Evaluation of Non-linear Fluid Flow Through Rough-walled Fractures

Document Type : Research Article



In many geological structures, the matrix permeability is negligible and the fractures are the main flow paths. The fluid flow and particle transport through rock fracture are increasingly important research topics mainly to the demands for design, operation and safety assessments of underground/ surface constructions. In this paper, single-phase fluid flow through a rock fracture is studied. Computational domain for an artificial three-dimensional fracture is generated and used for numerical fluid flow simulations. Both laminar and turbulent flow simulations are performed by using finite element method for a wide range of inlet velocities. The calculated average pressure drops, between consecutive vertical sections are compared to describe the flow rate dependant pressure drop. The simulations results show that; (i) the predicted static pressure drop for turbulent flow simulation was roughly 3% to 17% more than laminar simulation at Reynolds number of 4.5 to 89.5, respectively, and (ii) the Forchheimer law is fitted very well to flow simulation results and critical Reynolds number of 15 is suggested.


[1]Zimmerman, R. W., Bodvarsson, G. S; “Hydraulic conductivity of rock fractures”, Transport Porous Media, 23, 1-30, 1996._
[2] Louis, C; “A study of groundwater flow in jointed rock and influence on the stability of rock masses”,Imp coll. of London rock mech., Res. Rep. 10, 90,1969._
[3]Lomize, G.M; “Filtratsia v treshchinovatykh porodakh (Seepage in Jointed Rocks)”,Gosudarstvennoe Energetitcheskoe Izdatel’stvo,
Moskva-Leningrad, 1951._
[4]Elsworth, D., Goodman, R. E; “Characterization of rock fissure hydraulic conductivity using idealized wall roughness profiles”, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 23, 233-243, 1986._
[5]Wilson, C. R., Witherspoon, P. A; “Steady state flow in rigid networks of fractures”, Water Res. Res., 10, 328–335, 1974._
[6]Neuzil, C.E., Tracy, J. V; “Flow Through Fractures”, Water Resources Research, 17(1), 191-199, 1981._
[7]Moreno, L., Neretnieks, I., Eriksen, T; “Analysis of some laboratory tracer runs in natural fissures”,Water Resources Research, 2 (7), 951-958, 1985.
[8]Silliman, S. E; “An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture”, Water Res.Res.25, 2275-2283, 1989._
[9]Walsh, J. B., Brown, S. R., Durham. W. B; “Effective media theory with spatial correlation for flow in a fracture”, Journal of Geophysical Research., 102(22), 587-22,594, 1997._
[10]Bear, J., Tsang, C. F., De Marsily, G; “Flow and Contaminant Transport in Fractured Rock”,Academic Press, San Diego, 1993
[11]Tsang, Y. W., Witherspoon, P. A; . “Hydromechanical behavior of a deformable rock fracture subject to normal stress”, J. Geophys.
Res.,86, 9287-9298, 1981._
[12]Tsang, Y. W; “The effect of tortuosity on fluid flow through a single fracture”, Water Resources Research., 20(9), 1209-1215, 1984._
[13]Moreno, L., Tsang, Y. W., Tsang, C. F., Hale, F. V., Neretnieks, I; “Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations” Water Resources Research 24 (12), 2033–2048, 1988.
[14]Tsang, Y.W., Tsang, C.F; “Flow Channeling in a Single Fracture as a Two- Dimensional Strongly Heterogeneous Permeable Medium”, Water Resources Research, 25(9), 2076-2080, 1989.
[15]Piggott, A. R., Elsworth, D; “Laboratory assesment of the equivalent apertures of a rock fracture”, Geophysical Research Letters 2, 1387-1390, 1993.
[16]David, C; “Geometry of flow paths for fluid .transport in rocks”, Journal of Geophysical Research., 98, 12,267-12,278, 1993.
[17]Brown, S. R; “Fluid flow through rock joints: the . effect of surface roughness”, Journal of Geophysical Research 92 (B2), 1337-1347, 1987.
[18]Renshaw, C. E; “On the relationship between . mechanical and hydraulic apertures in roughwalled fractures”, Journal of Geophysical
Research, 100 (B12), 629-636, 1995.
[19]Thompson, M. E., Brown, S. R; “The effect of anisotropic surface roughness on flow and transport in fracture”, Journal of Geophysical Research 96 (B13), 923–932, 1991.
[20]Brown, S. R; “Transport of fluid and electric current through a single fracture”, Journal of Geophysical Research, 94, 9429-9438, 1989.
[21]Koyama, T., Li, B., Jiang, Y., Jing, L; “Numerical simulations for the effects of normal loading on particle transport in rock fractures during shear”,International Journal of Rock Mechanics & Mining Sciences, 45(5), 1403-1419, 2008.
[22]Koyama, T., Fardin, N., Jing, L., Stephansson, “Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas”,International Journal of Rock Mechanics & Mining Sciences, 43, 89–106, 2006.
[23]Brown, S.R., Stockman, H.W., Reeves, S.J; “Applicability of the Reynolds equation for modeling fluid flow between rough surfaces”,Geophys. Res. Lett, 22(18), 2537–2540, 1995.
[24]Oron, A. P., Berkowitz, B; “Flow in rock fractures: the local cubic law assumption reexamined”, Water Resources Research. 34:2811-24, 1998.
[25]Nicholl, M., Rajaram, J. H., Glass, R., Detwiler, R; “Saturated flow in a single fracture: Evaluation of the Reynolds equation in measured aperture field”,Water Res., Res., 35(11), 3361-3373, 1999.
[26]Ge, S; “A governing equation for fluid flow in rough fractures”, Water Resources Research 33 (1),53–61, 1997.
[27]Yeo, I. W., Ge, S; ‘Applicable range of the Reynolds equation for fluid flow in a rock Fracture”, Geosciences Journal 9 (4), 347-352,
[28]Qian, J., Zhan, H., Zhao, W., Sun, F; “Experimental study of turbulent unconfined groundwater flow in a single fracture”, Journal of
Hydrology, 311, 134–142, 2005.
[29]Koyama, T., Neretnieks, I., Jing, L; “A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear”, International Journal of Rock Mechanics and Mining Science 45, 1082–1101, 2008.
[30]Zimmerman, R. W., Al-Yaarubi, A. H., Pain, C. C., Grattoni, C. A; “Non-linear regimes of fluid flow in rock fractures”, International Journal of Rock Mechanics and Mining Science, 41 (3), 163-169,2004.
[31]Nazridoust, K., Ahmadi, G., Smith, D. H; “A new friction factor correlation for laminar, single-phase flows through rock fractures”, Journal of Hydrology 329, 315– 328, 2006.
[32]Brush, D., Thomson, N. R; “Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations”, Water Resources Research 39 (4), 1085-1099, 2003.
[33]Chen, Z. X., Lyons, S. L., Qin, G; “Derivation of the Forchheimer law via homogenization”, Transp. Porous Media, 44, 325-35, 2001.