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Towards a Better Understanding of the Impact of Fracture Roughness on Permeability-Stress Relationships using First Principles (2011-2017)

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Investigator(s): Carla Co

Accurate modeling of fracture flow behavior is important for tight reservoirs, such as shale gas and geothermal systems, where faults and fractures are the main conduits for flow. In enhanced geothermal systems (EGS), hydraulic fracturing is used to increase permeability by creating new fractures or inducing slip on preexisting fractures (McClure and Horne, 2011). If appropriate investments in research and development are made, EGS has a potential of having up to 100 GWe of generating capacity in the next 50 years (Tester et al., 2006). Considering the great potential for EGS, a fundamental understanding of the physics of fracture deformation and flow are necessary for optimizing geothermal energy production. Typically, it is assumed that faults and fractures have smooth surfaces with constant aperture and permeability values. However, field data have shown that real faults and fractures have rough surfaces that can modify fluid flow pathways significantly (Ritz et al., 2012). Moreover, flow experiments conducted on rough-walled fractures have demonstrated channeling flow behavior, where only 30 percent of the fracture area was conducive to flow (Ishibashi et al., 2012). Flow channeling also reduces the cross-sectional area available for heat conduction, which can lead to inadequate heating of injected fluids in the reservoir. The spatial distribution of aperture and permeability values within the fracture plane can be modified by the application of stress. Numerous experiments have demonstrated the evolution of fracture aperture and permeability due to applied normal and shear stresses (Barton et al., 1985; Esaki et al., 1999; Lee and Cho, 2002; Gutierrez et al., 2000). However, due to limitations in equipment capabilities and configurations, local normal and shear displacement values cannot be measured. Moreover, inelastic deformation and local stress concentrations constantly alter the local surface roughness, making it difficult to isolate the impact of fracture roughness. Inelastic effects such as gouge formation and rock breakage change the fracture permeability. Thus, it is hard to develop a fundamental understanding of the impact of roughness due to the complexity of the interacting mechanisms in the model. Several empirical models have likewise been developed to quantify the impact of applied stress conditions on the fracture permeability (Barton et al., 1985; Willis-Richards et al., 1996; Dempsey et al., 2013). These empirical models are used commonly in geomechanical simulation models (McClure and Horne, 2011). Though these empirical models are useful for general estimations of changes in permeability with stress, it is very difficult to determine the appropriate values for model constants that are applicable for a specific system under a wide range of stress conditions. Furthermore, performing the necessary experiments to determine the correct constants requires significant effort. Because of the limitations of empirical equations and laboratory experiments, a consistent physical model is needed for the accurate modeling of fracture permeability evolution with stress. Thus, the displacement discontinuity boundary element method with integrated complementarity (DDM) is a viable alternative. In this study, the main objective was to investigate the impact of fracture surface roughness on permeability-stress relationships using the DDM model. Furthermore, the changes in the spatial distribution of the fracture aperture and flow pathways due to stress application were also analyzed. For reservoirs found in tight rocks, such as shale gas and geothermal reservoirs, faults and fractures are the main conduits for flow. Thus, a fundamental understanding of the influence of fracture surface roughness on the fracture flow behavior is necessary for optimizing production in these systems. In addition, an accurate model of fracture permeability evolution with stress is essential for incorporating geomechanical effects in field scale simulations. Laboratory experiments in literature have demonstrated flow channeling effects due to fracture surface roughness. In this study, the displacement discontinuity boundary element method with integrated complementarity (DDM) was used to investigate the changes in the spatial distribution of aperture and slip due to stress applied on a rough fracture surface. Shear stress was applied in the longitudinal and lateral directions with respect to the original fracture surface. In addition, steady-state flow simulations were conducted on the aperture maps generated from the DDM models to calculate the fracture permeability and evaluate the fracture flow behavior. Results exhibited heterogeneous aperture and slip distributions within the fracture plane for different stress conditions. In addition, fracture permeability and slip values were generated at various stress conditions. Both fracture permeability and slip increased with shear stress and decreased with normal stress. Moreover, the overall trend of the change in fracture permeability with slip was consistent with experimental results and empirical models found in literature. Higher rates of permeability changes were observed at lower shear stress and slip conditions. Another significant finding of this study was the permeability anisotropy with respect to the applied shear stress direction. The permeability was consistently higher in the direction perpendicular to the applied shear stress compared to the parallel direction. Moreover, channelized flow patterns were observed for the perpendicular flow direction while distributed flow patterns were observed in the parallel flow direction. Because the DDM is a consistent physical model, it provides a comprehensive approach for understanding the fundamental effects of fracture roughness on the permeability and slip evolution of fractures under different stress conditions. In addition, flow patterns can be modeled and observed because this approach considers the spatial distribution of aperture in the fracture plane. For instance, a two-dimensional fracture aperture distribution is essential for modeling permeability anisotropy with respect to shear stress. For future work, a three-dimensional DDM (Kaven et al., 2012) application on rough fracture surfaces will be needed to account for the stress interactions between fracture traces and across fractures. In addition, the integration of inelastic effects on the local aperture development with the DDM model will create a broader understanding of the permeability evolution with stress.


Barton, N., Bandis, S., and Bakhtar, K.: Strength, Deformation and Conductivity Coupling of Rock Joints, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 22, (1985), 121-140.

Co, C. and R. Horne.: Stress-Permeability Relationships in Low Permeability Systems: Application to Shear Fractures, Proceedings, 39th Stanford Geothermal Workshop, Stanford, CA (2015).

Co, C. and Horne, R.: Artificial Rough Fracture Generation using Sequential Gaussian Simulation (SGSIM): Correlating Spatial Aperture Characteristics to Flow Channeling Behavior, 2015 International Association for Mathematical Geosciences (IAMG) Conference, Freiberg, Germany, (2015).

Crouch, S.L., Starfield, A.M.: Boundary Element Methods in Solid Mechanics, Allen & Unwin, London, 1983.

Dempsey, D., Kelkar, S., Lewis, K., Hickman, S., Davatzes, N., Moos, D., and Zemach, E.: Modeling Shear Stimulation of the Desert Peak EGS Well 27-15 Using a Coupled Thermal-Hydrological-Mechanical Simulator, Proceedings, 47th US Rock Mechanics / Geomechanics Symposium, San Francisco, CA (2013).

Esaki, T., Du, S., Mitani, Y., Ikusada, K., and Jing, L.: Development of a Shear-Flow Test Apparatus and Determination of Coupled Properties for a Single Rock Joint. 
International Journal of Rock Mechanics and Mining Sciences, 36(5), (1999), 641-650.

Ishibashi, T., Watanabe, N., Hirano, N., Okamoto, A., and Tsuchiya, N.: Upgrading of Aperture Model based on Surface Geometry of Natural Fracture for Evaluating Channeling Flow, GRC Transactions, 36, (2012), 481-486.

Kaven, J. O., Hickman, S. H., Davatzes, N. C., and Mutlu, O.: Linear Complementarity Formulation for 3D Frictional Sliding Problems, Computational Geosciences, 16(3), (2012), 613-624.

Lee, H. and Cho, T.: Hydraulic Characteristics of Rough Fractures in Linear Flow under Normal and Shear Load, Rock Mechanics and Rock Engineering, 35(4), (2002), 299-318.

Matsuki, K., Y. Chida, K. Sakaguchi, and P. W. J. Glover (2006), Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures, Int. J. Rock Mech. Min. Sci., 43, 726–755.

McClure, M. W. and Horne, R. N.: Investigation of Injection-Induced Seismicity Using a Coupled Fluid Flow and Rate/State Friction Model. Geophysics, 76(6), (2011), WC181-WC198.

Nemoto, K., N. Watanabe, N. Hirano, and N. Tsuchiya (2009), Direct Measurement of Contact Area and Stress Dependence of Anisotropic Flow through Rock Fracture with Heterogeneous Aperture Distribution, Earth Planet. Sci. Lett., 281, 81–87.

Pollard, D. D. and Fletcher, R. C.: Fundamentals of Structural Geology, Cambridge University Press, (2005).

Ritz, E., Mutlu, O., and Pollard, D. D.: Integrating Complementarity into the 2D Displacement Discontinuity Boundary Element Method to Model Faults and Fractures with Frictional Contact Properties, Computers & Geosciences, 45, (2012), 304-312.

Roberts, J., and T. D. Roberts (1978), Use of the Butterworth Low-Pass Filter for Oceanographic Data, J. Geophys. Res., 83(C11), 5510–5514, doi:10.1029/JC083iC11p05510.

Tester, J., Anderson, B. J., Batchelor, A. S., Blackwell, D. D., DiPippo, R., Drake, E. M., Garnish, J., Livesay, B., Moore, M. C., Nichols, K., et al.: The Future of Geothermal Energy, Massachusetts Institute of Technology, (2006).

Willis-Richards, J., Watanabe, K., and Takahashi, H.: Progress Toward a Stochastic Rock Mechanics Model of Engineered Geothermal Systems, Journal of Geophysical Research: Solid Earth, 101(B8), (1996), 17481-17496.

Witherspoon, P., Wang, J., Iwai, K., and Gale, J.: Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture, Water Resources Research, 16(6), (1980), 1016-1024.