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A dimensionally reduced Stokes–Darcy model for fluid flow in fractured porous media

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  • Rybak, Iryna
  • Metzger, Stefan

Abstract

Dimensionally reduced models are effective approximations of flow and transport processes in structures containing thin layers. We propose and analyse such a model for flow in fractured porous media. The fractures can store and transport fluid and they are modelled as lower-dimensional entities in the surrounding porous medium. The flow system of interest in this work is single-phase, isothermal and non-compositional. The model consists of the full-dimensional Darcy’s law in the rock matrix coupled to the Stokes equations of co-dimension one in the fracture. The well-posedness of the reduced coupled problem is proved and the reduced model is validated against the full-dimensional model numerically. The simulation results demonstrate that the proposed model is indeed a cost effective alternative to full-dimensional models.

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  • Rybak, Iryna & Metzger, Stefan, 2020. "A dimensionally reduced Stokes–Darcy model for fluid flow in fractured porous media," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    • Handle: RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320302290
    DOI: 10.1016/j.amc.2020.125260
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    1. Ahmed, Elyes & Jaffré, Jérôme & Roberts, Jean E., 2017. "A reduced fracture model for two-phase flow with different rock types," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 49-70.
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