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Advanced Computing pp 81–98Cite as

Optimal Control of Partially Miscible Two-Phase Flow with Applications to Subsurface CO2 Sequestration

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 93))

Abstract

Motivated by applications in subsurface CO2 sequestration, we investigate constrained optimal control problems with partially miscible two-phase flow in porous media. The objective is, e.g., to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, where the time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE system and formulate the optimal control problem. For the discretization we use a variant of the BOX method, a locally conservative control-volume FE method. The timestep-wise Lagrangian of the control problem is implemented as a functional in the PDE toolbox Sundance, which is part of the HPC software Trilinos. The resulting MPI parallelized Sundance state and adjoint solvers are linked to the interior point optimization package IPOPT. Finally, we present some numerical results in a heterogeneous model reservoir.

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Acknowledgements

This publication is based on work supported by Award No. UK-C0020, made by King Abdullah University of Science and Technology (KAUST). The work was conducted for the MAC-KAUST project K1 “Simulating CO2 Sequestration” within the Munich Centre of Advanced Computing (MAC) at TUM. The authors gratefully acknowledge this support as well as the grant DFG INST 95/919-1 FUGG that provided partial funding of the compute cluster used for the computations. Moreover, the authors would like to thank Michael Bader for handling the paper and the three referees for their valuable comments.

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Authors and Affiliations

  1. Chair of Mathematical Optimization, Department of Mathematics, Technische Universität München, Boltzmannstr. 3, 85748, Garching b. München, Germany

    Moritz Simon & Michael Ulbrich

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  1. Moritz Simon
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  2. Michael Ulbrich
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Correspondence to Moritz Simon .

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Editors and Affiliations

  1. Department of Informatics, Technische Universität München, Munich, Germany

    Michael Bader

  2. Department of Informatics, Technische Universität München, Munich, Germany

    Hans-Joachim Bungartz

  3. Department of Informatics, Technische Universität München, Munich, Germany

    Tobias Weinzierl

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Simon, M., Ulbrich, M. (2013). Optimal Control of Partially Miscible Two-Phase Flow with Applications to Subsurface CO2 Sequestration. In: Bader, M., Bungartz, HJ., Weinzierl, T. (eds) Advanced Computing. Lecture Notes in Computational Science and Engineering, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38762-3_4

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