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Non-intrusive subdomain POD-TPWL for reservoir history matching

  • Cong XiaoEmail author
  • Olwijn Leeuwenburgh
  • Hai Xiang Lin
  • Arnold Heemink
Open Access
Original Paper
  • 71 Downloads

Abstract

This paper presents a non-intrusive subdomain POD-TPWL (SD POD-TPWL) for reservoir history matching through integrating domain decomposition (DD), proper orthogonal decomposition (POD), radial basis function (RBF) interpolation, and the trajectory piecewise linearization (TPWL). It is an efficient approach for model reduction and linearization of general non-linear time-dependent dynamical systems without accessing to the legacy source code. In the subdomain POD-TPWL algorithm, firstly, a sequence of snapshots over the entire computational domain is saved and then partitioned into subdomains. From the local sequence of snapshots over each subdomain, a number of local basis vectors is formed using POD, and then the RBF interpolation is used to estimate the derivative matrices for each subdomain. Finally, those derivative matrices are substituted into a POD-TPWL algorithm to form a reduced-order linear model in each subdomain. This reduced-order linear model makes the implementation of the adjoint easy and results in an efficient adjoint-based parameter estimation procedure. Comparisons with the classic finite-difference-based history matching show that our proposed subdomain POD-TPWL approach is obtaining comparable results. The number of full-order model simulations required is roughly 2–3 times the number of uncertain parameters. Using different background parameter realizations, our approach efficiently generates an ensemble of calibrated models without additional full-order model simulations.

Keywords

Data assimilation Reduced-order modeling Model linearization Domain decomposition 

Abbreviations

POD

Proper orthogonal decomposition

PCA

Principal component analysis

RBF

Radial basis function

TPWL

Trajectory piecewise linearizaton

DD

Domain decomposition

FOM

Full-order model

Notes

Acknowledgements

We thank the research funds by China Scholarship Council (CSC) and Delft University of Technology. We are also very grateful to the editor and reviewers for their reviews and insightful comments.

Funding information

This study received research funds from China Scholarship Council (CSC) and Delft University of Technology.

Supplementary material

10596_2018_9803_MOESM1_ESM.pdf (694 kb)
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Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Cong Xiao
    • 1
    Email author
  • Olwijn Leeuwenburgh
    • 2
    • 3
  • Hai Xiang Lin
    • 1
  • Arnold Heemink
    • 1
  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands
  3. 3.TNOUtrechtThe Netherlands

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