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    Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media

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    Type
    Article
    Authors
    Amir, Sahar cc
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2018-01-02
    Online Publication Date
    2018-01-02
    Print Publication Date
    2018-04
    Permanent link to this record
    http://hdl.handle.net/10754/626880
    
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    Abstract
    The heterogeneous natures of rock fabrics, due to the existence of multi-scale fractures and geological formations, led to the deviations from unity in the flux-equations fractional-exponent magnitudes. In this paper, the resulting non-Newtonian non-Darcy fractional-derivatives flux equations are solved using physics-preserving averaging schemes that incorporates both, original and shifted, Grunwald-Letnikov (GL) approximation formulas preserving the physics, by reducing the shifting effects, while maintaining the stability of the system, by keeping one shifted expansion. The proposed way of using the GL expansions also generate symmetrical coefficient matrices that significantly reduces the discretization complexities appearing with all shifted cases from literature, and help considerably in 2D and 3D systems. Systems equations derivations and discretization details are discussed. Then, the physics-preserving averaging scheme is explained and illustrated. Finally, results are presented and reviewed. Edge-based original GL expansions are unstable as also illustrated in literatures. Shifted GL expansions are stable but add a lot of additional weights to both discretization sides affecting the physical accuracy. In comparison, the physics-preserving averaging scheme balances the physical accuracy and stability requirements leading to a more physically conservative scheme that is more stable than the original GL approximation but might be slightly less stable than the shifted GL approximations. It is a locally conservative Single-Continuum averaging scheme that applies a finite-volume viewpoint.
    Citation
    Amir SZ, Sun S (2018) Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media. Journal of Petroleum Science and Engineering. Available: http://dx.doi.org/10.1016/j.petrol.2017.12.078.
    Sponsors
    We acknowledge that this work is supported by the KAUST research fund awarded through the KAUST-KFUPM Initiative (KKI) Program to the collaborative project on "Fractional Diffusion Modeling of Transport in the Environment".
    Publisher
    Elsevier BV
    Journal
    Journal of Petroleum Science and Engineering
    DOI
    10.1016/j.petrol.2017.12.078
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0920410517310355
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.petrol.2017.12.078
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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