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

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    Type
    Book Chapter
    Authors
    Simon, Moritz
    Ulbrich, Michael
    KAUST Grant Number
    UK-C0020
    Date
    2013-07-31
    Online Publication Date
    2013-07-31
    Print Publication Date
    2013
    Permanent link to this record
    http://hdl.handle.net/10754/599090
    
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    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.
    Citation
    Simon M, Ulbrich M (2013) Optimal Control of Partially Miscible Two-Phase Flow with Applications to Subsurface CO2 Sequestration. Advanced Computing: 81–98. Available: http://dx.doi.org/10.1007/978-3-642-38762-3_4.
    Sponsors
    This publication is based on work supported by Award No. UK-C0020, madeby King Abdullah University of Science and Technology (KAUST). The work was conductedfor the MAC-KAUST project K1 “Simulating CO2 Sequestration” within the Munich Centre ofAdvanced Computing (MAC) at TUM. The authors gratefully acknowledge this support as well asthe grant DFG INST 95/919-1 FUGG that provided partial funding of the compute cluster used forthe computations. Moreover, the authors would like to thank Michael Bader for handling the paperand the three referees for their valuable comments.
    Publisher
    Springer Nature
    Journal
    Lecture Notes in Computational Science and Engineering
    DOI
    10.1007/978-3-642-38762-3_4
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-642-38762-3_4
    Scopus Count
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