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Upscaling non-Darcy flow using mixed finite element method Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/4j03d236h

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  • In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite element spaces. The resulting non-linear system is solved using fixed point iteration; we provide sufficient conditions for this iteration to converge. Then we formulate an upscaling method for non-Darcy flow extending a method by Durlofsky originally given for Darcy flow. The method computes effective coefficients which can be used to simulate the Darcy flow on a coarse grid. We compare numerical results for Darcy and non-Darcy flow and upscaling results for two scenarios; in all cases results apply to a problem with rate-specified wells.
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