Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

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, Journal Name: Advances in Water Resources Journal Issue: C Vol. 114; ISSN 0309-1708
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (33)

A Multigrid Method Based on Incomplete Gaussian Elimination journal September 1996
Some Preconditioning Techniques for Saddle Point Problems book January 2008
Results of the MoMaS benchmark for gas phase appearance and disappearance using generalized MHFE journal November 2014
A Preconditioned Iterative Method for Saddlepoint Problems journal July 1992
On the Approximate Cyclic Reduction Preconditioner journal January 1999
A Multigrid Method Based on Incomplete Gaussian Elimination journal September 1996
Multilevel block factorizations in generalized hierarchical bases journal January 2002
An algorithm for profile and wavefront reduction of sparse matrices journal February 1986
hypre: A Library of High Performance Preconditioners
  • Falgout, Robert D.; Yang, Ulrike Meier; Goos, Gerhard
  • Computational Science — ICCS 2002: International Conference Amsterdam, The Netherlands, April 21–24, 2002 Proceedings, Part III https://doi.org/10.1007/3-540-47789-6_66
book April 2002
Schur-complement multigrid journal February 1997
Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository journal August 2008
Fully coupled generalised hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part II: numerical scheme and numerical results journal February 2012
Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase journal October 2012
Method of Negative Saturations for Modeling Two-phase Compositional Flow with Oversaturated Zones journal December 2008
A note on MGR methods journal February 1983
Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media journal January 1995
BoomerAMG: A parallel algebraic multigrid solver and preconditioner journal April 2002
On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media journal April 2001
A new approach for phase transitions in miscible multi-phase flow in porous media journal August 2011
A generalized Block FSAI preconditioner for nonsymmetric linear systems journal January 2014
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations journal January 2008
Constrained pressure residual multiscale (CPR-MS) method for fully implicit simulation of multiphase flow in porous media journal October 2015
Analytical decoupling techniques for fully implicit reservoir simulation journal May 2017
Gas phase appearance and disappearance as a problem with complementarity constraints journal May 2014
Block Preconditioners Based on Approximate Commutators journal January 2006
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems journal July 1986
Parallel Time Integration with Multigrid journal January 2014
ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier--Stokes Equations journal January 2015
Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media journal January 2017
The Primal-Dual Active Set Strategy as a Semismooth Newton Method journal January 2002
The Incomplete Factorization Multigraph Algorithm journal January 1999
On the Approximate Cyclic Reduction Preconditioner journal January 1999
A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils1 journal January 1980

Figures / Tables (13)

Fig. 1(p. 11)figure Fig. 1
Fig. 2(p. 12)figure Fig. 2
Table 1(p. 12)table Table 1
Table 2(p. 12)table Table 2
Table 3(p. 12)table Table 3
Fig. 3(p. 13)figure Fig. 3
Fig. 4(p. 14)figure Fig. 4
Fig. 5(p. 14)figure Fig. 5
Table 4(p. 15)table Table 4
Table 5(p. 15)table Table 5
Table 6(p. 15)table Table 6
Fig. 6(p. 16)figure Fig. 6
Fig. 7(p. 16)figure Fig. 7

Similar Records

Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media
Journal Article · Wed Oct 25 20:00:00 EDT 2017 · SIAM Journal on Scientific Computing · OSTI ID:1505960
Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems
Conference · Mon Feb 21 23:00:00 EST 2000 · OSTI ID:15006488
A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media
Journal Article · Wed Mar 11 20:00:00 EDT 2020 · SIAM Journal on Scientific Computing · OSTI ID:1607853

Related Subjects

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