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    Fast multiscale reservoir simulations using POD-DEIM model reduction

    Access Status
    Fulltext not available
    Authors
    Ghasemi, M.
    Yang, Y.
    Gildin, E.
    Efendiev, Y.
    Calo, Victor
    Date
    2015
    Type
    Conference Paper
    
    Metadata
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    Citation
    Ghasemi, M. and Yang, Y. and Gildin, E. and Efendiev, Y. and Calo, V. 2015. Fast multiscale reservoir simulations using POD-DEIM model reduction, in SPE Reservoir Simulation Symposium, 23-25 February, Houston, Texas, USA, pp. 1393-1410.
    Source Title
    Society of Petroleum Engineers - SPE Reservoir Simulation Symposium 2015
    DOI
    10.2118/173271-MS
    ISBN
    9781510800618
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51318
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we present a global-local model reduction for fast multiscale reservoir simulations in highly heterogeneous porous media with applications to optimization and history matching. Our proposed approach identifies a low dimensional structure of the solution space. We introduce an auxiliary variable (the velocity field) in our model reduction that allows achieving a high degree of model reduction. The latter is due to the fact that the velocity field is conservative for any low-order reduced model in our framework. Because a typical global model reduction based on POD is a Galerkin finite element method, and thus it can not guarantee local mass conservation. This can be observed in numerical simulations that use finite volume based approaches. Discrete Empirical Interpolation Method (DEIM) is used to approximate the nonlinear functions of fine-grid functions in Newton iterations. This approach allows achieving the computational cost that is independent of the fine grid dimension. POD snapshots are inexpensively computed using local model reduction techniques based on Generalized Multiscale Finite Element Method (GMsFEM) which provides (1) a hierarchical approximation of snapshot vectors (2) adaptive computations by using coarse grids (3) inexpensive global POD operations in a small dimensional spaces on a coarse grid. By balancing the errors of the global and local reduced-order models, our new methodology can provide an error bound in simulations. Our numerical results, utilizing a two-phase immiscible flow, show a substantial speed-up and we compare our results to the standard POD-DEIM in finite volume setup.

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