Two-Stage Algebraic Multiscale Linear Solver for Highly Heterogeneous Reservoir Models
- Authors
- Hui Zhou (ConocoPhillips Subsurface Technology) | Hamdi A. Tchelepi (Stanford University)
- DOI
- https://doi.org/10.2118/141473-PA
- Document ID
- SPE-141473-PA
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Journal
- Volume
- 17
- Issue
- 02
- Publication Date
- June 2012
- Document Type
- Journal Paper
- Pages
- 523 - 539
- Language
- English
- ISSN
- 1086-055X
- Copyright
- 2012. Society of Petroleum Engineers
- Disciplines
- 4.1.2 Separation and Treating, 4.3.4 Scale
- Keywords
- Large-scale simulation, Reservoir Simulation, Multiscale method
- Downloads
- 1 in the last 30 days
- 445 since 2007
- Show more detail
- View rights & permissions
| SPE Member Price: | USD 10.00 |
| SPE Non-Member Price: | USD 30.00 |
Summary
An efficient two-stage algebraic multiscale solver (TAMS) that converges to the fine-scale solution is described. The first (global) stage is a multiscale solution obtained algebraically for the given fine-scale problem. In the second stage, a local preconditioner, such as the Block ILU (BILU) or the Additive Schwarz (AS) method, is used. Spectral analysis shows that the multiscale solution step captures the low-frequency parts of the error spectrum quite well, while the local preconditioner represents the high-frequency components accurately. Combining the two stages in an iterative scheme results in efficient treatment of all the error components associated with the fine-scale problem. TAMS is shown to converge to the reference fine-scale solution. Moreover, the eigenvalues of the TAMS iteration matrix show significant clustering, which is favorable for Krylov-based methods. Accurate solution of the nonlinear saturation equations (i.e., transport problem) requires having locally conservative velocity fields. TAMS guarantees local mass conservation by concluding the iterations with a multiscale finite-volume step. We demonstrate the performance of TAMS using several test cases with strong permeability heterogeneity and large-grid aspect ratios. Different choices in the TAMS algorithm are investigated, including the Galerkin and finite-volume restriction operators, as well as the BILU and AS preconditioners for the second stage. TAMS for the elliptic flow problem is comparable to state-of-the-art algebraic multigrid methods, which are in wide use. Moreover, the computational time of TAMS grows nearly linearly with problem size.
| File Size | 4 MB | Number of Pages | 17 |
References
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