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

Iryna Rybak and Stefan Metzger

Applied Mathematics and Computation, 2020, vol. 384, issue C

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.

Keywords: Porous medium; Fracture; Interface conditions; Darcy’s law; Stokes equations (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320302290

DOI: 10.1016/j.amc.2020.125260

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