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Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Kourounis, Drosos ; Durlofsky, Louis ; Jansen, Jan ; Aziz, Khalid

In: Computational Geosciences, 2014, vol. 18, no. 2, p. 117-137

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    Titre
    • Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow
    Auteur
    • Kourounis, Drosos. Department of Energy Resources Engineering, Stanford University, 94305-2220, Stanford, CA, USA
    • Durlofsky, Louis. Department of Energy Resources Engineering, Stanford University, 94305-2220, Stanford, CA, USA
    • Jansen, Jan. Department of Geoscience and Engineering, Delft University of Technology, Delft, Netherlands
    • Aziz, Khalid. Department of Energy Resources Engineering, Stanford University, 94305-2220, Stanford, CA, USA
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Computational Geosciences, 2014, vol. 18, no. 2, p. 117-137. Springer International Publishing
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:326550
    Summary
    An adjoint formulation for the gradient-based optimization of oil-gas compositional reservoir simulation problems is presented. The method is implemented within an automatic differentiation-based compositional flow simulator (Stanford's Automatic Differentiation-based General Purpose Research Simulator, AD-GPRS). The development of adjoint procedures for general compositional problems is much more challenging than for oil-water problems due to the increased complexity of the code and the underlying physics. The treatment of nonlinear constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well bottom-hole pressures, poses a particular challenge. Two approaches for handling these constraints are presented—a formal treatment within the optimizer and a simpler heuristic treatment in the forward model. The relationship between discrete and continuous adjoint formulations is also elucidated. Results for four example cases of increasing complexity are presented. Improvements in the objective function (cumulative oil produced) relative to reference solutions range from 4.2 to 11.6 %. The heuristic treatment of nonlinear constraints is shown to offer a cost-effective means for obtaining feasible solutions, which are, in some cases, better than those obtained using the formal constraint handling procedure.