Roughness decomposition and nonlinear fluid flow in a single rock fracture

International Journal of Rock Mechanics and Mining Sciences

Volumn 75, Issue , 2015, Pages 102-118

  Zou, Liangchao ^a   Jing, Lanru ^a   Cvetkovic, Vladimir ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Hydraulic aperture; Navier Stokes equations; Rock fractures; Roughness decomposition; Wavelet analysis

Indexed keywords

BOUNDARY LAYERS; FINITE VOLUME METHOD; FLOW FIELDS; FRACTURE; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS; REYNOLDS NUMBER; ROCK MECHANICS; ROCKS; VISCOUS FLOW;

FLUID-FLOW; FRACTURED ROCK MASS; HIGH FREQUENCY HF; HYDRAULIC APERTURE; NAVIER-STOKES EQUATION; NONLINEAR FLUIDS; ROCK FRACTURES; ROUGHNESS DECOMPOSITION; WALL SURFACES; WAVELET-ANALYSIS;

SURFACE ROUGHNESS;

FINITE VOLUME METHOD; FLUID FLOW; FRACTURE MECHANICS; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; ROCK MECHANICS; ROUGHNESS; TWO-DIMENSIONAL MODELING; WAVELET ANALYSIS;

EID: 84922989675     PISSN: 13651609     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijrmms.2015.01.016     Document Type: Article

References (50)

1. 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(6):1016-1024.
2. Oron A.P., Berkowitz B. Flow in rock fractures: the local cubic law assumption reexamined. Water Resour Res 1998, 34(11):2811-2825.
3. Brown S.R., Stockman H.W., Reeves S.J. Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys Res Lett 1995, 22(18):2537-2540.
4. 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(4):1085.
5. Yeo I.W., Ge S. Applicable range of the Reynolds equation for fluid flow in a rock fracture. Geosci J 2005, 9(4):347-352.
6. 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. Int J Rock Mech Min Sci 2008, 45(7):1082-1101.
7. Zimmerman R.W., Kumar S., Bodvarsson G.S. Lubrication theory analysis of the permeability of rough-walled fractures. Int J Rock Mech Min Sci 1991, 28(4):325-331.
8. Zimmerman R.W., Bodvarsson G.S. Hydraulic conductivity of rock fractures. Transp Porous Media 1996, 23:1-30.
9. V.Di Federico Estimates of equivalent aperture for non-Newtonian flow in rough-walled fracture. Int J Rock Mech Min Sci 1997, 34(7):1133-1137.
10. Sisavath S., Al-Yaarubi A., Pain C.C., Zimmerman R.W. A simple model for deviations from the cubic law for a fracture undergoing dilation or closure. Pure Appl Geophys 2003, 160:1009-1022.
11. Basha H.A., El-Asmar W. The fracture flow equation and its perturbation solution. Water Resour Res 2003, 39(12):1365.
12. Zimmerman R.W., Al-Yaarubi A., Pain C.C., Grattoni C.A. Nonlinear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 2004, 41(3):163-169.
13. Al-Yaarubi A.H., Pain C.C., Grattoni C.A., Zimmerman R.W. Navier-Stokes simulations of fluid flow through a rough fracture. Dynamics of fluids and transport in fractured rock, geophysics monograph series 2005, 162:55-64. (AGU).
14. Lee S.H., Lee K.K., Yeo I.W. Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging. Geophys Res Lett 2014, 41(13):4578-4585.
15. Cardenas M.B., Slottke D.T., Ketcham R.A., Sharp J.M. Navier-Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies. Geophys Res Lett 2007, 34:L14404.
16. Cardenas M.B. Three-dimensional vortices in single pores and their effects on transport. Geophys Res Lett 2008, 35:L18402.
17. Cardenas M.B., Slottke D.T., Ketcham R.A., Sharp J.M. Effects of inertia and directionality on flow and transport in a rough asymmetric fracture. J Geophys Res 2009, 114:B06204.
18. Crandall D., Bromhal G., Karpyn Z.T. Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures. Int J Rock Mech Min Sci 2010, 47:784-796.
19. Barton N. Review of a new shear-strength criterion for rock joints. Eng Geol 1973, 7(4):287-332.
20. Xie H., Wang J.A., Xie W.H. Fractal effects of surface roughness on the mechanical behavior of rock joints. Chaos Solitons Fractals 1997, 8(2):221-252.
21. Ge Y., PHSW Kulatilake, Tang H., Xiong C. Investigation of natural rock joint roughness. Comput Geotech 2014, 55:290-305.
22. Gadelmawla E.S., Koura M.M., Maksoud T.M.A., Elewa I.M., Soliman H.H. Roughness parameters. J Mater Process Tech 2002, 123(1):133-145.
23. Tse R., Cruden D.M. Estimating joint roughness coefficients. Int J Rock Mech Min Sci 1979, 1979(16):303-307.
24. Fardin N., Stephansson O., Jing L. The scale dependence of rock joint surface roughness. Int J Rock Mech Min Sci 2001, 38:659-669.
25. Lanaro F. A random field model for surface roughness and aperture of rock fractures. Int J Rock Mech Min Sci 2000, 37(8):1195-1210.
26. Belem T., Homand-Etienne F., Souley M. Quantitative parameters for rock joint surface roughness. Rock Mech Rock Eng 2000, 33(4):217-242.
27. ISRM Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci 1978, 15:319-368.
28. Jing L., Nordlund E., Stephansson O. An experimental study on the anisotropy and stress-dependency of the strength and deformability of rock joints. Int J Rock Mech Min Sci 1992, 29:535-542.
29. Chae B., Ichikawa Y., Jeong G., Seo Y., Kim B. Roughness measurement of rock discontinuities using a confocal laser scanning microscope and the Fourier spectral analysis. Eng Geol 2004, 72(3-4):181-199.
30. Khoshelham K., Altundag D., Ngan-Tillard D., Menenti M. Influence of range measurement noise on roughness characterization of rock surfaces using terrestrial laser scanning. Int J Rock Mech Min Sci 2011, 48(8):1215-1223.
31. Mehrishal A., Sharifzadeh M. Evaluation of the hydraulic aperture of a rock joint using wavelet theory. Geosyst Eng 2013, 16(1):119-127.
32. Daubechies I. Ten lectures on wavelets 1992, Society for Industrial and Applied Mathematics, Philadelphia.
33. Mallat S. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Pattern Anal Mach Intell 1989, 7:674-693.
34. Pradhan P.S., King R.L. Estimation of the number of decomposition levels for a wavelet-based multiresolution multisensor image fusion. IEEE Trans Geosci Remote Sens 2006, 44(12):3674-3686.
35. Kharate GK, Ghatol AA, Rege PP. Selection of mother wavelet for image compression on basis of image. In: Proceedings of the International Conference on Signal Processing, Communications and Networking; 22-24 Feb. 2007. p. 281-85.
36. Rafiee J., Tse P.W., Harifi A., Sadeghi M.H. A novel technique for selecting mother wavelet function using an intelligent fault diagnosis system. Expert Syst Appl 2009, 36(3):4862-4875.
37. Matlab. 2013. http://www.mathworks.se/help/wavelet/ref/waveletfamilies.html.
38. Thomas T.R. Rough surfaces 1999, Imperial College Press, London. 2nd Ed.
39. Shapiro S., Wilk M. An analysis of variance test for normality (complete samples). Biometrika 1965, 52(3):591-611.
40. Kim J., Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J Comput Phys 1985, 59(2):308-323.
41. Armfield S., Street R. An analysis and comparison of the time accuracy of fractional-step methods for the Navier-Stokes equations on staggered grids. Int J Numer Methods Fluids 2002, 38:255-282.
42. Rhie C.M., Chow W.L. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J 1983, 21(11):1525-1532.
43. Kim D., Choi H. A second-order time-accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids. J Comput Phys 2000, 162(2):411-428.
44. Ghia U., Ghia K., Shin C. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J Comput Phys 1982, 48:387-411.
45. Erturk E., Corke T., Gökçöl C. Numerical solutions of 2D steady incompressible driven cavity flow at high Reynolds numbers. Int J Numer Methods Fluids 2005, 48:747-774.
46. Olsson R. Mechanical and hydromechanical behaviour of hard rock joints - a laboratory study 1998, University of Chalmers, Sweden, (Ph.D. thesis).
47. Yeo I.W. Effect of fracture roughness on solute transport. Geosci J 2001, 5(2):145-151.
48. Boutt D.F., Grasselli G., Fredrich J.T., Cook B.K., Williams J.R. Trapping zones: The effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture. Geophys Res Lett 2006, 33:L21402.
49. Wang L., Cardenas M.B. Non-Fickian transport through two-dimensional rough fractures: assessment and prediction. Water Resour Res 2014, 50(2):871-884.
50. Neretnieks I. Channeling with diffusion into stagnant water and into a matrix in series. Water Resour Res 2006, 42:W11418.