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A Fully-Implicit, Iterative Scheme for the Simulation of Two-Phase Flow in Porous Media

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

In this work, we present a new implicit scheme for two-phase flow in porous media. The proposed scheme is based on the iterative IMPES (IMplicit Pressure Explicit Saturation) method and, therefore, preserves its efficiency in treatment of nonlinearities, while relaxing the time step condition common for explicit methods. At the same time, it does not involve costly computation of Jacobian matrix required for generic Newtons type methods.

Implicit treatment of capillary pressure term ensures the stability and convergence properties of the new scheme. This choice of stabilization is supported by mathematical analysis of the method which also includes the rigorous proof of convergence.

Our numerical results indicate that the scheme has superior performance compared with standard IMPES and fully implicit methods on benchmark problems.

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Acknowledgements

The first author acknowledges the Research Council of Norway and the industry partners; ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Maersk Oil Norway AS, Statoil Petroleum AS, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS and DEA Norge AS of The National IOR Centre of Norway for support.

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Authors and Affiliations

  1. The National IOR Centre of Norway/UiS, Stavanger, Norway

    Anna Kvashchuk

  2. University of Bergen, Bergen, Norway

    Florin Adrian Radu

Authors
  1. Anna Kvashchuk
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  2. Florin Adrian Radu
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Corresponding author

Correspondence to Anna Kvashchuk .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Kvashchuk, A., Radu, F.A. (2019). A Fully-Implicit, Iterative Scheme for the Simulation of Two-Phase Flow in Porous Media. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_57

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