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An iterative representer-based scheme for data inversion in reservoir modeling
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Iglesias, Marco and Dawson, Clint (2009) An iterative representer-based scheme for data inversion in reservoir modeling. Inverse Problems, Vol.25 (No.3). Article no. 035006. doi:10.1088/0266-5611/25/3/035006 ISSN 0266-5611.
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Official URL: http://dx.doi.org/10.1088/0266-5611/25/3/035006
Abstract
In this paper, we develop a mathematical framework for data inversion in reservoir models. A general formulation is presented for the identification of uncertain parameters in an abstract reservoir model described by a set of nonlinear equations. Given a finite number of measurements of the state and prior knowledge of the uncertain parameters, an iterative representer-based scheme (IRBS) is proposed to find improved parameters. In this approach, the representer method is used to solve a linear data assimilation problem at each iteration of the algorithm. We apply the theory of iterative regularization to establish conditions for which the IRBS will converge to a stable approximation of a solution to the parameter identification problem. These theoretical results are applied to the identification of the second-order coefficient of a forward model described by a parabolic boundary value problem. Numerical results are presented to show the capabilities of the IRBS for the reconstruction of hydraulic conductivity from the steady-state of groundwater flow, as well as the absolute permeability in the single-phase Darcy flow through porous media.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Inverse Problems | ||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||
| ISSN: | 0266-5611 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.25 | ||||
| Number: | No.3 | ||||
| Page Range: | Article no. 035006 | ||||
| DOI: | 10.1088/0266-5611/25/3/035006 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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