Physics-preserving averaging scheme based on Grunwald-Letnikov formula for gas flow in fractured media
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ArticleAuthors
Amir, Sahar
Sun, Shuyu

KAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2018-01-02Online Publication Date
2018-01-02Print Publication Date
2018-04Permanent link to this record
http://hdl.handle.net/10754/626880
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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 BVAdditional Links
http://www.sciencedirect.com/science/article/pii/S0920410517310355ae974a485f413a2113503eed53cd6c53
10.1016/j.petrol.2017.12.078