Constrained pressure residual multiscale (CPR-MS) method for fully implicit simulation of multiphase flow in porous media

Cusini, Matteo; Lukyanov, Alexander A.; Natvig, Jostein R.; Hajibeygi, Hadi

doi:10.1016/j.jcp.2015.07.019

Cited by 48 publications

(29 citation statements)

References 36 publications

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“…which means that the fracture-matrix coupling term is completely omit-ted in Eq (18). The prolongation is solved algebraically, as described in Appendix A.1.…”

Section: Basis Function Formulationsmentioning

confidence: 99%

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

źene

Kobaisi

Hajibeygi

2016

Journal of Computational Physics

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This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, a map between coarse-and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated:(1) Decoupled-AMS, in which the two media are completely decoupled, (2) Frac-AMS and (3) Rock-AMS, which take into account only one-way transmissibilities, and (4) Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two-and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.

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“…which means that the fracture-matrix coupling term is completely omit-ted in Eq (18). The prolongation is solved algebraically, as described in Appendix A.1.…”

Section: Basis Function Formulationsmentioning

confidence: 99%

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

źene

Kobaisi

Hajibeygi

2016

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

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“…When a large number of processor cores are used, a robust and scalable preconditioner is needed to keep the compute time at an acceptable level while maintaining the number of Krylov iterations. The constrained pressure residual (CPR) preconditioner is widely used in the community of reservoir simulation [15,38]. This is based on subblocks of the Jacobian matrix and uses an approximate pressure solve such as algebraic multigrid (AMG) [25] to constrain the residual of the full system, and thus is known as a physics-splitting approach.…”

Section: Introductionmentioning

confidence: 99%

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

Luo

Liu

Cai

et al. 2020

Journal of Computational Physics

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“…The standard reservoir simulator implementation [3][4][5][6][7][8][9] couples Incomplete LU (ILU) factorizations, effective for the hyperbolic part, with an algebraic multigrid (AMG) method, well-suited for the elliptic part. A variant of CPR preconditioning that replaces AMG by a multiscale finite volume (MSFV) or finite element (MSFE) solver was proposed in [10]. Using a multigrid reduction (MGR) approach [11], the CPR method has been generalized in a broader multigrid framework and successfully applied to multiphase flow and transport with phase transitions in [12,13].…”

Section: Introductionmentioning

confidence: 99%

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

White

Castelletto

Klevtsov

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Many applications involving porous media-notably reservoir engineering and geologic applications-involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton-Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. The key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

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Constrained pressure residual multiscale (CPR-MS) method for fully implicit simulation of multiphase flow in porous media

Cited by 48 publications

References 36 publications

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

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