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    Complexity reduction of multi-phase flows in heterogeneous porous media

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    Type
    Conference Paper
    Authors
    Ghommem, Mehdi
    Calo, Victor M. cc
    Efendiev, Yalchin R. cc
    Gildin, Eduardo G.
    KAUST Department
    Applied Mathematics and Computational Science Program
    Biological and Environmental Sciences and Engineering (BESE) Division
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2013-10-08
    Online Publication Date
    2013-10-08
    Print Publication Date
    2013
    Permanent link to this record
    http://hdl.handle.net/10754/564668
    
    Metadata
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    Abstract
    In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in highly heterogeneous porous media. We propose intrusive and non-intrusive model reduction approaches that enable a significant reduction in the dimension of the flow problem size while capturing the behavior of the fully-resolved solutions. In one approach, we employ the dynamic mode decomposition (DMD) and the discrete empirical interpolation method (DEIM). This approach does not require any modification of the reservoir simulation code but rather postprocesses a set of global snapshots to identify the dynamically-relevant structures associated with the flow behavior. In a second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper orthogonal decomposition (POD) modes. Furthermore, we use DEIM to approximate the mobility related term in the global system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE 10 benchmark permeability field and present a variety of numerical examples of two-phase flow and transport. The proposed model reduction methods can be efficiently used when performing uncertainty quantification or optimization studies and history matching.
    Citation
    Ghommem, M., Calo, V., Efendiev, Y., & Gildin, E. (2013). Complexity Reduction of Multi-Phase Flows in Heterogeneous Porous Media. SPE Kuwait Oil and Gas Show and Conference. doi:10.2118/167295-ms
    Publisher
    Society of Petroleum Engineers (SPE)
    Journal
    SPE Kuwait Oil and Gas Show and Conference
    Conference/Event name
    Kuwait Oil and Gas Show and Conference, KOGS 2013
    ISBN
    9781629932149
    DOI
    10.2118/167295-ms
    ae974a485f413a2113503eed53cd6c53
    10.2118/167295-ms
    Scopus Count
    Collections
    Conference Papers; Biological and Environmental Science and Engineering (BESE) Division; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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