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reservoir description BY USING A PIECEWISE CONSTANT LEVEL SET METHOD

Journal of Computational Mathematics 2008年第3期26卷 365-377页

作者： Hongwei Li Center for Integrated Petroleum Research,University of Bergen,Norway Department of Mathematics,Capital Normal University,Beijing 100037,China Xuecheng Tai Department of Mathematics,University of Bergen,Norway Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore Sigurd Ivar Aanonsen Center for Integrated Petroleum Research,University of Bergen,Norway Department of Mathematics,University of Bergen,Norway Center for Integrated Petroleum Research University of Bergen Norway Department of Mathematics Capital Normal University Beijing 100037 China Department of Mathematics University of Bergen Norway Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore

We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.

关键词： Inverse problem Level set method Piecewise constant operator splitting,reservoir description

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