On mapping fracture networks onto continuum

Water Resources Research

Volumn 44, Issue 8, 2008, Pages

  Botros, Farag E ^a,c,d   Hassan, Ahmed E ^b,c   Reeves, Donald M ^a   Pohll, Greg ^a  

^a DESERT RESEARCH INSTITUTE   (United States)

^b DESERT RESEARCH INSTITUTE   (United States)

^c CAIRO UNIVERSITY   (Egypt)

^d Daniel B Stephens and Associates   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMAL MAPPING; FLOW OF FLUIDS; NETWORK PROTOCOLS; SENSOR NETWORKS; SOLUTE TRANSPORT; STOCHASTIC PROGRAMMING;

COMPUTATIONALLY EFFICIENT; CORRECTION FACTORS; DEGREE OF CONNECTIVITY; DISCRETE FRACTURE NETWORK; DISCRETE FRACTURES; FINITE DIFFERENCING; FLOW EQUATIONS; FLOW PATHS; FLUID FLOWING; FRACTURE DENSITY; FRACTURE NETWORKS; FRACTURE STATISTICS; FRACTURED MEDIA; GRID CELL SIZE; GRID CELLS; GRID RESOLUTIONS; MODELING APPROACHES; MONTE CARLO; NETWORK CONNECTIVITY; ROCK MATRIX; SINGLE-PHASE FLOWS;

FRACTURE;

COMPARATIVE STUDY; FLOW MODELING; FLOW PATTERN; FLUID FLOW; FRACTURE NETWORK; HYDROLOGICAL MODELING; MONTE CARLO ANALYSIS; SOLUTE TRANSPORT; STOCHASTICITY;

EID: 53849100000     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2007WR006092     Document Type: Article

References (63)

1. Adler, P. M., and J.-F. Thovert (1999), Fractures and Fracture Networks, Theories and Applications of Transport in Porous Media, Springer, New York.
2. Ando, K., A. Kostner, and S. P. Neuman (2003), Stochastic continuum modeling of flow and transport in crystalline rock mass: Fanay-Augeres, France, revisited, Hydrogeol. J., 11, 521-535.
3. Bandis, S. C., A. Makurat, and G. Vik (1985), Predicted and measured hydraulic conductivity of rock joints, in Proceedings of the International Symposium on Fundamentals of Rock Joints, edited by O. Stephansson, pp. 269-280, Centek Publishers, Bjorkliden, Sweden.
4. Benke, R., and S. Painter (2003), Modeling conservative tracer transport in fracture networks with a hybrid approach based on the Boltzmann transport equation, Water Resour. Res., 39(11), 1324, doi:10.1029/2003WR001966.
5. Berkowitz, B. (1995), Analysis of fracture network connectivity using percolation theory, Math. Geol., 27(4), 467-483.
6. Berkowitz, B. (2002), Characterizing flow and transport in fractured geological media: A review, Adv. Water Resour., 25, 861-884.
7. Berkowitz, B., and I. Balberg (1993), Percolation theory and its application to groundwater hydrology, Water Resour. Res., 29(4), 775-794.
8. Berkowitz, B., and H. Scher (1997), Anomalous transport in random fracture networks, Phys. Rev. Lett., 79(20), 4038-4041.
9. Best, D. J., and N. I. Fisher (1979), Efficient simulation of the von Mises distribution, Appl. Stat., 28(2), 152-157.
10. Bodin, J., G. Porel, F. Delay, F. Ubertosi, S. Bernard, and J.-R. de Dreuzy (2007), Simulation and analysis of solute transport in 2D fracture/pipe networks: The SOLFRAC program, J. Contam. Hydrol., 89(1-2), 1-28.
11. Bour, O., and P. Davy (1997), Connectivity of random fault networks following a power law fault length distribution, Water Resour. Res., 33(7), 1567-1583.
12. Bour, O., and P. Davy (1998), On the connectivity of three-dimensional fault networks, Water Resour. Res., 34(10), 2611-2622.
13. Cacas, M. C., E. Ledoux, G. de Marsily, B. Tillie, B. Barbreau, A. Durand, B. Feuga, and P. Peaudecerf (1990), Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 1. The flow model, Water Resour. Res., 26(3), 479-489.
14. Chen, Z., and R. E. Ewing (1999), Numerical Treatment of Multiphase Flows in Porous Media, Springer, Beijing, China.
15. Cvetkovic, V., S. Painter, N. Outters, and J.-O. Selroos (2004), Stochastic simulation of radionuclide migration in discretely fractured rock near Aspo hard rock laboratory, Water Resour. Res., 40, W02404, doi:10.1029/2003WR002655.
16. de Dreuzy, J.-R., P. Davy, and O. Bour (2001), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on log-normal distribution of apertures, Water Resour. Res., 37(8), 2079-2095.
17. de Dreuzy, J.-R., P. Davy, and O. Bour (2002), Hydraulic properties of two-dimensional random fracture networks following power law distribution of length and aperture, Water Resour. Res., 38(12), 1276, doi:10.1029/2001WR001009.
18. de Dreuzy, J.-R., C. Darcel, P. Davy, and O. Bour (2004), Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution, Water Resour. Res., 40, W01502, doi:10.1029/2003WR002260.
19. Dershowitz, W., S. Follin, T. Eiben, and J. Anderson (1999), SR 97-Alternative models project: Discrete fracture network modeling for performance assessment of Aberg, SKB Report R-99-43, Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden.
20. Englman, R., Y. Gur, and Z. Jaeger (1983), Fluid flow through a crack network in rocks, J. Appl. Mech., 50, 707-711.
21. Fisher, R. (1953), Dispersion on a sphere, Proc. R. Soc. Lond., (A217), 295-305.
22. Follin, S., and R. Thunvik (1994), On the use of continuum approximations for regional modeling of groundwater flow through crystalline rocks, Adv. Water Resour., 17(4), 133-145.
23. Harbaugh, A. W., E. R. Banta, M. C. Hill, and M. G. McDonald (2000), MODFLOW-2000, the U. S. Geological Survey modular ground-water model - User guide to modularization concepts and the ground-water flow process, U.S. Geological Survey Open-File Report 00-92.
24. Harlow, F. H., and J. E. Welch (1965), Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8, 2182.
25. Hestir, K., and J. C. S. Long (1990), Analytical expressions for the permeability of random two-dimensional Poisson fracture networks based on regular lattice percolation and equivalent media theories, J. Geophys. Res., 95(B13), 21,565-21,581.
26. Jackson, C. P., A. R. Hoch, and S. Todman (2000), Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium, Water Resour. Res., 36(1), 189-202.
27. Kirkpatrick, S. (1973), Percolation and conduction, Rev. Mod. Phys., 574-588.
28. Langevin, C. D. (2003), Stochastic groundwater flow simulation with a fracture zone continuum model, Ground Water, 41(5), 587-601.
29. Liu, H. H., and G. S. Bodvarsson (2001), Constitutive relations for unsaturated flow in fracture networks, J. Hydrol., 252, 116-125.
30. Long, J. C. S., J. S. Remer, C. R. Wilson, and P. A. Witherspoon (1982), Porous media equivalent for networks of discontinuous fractures, Water Resour. Res., 18(3), 645-658.
31. McKenna, S. A., and P. C. Reeves (2006), Fractured continuum approach to stochastic permeability modeling, in Stochastic Modeling and Geostatistics: Principles, Methods and Case Studies, vol. II, AAPG Comput. Appl. Geol. 5, edited by T. C. Coburn, J. M. Yarus, and R. L. Chambers, pp. 173-186, AAPG, Tulsa, Okla.
32. National Research Council (1996), Rock Fractures and Fluid Flow, Contemporary Understanding and Applications, National Academy Press, Washington, D. C.
33. Neuman, S. P. (1987), Stochastic continuum presentation of fractured rock permeability as an alternative to REV and fracture network concepts, in Proceedings of the 28th U.S. Symposium on Rock Mechanics, Tucson, pp. 533-561.
34. Neuman, S. P. (1988), A Proposed Conceptual Framework and Methodology for Investigating Flow and Transport in Swedish Crystalline Rocks, Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden.
35. Neuman, S. P. (2005), Trends, prospects and challenges in quantifying flow and transport through fractured rocks, Hydrogeol. J., 13, 124-147.
36. Neuman, S. P., and J. S. Depner (1988), Use of variable-scale pressure test data to estimate the log hydraulic conductivity covariance and dispersivity of fractured granites near Oracle, Arizona, J. Hydrol., 102, 475-501.
37. Nguyen, T. S., L. Borgesson, M. Chijimatsu, J. Rutqvist, T. Fujita, J. Hernelind, A. Kobayashi, Y. Ohnishi, M. Tanaka, and L. Jing (2001), Hydro-mechanical response of a fractured granitic rock mass to excavation of a test pit - the Kamaishi Mine experiment in Japan, Int. J. Rock Mech. Mining Sci., 38(1), 79-94.
38. Niemi, A., K. Kontio, A. Kuusela-Lahtinen, and A. Poteri (2000), Hydraulic characterization and upscaling of fracture networks based on multiple-scale well test data, Water Resour. Res., 36(12), 3481-3497.
39. Oda, M. (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35(4), 483-495.
40. Ohman, J., and A. Niemi (2003), Upscaling of facture hydraulics by means of an oriented correlated stochastic continuum model, Water Resour. Res., 39(10), 1277, doi:10.1029/2002WR001776.
41. Painter, S., and V. Cvetkovic (2005), Upscaling discrete fracture network simulations: An alternative to continuum transport models, Water Resour. Res., 41, W02002, doi:10.1029/2004WR003682.
42. Park, Y.-J., J.-R. de Dreuzy, K.-K. Lee, and B. Berkowitz (2001), Transport and intersection mixing in random fracture networks with power law length distributions, Water Resour. Res., 37(10), 2493-2501.
43. Parney, R. W. (1999), Statistical continuum modeling of mass transport through fractured media in two and three dimensions, Ph.D. dissertation, Univ. of British Columbia, Vancouver, Canada.
44. Pohlmann, K. F., G. Pohll, J. B. Chapman, A. E. Hassan, R. Carroll, C. Shirley (2004), Modeling to Support Groundwater Contaminant Boundaries for the Shoal Underground Nuclear test, DOE/NV13609-13, DRI Report 45184.
45. Pohlmann, K. F., M. Ye, D. M. Reeves, M. Zavarin, and D. Decker (2007), Modeling of Groundwater Flow and Radionuclide Transport at the Climax Mine sub-CAU, Nevada Test Site, DOE/NV26383-05, DRI Report, 45226.
46. Priest, S. D. (1993), Discontinuity Analysis for Rock Engineering, 1st ed., Chapman and Hall, London.
47. Reeves, D. M., D. A. Benson, and M. M. Meerschaert (2008), Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation, Water Resour. Res., 44, W05404, doi:10.1029/2007WR006069.
48. Renshaw, C. E. (1999), Connectivity of joint networks with power law length distributions, Water Resour. Res., 35(9), 2661-2670.
49. Robinson, P. C. (1983), Connectivity of fracture systems - a percolation theory approach, J. Phys. A: Math. Gen., 16, 605-614.
50. Robinson, P. C. (1984), Numerical calculations of critical densities for lines and planes, J. Phys. A: Math. Gen., 17, 2823-2830.
51. Sahimi, M. (1995), Flow and Transport in Porous Media and Fractured Rock, 1st ed., VCH, Weinheim.
52. Schwartz, F. W., and L. Smith (1988), A continuum approach for modeling mass transport in fractured media, Water Resour. Res., 24(8), 1360-1372.
53. Selroos, J.-O., D. D. Walker, A. Strom, B. Gylling, and S. Follin (2002), Comparison of alternative modeling approaches for groundwater flow in fractured rock, J. Hydrol., 257, 174-188.
54. Smith, L., C. W. Mase, and F. W. Schwartz (1987), Estimation of fracture aperture using hydraulic and tracer tests, in Proceedings of the 28th U.S. Symposium on Rock Mechanics, edited by I. W. Farmer et al., pp. 453-463, Tucson, Ariz.
55. Snow, D. T. (1969), Anisotropic permeability of fractured media, Water Resour. Res., 5(6), 1273-1289.
56. Svensson, U. (2001a), A continuum representation of fracture networks: part I. Method and basic test cases, J. Hydrol., 250, 170-186.
57. Svensson, U. (2001b), A continuum representation of fracture networks: part II. Application to the Aspo Hard Rock Laboratory, J. Hydrol., 250, 187-205.
58. Tsang, Y. W. (1992), Usage of "equivalent apertures" for rock fractures as derived from hydraulic and tracer tests, Water Resour. Res., 28(5), 1451-1455.
59. Tsang, Y. W., C.-F. Tsang, F. V. Hale, and B. Dverstorp (1996), Tracer transport in a stochastic continuum model of fractured media, Water Resour. Res., 32(10), 3077-3092.
60. Vesselinov, V. V., S. P. Neuman, and W. A. Illman (2001), Three-dimensional numerical inversion of pneumatic cross-hole test in unsaturated fractured tuff: 2. Equivalent parameters, high-resolution stochastic imaging and scale effects, Water Resour. Res., 37(12), 3019-3041.
61. Widen, H., and D. D. Walker (1999), Alternative models project: Stochastic continuum modeling of Aberg, SKB Rep. R-99-42, Swedish Nuclear Fuel and Waste Management Co., Stockholm, Sweden.
62. Zhang, X., and D. J. Sanderson (2002), Numerical Modeling and Analysis of Fluid Flow and Deformation of Fractured Rock Masses, Elsevier, New York.
63. Zimmerman, R. W., and G. S. Bodvarsson (1996), Effective transmissivity of two-dimensional fracture network, Int. J. Rock Mech. Min. Sci. Geochem. Abstr., 33(4), 433-438.