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Numerical validation of an adaptive model for the determination of nonlinear-flow regions in highly heterogeneous porous media (2405.02094v1)

Published 3 May 2024 in math.NA and cs.NA

Abstract: An adaptive model for the description of flows in highly heterogeneous porous media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of the fluid's velocity, the constitutive law linking velocity and pressure gradient is selected between two possible options, one better adapted to slow motion and the other to fast motion. We propose here to validate further this adaptive approach by means of more extensive numerical experiments, including a three-dimensional case, as well as to use such approach to determine a partition of the domain into slow- and fast-flow regions.

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References (34)
  1. https://github.com/pmgbergen/porepy.
  2. A multiscale flux basis for mortar mixed discretizations of reduced Darcy–Forchheimer fracture models. Comput. Methods Appl. Mech. Eng., 354:16–36, 2019.
  3. On the well-posedness of generalized Darcy–Forchheimer equation. Bound. Value Probl., 2018(123), 2018.
  4. Analysis of generalized Forchheimer flows of compressible fluids in porous media. J. Math. Phys., 50(10):103102, 2009.
  5. Numerical approach to non-Darcy mixed convective flow of non-Newtonian fluid on a vertical surface with varying surface temperature and heat source. Karbala Int. J. Mod. Sci., 6(3), 2020.
  6. Numerical solution of skin friction in porous medium using Brinkman Forchheimer model under fuzzy environment. Int. J. Appl. Comput., preprint, 2022.
  7. On a Class of Incomplete Gamma Functions with Applications. Chapman & Hall, 2001.
  8. SPE-66599-MS, chapter Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques, page 13. Soc. Pet. Eng., Houston, Texas, 2001.
  9. Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. Math. Comp., 84:153–186, 2015.
  10. Domain decomposition methods for flow in heterogeneous porous media. Contemp. Math., 218:104–120, 1998.
  11. Nonlinear corrections to Darcy’s law at low Reynolds numbers. J. Fluid Mech., 343:331–350, 1997.
  12. A. Fumagalli and F. S. Patacchini. https://github.com/compgeo-mox/validate_adaptative.
  13. A. Fumagalli and F. S. Patacchini. Model adaptation for non-linear elliptic equations in mixed form: existence of solutions and numerical strategies. ESAIM: Math. Model. Numer. Anal., 56(2):565–592, 2022.
  14. A. Fumagalli and F. S. Patacchini. Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media. J. Comput. Phys., 475:111844, 2023.
  15. Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal–dual gap estimators. Comput. Methods Appl. Mech. Eng., 418:116558, 2024.
  16. L. Hoang and A. Ibragimov. Structural stability of generalized Forchheimer equations for compressible fluids in porous media. Nonlinearity, 24(1):1–41, 2011.
  17. Porepy: An open-source software for simulation of multiphysics processes in fractured porous media. Comput. Geosci., 2020.
  18. Generalization of the Forchheimer-extended Darcy flow model to the tensor premeability case via a variational principle. J. Fluid Mech., 299:97–104, 1995.
  19. V. A. Kovtunenko. Mixed variational problem for a generalized Darcy–Forchheimer model driven by hydraulic fracture. J. Vib. Test. Dyn. Syst., 7(1):15–21, 2023.
  20. Laboratory measurements of non-Darcy flow coefficients in natural and artificial unconsolidated porous media. J. Pet. Sci. Eng., 77(3):365–374, 2011.
  21. E. Marušić-Paloka and A. Mikelić. The derivation of a nonlinear filtration law including the inertia effects via homogenization. Nonlinear Anal. Theory Methods Appl., 42(1):97–137, 2000.
  22. S. P. Neuman. Theoretical derivation of Darcy’s law. Acta Mech., 25(3-4):153–170, 1977.
  23. D. W. Peaceman. Interpretation of well-block pressures in numerical reservoir simulation (includes associated paper 6988). Soc. Pet. Eng. J., 18(03):183–194, 1978.
  24. D. W. Peaceman. Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability. Soc. Pet. Eng. J., 23(03):531–543, 1983.
  25. F. Russo Spena and A. Vacca. A potential formulation of non-linear models of flow through anisotropic porous media. Transp. Porous Media, 45:405–421, 2001.
  26. D. Ruth and H. Ma. On the derivation of the Forchheimer equation by means of the averaging theorem. Transp. Porous Media, 7(3):255–264, 1992.
  27. Domain decomposition strategies for nonlinear flow problems in porous media. J. Comput. Phys., 234:439–451, 2013.
  28. W. Sobieski and A. Trykozko. Darcy’s and Forchheimer’s laws in practice. Part 1. The experiment. Tech. Sci., 17(4):321–335, 2014.
  29. W. Sobieski and A. Trykozko. Darcy’s and Forchheimer’s laws in practice. Part 2. The numerical model. Tech. Sci., 17(4):337–350, 2014.
  30. S. Whitaker. Flow in porous media I: A theoretical derivation of Darcy’s law. Transp. Porous Media, 1(1):3–25, 1986.
  31. S. Whitaker. The Forchheimer equation: A theoretical development. Transp. Porous Media, 25(1):27–61, 1996.
  32. A study on Darcy versus Forchheimer models for flow through heterogeneous landfills including macropores. Water, 14(4), 2022.
  33. Z. Zeng and R. Grigg. A criterion for non-Darcy flow in porous media. Transp. Porous Media, 63:57–69, 2006.
  34. Experimental investigation of Forchheimer coefficients for non-Darcy flow in conglomerate-confined aquifer. Geofluids, pages 1–21, 2018.
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