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Reservoir description using a binary level set model

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Computing and Visualization in Science

Abstract

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from time-lapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.

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Author notes

  1. Lars Kristian Nielsen

    Present address: Laksevåg Upper Secondary/High School, Bergen, Norway

Authors and Affiliations

  1. Department of Mathematics, University of Bergen, 5020, Bergen, Norway

    Lars Kristian Nielsen, Xue-Cheng Tai, Sigurd Ivar Aanonsen & Magne Espedal

  2. CIPR-Centre for Integrated Petroleum Research, University of Bergen, 5020, Bergen, Norway

    Lars Kristian Nielsen, Hongwei Li, Sigurd Ivar Aanonsen & Magne Espedal

  3. Department of Mathematics, Capital Normal University, 10037, Beijing, People’s Republic of China

    Hongwei Li

  4. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637616, Singapore

    Xue-Cheng Tai

Authors
  1. Lars Kristian Nielsen
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  2. Hongwei Li
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  3. Xue-Cheng Tai
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  4. Sigurd Ivar Aanonsen
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  5. Magne Espedal
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Corresponding author

Correspondence to Sigurd Ivar Aanonsen.

Additional information

Communicated by G. Wittum.

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Nielsen, L.K., Li, H., Tai, XC. et al. Reservoir description using a binary level set model. Comput. Visual Sci. 13, 41 (2010). https://doi.org/10.1007/s00791-008-0121-1

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