Numerical aspects of hydro-mechanical coupling of fluid-filled fractures using hybrid-dimensional element formulations and non-conformal meshes

Abstract

In the field of porous and fractured media, subsurface flow provides insight into the characteristics of fluid storage and properties connected to underground matter and heat transport. Subsurface flow is precisely described by many diffusion based models in the literature. However, diffusion-based models lack to reproduce important hydro-mechanical coupling phenomena like inverse water-level fluctuations (Noordbergum effect). In theory, contemporary modeling approaches, such as direct numerical simulations (DNS) of surface-coupled fluid-solid (fracture) interactions or coarse-grained continuum approaches like Biot’s theory, are capable of capturing such phenomena. Nevertheless, during modeling processes of fractures with high aspect ratios, DNS methods with the explicit discretization of the fluid domain fail, and coarse-grained continuum approaches require a non-linear formulation for the fracture deformation since large deformation can be reached easily within fractures. Hence a hybrid-dimensional approach uses a parabolic velocity profile to avoid an explicit discretization of the fluid domain within the fracture. For fracture flow, the primary variable is the pressure field only, and the fracture domain is reduced by one dimension. The interaction between the fracture and the surrounding matrix domain, respectively, is realized by modified balance equations. The coupled system is numerically stiff when fluids are described with a low compressibility modulus. Two algorithms are proposed within this work, namely the weak coupling scheme, which uses an implicit staggered-iterative algorithm to find the residual state and the strong coupling scheme which directly couples both domains by implementing interface elements. In the course of this work, a consistent implementation scheme for the coupling of hybrid-dimensional elements with a surrounding bulk matrix is proposed and validated and tested throughout different numerical experiments.

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Acknowledgements

The authors gratefully acknowledge the funding provided by the German Federal Ministry of Education and Research (BMBF) for the GeomInt project, Grant Number 03A0004E, within the BMBF Geoscientific Research Program “Geo:N Geosciences for Sustainability”.

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Correspondence to Patrick Schmidt.

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Schmidt, P., Steeb, H. Numerical aspects of hydro-mechanical coupling of fluid-filled fractures using hybrid-dimensional element formulations and non-conformal meshes. Int J Geomath 10, 14 (2019). https://doi.org/10.1007/s13137-019-0127-5

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Keywords

  • Fracture flow
  • Hydromechanical coupling
  • Deformation-induced flow
  • Pressure diffusion

Mathematics Subject Classification

  • 86-08