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Effects of intersection and dead-end of fractures on nonlinear flow and particle transport in rock fracture networks

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Abstract

Fluid flow tests were conducted on three artificial rock fracture network models to visually investigate the behaviors of fluid flow and solute transport within the fracture intersections, by using the visualization techniques with a CCD camera. Numerical simulations by solving the Navier-Stokes equations were performed to simulate the fluid flow and solute transport based on the experimental models, and to extensively estimate the effects of fracture intersection and dead-end in fracture networks. The results show that for the crossed fracture models, when the Reynolds number (Re) of the inlet is larger than 1, a nonlinear flow regime starts to appear where the proportion of the flow rates in the two outlets change nonlinearly. When calculating the fluid flow in discrete fracture network (DFN) models, it is found that the critical condition of applying the local cubic law to model fluid flow in each single fracture in DFNs is J ≤ 10–5, where J is the hydraulic gradient. Beyond this value, the deviation of applying the cubic law increases remarkably with increasing hydraulic gradient. The effects of dead-ends of fractures on fluid flow are negligible, however, they have a strong impact on the breakthrough curves of particles in DFNs with the relative time deviation rate in the range of 5–35%.

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References

  • Aharwal, K.R., Gandhi, B.K., and Saini, J.S., 2008, Experimental investigation on heat-transfer enhancement due to a gap in an inclined continuous rib arrangement in a rectangular duct of solar air heater. Renewable Energy, 33, 585–596.

    Article  Google Scholar 

  • Baghbanan, A. and Jing, L., 2007, Hydraulic properties of fracture rock masses with correlated fracture length and aperture. International Journal of Rock Mechanics and Mining Sciences, 44, 704–719.

    Article  Google Scholar 

  • Baghbanan, A. and Jing, L., 2008, Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. International Journal of Rock Mechanics and Mining Sciences, 45, 1320–1334.

    Article  Google Scholar 

  • Brush, D.J. and Thomson, N.R., 2003, Fluid flow in synthetic roughwalled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resources Research, 39, 1085. doi:10.1029/2002WR001346

    Article  Google Scholar 

  • Cvetkovic, V., Painter, S., Outters, N., and Selroos, J.O., 2004, Stochastic simulation of radionuclide migration in discretely fractured rock near the Äspö Hard Rock Laboratory. Water Resources Research, 40, W02404. doi:10.1029/2003WR002655

    Article  Google Scholar 

  • Fluent, Inc., 2006, Fluent 6.3 Users Guide. Fluent Inc., Lebanon, 2501 p.

  • Forchheimer, P., 1901, Wasserbewegung durch boden. Zeitschrift des Vereines Deutscher Ingenieure, 45, 1782–1788.

    Google Scholar 

  • Frampton, A. and Cvetkovic, V., 2007a, Upscaling particle transport in discrete fracture networks: 1. Nonreactive tracers. Water resources research, 43, W10428. doi:10.1029/2006WR005334

    Google Scholar 

  • Frampton, A. and Cvetkovic, V., 2007b, Upscaling particle transport in discrete fracture networks: 2. Reactive tracers. Water resources research, 43, W10429. doi:10.1029/2006WR005336

    Google Scholar 

  • Gale, S.J., 1984, The hydraulics of conduit flow in carbonate aquifers. Journal of Hydrology, 70, 309–327.

    Article  Google Scholar 

  • Hull, L.C. and Koslow, K.N., 1986, Streamline routing through fracture junctions. Water Resources Research, 22, 1731–1734.

    Article  Google Scholar 

  • Jafari, A. and Babadagli, T., 2013, Relationship between percolation–fractal properties and permeability of 2-D fracture networks. International Journal of Rock Mechanics and Mining Sciences, 60, 353–362.

    Article  Google Scholar 

  • Javadi, M., Sharifzadeh, M., and Shahriar, K., 2010, A new geometrical model for nonlinear fluid flow through rough fractures. Journal of Hydrology, 389, 18–30.

    Article  Google Scholar 

  • Johnson, J., Brown, S., and Stockman, H., 2006, Fluid flow and mixing in rough - walled fracture intersections. Journal of Geophysical Research: Solid Earth (1978–2012), 111(B12).

    Google Scholar 

  • Johnson, J. and Brown, S., 2001, Experimental mixing variability in intersecting natural fractures. Geophysical Research Letters, 28, 4303–4306.

    Article  Google Scholar 

  • Klimczak, C., Schultz, R.A., Parashar, R., and Reeves, D.M., 2010, Cubic law with aperture-length correlation: implications for network scale fluid flow. Hydrogeology Journal, 18, 851–862.

    Article  Google Scholar 

  • Kohl, T., Evans, K.F., Hopkirk, R.J., Jung, R., and Rybach, L., 1997, Observation and simulation of non-Darcian flow transients in fractured rock. Water Resources Research, 33, 407–418.

    Article  Google Scholar 

  • Kosakowski, G. and Berkowitz, B., 1999, Flow pattern variability in natural fracture intersections. Geophysical Research Letters, 26, 1765–1768.

    Article  Google Scholar 

  • Latham, J.P., Xiang, J., Belayneh, M., Nick, H.M., Tsang, C.F., and Blunt, M.J., 2013, Modelling stress-dependent permeability in fractured rock including effects of propagating and bending fractures. International Journal of Rock Mechanics and Mining Sciences, 57, 100–112.

    Article  Google Scholar 

  • Leung, C.T.O. and Zimmerman, R.W., 2012, Estimating the hydraulic conductivity of two-dimensional fracture networks using network geometric properties. Transport in Porous Media, 93, 777–797.

    Article  Google Scholar 

  • Lever, D.A., Bradbury, M.H., and Hemingway, S.J., 1985, The effect of dead-end porosity on rock-matrix diffusion. Journal of Hydrology, 80, 45–76.

    Article  Google Scholar 

  • Li, B., Jiang, Y., Koyama, T., Jing, L., and Tanabashi, Y., 2008, Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures. International Journal of Rock Mechanics and Mining Sciences, 45, 362–375.

    Article  Google Scholar 

  • Liu, R., Jiang, Y., Li, B., and Wang, X., 2015a, A fractal model for charactering fluid flow in fractured rock masses on randomly distributed rock fracture networks. Computers and Geotechnics, 65, 45–55.

    Article  Google Scholar 

  • Liu, R., Jiang, Y., Li, B., and Wang, X., 2015b, Study of nonlinear hydraulic characteristics and hydraulic aperture calculation of crossed fracture. Rock and Soil Mechanics, 36, 1581–1590. (in Chinese)

    Google Scholar 

  • Liu, R., Jiang, Y., Li, B., and Wang, X., 2014, Numerical calculation of directivity of equivalent permeability of fractured rock masses network. Rock and Soil Mechanics, 35, 2394–2400. (in Chinese)

    Google Scholar 

  • Long, J.C.S., Remer, J.S., Wilson, C.R., and Witherspoon, P.A., 1982, Porous media equivalents for networks of discontinuous fractures. Water Resources Research, 18, 645–658.

    Article  Google Scholar 

  • Miao, T., Yu, B., Duan, Y., and Fang, Q., 2015, A fractal analysis of permeability for fractured rocks. International Journal of Heat and Mass Transfer, 81, 75–80.

    Article  Google Scholar 

  • Min, K.B., Rutqvist, J., Tsang, C.F., and Jing, L., 2004, Stress-dependent permeability of fractured rock masses: a numerical study. International Journal of Rock Mechanics and Mining Sciences, 41, 1191–1210.

    Article  Google Scholar 

  • Murphy, H., Huang, C., Dash, Z., Zyvoloski, G., and White, A., 2004, Semianalytical solutions for fluid flow in rock joints with pressure-dependent openings. Water Resources Research, 40, W12506. http://dx.doi.org/10.1029/2004WR003005

    Article  Google Scholar 

  • Parashar, R. and Reeves, D.M., 2012, On iterative techniques for computing flow in large two-dimensional discrete fracture networks. Journal of Computational and Applied Mathematics, 236, 4712–4724.

    Article  Google Scholar 

  • Park, Y.J., Lee, K.K., and Berkowitz, B., 2001, Effects of junction transfer characteristics on transport in fracture networks. Water Resources Research, 37, 909–923.

    Article  Google Scholar 

  • Park, Y.J. and Lee, K.K., 1999, Analytical solutions for solute transfer characteristics at continuous fracture junctions. Water Resources Research, 35, 1531–1537.

    Article  Google Scholar 

  • Reeves, D.M., Parashar, R., Pohll, G., Carroll, R., Badger, T., and Willoughby, K., 2013, The use of discrete fracture network simulations in the design of horizontal hillslope drainage networks in fractured rock. Engineering Geology, 163, 132–143.

    Article  Google Scholar 

  • Stockman, H.W., Johnson, J., and Brown, S.R., 2001, Mixing at fracture intersections: Influence of channel geometry and the Reynolds and Peclet numbers. Geophysical Research Letters, 28, 4299–4302.

    Article  Google Scholar 

  • Stockman, H.W., Li, C., and Wilson, J.L., 1997, A lattice-gas and lattice Boltzmann study of mixing at continuous fracture Junctions: Importance of boundary conditions. Geophysical Research Letters, 24, 1515–1518.

    Article  Google Scholar 

  • Wilson, C.R. and Witherspoon, P.A., 1976, Flow interference effects at fracture intersections. Water Resources Research, 12, 102–104.

    Article  Google Scholar 

  • Xiong, X., Li, B., Jiang, Y., Koyama, T., and Zhang, C., 2011, Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. International Journal of Rock Mechanics and Mining Sciences, 48, 1292–1302.

    Article  Google Scholar 

  • Zhang, X., Powrie, W., Harkness, R., and Wang, S., 1999, Estimation of permeability for the rock mass around the shiplocks of the Three Gorges Project, China. International Journal of Rock Mechanics and Mining Sciences, 36, 381–397.

    Article  Google Scholar 

  • Zhang, X., Sanderson, D.J., Harkness, R.M., and Last, N.C., 1996, Evaluation of the 2-D permeability tensor for fractured rock masses. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33, 17–37.

    Article  Google Scholar 

  • Zhang, X. and Sanderson, D.J., 1996, Effects of stress on the twodimensional permeability tensor of natural fracture networks. Geophysical Journal International, 125, 912–924.

    Article  Google Scholar 

  • Zhao, Z., Jing, L., Neretnieks, I., and Moreno, L., 2011, Numerical modeling of stress effects on solute transport in fractured rocks. Computers and Geotechnics, 38, 113–126.

    Article  Google Scholar 

  • Zhao, Z., Jing, L., and Neretnieks, I., 2010, Evaluation of hydrodynamic dispersion parameters in fractured rocks. Journal of Rock Mechanics and Geotechnical Engineering, 2, 243–254.

    Article  Google Scholar 

  • Zhao, Z., Li, B., and Jiang, Y., 2013, Effects of fracture surface roughness on macroscopic fluid flow and solute transport in fracture networks. Rock Mechanics and Rock Engineering, Doi: 10.1007/s00603–013–0497–1.

    Google Scholar 

  • Zimmerman, R.W., Al-Yaarubi, A., Pain, C.C., and Grattoni, C.A., 2004, Non-linear regimes of fluid flow in rock fractures. International Journal of Rock Mechanics and Mining Sciences, 41, 163–169.

    Article  Google Scholar 

  • Zimmerman, R.W. and Bodvarsson, G.S., 1996, Hydraulic conductivity of rock fractures. Transport in Porous Media, 23, 1–30.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Graduate School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki, 8528521, Japan

    Richeng Liu

  2. School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, Nagasaki, 8528521, Japan

    Yujing Jiang & Bo Li

  3. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, 266510, China

    Yujing Jiang

  4. Rock Mechanics and Geo-Hazards Center, Shaoxing University, Shaoxing, 312000, China

    Bo Li

Authors
  1. Richeng Liu
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  2. Yujing Jiang
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  3. Bo Li
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Correspondence to Yujing Jiang.

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Liu, R., Jiang, Y. & Li, B. Effects of intersection and dead-end of fractures on nonlinear flow and particle transport in rock fracture networks. Geosci J 20, 415–426 (2016). https://doi.org/10.1007/s12303-015-0057-7

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  • DOI: https://doi.org/10.1007/s12303-015-0057-7

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