On an asymptotic expansion for porous media flow of Carreau fluids

• Porous media flow of polymers with Carreau law viscosities and their application to enhanced oil recovery (EOR) is considered. Applying the homogenization method leads to a nonlinear two-scale problem. In case of a small difference between the Carreau and the Newtonian case an asymptotic expansion based on the small deviation of the viscosity from the Newtonian case is introduced. For uni-directional pressure gradients, which is a reasonable assumption in applications like EOR, auxiliary problems to decouple the micro- from the macrovariables are derived. The microscopic flow field obtained by the proposed approach is compared to the solution of the two-scale problem. Finite element calculations for an isotropic and an anisotropic pore cell geometries are used to validate the accuracy and speed-up of the proposed approach. The order of accuracy has been studied by performing the simulations up to the third order expansion for the isotropic geometry.

Author: Thomas Götz, Hanna Parhusip urn:nbn:de:hbz:386-kluedo-13473 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (260) Preprint English 2004 2004 Technische Universität Kaiserslautern 2004/09/09 Carreau law; porous media flow ; two-scale expansion Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Sxx Flows in porous media; filtration; seepage / 76S05 Flows in porous media; filtration; seepage Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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