Advertisement

Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media

  • Konstantin Brenner
  • Mayya Groza
  • Cindy Guichard
  • Roland Masson
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)

Abstract

This paper presents the Vertex Approximate Gradient (VAG) discretization of a two-phase Darcy flow in discrete fracture networks (DFN) taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain with continuous pressures at the matrix fracture interface. Compared with Control Volume Finite Element (CVFE) approaches, the VAG scheme has the advantage to avoid the mixing of the fracture and matrix rocktypes at the interfaces between the matrix and the fractures, while keeping the low cost of a nodal discretization on unstructured meshes. The convergence of the scheme is proved under the assumption that the relative permeabilities are bounded from below by a strictly positive constant but cover the case of discontinuous capillary pressures. The efficiency of our approach compared with CVFE discretizations is shown on a 3D fracture network with very low matrix permeability.

Keywords

Capillary Pressure Fracture Network Discrete Fracture Network Homogeneous Dirichlet Boundary Condition Fracture Porous Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors would like to thank GDFSuez EP and Storengy for partially supporting this work.

References

  1. 1.
    Alboin, C., Jaffré, J., Roberts, J., Serres, C.: Modeling fractures as interfaces for flow and transport in porous media. Fluid flow transp. porous media 295, 13–24 (2002)CrossRefGoogle Scholar
  2. 2.
    Brenner, K., Groza, M., Guichard, C., Masson, R.: Vertex approximate gradient scheme for hybrid dimensional two-phase darcy flows in fractured porous media. Preprinted, http://hal.archives-ouvertes.fr/hal-00910939 (2013)
  3. 3.
    Eymard, R., Guichard, C., Herbin, R.: Small-stencil 3d schemes for diffusive flows in porous media. ESAIM: M2AN 46, 265–290 (2010)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Eymard, R., Guichard, C., Herbin, R., Masson, R.: Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation. ZAMM—J. Appl. Math. Mech. (2013). doi: 10.1002/zamm.201200206
  5. 5.
    Firoozabadi, A., Monteagudo, J.E.: Control-volume model for simulation of water injection in fractured media: incorporating matrix heterogeneity and reservoir wettability effects. SPE J. 12, 355–366 (2007)Google Scholar
  6. 6.
    Reichenberger, V., Jakobs, H., Bastian, P., Helmig, R.: A mixed-dimensional finite volume method for multiphase flow in fractured porous media. Adv. Water Resour. 29, 1020–1036 (2006)CrossRefGoogle Scholar
  7. 7.
    Si, H.: TetGen. A quality tetrahedral mesh generator and three-dimensional delaunay triangulator. (2007). http://tetgen.berlios.de

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Konstantin Brenner
    • 1
  • Mayya Groza
    • 1
  • Cindy Guichard
    • 2
  • Roland Masson
    • 1
  1. 1.Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7251 and team CoffeeUniversité Nice Sophia Antipolis, CNRS and INRIA Sophia Antipolis MéditerranéeNiceFrance
  2. 2.Laboratoire Jacques-Louis Lions, CNRS, UMR 7598Sorbonne Universités, UMPC Univ Paris 06ParisFrance

Personalised recommendations