Microflow effects on the hydraulic aperture of single rough fractures

Ge Zhang, Yudong Zhang, Aiguo Xu, Yingjun Li

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The understanding of flow behavior in rough fractures is essential for many engineering activities. When the aperture of a rough fracture approaches the mean free path of fluid molecules, the microflow effect, sometimes also referred to relative rarefaction effect, relative discrete effect or non-equilibrium effect, becomes pronounced. It was found often to enhance the flow rate. However, the surface roughness shows completely contrary influence. In order to clarify the influences of the two factors, a computer simulation work accompanied with theoretical analyses is conducted. Previous empirical models for hydraulic aperture which already containing roughness effect are modified with consideration of the microflow effect. Direct simulation using the lattice Boltzmann method is conducted on artificially created 2D fractures with random roughness following Gaussian distribution to reveal the competitive relationship of two effects. The simulation results also verify modified models. Among them, the one based on Rasouli and Hosseinian's model agrees with the simulation on the relationship between hydraulic aperture and mechanical aperture for both cases with very rough fractures and relatively smooth fractures. Further investigation confirms that, under various roughness, the ratio of hydraulic aperture over mechanical aperture shows quantitatively different trends as mechanical aperture decreases. This phenomenon exists on a relatively wide scale. An equilibrium point of two effects is also found through analysis of the relationship. The results reveal the mechanism of microflow in 2D rough fractures and also provide a reference for engineering problems like the transport of natural gas through microfractures.

Cited as: Zhang, G., Zhang, Y., Xu, A., Li, Y. Microflow effects on the hydraulic aperture of single rough fractures. Advances in Geo-Energy Research, 2019, 3(1): 104-114, doi: 10.26804/ager.2019.01.09


Microflow, single fracture, roughness, hydraulic aperture, lattice Boltzmann method

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Ansumali, S., Karlin, I.V. Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 2002, 66(2): 026311.

Barton, N., Choubey, V. The shear strength of rock joints in theory and practice. Rock Mech. 1977, 10(1-2): 1-54.

Boutt, D.F., Grasselli, G., Fredrich, J.T., et al. Trapping zones: The effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture. Geophys. Res. Lett. 2006, 33(21): L21402.

Brown, S.R. Simple mathematical model of a rough fracture. J. Geophys. Res. Sol. Ea. 1995, 100(B4): 5941-5952.

Cacas, M.C., Ledoux, E., Marsily, G.D., et al. Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 1. The flow model. Water Resour. Res. 1990, 26(3): 479-489.

Cai, J., Yu, B., Zou, M., et al. Fractal analysis of surface roughness of particles in porous media. Chinese Phys. Lett. 2010, 27(2): 024705.

Ciezobka, J., Courtier, J., Wicker, J. Hydraulic fracturing test site (HFTS)-Project overview and summary of results. Paper URTEC2937168 Presented at the Unconventional Resources Technology Conference, Houston, Texas, USA, 23-25 July, 2018.

Darabi, H., Ettehad, A., Javadpour, F., et al. Gas flow in ultra-tight shale strata. J. Fluid Mech. 2012, 710: 641-658.

Eker, E., Akin, S. Lattice Boltzmann simulation of fluid flow in synthetic fractures. Transp. Porous Media 2006, 65(3): 363-384.

Golparvar, A., Zhou, Y., Wu, K., et al. A comprehensive review of pore scale modeling methodologies for multiphase flow in porous media. Adv. Geo-Energy Res. 2018, 2(4): 418-440.

Karniadakis, G., Beskok, A., Aluru, N. Microflows and Nanoflows: Fundamentals and Simulation. New York, Springer Science & Business Media, 2006.

Li, J., Ho, M.T., Wu, L., et al. On the unintentional rarefaction effect in LBM modeling of intrinsic permeability. Adv. Geo-Energy Res. 2018, 2(4): 404-409.

Liu, H., Zhang, X., Lu, X., et al. Study on flow in fractured porous media using pore-fracture network modeling. Energies 2017, 10(12): 1984.

Liu, R., Jiang, Y., Huang, N., et al. Hydraulic properties of 3D crossed rock fractures by considering anisotropic aperture distributions. Adv. Geo-Energy Res. 2018, 2(2): 113-121.

Louis, C. Rock hydraulics, in Rock Mechanics, edited by L. M ¨uller, Vienna, Springer, pp. 299-387, 1972.

Luo, S., Zhao, Z., Peng, H., et al. The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks. Int. J. Rock Mech. Min. 2016, 87: 29-38.

Myers, N. Characterization of surface roughness. Wear 1962, 5(3): 182-189.

Oron, A.P., Berkowitz, B. Flow in rock fractures: The local cubic law assumption reexamined. Water Resour. Res. 1998, 34(11): 2811-2825.

Patir, N., Cheng, H. An average flow model for determining effects of three-dimensional roughness on partial hy-drodynamic lubrication. J. Lubr. Technol. 1978, 100(1): 12-17.

Rasouli, V., Hosseinian, A. Correlations developed for estimation of hydraulic parameters of rough fractures through the simulation of JRC flow channels. Rock Mech. Rock Eng. 2011, 44(4): 447-461.

Renshaw, C.E. On the relationship between mechanical and hydraulic apertures in roughwalled fractures. J. Geophys. Res. Sol. Ea. 1995, 100(B12): 24629-24636.

Succi, S. The Lattice Boltzmann Equation: For Fluid Dy-namics and Beyond. New York, USA, Oxford University Press, 2001.

Tang, G., Tao, W., He, Y. Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions. Phys. Fluids 2005, 17(5): 058101.

Wang, M., Chen, Y., Ma, G., et al. Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Adv. Water Resour. 2016, 96: 373-388.

Wang, Z., Wang, M., Chen, S. Coupling of high Knudsen number and non-ideal gas effects in microporous media. J. Fluid Mech. 2018, 840: 56-73.

Witherspoon, P.A., Wang, J.S., Iwai, K., et al. Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res. 1980, 16(6): 1016-1024.

Xu, A., Gonnella, G., Lamura, A. Phase-separating binary fluids under oscillatory shear. Phys. Rev. E 2003, 67(5): 056105.

Xu, A., Gonnella, G., Lamura, A., et al. Scaling and hydrody-namic effects in lamellar ordering. EPL-Europhys. Lett. 2005, 71(4): 651.

Xu, A., Gonnella, G., Lamura, A. Simulations of complex fluids by mixed lattice Boltzmann-finite difference methods. Phys. A 2006a, 362(1): 42-47.

Xu, A., Gonnella, G., Lamura, A. Morphologies and flow patterns in quenching of lamellar systems with shear. Phys. Rev. E 2006b, 74(1): 011505.

Zhang, G., Feng, C., Gong, W., et al. Simulation and analysis of the effect of roughness elements on fluid flow through single fracture based on lattice Boltzmann method. Scientia Sinica Physica, Mechanica & Astronomica 2017, 47(2): 024701. (in Chinese)

Zhang, G., Tian, Y., Li, Y. Numerical study on the mechanism of fluid flow through single rough fractures with different JRC. Scientia Sinica Physica, Mechanica & Astronomica 2018b, 49(1): 014701. (in Chinese)

Zhang, Y., Xu, A., Zhang, G., et al. Discrete Boltzmann method with Maxwell-type boundary condition for slip flow. Commun. Theor. Phys. 2018a, 69(1): 77.

Zhao, J., Yao, J., Li, A., et al. Simulation of microscale gas flow in heterogeneous porous media based on the lattice Boltzmann method. J. Appl. Phys. 2016, 120(8): 084306.

Zhao, Z., Li, B. On the role of fracture surface roughness in fluid flow and solute transport through fractured rocks. Paper ISRM-13CONGRESS-2015-051 Presented at the 13th ISRM International Congress of Rock Mechanics, Montreal, Canada, 10-13 May, 2015.

Zhao, Z., Peng, H., Wu, W., et al. Characteristics of shear-induced asperity degradation of rock fractures and implications for solute retardation. Int. J. Rock Mech. Min. 2018, 105: 53-61.

Zhou, J., Wang, M., Wang, L., et al. Emergence of nonlinear laminar flow in fractures during shear. Rock Mech. Rock Eng. 2018, 51(11): 3635-3643.

Zimmerman, R.W., Bodvarsson, G.S. Hydraulic conductivity of rock fractures. Transp. Porous Media 1996, 23(1): 1-30.

Zimmerman, R.W., Kumar, S., Bodvarsson, G. Lubrication theory analysis of the permeability of rough-walled frac-tures. Berkeley, Lawrence Berkeley National Laboratory, 1991.

Zou, L., Jing, L., Cvetkovic, V. Roughness decomposition and nonlinear fluid flow in a single rock fracture. Int. J. Rock Mech. Min. 2015, 75: 102-118.

Zou, Q., He, X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 1997, 9(6): 1591-1598.


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