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Flow and transport in fractured poroelastic media

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Abstract

We study flow and transport in fractured poroelastic media using Stokes flow in the fractures and the Biot model in the porous media. The Stokes–Biot model is coupled with an advection–diffusion equation for modeling transport of chemical species within the fluid. The continuity of flux on the fracture-matrix interfaces is imposed via a Lagrange multiplier. The coupled system is discretized by a finite element method using Stokes elements, mixed Darcy elements, conforming displacement elements, and discontinuous Galerkin for transport. The stability and convergence of the coupled scheme are analyzed. Computational results verifying the theory as well as simulations of flow and transport in fractured poroelastic media are presented.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Ilona Ambartsumyan, Eldar Khattatov, Truong Nguyen & Ivan Yotov

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  1. Ilona Ambartsumyan
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  2. Eldar Khattatov
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  3. Truong Nguyen
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  4. Ivan Yotov
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Correspondence to Ivan Yotov.

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Partially supported by DOE Grant DE-FG02-04ER25618 and NSF Grants DMS 1418947 and DMS 1818775.

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Ambartsumyan, I., Khattatov, E., Nguyen, T. et al. Flow and transport in fractured poroelastic media. Int J Geomath 10, 11 (2019). https://doi.org/10.1007/s13137-019-0119-5

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