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    Fast multiscale reservoir simulations with POD-DEIM model reduction

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    Type
    Conference Paper
    Authors
    Yang, Yanfang
    Ghasemi, Mohammadreza
    Gildin, Eduardo
    Efendiev, Yalchin R. cc
    Calo, Victor
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-12-14
    Online Publication Date
    2015-02-23
    Print Publication Date
    2015
    Permanent link to this record
    http://hdl.handle.net/10754/593278
    
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    Abstract
    We present a global/local model reduction for fast multiscale reservoir simulations in highly heterogeneous porous media. Our approach identifies a low-dimensional structure in the solution space. We introduce an auxiliary variable (the velocity field) in our model reduction that achieves a high compression of the model. This compression is achieved because the velocity field is conservative for any low-order reduced model in our framework, whereas a typical global model reduction that is based on proper-orthogonaldecomposition (POD) Galerkin projection cannot guarantee local mass conservation. The lack of mass conservation can be observed in numerical simulations that use finite-volume-based approaches. The discrete empirical interpolation method (DEIM) approximates fine-grid nonlinear functions in Newton iterations. This approach delivers an online computational cost that is independent of the fine-grid dimension. POD snapshots are inexpensively computed with local model-reduction techniques that are based on the generalized multiscale finite-element method (GMsFEM) that provides (1) a hierarchical approximation of the snapshot vectors, (2) adaptive computations with coarse grids, and (3) inexpensive global POD operations in small dimensional spaces on a coarse grid. By balancing the errors of the global and local reduced-order models, our new methodology provides an error bound in simulations. Our numerical results, by use of a two-phase immiscible flow, show a substantial speedup, and we compare our results with the standard POD-DEIM in a finite-volume setup.
    Citation
    Yang, Y., Ghasemi, M., Gildin, E., Efendiev, Y., & Calo, V. (2016). Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction. SPE Journal, 21(06), 2141–2154. doi:10.2118/173271-pa
    Sponsors
    Eduardo Gildin and Yalchin Efendiev acknowledge the partial support of the US Department of Defence Army ARO Project under grant number W911NF-12-1-0206. This publication also was made possible by National Priorities Research Program grant 7-1482-1278 from the Qatar National Research Fund (a member of The Qatar Foundation). Yalchin Efendiev would like to thank the partial support from the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under award number DE-FG02-13ER26165.
    Publisher
    Society of Petroleum Engineers (SPE)
    Journal
    SPE Reservoir Simulation Symposium
    Conference/Event name
    SPE Reservoir Simulation Symposium
    DOI
    10.2118/173271-PA
    Additional Links
    http://www.onepetro.org/doi/10.2118/173271-PA
    ae974a485f413a2113503eed53cd6c53
    10.2118/173271-PA
    Scopus Count
    Collections
    Conference Papers; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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