Calculation of tensorial flow properties on pore level: Exploring the influence of boundary conditions on the permeability of three-dimensional stochastic reconstructions

Kirill M. Gerke, Marina V. Karsanina, Regina Katsman

Research output: Contribution to journalArticlepeer-review


While it is well known that permeability is a tensorial property, it is usually reported as a scalar property or only diagonal values are reported. However, experimental evaluation of tensorial flow properties is problematic. Pore-scale modeling using three-dimensional (3D) images of porous media with subsequent upscaling to a continuum scale (homogenization) is a valuable alternative. In this study, we explore the influence of different types of boundary conditions on the external walls of the representative modeling domain along the applied pressure gradient on the magnitude and orientation of the computed permeability tensor. To implement periodic flow boundary conditions, we utilized stochastic reconstruction methodology to create statistically similar (to real porous media structures) geometrically periodic 3D structures. Stochastic reconstructions are similar to encapsulation of the porous media into statistically similar geometrically periodic one with the same permeability tensor. Seven main boundary conditions (BC) were implemented: Closed walls, periodic flow, slip on the walls, linear pressure, translation, symmetry, and immersion. The different combinations of BCs amounted to a total number of 15 BC variations. All these BCs significantly influenced the resulting tensorial permeabilities, including both magnitude and orientation. Periodic boundary conditions produced the most physical flow patterns, while other classical BCs either suppressed crucial transversal flows or resulted in unphysical currents. Our results are crucial to performing flow properties upscaling and will be relevant to computing not only single-phase but also multiphase flow properties. Moreover, other calculation of physical properties such as some mechanical, transport, or heat conduction properties may benefit from the technique described in this study.

Original languageEnglish
Article number053312
JournalPhysical Review E
Issue number5
StatePublished - 20 Nov 2019

Bibliographical note

Funding Information:
We thank our colleagues Dr. Dina Gafurova and Prof. Elena Skvortsova for the 2D images of porous media used in this work. We also thank Peleg Haruzi and Prof. Igor Bogdanov for sharing their experiences on modeling with Comsol. K.M.G. acknowledges early fruitful tensor discussions with Prof. Pavel Bedrikovetsky and Dr. Mohammad Sedaghat. We are indebted to Dr. Sergey Yankin from Russian Comsol Support for providing technical assistance that contributed to the completion of this study. This research was supported by the Russian Science Foundation Grant No. 17-17-01310 and by Institutional Postdoctoral Fellowships from the University of Haifa, Israel. Collaborative effort of the authors is within the Flow and Transport in Media with Pores research group and uses some of its software. We thank two anonymous reviewers for constructive comments which helped to improve our original manuscript. Author contributions: K.M.G. conceived this research; M.V.K. performed stochastic reconstructions and provided programming support; K.M.G. and R.K. performed modeling and all simulations; K.M.G. analyzed the results and wrote the manuscript; all authors reviewed the final version of the paper.

Publisher Copyright:
© 2019 American Physical Society.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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