Introduction to PDE-Constrained Optimization in the Oil and Gas Industry

  • Jeremy BrandmanEmail author
  • Huseyin Denli
  • Dimitar Trenev
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 163)


This article is an expanded version of a tutorial on applications of PDE-constrained optimization in the oil and gas industry that was given at the Frontiers in PDE-Constrained Optimization workshop. (The workshop was held at the Institute for Mathematics and its Applications June 6–10, 2016.) We begin with an overview of the oil and gas supply chain that highlights the importance of PDE-constrained optimization. Next, we take an in-depth look at two key applications: full-wavefield inversion and reservoir history matching. For each application, we introduce a PDE model, derive the gradient of the objective function using the adjoint-state method, and present simple numerical results. We conclude with a discussion of key challenges.



The authors thank ExxonMobil for permission to publish this work. The authors also thank Martin Lacasse, Laurent White, Rohan Panchadhara, Anatoly Baumstein, Tom Dickens, Dave Stern, Klaus Wiegand, and Xiao-Hui Wu for their feedback on an earlier version of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jeremy Brandman
    • 1
    Email author
  • Huseyin Denli
    • 1
  • Dimitar Trenev
    • 1
  1. 1.Corporate Strategic ResearchExxonMobil Research and Engineering CompanyAnnandaleUSA

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