Transport in Porous Media

, Volume 128, Issue 1, pp 243–269 | Cite as

3D Microscale Flow Simulation of Shear-Thinning Fluids in a Rough Fracture

  • Min ZhangEmail author
  • Maša Prodanović
  • Maryam Mirabolghasemi
  • Jianlin Zhao


The shear-thinning fluid flow in rough fractures is of wide interest in subsurface engineering. Inertial effects due to flow regime, fracture aperture variations as well as fluid rheology affect the macroscopic flow parameters in an interrelated way. We present a 3D microscale flow simulation for both Newtonian and Cross power-law shear-thinning fluids through a rough fracture over a range of flow regimes, thus evaluating the critical Reynolds number above which the linear Darcy’s law is no longer applicable. The flow domain is extracted from a computed microtomography image of a fractured Berea sandstone. The fracture aperture is much more variable than any of the previous numerical or experimental work involving shear-thinning fluids, and simulations are 3D for the first time. We quantify the simulated velocity fields and propose a new correlation for shift factor (parameter relating in situ porous medium viscosity with bulk viscosity). The correlation incorporates tortuosity (parameter calculated either based only on fracture image or on detailed velocity field, if available) as well as a fluid-dependent parameter obtained from the analytical/semi-analytical solutions of the same shear-thinning fluids flow in a smooth slit. Our results show that the shift factor is dependent on both the fracture aperture distribution (not only the hydraulic/equivalent aperture) and fluid rheology properties. However, both the inertial coefficient and critical Reynolds number are functions of the fracture geometry only, which is consistent with a recent experimental study.


Shear-thinning fluid Computational fluid dynamics Realistic rough fracture Forchheimer’s law Shift factor 



M. Z. would like to thank China Scholarship Council (CSC) for supporting her Ph.D. study at The University of Texas at Austin. M. P. has been supported by NSF EarthCube Grant 1541008. The authors also would like to thank the Texas Advanced Computing Center (TACC) for providing valuable technical support and its state-of-the-art computing resources ( The fracture image used in this study is publicly available on Digital Rocks Portal (Karpyn et al. 2016); before the final version of this paper is accepted, we will post a selection of flow fields from this study in the same repository.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Hildebrand Department of Petroleum and Geosystems EngineeringThe University of Texas at AustinAustinUSA
  2. 2.Dave C. Swalm School of Chemical EngineeringMississippi State UniversityStarkvilleUSA
  3. 3.Chair of Building Physics, Department of Mechanical and Process EngineeringETH Zurich (Swiss Federal Institute of Technology in Zurich)ZurichSwitzerland

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