Effects of fractal surface roughness and lithology on single and multiphase flow in a single fracture: An experimental investigation

International Journal of Multiphase Flow

Volumn 68, Issue , 2015, Pages 40-58

  Babadagli, Tayfun ^a   Ren, Xiaojuan ^b   Develi, Kayhan ^c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b XI'AN SHIYOU UNIVERSITY   (China)

^c ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Fractal dimension; Fracture roughness; Hydraulic conductivity; Multiphase flow in single fractures; Single phase flow; Unsteady state displacement in fractures

Indexed keywords

HYDRAULIC CONDUCTIVITY;

EXPERIMENTAL INVESTIGATIONS; FRACTURE ROUGHNESS; SINGLE FRACTURE; SINGLE-PHASE FLOW; UNSTEADY STATE;

FRACTAL DIMENSION;

EID: 84910066632     PISSN: 03019322     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmultiphaseflow.2014.10.004     Document Type: Article

References (85)

1. Amundsen H., Wagner G., Oxaal U., Meakin P., Feder J., Jøssang T. Slow two-phase flow in artificial fractures: experiments and simulations. Water Resour. Res. 1999, 35:2619-2626.
2. Auradou H., Hulin J.P., Roux S. Experimental study of miscible displacement fronts in rough self-affine fractures. Phys. Rev. E 2001, 63:066306. 1-10.
3. Auradou H., Maloy K.J., Schmittbuhl J., Hansen A. Drainage in a rough gouge-filled fracture. Transp. Porous Media 2003, 50:267-305.
4. Babadagli T., Develi K. On the application of methods used to calculate fractal dimension of fracture surfaces. Fractals 2001, 9:105-128.
5. Babadagli T., Develi K. Fractal characteristics of rocks fractured under tension. Theor. Appl. Fract. Mech. 2003, 39:73-88.
6. Babadagli, T., Raza, S., Ren, X., Develi, K., 2014. Effect of surface roughness and lithology on the water-gas and water-oil relative permeabilities of single fractures. Transp. Porous Media (submitted for publication).
7. Berkowitz B. Characterizing flow and transport in fractured geological media: a review. Adv. Water Resour. 2002, 25:861-884.
8. Bogdanov I.I., Mourzenko V.V., Thovert J.F., Adler P.M. Two-phase flow through fractured porous media. Phys. Rev. E 2003, 68. 10.1103/PhysRevE.68.026703.
9. Brown S.R. Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. 1987, 92:1337-1347.
10. Brown S.R. A note on the description of surface roughness using fractal dimension. Geophys. Res. Lett. 1987, 14:1095-1098.
11. Brown S.R., Scholz S.H. Broad bandwidth study of the topography of natural rock surfaces. J. Geophys. Res. 1985, 90:12575-12582.
12. Brush D.J., Thomson N.R. Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour. Res. 2003, 39:1058. 10.1029/2002WR001346.
13. Chen C.-Y., Horne R.N. Experimental study of liquid-gas flow structure effects on relative permeabilities in a fracture. Water Resour. Res. 2004, 40:W08301. 10.1029/2004WR003026.
14. Chen C.-Y., Horne R.N. Two-phase flow in rough-walled fractures: experimental and a flow structure model. Water Resour. Res. 2006, 42:W03430. 10.1029/2004WR003837.
15. Chen Z., Narayan S.P., Yang Z., Rahman S.S. An experiment investigation of hydraulic behaviour of fractures and joints in granitic rock. Int. J. Rock Mech. Min. Sci. 2000, 37:1061-1071.
16. Chen Z., Qian J.Z., Luo S.H., Zhan H.B. Experimental study of friction factor for groundwater flow in a single rough fracture. J. Hydrodyn. 2009, 21:820-825.
17. Den Outer A., Kasshoek J.F., Hack H.R.G.K. Difficulties with using continuous fractal theory for discontinuity surfaces. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1995, 32:3-9.
18. Develi, K., 2006. Quantification of Surface Roughness with Theoretical and Experimental Methods for Mechanical Modelling of Jointed Rocks. PhD Thesis. Dep. of Geol. Eng., Istanbul Technical University, Istanbul, Turkey.
19. Develi K., Babadagli T. Quantification of natural fracture surfaces using fractal geometry. Math. Geol. 1998, 30:971-998.
20. Develi, K., Babadagli, T., 2014. Experimental analysis of single-phase flow through deformable rough rock fractures. Int. J. Rock Mech. Min. Sci. (submitted for publication).
21. Develi K., Babadagli T., Comlekci C. A new computer controlled surface scanning device for measurements of joint surface roughness. Comput. Geosci. 2001, 27:265-277.
22. Dubuc B., Quiniou J.F., Roques-Carmes C., Tricot C., Zucker S.W. Evaluating the fractal dimension of profiles. Phys. Rev. A 1989, 39:1500-1512.
23. Faoro I., Niemeijer A., Marone C., Elsworth D. Influence of shear and deviatoric stress on the evolution of permeability in fractured rock. J. Geophys. Res. 2009, 114:B01201. 1-10.
24. Fourar M., Bories S. Experimental study of air-water two-phase flow through a fracture (narrow channel). Int. J. Multiphase Flow 1995, 21:621-637.
25. Fourar M., Lenormand R. A new model for two-phase flows at high velocities through porous media and fractures. J. Pet. Sci. Eng. 2001, 30:121-127.
26. Fourar M., Bories S., Lenormand R., Persoff P. Two-phase flow in smooth and rough fractures: measurement and correlation by porous-medium and pipe flow models. Water Resour. Res. 1993, 29:3699-3708.
27. Genabeek O.V., Rothman D.H. Critical behavior in flow through a rough-walled channel. Phys. Lett. A 1999, 255:31-36.
28. Glover P.W.J., Matsuki K., Hikima R., Hayashi K. Fluid flow in synthetic rough fractures and application to the Hachimantai geothermal hot dry rock test site. J. Geophys. Res. 1998, 103:9621-9635.
29. Huang S.L., Oelfke S.M., Speck R.C. Applicability of fractal characterization and modeling to joint profiles. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1992, 29:89-98.
30. Inoue J., Sugita H. Forth-order approximation of fluid flow through rough-walled rock fracture. Water Resour. Res. 2003, 39:1202. 1-10. 10.1029/2002WR001411.
31. Isakov E., Ogilvie R.S.R., Taylor C.W., Glover P.W.J. Fluid flow through fractures in rocks I: high resolution aperture determinations. Earth Planet. Sci. Lett. 2001, 191:267-282.
32. Karperien, A., 1999-2013. FracLac for ImageJ, http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm.
33. Klinkenberg B. A review of methods used to determine the fractal dimension of linear features. Math. Geol. 1994, 36:23-46.
34. Kobayashi, A., Yamashita, R., 1990. Numerical studies of fluid flow through channels on fracture plane. In: Int. Conf. Mech. Joint Fault. Rock, pp. 613-620.
35. Kostakis, K., Harrison, J.P., Young, A.T., 1996. Investigation of two-phase flow in single rough fracture. In: Eurock '96. Balkema, Rotterdam, pp. 1215-1220.
36. Kwasiniewski M.A., Wang J.A. Surface roughness evolution and mechanical behavior of rock joints. Chaos, Soliton Fract. 1997, 34:709.
37. Lee J., Kang J.M., Choe J. Experimental analysis on the effects of variable apertures on tracer transport. Water Resour. Res. 2003, 39:1-11.
38. Louis, C., Maini, Y., 1970. Determination of in-situ hydraulic parameters in jointed rock. In: Proc. 2nd Congr. Rock Mechanics, 21-26 September 1970, Belgrade, Inst. Dev. Water Resour., vol. 1, Belgrade, pp. 235-243.
39. Mandelbrot B.B., Passoja D.E., Paullay A.J. Fractal character of fracture surfaces of metals. Nature 1984, 308:721-722.
40. Miller S.M., McWilliams P.C., Kerkering J.C. Ambiguities in estimating fractal dimensions of rock fracture surfaces. Rock Mech. Contribution Challenges 1990, 471-478. Balkema, Rotterdam. W. Hustrulid, G.A. Johnson (Eds.).
41. 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 relations to some field observations. Water Resour. Res. 1988, 24:2033-2048.
42. Mourzenko V.V., Thovert J.-F., Adler P.M. Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities. Phys. Rev. E 2011, 84. 10.1103/PhysRevE.84.036307.
43. Murata S., Saito T. Estimation of tortuosity of fluid flow through a single fracture. J. Can. Pet. Technol. 2003, 42:39-45.
44. Murata, S., Mitsuishi, H., Saito, T., 2002. Characterization of Fracture Permeability by Using a Fractal Model. SPE 77881 Paper Presented at the Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, Australia, 2002, 1-8.
45. Naderi K., Babadagli T. Visual analysis of displacement processes in porous media under ultrasound effect. Phys. Rev. E 2011, 83:056323/1-056323/14.
46. Nemoto K., Watanabe N., Hirano N., Tsuchiya N. Direct measurement of contact area and stress dependence of anisotropic flow through rock fracture with heterogeneous aperture distribution. Earth Planet. Sci. Lett. 2009, 281.
47. Neuzil C.C., Tracy J.V. Flow through fractures. Water Resour. Res. 1981, 17:191-199.
48. Nowamooz A., Radilla G., Fourar M. Non-Darcian two-phase flow in a transparent replica of rough-walled rock fracture. Water Resour. Res. 2009, 45:W07406. 10.1029/2008WR007315.
49. Oron A.P., Berkowitz B. Flow in rock fractures: the local cubic law assumption reexamined. Water Resour. Res. 1998, 34:2811-2825.
50. Pan X., Wong R.C., Maini B.B. Effects of viscous coupling on the flow of oil and water in a fracture. CIM 1998, 98-15.
51. Pande C.S., Richards L.R., Smith S. Fractal characteristics of fractured surfaces. J. Mater. Sci. Lett. 1987, 6:295-297.
52. Persoff P., Pruess K. Two-phase flow visualization and relative permeability measurements in natural rough-walled rock fractures. Water Resour. Res. 1995, 3:1175-1186.
53. Piggott, A.R., Elsworth, D., 1990. Laboratory studies of transport within a single rock fracture. In: Barton, Stephansson (Eds.), Rock Joints. Belkema, Rotterdam, pp. 397-404.
54. Plouraboué F., Kurowski P., Boffa J.M., Hulin J.P., Roux S. Experimental study of the transport properties of rough self-affine fractures. J. Contam. Hydrol. 2000, 46:295-318.
55. Pruess K., Tsang Y.W. On two-phase relative permeability and capillary pressure of rough-walled rock fractures. Water Resour. Res. 1990, 26:1915-1926.
56. Qian J., Zhan H., Zhao W., Sun F. Experimental study of turbulent unconfined groundwater flow in a single fracture. J. Hydrol. 2005, 311:134-142.
57. Radilla G., Nowamooz A A., Fourar M. Modeling Non-Darcian single- and two-phase flow in transparent replicas of rough-walled rock fractures. Transp. Porous Media 2013, 98:401-426.
58. Romm, E.S., 1966. Fluid flow in fractured rocks, Nedra, Moscow (English translation by W.R. Blake, Bartleville, Okla., 1972).
59. Rossen, W.R., Kumar, A.T.A., 1992. Single- and Two-phase Flow in Natural Fractures. SPE, Abstr., Presented at the 67th Ann. Tech. Conf. Exh. SPE, Washington, DC, 4-7 October, pp. 595-603.
60. Rutqvist J., Stephansson O. The role of hydromechanical coupling in fractured rock engineering. Hydrogeol. J. 2003, 11:7-40.
61. Rutqvist, J., Tsang, C.-F., Ekman, D., Stephansson, O., 1997. Evaluation of In Situ Hydromechanical Properties of Rock Fractures at Laxemar in Sweden. Paper Presented at 1st Asian Rock Mechanics Symposium ARMS 97, Seoul, Korea.
62. Schmittbuhl J., Vilotte J.P., Roux S. Reliability of self-affine measurements. Phys. Rev. E 1995, 51:131-147.
63. Schmittbuhl J., Steyer A., Jouniaux L., Toussaint R. Fracture morphology and viscous transport. Int. J. Rock Mech. Min. Sci. 2008, 422-430.
64. Shad S., Gates A.D. Multiphase flow in fractures: co-current and counter-current flow in a fracture. J. Can. Pet. Technol. 2010, 49:48-55. 10.2118/133205-PA.
65. Shad, S., Maini, B.B., Gates, I.D., 2010. Effect of Fracture and Flow Orientation on Two-phase Flow in an Oil-Wet Fracture: Relative Permeability Curves and Flow Structure. SPE, 132229, Presented at the 2010 SPE Western Regional Meeting, Anaheim, CA, 27-29 May.
66. Shapiro A.M., Nicholas J.R. Assessing the validity of the channel model of fracture aperture under field conditions. Water Resour. Res. 1989, 25:817-828.
67. Tsang Y.W. The effect of tortuosity on fluid flow through a single fracture. Water Resour. Res. 1984, 20:1209-1215.
68. Tsang Y.W., Tsang C.F. Channel model of flow through fractured media. Water Resour. Res. 1987, 23:467-479.
69. Tsang Y.W., Tsang C.F., Neretnieks I., Moreno L. Flow and tracer transport in fractures media: a variable aperture channel model and its properties. Water Resour. Res. 1988, 24:2049-2060.
70. Unger A.J.A., Mase C.W. Numerical study of the hydrochemical behavior of two rough fracture surfaces in contact. Water Resour. Res. 1993, 29:2101-2114.
71. van Dam, D.B., de Pater, C.J., 1999. Roughness of Hydraulic Fractures: The Importance of In-situ Stress and Tip Processes. SPE 56596, Presented at 1993 SPE Annual Technol. Conf. Ex., Houston, TX, 3-6 October.
72. Vu M.N., Pouya A., Seyedi D.M. Modelling of steady-state fluid flow in 3D fractured isotropic porous media: application to effective permeability calculation. Int. J. Numer. Anal. Meth. Geomech. 2013, 37:2257-2277. 10.1002/nag.2134.
73. Vu M.N., Pouya A., Seyedi D.M. Theoretical and numerical study of the steady-state flow through finite fractured porous media. Int. J. Numer. Anal. Meth. Geomech. 2014, 38:221-235. 10.1002/nag.2200.
74. Wang J.S.Y., Narasimhan T.N., Scholz C.H. Aperture correlation of a fractal fracture. J. Geophys. Res. 1988, 93:2216-2224.
75. Watanabe N., Hirano N., Tamagawa T., Tezuka K., Tsuchiya N. Numerical estimation of aperture structure and flow wetted field in rock fracture. GRC Trans. 2005, 29.
76. Watanabe N., Hirano N., Tsuchiya N. Diversity of channeling flow in heterogeneous aperture distribution inferred from integrated experimental-numerical analysis on flow through shear fracture in granite. J. Geophys. Res. 2009, 114:BO4208. 10.1029/2008JB005959.
77. Witherspoon P.A., Wang J.S.Y., Iwai K., Gale J.E. Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res. 1980, 16:1016-1024.
78. Wong, D.A., Walters, D.A., Maini, B., 1996. The Effect of a Variable Aperture System on the Two-phase Flow Response in an Oil Sand Fracture. CMI, Presented at the 47th Annual Technol. Meet. Petr. Soc., Calgary, AB, 10-12 June, pp. 1-10.
79. Wong R.C.K., Pan Z., Maini B.B. Correlation between pressure gradient and phase saturation for oil-water flow in smooth- and rough-walled parallel-plate models. Water Resour. Res. 2008, 44:WO2418. 10.1029/2007WR006043.
80. Xie H., Wang J., Kwasniewski M.A. Multifractal characterization of rock fracture surfaces. Int. J. Rock Mech. Min. Sci. 1997, 36:19-27.
81. Yamatomi J., Mogi G., Adachi T., Sugiura K. Modeling and analysis of fluid flow through a rock fracture with wall roughness. Rock Mech. Nat. Int. 2001, 705-712.
82. Yeo, I.W., Zimmerman, R.W., de Freitas, M.H., 1996. Design and analysis of an experimental system to measure directional permeabilities of a rock fracture under normal and shear loading. In: Barla (Ed.), ISRM-Eurock'96. Balkema, Rotterdam, pp. 1223-1227. ISBN:90 5410 843 6.
83. Yeo I.W., De Freitas M.H., Zimmerman R.W. Effect of shear displacement on the aperture and permeability of a rock fracture. Int. J. Rock Mech. Min. Sci. 1998, 35:1051-1070.
84. Zimmerman R.W., Bodvarsson G.S. Review article: hydraulic conductivity of rock fractures. Transp. Porous Media 1996, 23:1-30.
85. Zimmerman R.W., Al-Yaarubi A., Pain C.C., Grattoni C.A. Non-linear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. Abstr. 2004, 41.