Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir

Andrea Capolei, Carsten Völcker, Jan Frydendall, John Bagterp Jørgensen

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Conventional recovery techniques enable recovery of 10-50% of the oil in an oil eld. Advances in smart well technology and enhanced oil recovery techniques enable signicant larger recovery. To realize this potential, feedback model-based optimal control technologies are needed to manipulate the injections and oil production such that ow is uniform in a given geological structure. Even in the case of conventional water ooding, feedback based optimal control technologies may enable higher oil recovery than with conventional operational strategies. The optimal control problems that must be solved are large-scale problems and require specialized numerical algorithms. In this paper, we combine a single shooting optimization algorithm based on sequential quadratic programming (SQP) with explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods and a continuous adjoint method for sensitivity computation. We demonstrate the procedure on a water ooding example with conventional injectors and producers.
Original languageEnglish
Title of host publicationProceedings of the 17th Nordic Process Control Workshop
EditorsJohn Bagterp Jørgensen, Jakob Kjøbsted Huusom, Gürkan Sin
Place of PublicationKogens Lyngby
PublisherTechnical University of Denmark
Publication date2012
ISBN (Print)978-87-643-0946-1
Publication statusPublished - 2012
Event17th Nordic Process Control Workshop - Kongens Lyngby, Denmark
Duration: 25 Jan 201227 Jan 2012
Conference number: 17


Conference17th Nordic Process Control Workshop
CityKongens Lyngby
Internet address


  • Oil Reservoir
  • Optimal Control
  • Numerical Methods
  • Optimization


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