Physics-based Pre-conditioners for Large-scale Subsurface Flow Simulation

Gabriela Diaz Cortes, Kees Vuik, Jan Dirk Jansen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)
16 Downloads (Pure)


We consider deflation-based pre-conditioning of the pressure equation for large-scale reservoir models with strong spatial variations in the permeabilities. The use of deflation techniques involves the search for good deflation vectors, which usually are problem-dependent. We propose the use of proper orthogonal decomposition (POD) to generate physics-based problem-specific deflation vectors. The use of POD to construct pre-conditioners has been attempted before but in those applications, a snap-shot-based reducedorder basis was used as pre-conditioner directly whereas we propose the use of basis vectors as deflation vectors. We investigate the effectiveness of the method with numerical experiments using the conjugate gradient iterative method in combination with Incomplete Cholesky preconditioning (ICCG) and PODbased deflation (DICCG). We consider incompressible and compressible single-phase flow in a layered model with large variations in the permeability coefficients, and the SPE10 benchmark model. We obtain an important reduction for the number of iterations with our proposed DICCG method in comparison with the ICCG method. In some test problems, we achieve convergence within one DICCG iteration. However, our method requires a number of preparatory reservoir simulations proportional to the number of wells and the solution of an eigenvalue problem to compute the deflation vectors. This overhead will be justified in case of a large number of subsequent simulations with different control settings as typically required in numerical optimization or sensitivity studies.
Original languageEnglish
Title of host publicationProceedings of the 15th European Conference on the Mathematics of Oil Recovery
EditorsJ.D. Jansen
Place of PublicationHouten
Number of pages21
ISBN (Electronic)978-94-6282-193-4
Publication statusPublished - 2016
EventECMOR XV: 15th European Conference on the Mathematics of Oil Recovery - Amsterdam, Netherlands
Duration: 29 Aug 20161 Sep 2016


ConferenceECMOR XV
Abbreviated titleECMOR XV
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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  • POD-Based Deflation Method For Reservoir Simulation

    Diaz Cortes, G., 2019, Delft, the Netherlands. 156 p.

    Research output: ThesisDissertation (TU Delft)

    Open Access
    98 Downloads (Pure)

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