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

Moritz Simon; Michael Ulbrich

doi:10.1007/978-3-642-38762-3_4

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

Moritz Simon, Michael Ulbrich

Research output: Chapter in Book/Report/Conference proceeding › Chapter

5 Scopus citations

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computational Science and Engineering
Publisher	Springer Nature
Pages	81-98
Number of pages	18
ISBN (Print)	9783642387616
DOIs	https://doi.org/10.1007/978-3-642-38762-3_4
State	Published - Jul 31 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): UK-C0020
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Optimal Control of Partially Miscible Two-Phase Flow with Applications to Subsurface CO2 Sequestration",

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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N2 - 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.

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

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