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Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

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  • Published: 09 November 2022
  • volume 48, Article number: 73 (2022)
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Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery
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  • Tim Keil1,
  • Hendrik Kleikamp1,
  • Rolf J. Lorentzen2,
  • Micheal B. Oguntola  ORCID: orcid.org/0000-0001-6692-639X2,3 &
  • …
  • Mario Ohlberger1 

  • 328 Accesses

  • 1 Citation

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Abstract

In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive training procedure of a neural network that directly approximates an input-output map of the underlying PDE-constrained optimization problem. The training process thereby focuses on the construction of an accurate surrogate model solely related to the optimization path of an outer iterative optimization loop. True evaluations of the objective function are used to finally obtain certified results. Numerical experiments are given to evaluate the accuracy and efficiency of the approach for a heterogeneous five-spot benchmark problem.

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Funding

Open access funding provided by University Of Stavanger • Tim Keil, Hendrik Kleikamp, Micheal Oguntola and Mario Ohlberger received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 –390685587, Mathematics Münster: Dynamics–Geometry–Structure.

• Tim Keil and Mario Ohlberger received funding from the Deutsche Forschungsgemeinschaft under contract OH 98/11-1.

• Micheal Oguntola and Rolf Lorentzen received funding from the Research Council of Norway and the industry partners, ConocoPhillips Skandinavia AS, Aker BP ASA, Vår Energi AS, Equinor Energy AS, Neptune Energy Norge AS, Lundin Energy Norway AS, Halliburton AS, Schlumberger Norge AS, and Wintershall Dea Norge AS, of The National IOR Centre of Norway.

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Authors and Affiliations

  1. Institute for Analysis and Numerics and Mathematics Münster, University of Münster, Einsteinstrasse 62, D-48149, Münster, Germany

    Tim Keil, Hendrik Kleikamp & Mario Ohlberger

  2. NORCE-Norwegian Research Center AS, 5838, Bergen, Norway

    Rolf J. Lorentzen & Micheal B. Oguntola

  3. University of Stavanger, 4036, Stavanger, Norway

    Micheal B. Oguntola

Authors
  1. Tim Keil
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  2. Hendrik Kleikamp
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  3. Rolf J. Lorentzen
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  4. Micheal B. Oguntola
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  5. Mario Ohlberger
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Corresponding author

Correspondence to Micheal B. Oguntola.

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Communicated by: Gianluigi Rozza

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Keil, T., Kleikamp, H., Lorentzen, R.J. et al. Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery. Adv Comput Math 48, 73 (2022). https://doi.org/10.1007/s10444-022-09981-z

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  • Received: 04 March 2022

  • Accepted: 15 September 2022

  • Published: 09 November 2022

  • DOI: https://doi.org/10.1007/s10444-022-09981-z

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Keywords

  • PDE-constrained optimization
  • Enhanced oil recovery
  • Machine learning
  • Neural networks
  • Surrogate modeling
  • Ensemble-based optimization

Mathematics Subject Classification (2010)

  • 49M41
  • 68T07
  • 90C90
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