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

  • Anna KvashchukEmail author
  • Florin Adrian Radu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


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.



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.The National IOR Centre of Norway/UiSStavangerNorway
  2. 2.University of BergenBergenNorway

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