Analysis of upscaling absolute permeability

By Xiao-hui Wu, Yalchin R. Efendiev, Thomas Y. Hou. 2002

293 citations recorded by the source corpus.

Flow based upscaling of absolute permeability has become an important step in practical simulations of flow through heterogeneous formations. The central idea is to compute upscaled, grid-block permeability from fine scale solutions of the flow equation. Such solutions can be either local in each grid-block or global in the whole domain. It is well-known that the grid-block permeability may be strongly influenced by the boundary conditions imposed on the flow equations and the size of the grid-blocks. We show that the upscaling errors due to both effects manifest as the resonance between the small physical scales of the media and the artificial size of the grid blocks. To obtain precise error estimates, we study the scale-up of single phase steady flows through media with periodic small scale heterogeneity. As demonstrated by our numerical experiments, these estimates are also useful for understanding the upscaling of general random media. It is further shown that the oversampling technique introduced in our previous work can be used to reduce the resonance error and obtain boundary-condition independent, grid-block permeability. Some misunderstandings in scale up studies are also clarified in this work.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b0b95556e6d1214e4b7856df7b340d279fbacbb1

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation (2004, background): “[25]), which is characterized by the ratio between the small scale of the media and the grid scale (size).”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “The multiscale finite element method can be used for such a purpose [122].”
Permeability tensor of three‐dimensional fractured porous rock and a comparison to trace map predictions (2014, background): “Other authors refer to similar approaches as “flow jacket” or “oversampling” and find that this procedure reduces boundary effects and better reflects the connectivity of the sampling domain [e.g., Holden and Lia, 1992; Wu et al., 2002].”