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Title: Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]

Journal Article · · Advances in Water Resources
 [1];  [2];  [2]
  1. Univ. of Maryland, College Park, MD (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
+ Show Author Affiliations

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 two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1438746
Alternate ID(s):
OSTI ID: 2325525
Report Number(s):
LLNL-JRNL-734458
Journal Information:
Advances in Water Resources, Vol. 114, Issue C; ISSN 0309-1708
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 16 works
Citation information provided by
Web of Science

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Figures / Tables (13)

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Related Subjects

58 GEOSCIENCES
02 PETROLEUM
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Algebraic multigrid
Preconditioning
Compositional two-phase flow
Phase transitions
Nonlinear complementarity problem