Algebraic multigrid preconditioners for twophase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]
Abstract
Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to dealmore »
 Authors:

 Univ. of Maryland, College Park, MD (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1438746
 Report Number(s):
 LLNLJRNL734458
Journal ID: ISSN 03091708
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Advances in Water Resources
 Additional Journal Information:
 Journal Volume: 114; Journal Issue: C; Journal ID: ISSN 03091708
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES; 02 PETROLEUM; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Algebraic multigrid; Preconditioning; Compositional twophase flow; Phase transitions; Nonlinear complementarity problem
Citation Formats
Bui, Quan M., Wang, Lu, and OseiKuffuor, Daniel. Algebraic multigrid preconditioners for twophase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]. United States: N. p., 2018.
Web. doi:10.1016/j.advwatres.2018.01.027.
Bui, Quan M., Wang, Lu, & OseiKuffuor, Daniel. Algebraic multigrid preconditioners for twophase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]. United States. doi:10.1016/j.advwatres.2018.01.027.
Bui, Quan M., Wang, Lu, and OseiKuffuor, Daniel. Tue .
"Algebraic multigrid preconditioners for twophase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]". United States. doi:10.1016/j.advwatres.2018.01.027. https://www.osti.gov/servlets/purl/1438746.
@article{osti_1438746,
title = {Algebraic multigrid preconditioners for twophase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]},
author = {Bui, Quan M. and Wang, Lu and OseiKuffuor, Daniel},
abstractNote = {Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of twophase, twocomponent flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.},
doi = {10.1016/j.advwatres.2018.01.027},
journal = {Advances in Water Resources},
number = C,
volume = 114,
place = {United States},
year = {2018},
month = {2}
}
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