Computational Geosciences

, Volume 22, Issue 3, pp 925–950 | Cite as

Hybrid three-scale model for evolving pore-scale geometries

  • Timothy B. Costa
  • Kenneth Kennedy
  • Malgorzata Peszynska
Original paper


We consider flow and upscaling of flow properties from pore scale to Darcy scale, when the pore-scale geometry is changing. The idea is to avoid having to solve for the pore evolution at the pore scale, because this results in unmanageable complexity. We propose to use stochastic modeling to parametrize plausible modifications of the pore geometry and to construct distributions of permeability parametrized by Darcy-scale variables. To localize the effects of, e.g., clogging, we introduce an intermediate scale of pore-network models. We use local Stokes solvers to calibrate the throat permeability.


Pore-scale simulations Pore-network models Flow and transport evolving geometries Upscaling Downscaling Random geometries Immersed volume Stokes model 


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Wewould like to gratefully acknowledge the collaborations with two colleagues, and our financial support. We also appreciate the comments from anonymous reviewers which helped to improve this manuscript.

Dr Anna Trykozko from University of Warsaw helped us to validate the software HybGe-Flow3D by running comparisons of permeabilities we obtained with those reported in [46], which were based on flow simulations with ANSYS Fluent.

We also want to thank Dr Masa Prodanovic from The University of Texas at Austin who helped us with the software 3DMA-Rock for pore–network extraction [33].

Funding information

This work was partially supported by the grants NSF DMS-1115827 and NSF DMS-1522734. This research was partially supported by the grants NSF DMS-1115827 and NSF DMS-1522734.


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Authors and Affiliations

  1. 1.Numerical Solutions, IncCorvallisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

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