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Fingering patterns in hierarchical porous media

Si Suo1, Mingchao Liu2,3, and Yixiang Gan1,*

  • 1School of Civil Engineering, University of Sydney, Sydney, New South Wales 2006, Australia
  • 2Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
  • 3Department of Engineering Mechanics, CNMM & AML, Tsinghua University, Beijing 100084, China

  • *Corresponding author: yixiang.gan@sydney.edu.au
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Phys. Rev. Fluids 5, 034301 – Published 9 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034301

Abstract

Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes, and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviors in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. Divided by the breakthrough, such a displacement process includes pre- and postbreakthrough stages during which the fingering evolution is dominated by viscous and capillary effects, respectively. Through conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterize the fingering dynamics in hierarchical porous media, a phase diagram, which describes the switch among the three fingering modes (the suppressing, crossover, and dendrite mode), is constructed by introducing a scaling parameter, i.e., the ratio of timescales considering the combined effect of characteristic pore sizes and wettability. The findings presented in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.

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Phys. Rev. Fluids 5, 034301– Published 9 March, 2020
  • Received 22 April 2019
  • Accepted 11 February 2020
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