Influence of multiscale surface roughness on permeability in fractures


Flow through rough fracture is common in numerous geotechnical and geological applications. Therefore, understanding this flow is important for improving the accuracy of mass- and energy-transport modeling and transportation. Several methods are available for quantifying fluid flow through rough fractures. Although this flow can be described fully using Navier-Stokes equations, these equations are generally difficult to solve due to the presence of a nonlinear term due to inertia. Simplified Navier-Stokes equations have been applied to overcome this problem, including ignoring the inertia term and reducing the equation to the Reynolds equation. Nevertheless, the applicability of Reynolds equation is limited due to the effects of roughness or inertia force.

With recent advancements in numerical methods for solving nonlinear Navier-Stokes equations, there is remarkable progress in studying the impact of surface fracture on the flow of fluid in rough fractures. Additionally, the roughness in the random rough surfaces can be categorized as small-scale unevenness or large-scale unevenness, also known as primary and secondary roughness, respectively. To this end, wavelet analysis technique has been adopted to study the impact of roughness on nonlinear flow in different rough fractures. It is effective for investigating the effects of the roughness of different scales. However, its drawbacks, including the difficulty in defining the cut-off length separating the low- and high-frequency unevenness and the problem of quantifying the permeability-related error when some high-frequency roughness is neglected, limit its practical applications.

Herein, Dr. Zhongzheng Wang, Dr. Yanyao Bao, and Professor Yixiang Gan from The University of Sydney in collaboration with Professor Jean-Michel Pereira from Ecole des Ponts ParisTech and Professor Emilie Sauret from Queensland University of Technology studied the influence of multiscale surface roughness on the permeability of fluid flow in rough fractures. Wavelet analysis technique was employed to decompose the random rough fractal surfaces with controlled dimensions and different relative roughness. Different frequencies of the surface topology were progressively filtered in a level-by-level procedure while keeping the large-scale waviness constant. A series of direct numerical simulations were carried out across different fracture spacings, flow conditions, surface profiles and relative roughness to examine the individual effects of surface roughness on different scales. The work is published in the journal, Physical Review Fluids.

The research team revealed in-depth details about the impacts of relative surface roughness on the nonlinear flow behavior across a spectrum of length scales. The onset of the resulting nonlinear flow behavior was described using the pressure gradient vs flow rate curves. The effects were associated with the formation of eddy currents with an increase in the Reynolds number, which was attributed to the relative effects of the inertial force. This phenomenon was well illustrated using Forchheimer’s law.

Considering the effects of high-frequency roughness (smaller scale) improved the sensitivity of the apparent permeability to Reynolds number. Consequently, an increase in smaller fracture spacing enhanced the sensitivity of the apparent permeability to both Reynolds number and roughness. An error index was proposed to quantify the relative error in predicting permeability associated with limited resolution in describing the surface profile. The results showed that the relative error could be well described over a wide range of flow and fracture conditions using the proposed error index.

In summary, the study reported the effectiveness of direct numerical simulation in exploring the effects of multiscale roughness on the permeability in rough fracture. The study improved the understanding of the role of multiscale roughness on fluid flow in rough fractures and would facilitate the accurate determination of permeability and surface profile resolution for numerical and experimental investigations. In a statement to Advances in Engineering, Professor Yixiang Gan the corresponding author, said that their findings would significantly contribute to accurate modeling and interpretation of mass transport processes through fractured networks.

Influence of multiscale surface roughness on permeability in fractures - Advances in Engineering
Qualitatively show impact of approximation level & relative roughness

Influence of multiscale surface roughness on permeability in fractures - Advances in Engineering

About the author

Dr Yixiang Gan is currently Associate Professor at the School of Civil Engineering and Deputy Director of Sydney Nano Institute, The University of Sydney, Australia. He received his Dr.-Ing from Karlsruhe Institute of Technology, Germany. After joining The University in 2010, he has been developing his research group with unique data-driven modelling and experimental capabilities to optimize engineering solutions for energy storage.

His research contains a balance between engineering applications addressing grand challenges and curiosity-driven topics transforming fundamental understanding. He has been an active researcher in the mechanics and physics of granular materials from microstructure-informed approaches. His research areas include mechanics of granular and porous media, mechanics of interfaces, and energy geotechnics. He was a recipient of ARC Discovery Early Career Researcher Award (DECRA), SOAR Fellowship, and Endeavour Leadership Awards.


Wang, Z., Bao, Y., Pereira, J., Sauret, E., & Gan, Y. (2022). Influence of multiscale surface roughness on permeability in fracturesPhysical Review Fluids, 7(2), 024101-13.

Go To Physical Review Fluids

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