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The multiscale perturbation method for two-phase reservoir flow problems

Author

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  • Rocha, Franciane F.
  • Mankad, Het
  • Sousa, Fabricio S.
  • Pereira, Felipe

Abstract

In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible displacement in porous media approximated by an operator splitting method. The proposed procedure is based on domain decomposition and combines the Multiscale Perturbation Method (MPM) [Ali, et al., Appl. Math. and Comput., 387 (2020) pp. 125023] with the Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21]. When an update of the velocity field is called for by the operator splitting algorithm, the MPM-2P may provide, depending on the magnitude of a dimensionless algorithmic parameter, an accurate and computationally inexpensive approximation for the velocity field by reusing previously computed multiscale basis functions. Thus, a full update of all multiscale basis functions required by the MRCM for the construction of a new velocity field is avoided.

Suggested Citation

  • Rocha, Franciane F. & Mankad, Het & Sousa, Fabricio S. & Pereira, Felipe, 2022. "The multiscale perturbation method for two-phase reservoir flow problems," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300321009917
    DOI: 10.1016/j.amc.2021.126908
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    References listed on IDEAS

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    1. Al-Mamun, A. & Barber, J. & Ginting, V. & Pereira, F. & Rahunanthan, A., 2020. "Contaminant transport forecasting in the subsurface using a Bayesian framework," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Guiraldello, Rafael T. & Ausas, Roberto F. & Sousa, Fabricio S. & Pereira, Felipe & Buscaglia, Gustavo C., 2019. "Interface spaces for the Multiscale Robin Coupled Method in reservoir simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 103-119.
    3. Francisco, A. & Ginting, V. & Pereira, F. & Rigelo, J., 2014. "Design and implementation of a multiscale mixed method based on a nonoverlapping domain decomposition procedure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 125-138.
    4. Ali, Alsadig & Mankad, Het & Pereira, Felipe & Sousa, Fabrício S., 2020. "The multiscale perturbation method for second order elliptic equations," Applied Mathematics and Computation, Elsevier, vol. 387(C).
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    1. Ali, Alsadig & Mankad, Het & Pereira, Felipe & Sousa, Fabrício S., 2020. "The multiscale perturbation method for second order elliptic equations," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Guiraldello, Rafael T. & Ausas, Roberto F. & Sousa, Fabricio S. & Pereira, Felipe & Buscaglia, Gustavo C., 2019. "Interface spaces for the Multiscale Robin Coupled Method in reservoir simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 103-119.

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