1887

Abstract

Summary

Control-volume distributed multi-point flux approximation (CVD-MPFA) coupled with single-phase reduceddimensional discrete fracture models [1], are extended to two-phase flow, including gravity and capillary pressure.

Both continuous and discontinuous fracture models are considered coupled with higher resolution methods, leading to novel finite-volume schemes for flow in subsurface fractured porous media on unstructured grids. Performance comparisons are presented for tracer and two-phase flow problems on a number of 2D fractured media test cases including hybrid gravity and capillary pressure effects on unstructured meshes.

[1] R. Ahmed, M.G. Edwards, S. Lamine, B.A.H. Huisman and M. Pal

“Control Volume Distributed Multi-Point Flux Approximation coupled with a lower-dimensional fracture model” J. Comput. Phys vol 284 pp 462–489 March 2015

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802150
2018-09-03
2024-04-19
Loading full text...

Full text loading...

References

  1. H.A.Friis, M.G.Edwards & J.Mykkeltveit
    , 2008. Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell Centered Triangular Grids, SIAM J. Sci. Com-put. 31(2): 1192–1220, Doi 10.1137/070692182.
    https://doi.org/10.1137/070692182 [Google Scholar]
  2. R.Ahmed, M.G.Edwards, S.Lamine, B.A.H.Huisman, & M.Pal
    , 2015. Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model, Journal of Computational Physics, 284:462–489.
    [Google Scholar]
  3. J.Jaffré, V.Martin, J.E.Roberts
    , 2003. Modeling Fractures and Barriers as Interfaces for Flow in Porous Media, [Research Report] RR-4848, INRIA. [inria-00071735].
    [Google Scholar]
  4. V.Martin, J.Jaffré, and J.E.Roberts
    , 2005. Modeling fractures and barriers as interfaces for flow in porous media, SIAM Journal on Scientific Computing, 26(5):1667–1691.
    [Google Scholar]
  5. Y.S.Wu
    , 2016. Multiphase Fluid Flow in Porous and Fractured Reservoirs, https://doi.org/10.1016/B978-0-12-803848-2.01001-1, Elsevier.
    [Google Scholar]
  6. J.DouglasJr & T.Arbogast
    , 1990. Dual porosity models for flow in naturally fractured reservoirs Dynamics of Fluids in Hierarchical Porous Media, Academic Press London, UK, 177–221.
    [Google Scholar]
  7. J.E.Warren, & P.J.Root
    , 1963. The Behavior of Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, Society of Petroleum Engineers, 3:245–255.
    [Google Scholar]
  8. H.Kazemi, L. S.MerrillJr, K. L.Porterfield, & P. R.Zeman
    , 1976. Numerical simulation of water-oil flow in naturally fractured reservoirs, Society of Petroleum Engineers Journal, Society of Petroleum Engineers, 16:317–326.
    [Google Scholar]
  9. M.Karimi-Fard and A.Firoozabadi
    , 2003. Numerical Simulation of Water Injection in Fractured Media Using the Discrete Fractured Model and the Galerkin Method, SPE Reservoir Evaluation & Engineering, 6(2):117–126. SPE-71615-PA, doi:10.2118/83633‑PA.
    https://doi.org/http://dx.doi.org/10.2118/83633-PA [Google Scholar]
  10. M.Karimi-Fard, L.J.Durlofsky and K.Aziz
    , 2004. An Efficient Discrete Fracture Model Applicable for General Purpose Reservoir Simulators. SPE 79699, SPE Journal, 9(2):227–236, doi:10.2118/79699–MS.
    https://doi.org/http://dx.doi.org/10.2118/79699–MS [Google Scholar]
  11. H.Hoteit & A.Firoozabadi
    , 2008. An efficient numerical model for incompressible two-phase flow in fractured media. Adv. in Water Resources, 31:891–905.
    [Google Scholar]
  12. T.H.Sandve, I.Berre, and J.M.Nordbotten
    , 2012. An efficient multi-point flux approximation method for discrete fracture-matrix simulations, Journal of Computational Physics, 231(9):3784–3800.
    [Google Scholar]
  13. R.Ahmed, M. G.Edwards, S.Lamine, B.A.H.Huisman, & M.Pal
    , 2017. CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations, Journal of Computational Physics, 349:265–299.
    [Google Scholar]
  14. S.H.Lee and Y.Efendiev and H.A.Tchelepi
    , 2015. Hybrid upwind discretization of nonlinear two-phase flow with gravity, Advances in Water Resources, 82:27–38, http://dx.doi.org/10.1016/j.advwatres.2015.04.007.
    [Google Scholar]
  15. Z.Chen, G.Huan & Y.Ma
    , 2006. Computational Methods for Multiphase Flows in Porous Media, SIAM, 2.
    [Google Scholar]
  16. K.Aziz & A.Settari
    , 1979. Petroleum Reservoir Simulation, pub Elsevier.
    [Google Scholar]
  17. D.W.Peaceman
    , 1977. Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam/New York.
    [Google Scholar]
  18. T.Barth & D.C.Jespersen
    , 1989. The design and application of upwind schemes on unstructured meshes, AIAA paper 89–0366.
    [Google Scholar]
  19. J.G.Kim & M.D.Deo
    , (1999, January 1). Comparison of the Performance of a Discrete Fracture Multiphase Model With Those Using Conventional Methods, Society of Petroleum Engineers, doi:10.2118/51928‑MS.
    https://doi.org/10.2118/51928-MS [Google Scholar]
  20. J.Jaffré, M.Mnejja, & J.E.Roberts
    , 2011. A discrete fracture model for two-phase flow with matrix-fracture interaction, Procedia Computer Science, 4:967–973.
    [Google Scholar]
  21. Y.W.Xie & M.G.Edwards
    , 2017. Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids, Computational Geosciences, 21:921–936.
    [Google Scholar]
  22. J.G.Kim, & M.D.Deo
    , 2000. Finite element, discrete-fracture model for multiphase flow in porous media, AIChE Journal, Wiley Online Library, 46:1120–1130.
    [Google Scholar]
  23. I.Aavatsmark
    , 2002. An Introduction to Multipoint Flux Approximations for Quadrilateral Grids, Computational Geosciences, 6:405–432. https://doi.org/10.1023/A:1021291114475.
    [Google Scholar]
  24. T.Arbogast, M.Juntunen, J.Pool, & M. F.Wheeler
    , 2013. A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocity and continuous capillary pressure, Computational Geosciences, 17:1055–1078.
    [Google Scholar]
  25. M.G.Edwards, & H.Zheng
    , 2010. Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids, Journal of Computational & Applied Mathematics, 234:2152–2161.
    [Google Scholar]
  26. S.Buckley, & M.Leverett
    , 1942. Mechanism of fluid displacements in sands, Transactions of the AIME, 146:107–116.
    [Google Scholar]
  27. M.G.Edwards, & C.F.Rogers
    , 1998. Finite volume discretization with imposed flux continuity for the general tensor pressure equation Computational Geosciences, Springer, 2:259–290.
    [Google Scholar]
  28. J. R.Shewchuk
    , May 1996. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in: Ming C.Lin, DineshManocha (Eds.), Applied Computational Geometry: Towards Geometric Engineering Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1148:203–222.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201802150
Loading
/content/papers/10.3997/2214-4609.201802150
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error