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Prediction of the low-velocity distribution from the pore structure in simple porous media

Pietro de Anna1,*, Bryan Quaife2,†, George Biros3,‡, and Ruben Juanes4,§

  • 1Institut des Sciences de la Terre, University of Lausanne, Lausanne 1015, Switzerland
  • 2Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, USA
  • 3Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Austin, Texas 78712, USA
  • 4Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

  • *pietro.deanna@unil.ch
  • †bquaife@fsu.edu
  • ‡gbiros@acm.org
  • §juanes@mit.edu
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Phys. Rev. Fluids 2, 124103 – Published 22 December, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.124103

Abstract

The macroscopic properties of fluid flow and transport through porous media are a direct consequence of the underlying pore structure. However, precise relations that characterize flow and transport from the statistics of pore-scale disorder have remained elusive. Here we investigate the relationship between pore structure and the resulting fluid flow and asymptotic transport behavior in two-dimensional geometries of nonoverlapping circular posts. We derive an analytical relationship between the pore throat size distribution fλ∼λ−β and the distribution of the low fluid velocities fu∼u−β/2, based on a conceptual model of porelets (the flow established within each pore throat, here a Hagen-Poiseuille flow). Our model allows us to make predictions, within a continuous-time random-walk framework, for the asymptotic statistics of the spreading of fluid particles along their own trajectories. These predictions are confirmed by high-fidelity simulations of Stokes flow and advective transport. The proposed framework can be extended to other configurations which can be represented as a collection of known flow distributions.

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Phys. Rev. Fluids 2, 124103– Published 22 December, 2017
  • Received 18 July 2017
Article part of CHORUS

©2017 American Physical Society

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