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Abstract

Summary

Control volume finite element methods (CVFEM) are gaining increasing popularity for modeling multi-phase flow in porous media due to their inherited geometric flexibility for modeling complex shapes. Nonetheless, classical CVFEM suffer from two key problems; first, mass conservation is enforced by the use of control volumes that span element boundaries. Consequently, when modeling flow in regions with discontinuous material properties, control volumes that span geologic domain boundaries result in non-physical leakage that degrades the numerical solution accuracy. Another challenge is to provide an accurate solution for distorted elements; elements with high aspect ratio that are part of the discretized heterogeneous domain. In fact, most numerical methods struggle to provide a converged pressure solution for high aspect ratio elements of the domain.

Here, we introduce a numerical scheme that removes non-physical leakage across geologic domains and addresses the accuracy of classical control volume finite element method (CVFEM) in high aspect ratio elements. The scheme utilizes the frameworks of double-CVFEM (DCVFEM) where pressure is discretized CV-wise rather than element-wise. In addition, it introduces discontinuous control volumes by allowing pressure to be discontinuous between elements. The resultant finite element pair has an equal-order of velocity and pressure, with discontinuous linear elements for both the pressure and velocity fields P1DG–P1DG. This type of element pair is LBB unstable. The instability issue is circumvented by global enrichment of the finite element velocity interpolation space with an interior bubble function, given by the new element pair P1(BL)DG–P1DG. This element pair resolves both issues addressed earlier.

We demonstrate that the developed numerical method is mass conservative, and it accurately preserves sharp saturation changes across different material properties or discontinuous permeability fields as well as improves convergence to the pressure solution for distorted mesh, i.e. elements with high aspect ratio. We show the effectiveness of the presented formulation on realistic highly heterogeneous models.

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.202035153
2020-09-14
2024-04-26

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References

  1. Aavatsmark, I.
    [2002] An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences.
     [Google Scholar]
  2. Abushaikha, A., Blunt, M., Gosselin, O., Pain, C. and Jackson, M.
    [2015] Interface Control Volume Finite Element Method for Modelling Multi-phase Flow in Highly Heterogeneous and Fractured Reservoirs. Journal of Computational Physics.
     [Google Scholar]
  3. Anderson, D.
    [1965] Iterative Procedures for Nonlinear Integral Equations. Computing Machinery.
     [Google Scholar]
  4. Aziz, K. and Settari, A.
    [1979] Petroleum reservoir simulation. Applied Science Publishers.
     [Google Scholar]
  5. Belayneh, M., Geiger, S. and Matthäi, S.
    [2006] Numerical Simulation of Water Injection into Layered Fractured Carbonate Reservoir Analogs. AAPG Bulletin.
     [Google Scholar]
  6. Buckley, S. and Leverett, M.
    [1942] Mechanisms of Fluid Displacement in Sands. Transactions of the AIME.
     [Google Scholar]
  7. Douglas, J.
    [1983] Finite Difference Methods for Two-Phase Incompressible Flow in Porous Media. SIAM Journal on Numerical Analysis, 20(4), 681–696.
     [Google Scholar]
  8. Durlofsky, L.
    [1992] A Triangle Based Mixed Finite Element-Finite Volume Technique for Modeling Two Phase Flow through Porous Media. Journal of Computational Physics.
     [Google Scholar]
  9. Fung, L., Hiebert, A. and Nghiem, L.
    [1992] Reservoir Simulation with Control-Volume Finite Element Method. SPE Reservoir Engineering.
     [Google Scholar]
  10. Geiger, S., Roberts, S., Matthäi, S.K., Zoppou, C. and Burri, A.
    [2004] Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media. Geofluids.
     [Google Scholar]
  11. Gomes, J., Pavlidis, D., Salindas, P., Xie, Z., Percival, J., Melnikova, Y., Pain, C. and Jackson, M.
    [2016] A Force-balanced Control Volume Finite Element Method for Multi-phase Porous Media Flow Modeling. Numerical Methods in Fluids.
     [Google Scholar]
  12. Gunasekera, D., Cox, J. and Lindsey, P.
    [1997] The Generation and Application of K-Orthogonal Grid Systems. SPE Reservoir Simulation Symposium.
     [Google Scholar]
  13. Jackson, M., Percival, J., Mostaghimi, P., Tollit, B., Pavlidis, D., Pain, C., Gomes, J., El-Sheikh, A., Salinas, P., Muggeridge, A. and Blunt, M.
    [2015] Reservoir Modeling for Flow Simulation by Use of Surface, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method. SPE Reservoir Evaluation and Engineering.
     [Google Scholar]
  14. Nguyen-Xuana, H. and Liu, G.
    [2015] An Edge-based Finite Element Method (ES-FEM) with Adaptive Scaled-bubble Functions for Plane Strain Limit Analysis. Computer Methods in Applied Mechanics and Engineering.
     [Google Scholar]
  15. Pavlidis, D., Gomes, J., Xie, Z., Percival, J., Pain, C. and Matar, O.
    [2015] Compressive Advective and Multi-component Methods for Interface-capturing. Numerical Methods in Fluids.
     [Google Scholar]
  16. Salinas, P., Pavlidis, D., Xie, Z., Adam, A., Pain, C.C. and Jackson, M.D.
    [2017a] Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media. International Journal for Numerical Methods in Fluids, 84(8), 466–476.
     [Google Scholar]
  17. Salinas, P., Pavlidis, D., Xie, Z., Jacquemyn, C., Melnikova, Y., Jackson, M. and Pain, C.
    [2017b] Improving the Robustness of the Control Volume Finite Element Method with Application to Multiphase Porous Media Flow. Journal for Numerical Methods in Fluids.
     [Google Scholar]
  18. Salinas, P., Pavlidis, D., Xie, Z., Osman, H., Pain, C. and Jackson, M.
    [2018] A Discontinuous Control Volume Finite Element Method for Multi-phase Flow in Heterogeneous Porous Media. Journal of Computational Physics.
     [Google Scholar]
  19. Shewchuck, J.
    [2002] Delaunay Refinement Algorithms for Triangular Mesh Generation. Computational Geometry.
     [Google Scholar]
  20. Wu, X.H. and Parashkevov, R.
    [2009] Effect of Grid Deviation on Flow Solutions. SPE Journal.
     [Google Scholar]
  21. Zienkiewicz, O., Taylor, R. and Zhu, J.
    [2013] The Finite Element Method: its Basis and Fundamentals. Butterworth-Heinemann.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.202035153
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Discontinuous Control Volume Finite Element Method for Multiphase Flow in Porous Media on Challenging Meshes
Conference Proceedings 2020, 1 (2020); https://doi.org/10.3997/2214-4609.202035153
/content/papers/10.3997/2214-4609.202035153
/content/papers/10.3997/2214-4609.202035153
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