Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures

Journal of Hydrology

Volumn 529, Issue , 2015, Pages 993-1006

  Chen, Yi Feng ^a   Zhou, Jia Qing ^a   Hu, Shao Hua ^b   Hu, Ran ^a   Zhou, Chuang Bing ^c  

^a WUHAN UNIVERSITY   (China)

^b WUHAN UNIVERSITY OF TECHNOLOGY   (China)

^c NANCHANG UNIVERSITY   (China)

Author keywords

Forchheimer equation; Non Darcy flow; Rock fracture; Roughness

Indexed keywords

AQUIFERS; DEFORMATION; FLOW OF WATER; FLUID DYNAMICS; FRACTURE; GROUNDWATER FLOW; HYDROGEOLOGY; NONLINEAR EQUATIONS; PRESSURE GRADIENT; REGRESSION ANALYSIS; SEEPAGE; SENSITIVITY ANALYSIS; SURFACE ROUGHNESS;

EXPERIMENTAL EVALUATION; FORCHHEIMER EQUATION; NON-DARCY FLOW; NONLINEAR COEFFICIENT; PARAMETER EQUATIONS; PARAMETRIC EXPRESSIONS; ROCK FRACTURES; ROUGH-WALLED FRACTURES;

FLOW OF FLUIDS;

DARCY LAW; DEFORMATION; DISCHARGE; EXPERIMENTAL STUDY; FRACTURE; GRANITE; HYDRAULIC CONDUCTIVITY; NONLINEAR WAVE; NUMERICAL MODEL; PRESSURE GRADIENT; REGRESSION ANALYSIS; ROUGHNESS; SENSITIVITY ANALYSIS; STRESS; WALL ROCK;

EID: 84942245506     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2015.09.021     Document Type: Article

References (59)

1. Atkinson, L.C., 1986. A laboratory and Numerical Investigation of Steady-state, Two Regime Radial Flow to a Well From Rough, Horizontal, Deformable Fractures. PhD Thesis, Memorial University of Newfoundland, St. John's, NF.
2. Bandis S.C., Lumsden A.C., Barton N.R. Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1983, 20:249-268.
3. Barton N., de Quadros E.F. Joint aperture and roughness in the prediction of flow and groutability of rock masses. Int. J. Rock Mech. Min. Sci. 1997, 34(3-4):252.e1-252.e14.
4. Bear J. Dynamics of Fluids in Porous Media 1972, Am. Elsevier, New York.
5. Belhaj, H.A., Aghj, K.R., Nouri, A.M., Butt, S.D., Vaziri, H.H., Islam, M.R., 2003. Numerical and experimental modeling of non-Darcy flow in porous media. In: Society of Petroleum Engineers, SPE Latin America and Caribbean Petroleum Engineering Conference, Port of Spain, Trinidad, West Indies, pp. 1-9 (April 27-30, 2003).
6. Berkowitz B. Characterizing flow and transport in fractured geological media: a review. Adv. Water Resour. 2002, 25(8):861-884.
7. 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.
8. Chen Y., Hu S., Wei K., Hu R., Zhou C., Jing L. Experimental characterization and micromechanical modeling of damage-induced permeability variation in Beishan granite. Int. J. Rock Mech. Min. Sci. 2014, 71:64-76.
9. Chen Y.F., Hu S.H., Hu R., Zhou C.B. Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash's law-based empirical model. Water Resour. Res. 2015, 51(4):2096-2118.
10. Cherubini C., Giasi C.I., Pastore N. Bench scale laboratory tests to analyze non-linear flow in fractured media. Hydrol. Earth Syst. Sci. 2012, 9(4):5575-5609.
11. Develi K., Babadagli T. Experimental and visual analysis of single-phase flow through rough fracture replicas. Int. J. Rock Mech. Min. Sci. 2015, 73:139-155.
12. Di Federico V. Estimates of equivalent aperture for non-Newtonian flow in a rough-walled fracture. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1997, 34:1133-1137.
13. Douglas J., Paes-Leme P.J., Giorgi T. Generalized Forchheimer flow in porous media. Lecture Notes in Physics 1993, vol. 58:207-216. Elsevier Science Publishers B.V., North-Holland, Amsterdam.
14. Durham W.B., Bonner B.P. Self-propping and fluid flow in slightly offset joints at high effective pressures. J. Geophys. Res. 1994, 99(B5):9391-9399.
15. Eck B.J., Barrett M.E., Charbeneau R.J. Forchheimer flow in gently sloping layers: application to drainage of porous asphalt. Water Resour. Res. 2012, 48(1):W01530.
16. Elsworth D., Doe T.W. Application of non-linear flow laws in determining rock fissure geometry from single borehole pumping tests. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1986, 23(3):245-254.
17. Folch A., Menció A., Puig R., Soler A., Mas-Pla J. Groundwater development effects on different scale hydrogeological systems using head, hydrochemical and isotopic data and implications for water resources management: the Selva basin (NE Spain). J. Hydrol. 2011, 403(1):83-102.
18. 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(11):3699-3708.
19. Ghane E., Fausey N.R., Brown L.C. Non-Darcy flow of water through woodchip media. J. Hydrol. 2014, 519:3400-3409.
20. Javadi M., Sharifzadeh M., Shahriar K. A new geometrical model for non-linear fluid flow through rough fractures. J. Hydrol. 2010, 389(1):18-30.
21. Javadi M., Sharifzadeh M., Shahriar K., Mitani Y. Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour. Res. 2014, 50(2):1789-1804.
22. Jiang Q., Ye Z., Zhou C. A numerical procedure for transient free surface seepage through fracture networks. J. Hydrol. 2014, 519:881-891.
23. Konzuk J.S., Kueper B.H. Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour. Res. 2004, 40(2):W02402.
24. Li Y., Chen Y.F., Zhou C.B. Hydraulic properties of partially saturated rock fractures subjected to mechanical loading. Eng. Geol. 2014, 179:24-31.
25. Liu H.H., Birkholzer J. On the relationship between water flux and hydraulic gradient for unsaturated and saturated clay. J. Hydrol. 2012, 475:242-247.
26. Long J.C.S., Remer J.S., Wilson C.R., Witherspoon P.A. Porous media equivalents for networks of discontinuous fractures. Water Resour. Res. 1982, 18(3):645-658.
27. Louis, C., 1969. A study of groundwater flow in jointed rock and its influence on the stability of rock masses. Rock Mech. Res. Rep. 10, Imp. Coll., London, UK.
28. Macini P., Mesini E., Viola R. Laboratory measurements of non-Darcy flow coefficients in natural and artificial unconsolidated porous media. J. Petrol. Sci. Eng. 2011, 77(3):365-374.
29. Masciopinto C., Volpe A., Palmiotta D., Cherubini C. A combined PHREEQC-2/parallel fracture model for the simulation of laminar/non-laminar flow and contaminant transport with reactions. J. Contam. Hydrol. 2010, 117(1):94-108.
30. Miller R.J., Low P.F. Threshold gradient for water flow in clay systems. Soil. Sci. Soc. Am. Proc. 1963, 27(6):605-609.
31. Min K.B., Rutqvist J., Tsang C.F., Jing L. Stress-dependent permeability of fractured rock masses: a numerical study. Int. J. Rock Mech. Min. Sci. 2004, 41(7):1191-1210.
32. Moody L.F. Friction factors for pipe flow. Trans. ASME 1944, 66(8):671-684.
33. Moutsopoulos K.N., Papaspyros I.N.E., Tsihrintzis V.A. Experimental investigation of inertial flow processes in porous media. J. Hydrol. 2009, 374(3):242-254.
34. Neuville A., Toussaint R., Schmittbuhl J. Fracture aperture reconstruction and determination of hydrological properties: a case study at Draix (French Alps). Hydrol. Process. 2012, 26(14):2095-2105.
35. Noiriel C., Gouze P., Madé B. 3D analysis of geometry and flow changes in a limestone fracture during dissolution. J. Hydrol. 2013, 486:211-223.
36. Nowamooz A., Radilla G., Fourar M. Non-Darcian two-phase flow in a transparent replica of a rough-walled rock fracture. Water Resour. Res. 2009, 45(7):W07406.
37. Qian J., Zhan H., Chen A., Ye H. Experimental study of solute transport under non-Darcian flow in a single fracture. J. Hydrol. 2011, 399(3):246-254.
38. Qian J., Zhan H., Luo S., Zhao W. Experimental evidence of scale-dependent hydraulic conductivity for fully developed turbulent flow in a single fracture. J. Hydrol. 2007, 339(3-4):206-215.
39. Quinn P.M., Cherry J.A., Parker B.L. Quantification of non-Darcian flow observed during packer testing in fractured sedimentary rock. Water Resour. Res. 2011, 47(9):W09533.
40. Quinn P.M., Parker B.L., Cherry J.A. Using constant head step tests to determine hydraulic apertures in fractured rock. J. Contam. Hydrol. 2011, 126(1):85-99.
41. Ranjith P.G., Darlington W. Nonlinear single-phase flow in real rock joints. Water Resour. Res. 2007, 43(9):W09502.
42. Rivett M.O., Ellis P.A., Mackay R. Urban groundwater baseflow influence upon inorganic river-water quality: the River Tame headwaters catchment in the City of Birmingham, UK. J. Hydrol. 2011, 400(1):206-222.
43. Ruth D., Ma H. On the derivation of the Forchheimer equation by means of the averaging theorem. Transp. Porous Media 1992, 7(3):255-264.
44. Schrauf T.W., Evans D.D. Laboratory studies of gas flow through a single natural fracture. Water Resour. Res. 1986, 22(7):1038-1050.
45. Sidiropoulou M.G., Moutsopoulos K.N., Tsihrintzis V.A. Determination of Forchheimer equation coefficients a and b. Hydrol. Process. 2007, 21(4):534-554.
46. Skjetne E., Hansen A., Gudmundsson J.S. High-velocity flow in a rough fracture. J. Fluid Mech. 1999, 383:1-28.
47. Sukop M.C., Huang H., Alvarez P.F., Variano E.A., Cunningham K.J. Evaluation of permeability and non-Darcy flow in vuggy macroporous limestone aquifer samples with lattice Boltzmann methods. Water Resour. Res. 2013, 49(1):216-230.
48. Tse R., Cruden D.M. Estimating joint roughness coefficients. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1979, 16(5):303-307.
49. Tzelepis V., Moutsopoulos K.N., Papaspyros J.N.E., Tsihrintzis V.A. Experimental investigation of flow behavior in smooth and rough artificial fractures. J. Hydrol. 2015, 521:108-118.
50. Ulusay R., Hudson J.A. Suggested methods for determining tensile strength of rock materials. Part 2: Suggested method for determining indirect tensile strength by the Brazil test. Int. J. Rock Mech. Min. Sci. Geomech. 1978, 15:99-103.
51. 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.
52. Zeng Z., Grigg R. A criterion for non-Darcy flow in porous media. Transp. Porous Media 2006, 63(1):57-69.
53. Zhang Z., Nemcik J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J. Hydrol. 2013, 477:139-151.
54. Zhang Z., Nemcik J. Friction factor of water flow through rough rock fractures. Rock Mech. Rock Eng. 2013, 46(5):1125-1134.
55. Zhang Z., Nemcik J., Ma S. Micro-and macro-behaviour of fluid flow through rock fractures: an experimental study. Hydrogeol. J. 2013, 21(8):1717-1729.
56. 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. 2004, 41:163-169.
57. Zimmerman R.W., Bodvarsson G.S. Hydraulic conductivity of rock fractures. Transp. Porous Media 1996, 23(1):1-30.
58. Zou L., Jing L., Cvetkovic V. Roughness decomposition and nonlinear fluid flow in a single rock fracture. Int. J. Rock Mech. Min. Sci. 2015, 75:102-118.
59. Zou L., Tarasov B.G., Dyskin A.V., Adhikary D.P., Pasternak E., Xu W. Physical modelling of stress-dependent permeability in fractured rocks. Rock Mech. Rock Eng. 2013, 46(1):67-81.