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Volume 26, Issue 3
Reservoir Description by Using a Piecewise Constant Level Set Method

Hongwei Li, Xuecheng Tai & Sigurd Ivar Aanonsen

J. Comp. Math., 26 (2008), pp. 365-377.

Published online: 2008-06

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  • Abstract

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.

  • Keywords

Inverse problem, Level set method, Piecewise constant, Operator splitting, Reservoir description.

  • AMS Subject Headings

34A55, 35R30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-365, author = {Hongwei Li, Xuecheng Tai and Sigurd Ivar Aanonsen}, title = {Reservoir Description by Using a Piecewise Constant Level Set Method}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {3}, pages = {365--377}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8631.html} }
TY - JOUR T1 - Reservoir Description by Using a Piecewise Constant Level Set Method AU - Hongwei Li, Xuecheng Tai & Sigurd Ivar Aanonsen JO - Journal of Computational Mathematics VL - 3 SP - 365 EP - 377 PY - 2008 DA - 2008/06 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8631.html KW - Inverse problem, Level set method, Piecewise constant, Operator splitting, Reservoir description. AB -

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.

Hongwei Li, Xuecheng Tai and Sigurd Ivar Aanonsen. (2008). Reservoir Description by Using a Piecewise Constant Level Set Method. Journal of Computational Mathematics. 26 (3). 365-377. doi:
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