Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions

Journal of Geophysical Research: Solid Earth

Volumn 119, Issue 8, 2014, Pages 6288-6307

  Lang, P S ^a   Paluszny, A ^a   Zimmerman, R W ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

DFM; discrete fracture; effective permeability; finite element; unstructured grid; upscaling

Indexed keywords

FINITE ELEMENT METHOD; LAPLACE TRANSFORM; NUMERICAL MODEL; PERMEABILITY; POROUS MEDIUM; POWER LAW; SIZE DISTRIBUTION; UPSCALING;

EID: 84928039603     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1002/2014JB011027     Document Type: Article

References (51)

1. Adler, P., and, J. Thovert, (1999), Fractures and Fracture Networks, 431 pp., Springer, Amsterdam, Netherlands.
2. Amaziane, B., and, T. Hontans, (2002), Equivalent permeability and simulation of two-phase flow in heterogeneous porous media, Comput. Geosci., 5, 279-300, doi: 10.1023/A:1014508622020.
3. Azizmohammadi, S., and, J. D. Paul, (2012), Scale dependence of equivalent permeability tensor in naturally fractured reservoirs, in EGU General Assembly Conference Abstracts, vol. 14, edited by, A. Abbasi, and, N. Giesen, 9018 pp., SAO/NASA Astrophysics Data System. [Available at http://adsabs.harvard.edu/abs/2012EGUGA.14.9018A ].
4. Baghbanan, A., and, L. Jing, (2008), Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture, Int. J. Rock Mech. Min. Sci., 45 (8), 1320-1334, doi: 10.1016/j.ijrmms.2008.01.015.
5. Balberg, I., C. Anderson, S. Alexander, and, N. Wagner, (1984), Excluded volume and its relation to the onset of percolation, Phys. Rev. B, 30 (7), 3933-3943.
6. Belayneh, M., S. Geiger, and, S. K. Matthäi, (2006), Numerical simulation of water injection into layered fractured carbonate reservoir analogs, AAPG Bull., 90 (10), 1473-1493, doi: 10.1306/05090605153.
7. Berkowitz, B., and, P. M. Adler, (1998), Stereological analysis of fracture network structure in geological formations, J. Geophys. Res., 103 (B7), 15,339-15,360, doi: 10.1029/98JB01072.
8. Bogdanov, I., V. Mourzenko, J.-F. Thovert, and, P. Adler, (2007), Effective permeability of fractured porous media with power-law distribution of fracture sizes, Phys. Rev. E, 76 (3), 036,309, doi: 10.1103/PhysRevE.76.036309.
9. Bogdanov, I. I., V. V. Mourzenko, J.-F. Thovert, and, P. M. Adler, (2003), Effective permeability of fractured porous media in steady state flow, Water Resour. Res., 39 (1), 1023, doi: 10.1029/2001WR000756.
10. Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and, B. Berkowitz, (2001), Scaling of fracture systems in geological media, Rev. Geophys., 39 (3), 347-383.
11. Decroux, B., and, O. Gosselin, (2013), Computation of effective dynamic properties of naturally fractured reservoirs: Comparison and validation of methods, in 75th EAGE Conference and Exhibition Incorporating SPE EUROPEC, 10-13 June, London, UK, pp. 1-18, Soc. of Pet. Eng., doi: 10.2118/164846-MS.
12. Durlofsky, L. J., (1991), Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resour. Res., 27 (5), 699-708, doi: 10.1029/91WR00107.
13. Elfeel, M. A., and, S. Geiger, (2012), Static and dynamic assessment of DFN permeability upscaling, in SPE Europec/EAGE Annual Conference, 4-7 June, Copenhagen, Denmark, pp. 1-16, Soc. of Pet. Eng., doi: 10.2118/154369-MS.
14. Farmer, C. L., (2002), Upscaling: A review, Int. J. Numer. Methods Fluids, 40 (1-2), 63-78, doi: 10.1002/fld.267.
15. Gonzalez-Garcia, R., O. Huseby, J. Thovert, B. Ledésert, and, P. M. Adler, (2000), Three-dimensional characterization of a fractured granite and transport properties, J. Geophys. Res., 105 (B9), 21,387-21,401, doi: 10.1029/2000JB900149.
16. Holden, L., and, O. Lia, (1992), A tensor estimator for the homogenization of absolute permeability, Transp. Porous Media, 8 (1), 37-46, doi: 10.1007/BF00616891.
17. Koudina, N., R. Gonzalez Garcia, J.-F. Thovert, and, P. Adler, (1998), Permeability of three-dimensional fracture networks, Phys. Rev. E, 57 (4), 4466-4479, doi: 10.1103/PhysRevE.57.4466.
18. Leung, C. T. O., and, R. W. Zimmerman, (2012), Estimating the hydraulic conductivity of two-dimensional fracture networks using network geometric properties, Transp. Porous Media, 93 (3), 777-797, doi: 10.1007/s11242-012-9982-3.
19. Long, J. C. S., J. S. Remer, C. R. Wilson, and, P. A. Witherspoon, (1982), Porous media equivalents for networks of discontinuous fractures, Water Resour. Res., 18 (3), 645-658, doi: 10.1029/WR018i003p00645.
20. Malinouskaya, I., J.-F. Thovert, V. V. Mourzenko, P. M. Adler, R. Shekhar, S. Agar, E. Rosero, and, M. Tsenn, (2014), Fracture analysis in the Amellago outcrop and permeability predictions, Pet. Geosci., 20 (1), 93-107, doi: 10.1144/petgeo2012-094.
21. Marrett, R., (1996), Aggregate properties of fracture populations, J. Struct. Geol., 18 (2-3), 169-178, doi: 10.1016/S0191-8141(96)80042-3.
22. Matsumoto, M., and, T. Nishimura, (1998), Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Trans. Model. Comput. Simul., 8 (1), 3-30, doi: 10.1145/272991.272995.
23. Matthäi, S. K., and, M. Belayneh, (2004), Fluid flow partitioning between fractures and a permeable rock matrix, Geophys. Res. Lett., 31 (7), L07602, doi: 10.1029/2003GL019027.
24. Matthäi, S. K., et al. (2007), Numerical simulation of multi-phase fluid flow in structurally complex reservoirs, Geol. Soc. London Spec. Publ., 292 (1), 405-429, doi: 10.1144/SP292.22.
25. Min, K.-B., J. Rutqvist, C.-F. Tsang, and, L. Jing, (2004), Stress-dependent permeability of fractured rock masses: A numerical study, Int. J. Rock Mech. Min. Sci., 41 (7), 1191-1210, doi: 10.1016/j.ijrmms.2004.05.005.
26. Mourzenko, V., J.-F. Thovert, and, P. Adler, (2005), Percolation of three-dimensional fracture networks with power-law size distribution, Phys. Rev. E, 72 (3), 036,103, doi: 10.1103/PhysRevE.72.036103.
27. Mourzenko, V. V., J.-F. Thovert, and, P. M. Adler, (2011), Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities, Phys. Rev. E, 84 (3), 036,307, doi: 10.1103/PhysRevE.84.036307.
28. Nick, H. M., A. Paluszny, M. J. Blunt, and, S. K. Matthai, (2011), Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations, Phys. Rev. E, 84 (5), 056,301, doi: 10.1103/PhysRevE.84.056301.
29. Oda, M., (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35 (4), 483-495.
30. Odling, N. E., (1997), Scaling and connectivity of joint systems in sandstones from western Norway, J. Struct. Geol., 19 (10), 1257-1271, doi: 10.1016/S0191-8141(97)00041-2.
31. Olson, J. E., (2003), Sublinear scaling of fracture aperture versus length: An exception or the rule?, J. Geophys. Res., 108 (B9), 2413, doi: 10.1029/2001JB000419.
32. Olson, J. E., S. E. Laubach, and, R. H. Lander, (2007), Combining diagenesis and mechanics to quantify fracture aperture distributions and fracture pattern permeability, Geol. Soc. London Spec. Publ., 270 (1), 101-116, doi: 10.1144/GSL.SP.2007.270.01.08.
33. Paluszny, A., and, S. K. Matthai, (2010), Impact of fracture development on the effective permeability of porous rocks as determined by 2-D discrete fracture growth modeling, J. Geophys. Res., 115 (B2), B02203, doi: 10.1029/2008JB006236.
34. Paluszny, A., and, R. W. Zimmerman, (2011), Numerical simulation of multiple 3D fracture propagation using arbitrary meshes, Comput. Meth. Appl. Mech. Eng., 200 (9-12), 953-966, doi: 10.1016/j.cma.2010.11.013.
35. Piggott, A. R., (1997), Fractal relations for the diameter and trace length of disc-shaped fractures, J. Geophys. Res., 102 (B8), 18,121-18,125, doi: 10.1029/97JB01202.
36. Pouya, A., and, O. Fouché, (2009), Permeability of 3D discontinuity networks: New tensors from boundary-conditioned homogenisation, Adv. Water Resour., 32 (3), 303-314, doi: 10.1016/j.advwatres.2008.08.004.
37. Reeves, D. M., R. Parashar, G. Pohll, R. Carroll, T. Badger, and, K. Willoughby, (2013), The use of discrete fracture network simulations in the design of horizontal hillslope drainage networks in fractured rock, Eng. Geol., 163, 132-143, doi: 10.1016/j.enggeo.2013.05.013.
38. Renard, P., and, G. de Marsily, (1997), Calculating equivalent permeability: A review, Adv. Water Resour., 20 (5-6), 253-278, doi: 10.1016/S0309-1708(96)00050-4.
39. Rutqvist, J., C. Leung, A. Hoch, Y. Wang, and, Z. Wang, (2013), Linked multicontinuum and crack tensor approach for modeling of coupled geomechanics, fluid flow and transport in fractured rock, J. Rock Mech. Geotech. Eng., 5 (1), 18-31, doi: 10.1016/j.jrmge.2012.08.001.
40. Sanford, R. J., and, J. W. Dally, (1979), A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns, Eng. Fract. Mech., 11 (4), 621-633, doi: 10.1016/0013-7944(79)90123-1.
41. Snow, D. T., (1969), Anisotropie permeability of fractured media, Water Resour. Res., 5 (6), 1273-1289, doi: 10.1029/WR005i006p01273.
42. Stüben, K., (2001), A review of algebraic multigrid, J. Comput. Appl. Math., 128 (1-2), 281-309, doi: 10.1016/S0377-0427(00)00516-1.
43. Taylor, W. L., D. D. Pollard, and, A. Aydin, (1999), Fluid flow in discrete joint sets: Field observations and numerical simulations, J. Geophys. Res., 104 (B12), 28,983-29,006, doi: 10.1029/1999JB900179.
44. van Golf-Racht, T., (1982), Fundamentals of Fractured Reservoir Engineering, 732 pp., Elsevier BV, Amsterdam, Netherlands.
45. Wen, X., L. Durlofsky, and, M. Edwards, (2003), Use of border regions for improved permeability upscaling, Math. Geol., 35 (5), 521-547, doi: 10.1023/A:1026230617943.
46. Witherspoon, P. A., J. S. Y. Wang, K. Iwai, and, J. E. Gale, (1980), Validity of cubic law for fluid flow in a deformable rock fracture, Water Resour. Res., 16 (6), 1016-1024, doi: 10.1029/WR016i006p01016.
47. Wu, X., T. Hou, and, Y. Efendiev, (2002), Analysis of upscaling absolute permeability, Discrete Contin. Dyn. Syst. Ser. B, 2 (2), 185-204, doi: 10.3934/dcdsb.2002.2.185.
48. Wu, Y.-S., C. Haukwa, and, G. Bodvarsson, (1999), A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain, Nevada, J. Contam. Hydrol., 38 (1-3), 185-215, doi: 10.1016/S0169-7722(99)00014-5.
49. Zhang, X., D. Sanderson, R. Harkness, and, N. Last, (1996), Evaluation of the 2-D permeability tensor for fractured rock masses, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33 (1), 17-37, doi: 10.1016/0148-9062(95)00042-9.
50. Zimmerman, R., and, G. S. Bodvarsson, (1996), Effective transmissivity of two-dimensional fracture networks, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33 (4), 433-438.
51. Zimmerman, R., S. Kumar, and, G. Bodvarsson, (1991), Lubrication theory analysis of the permeability of rough-walled fractures, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28 (4), 325-331, doi: 10.1016/0148-9062(91)90597-F.