Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs

Handle URI:
http://hdl.handle.net/10754/597465
Title:
Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs
Authors:
Simon, Moritz; Ulbrich, Michael
Abstract:
© 2014, Springer Science+Business Media New York. With the target of optimizing CO2 sequestration in underground reservoirs, we investigate constrained optimal control problems with partially miscible two-phase flow in porous media. Our objective is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE system, formulate the optimal control problem and derive the continuous adjoint equations. For the discretization we apply a variant of the so-called BOX method, a locally conservative control-volume FE method that we further stabilize by a periodic averaging feature to reduce oscillations. The timestep-wise Lagrange function of the control problem is implemented as a variational form in Sundance, a toolbox for rapid development of parallel FE simulations, which is part of the HPC software Trilinos. We discuss the BOX method and our implementation in Sundance. The MPI parallelized Sundance state and adjoint solvers are linked to the interior point optimization package IPOPT, using limited-memory BFGS updates for approximating second derivatives. Finally, we present and discuss different types of optimal control results.
Citation:
Simon M, Ulbrich M (2014) Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs. Optim Eng 16: 103–130. Available: http://dx.doi.org/10.1007/s11081-014-9270-x.
Publisher:
Springer Science + Business Media
Journal:
Optimization and Engineering
KAUST Grant Number:
UK-C0020
Issue Date:
14-Nov-2014
DOI:
10.1007/s11081-014-9270-x
Type:
Article
ISSN:
1389-4420; 1573-2924
Sponsors:
The support from Award No. UK-C0020, made by King Abdullah University of Science and Technology (KAUST) is gratefully acknowledged. This work was conducted as part of the MAC-KAUST project K1 "Simulating CO<INF>2</INF> Sequestration" within the Munich Centre of Advanced Computing (MAC) at TUM. The computations were performed on a compute cluster that was partially funded by DFG INST 95/919-1 FUGG. Finally, we thank the referees for their valuable suggestions that helped us to improve the quality of the article.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSimon, Moritzen
dc.contributor.authorUlbrich, Michaelen
dc.date.accessioned2016-02-25T12:40:16Zen
dc.date.available2016-02-25T12:40:16Zen
dc.date.issued2014-11-14en
dc.identifier.citationSimon M, Ulbrich M (2014) Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs. Optim Eng 16: 103–130. Available: http://dx.doi.org/10.1007/s11081-014-9270-x.en
dc.identifier.issn1389-4420en
dc.identifier.issn1573-2924en
dc.identifier.doi10.1007/s11081-014-9270-xen
dc.identifier.urihttp://hdl.handle.net/10754/597465en
dc.description.abstract© 2014, Springer Science+Business Media New York. With the target of optimizing CO2 sequestration in underground reservoirs, we investigate constrained optimal control problems with partially miscible two-phase flow in porous media. Our objective is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE system, formulate the optimal control problem and derive the continuous adjoint equations. For the discretization we apply a variant of the so-called BOX method, a locally conservative control-volume FE method that we further stabilize by a periodic averaging feature to reduce oscillations. The timestep-wise Lagrange function of the control problem is implemented as a variational form in Sundance, a toolbox for rapid development of parallel FE simulations, which is part of the HPC software Trilinos. We discuss the BOX method and our implementation in Sundance. The MPI parallelized Sundance state and adjoint solvers are linked to the interior point optimization package IPOPT, using limited-memory BFGS updates for approximating second derivatives. Finally, we present and discuss different types of optimal control results.en
dc.description.sponsorshipThe support from Award No. UK-C0020, made by King Abdullah University of Science and Technology (KAUST) is gratefully acknowledged. This work was conducted as part of the MAC-KAUST project K1 "Simulating CO<INF>2</INF> Sequestration" within the Munich Centre of Advanced Computing (MAC) at TUM. The computations were performed on a compute cluster that was partially funded by DFG INST 95/919-1 FUGG. Finally, we thank the referees for their valuable suggestions that helped us to improve the quality of the article.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectAdjoint approachen
dc.subjectCO<inf>2</inf> sequestrationen
dc.subjectComplementarity conditionen
dc.subjectControl-volume FE methoden
dc.subjectOptimal controlen
dc.subjectPartially miscible two-phase flowen
dc.titleAdjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirsen
dc.typeArticleen
dc.identifier.journalOptimization and Engineeringen
dc.contributor.institutionTechnische Universitat Munchen, Munich, Germanyen
kaust.grant.numberUK-C0020en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.