A New Geometrical Model of Fluid Flow in Rock Fractures for Valid Application of the Cubic Law

Abstract:

The cubic law (CL) is one of the most commonly applied physical laws for flow through rock fractures and fractured media, but many studies indicate that the CL is often not adequate. We investigate the establishment conditions of valid applying the “cubic law” to flow in fractures. A dimensional analysis of the N-S equations yields three conditions for the applicability of cubic law, as a leading order approximation in a local fracture segment with parallel walls. These conditions may not be met in many natural rock fractures as whole and demonstrate that the “cubic law” should be exactly applied in local segments (local cubic law, LCL). In this way, a new 2D discrete equivalent model for natural rough fractures is introduced, and its equivalent aperture and flow formulation are derived. By comparing the developed model and experimental results of different fractures, good accuracy was found, and the model was validated. The model could be useful for theory studies of flows through real rock fractures.

• Periodical: Applied Mechanics and Materials (Volumes 580-583)
• Pages: 841-846
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.580-583.841
• Online since: July 2014
• Authors: Hong Guang Zhu*, Yao Dong Jiang, Cheng Yi, He Ping Xie
• Keywords: Fluid Flow, Geometrical Discrete-Equivalent Model, Local Cubic Law, Rock Fracture

References

[1] Neuman, S.P. Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeology Journal, 2005, 13(1): 124-147.

DOI: 10.1007/s10040-004-0397-2

[2] Amadei, B., Illangasekare, T. A mathematical model for flow and solute transport in non-homogeneous rock fractures, International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 1994, pp.719-731.

DOI: 10.1016/0148-9062(94)90011-6

[3] Nazridoust, K., Ahmadi, G., Smith, D.H. A new friction factor correlation for laminar, single-phase flows through rock fractures, Journal of Hydrology, 2006, pp.315-328.

DOI: 10.1016/j.jhydrol.2006.02.032

[4] Bear J, T.C.F., De Marsily G. Flow and Contaminant Transport in Fractured Rock., Academic Press, San Diego. (1993).

[5] Meheust, Y., Schmittbuhl, J. Geometrical heterogeneities and permeability anisotropy of rough fractures, Journal of geophysical research, 2001, pp.2089-2102.

DOI: 10.1029/2000jb900306

[6] Durham, W.B., Bonner, B.P. Self-propping and fluid-flow in slightly offset joints at high effective pressures, Journal of Geophysical Research-Solid Earth, 1994, pp.9391-9399.

DOI: 10.1029/94jb00242

[7] Novakowski, K.S., Lapcevic, P.A., Voralek, J., Bickerton, G. Preliminary interpretation of tracer experiments conducted in a discrete rock fracture under conditions of natural flow, Geophysical Research Letters, 1995, pp.1417-1420.

DOI: 10.1029/95gl00569

[8] Lee, H. -B., Yeo, I.W., Lee, K. -K. The modified Reynolds equation for non-wetting fluid flow through a rough-walled rock fracture, Advances in Water Resources, 2013, pp.242-249.

DOI: 10.1016/j.advwatres.2012.12.005

[9] Javadi, M., Sharifzadeh, M., Shahriar, K. A new geometrical model for non-linear fluid flow through rough fractures, Journal of Hydrology, 2010, pp.18-30.

DOI: 10.1016/j.jhydrol.2010.05.010

[10] Hongguang Zhu, Heping Xie, Cheng Yi, et al. Properties of fluid flow in rock fractures. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(4): 657-663. (In Chinese).