Modeling Non-Darcian Single- and Two-Phase Flow in Transparent Replicas of Rough-Walled Rock Fractures

Transport in Porous Media

Volumn 98, Issue 2, 2013, Pages 401-426

  Radilla, Giovanni ^a,b   Nowamooz, Ali ^a,b   Fourar, Mostafa ^a  

^a NANCY UNIVERSITÉ   (France)

^b ARTS ET MÉTIERS PARISTECH   (France)

Author keywords

Inertial effect; Non Darcian flow; Relative permeability; Rough fracture; Two phase flow

Indexed keywords

APPARENT PERMEABILITIES; HYDRODYNAMIC PARAMETERS; INERTIAL EFFECT; NON-DARCIAN FLOW; RELATIVE PERMEABILITY; ROUGH FRACTURES; SINGLE- AND TWO-PHASE FLOW; TWO-PHASE FLOW EXPERIMENTS;

FLOW OF GASES; FRACTURE; GROUNDWATER FLOW; IMAGE PROCESSING; LIQUIDS; POROUS MATERIALS; PRESSURE DROP; REYNOLDS NUMBER; SEEPAGE; TWO PHASE FLOW;

FLOW RATE;

FLOW MODELING; FRACTURED MEDIUM; HYDRODYNAMICS; IMAGE PROCESSING; PERMEABILITY; POROUS MEDIUM; REYNOLDS NUMBER; ROCK MECHANICS; SATURATION; TWO PHASE FLOW;

EID: 84878508487     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-013-0150-1     Document Type: Article

References (66)

1. Andrade, J. S., Costa, U. M. S., Almeida, M. P., Makse, H. A., Stanley, H. E.: Inertial effects on fluid flow through disordered porous media. Phys. Rev. Lett. 82, 5249-5252 (1999). doi: 10. 1103/PhysRevLett. 82. 5249.
2. Auriault, J.-L.: Nonsaturated deformable porous media: quasistatics. Transp. Porous Media 2, 45-64 (1987).
3. Barrère, J.: Modélisation des écoulements de Stokes et Navier-Stokes en milieu poreux. Ph. D. thesis, University of Bordeaux I, Bordeaux (1990).
4. Bauget, F., Fourar, M.: Non-Fickian dispersion in a single fracture. J. Contam. Hydrol. 100(3-4), 137-148 (2008). doi: 10. 1016/j. jconhyd. 2008. 06. 005.
5. Bear, J.: Dynamics of Fluids in Porous Media. Dover, Mineola (1972).
6. Brown, S. R.: Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. 92(B2), 1337-1347 (1987). doi: 10. 1029/JB092iB02p01337.
7. Brush, D. J., Thomson, N. R.: Fluid flow in synthetic roughwalled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour. Res. 39(4), 1085 (2003). doi: 10. 1029/2002WR001346.
8. Buchlin, J. M., Stubos, A.: Phase change phenomena at liquid saturated self heated particulate beds. In: Bear, J., Buchlin, J. M. (eds.) Modeling and Applications of Transport Phenomena in Porous Media. Kluwer Acad. Pub, Dordrecht (1987).
9. Buès, M., Panfilov, M., Oltean, C.: Macroscale model and inertia-viscous effects for Navier-Stokes flow in a radial fracture with corrugated walls. J. Fluid Mech. 504, 41-60 (2004). doi: 10. 1017/S002211200400816X.
10. Chauveteau, G., Thirriot, C.: Régimes d'écoulement en milieu poreux et limite de la loi de Darcy. La Houille Blanche 2, 141-148 (1967). doi: 10. 1051/lhb/1967009.
11. Chen, C., Horne, R. N., Fourar, M.: Experimental study of liquid-gas flow structure effect on relative permeabilities in a fracture. Water Resour. Res. 40, W08301 (2004). doi: 10. 1029/2004WR003026.
12. Chen, C., Horne, R. N.: Two-phase flow in rough-walled fractures: experiments and a flow structure model. Water Resour. Res. 42, W03430 (2006). doi: 10. 1029/2004WR003837.
13. Chen, Z., Lyons, S. L., Qin, G.: Derivation of the Forchheimer law via homogenization. Transp. Porous Media 44(2), 325-335 (2001). doi: 10. 1023/A: 1010749114251.
14. Corey, A. T.: The interrelationship between gas and oil relative permeabilities. Prod. Mon. 19(1), 38-41 (1954).
15. Cornell, D., Katz, D. L.: Flow of gases through consolidated porous media. Ind. Eng. Chem. 45(10), 2145-2153 (1953). doi: 10. 1021/ie50526a021.
16. Cvetkovic, V. D.: A continuum approach to high velocity flow in a porous medium. Transp. Porous Media 1(1), 63-97 (1986). doi: 10. 1007/BF01036526.
17. Darcy, H.: Les fontaines publiques de la ville de Dijon. Dalmont, Paris (1854).
18. de Gennes, P. G.: Theory of slow biphasic flows in porous media. Physico-Chem. Hydrodyn. 4, 175-185 (1983).
19. Detwiler, R. L., Pringle, S. E., Glass, R. J.: Measurement of fracture aperture fields using transmitted light: an evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture. Water Resour. Res. 35(9), 2605-2617 (1999). doi: 10. 1029/1999WR900164.
20. Diomampo, G. P.: Relative permeability through fractures. MS thesis, Stanford University, Stanford (2001).
21. Dullien, A. L., Azzam, M. I. S.: Flow rate-pressure gradient measurement in periodically nonuniform capillary tube. AIChE J. 19, 222-229 (1973). doi: 10. 1002/aic. 690190204.
22. Firdaouss, M., Guermond, J.-L., Le-quéré, P.: Nonlinear correction to Darcy's law at low Reynolds numbers. J. Fluid Mech. 343, 331-350 (1997). doi: 10. 1017/S0022112097005843.
23. Forchheimer, P.: Wasserberwegng durch Boden. Forschtlft ver. D. Ing. 45(50), 1782-1788 (1901).
24. Fourar, M., Bories, S.: Experimental study of air-water two-phase flow through a fracture (narrow channel). Int. J. Multiphase Flow 21(4), 621-637 (1995). doi: 10. 1016/0301-9322(95)00005-I.
25. Fourar, M., Bories, S., Lenormand, R., Persoff, P.: Two-phase flow in smooth and rough fractures: measurement and correlation by porous-media and pipe-flow models. Water Resour. Res. 29(11), 3699-3708 (1993). doi: 10. 1029/93WR01529.
26. Fourar, M., Lenormand, R.: A viscous coupling model for relative permeabilities in fractures. Paper SPE 49006 presented at the 1977 SPE annual technical conference and exhibition, New Orleans, 27-30 Sept 1998. doi: 10. 2118/49006-MS.
27. Fourar, M., Lenormand, R.: Inertial effects in two-phase flow through fractures. Oil Gas Sci. Tech. Rev. IFP 55(3), 259-268 (2000). doi: 10. 2516/ogst: 2000018.
28. Fourar, M., Lenormand, R.: A new model for two-phase flows at high velocities through porous media and fractures. J. Pet. Sci. Eng. 30(2), 121-127 (2001). doi: 10. 1016/S0920-4105(01)00109-7.
29. Fourar, M., Radilla, G., Lenormand, R., Moyne, C.: On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media. Adv. Water Resour. 27(6), 669-677 (2004). doi: 10. 1016/j. advwatres. 2004. 02. 021.
30. Geertsma, M.: Estimating the coefficient of inertial resistance fluid flow through porous media. SPE J. 14(5), 445-450 (1974). doi: 10. 2118/4706-PA.
31. Giorgi, T.: Derivation of the Forchheimer law via matched asymptotic expansions. Transp. Porous Media 29(2), 191-206 (1997). doi: 10. 1023/A: 1006533931383.
32. Hubbert, M. K.: Darcy law and the field equations of the flow of underground fluids. Trans. Am. Inst. Min. Mandal. Eng. 207, 222-239 (1956).
33. Isakov, E., Ogilvie, S. R., Taylor, C. W., Glover, P. W. J.: Fluid flow through rough fractures in rocks I: high resolution aperture determinations. Earth Planet. Sci. Lett. 191(3-4), 267-282 (2001). doi: 10. 1016/S0012-821X(01)00424-1.
34. Kalaydjian, F., Legait, B.: Perméabilités relatives couplées dans les écoulements en capillaries et en milieux poreux. C. R. Acad. Sci. Paris 304(série II), 1035-1038 (1987).
35. Lee H. S., Catton I. (1984) Two-phase flow in stratified porous media. 6th Information exchange meanding on debris coolability, Los Angeles.
36. Lipinski, R. J.: A one-dimensional particle bed dryout. Model. Trans. Am. Nucl. Soc. 38, 386-387 (1981).
37. Lipinski, R. J.: A model for boiling and dryout in particle beds. Report SAND 82-0756 (NUREG/CR-2646), Sandia Labs., Albuquerque (1982).
38. Lockhart, R. W., Martinelli, R. C.: Proposed correlation of data for isothermal two-phase, two-component flow in pipes. Chem. Eng. Prog. 45, 39-48 (1949).
39. MacDonald, I. F., El-Sayed, M. S., Mow, K., Dullien, F. A. L.: Flow through porous media, the Ergun equation revisited. Ind. Eng. Chem. Fundam. 18(3), 199-208 (1979). doi: 10. 1021/i160071a001.
40. Mahoney, D., Doggett, K.: Multiphase flow in fractures. In: Proceedings from the international symposium of the society of core analysts in Calgary, Calgary (1997).
41. Mei, C. C., Auriault, J.-L.: The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647-663 (1991). doi: 10. 1017/S0022112091001258.
42. Miskimins, J. L., Lopez-Hernandez, H. D., Barree, R. D.: Non-Darcy flow in hydraulic fractures: does it really matter? SPE 96389 annual technical conference and exhibition, Dallas, 9-12 Oct 2005.
43. Murphy, J. R., Thomson, N. R.: Two-phase flow in a variable aperture fracture. Water Resour. Res. 29(10), 3453-3476 (1993). doi: 10. 1029/93WR01285.
44. Muskat, M.: The flow of Homogeneous Fluids Through Porous Media. International Human Resources Development Corporation (reprint from McGraw-Hill), Boston (1937).
45. Neasham, J. W.: The morphology of dispersed clay in sandstone reservoirs and its effects on sandstone shaliness, pore space and fluid flow properties. Paper SPE 6858 presented at the 1977 SPE annual technical conference and exhibition, Denver, 9-12 Oct 1977 doi: 10. 2118/6858-MS.
46. Nicholl, M. J., Glass, R. J.: Wetting phase permeability in a partially saturated horizontal fracture. Proceedings of the 5th annual international high-level radioactive waste management conference 2007-2019, Las Vegas, 22-26 May 1994.
47. Noman, R., Archer, M. S.: The effect of pore structure on Non-Darcy gas flow in some low permeability reservoir rocks. Paper SPE 16400 presented at the SPE/DOE low permeability reservoirs symposium, Denver, 18-19 May 1987. doi: 10. 2118/16400-MS.
48. Nowamooz, A., Radilla, G., Fourar, M.: Non-Darcian flow in transparent replica of rough-walled rock fractures. Water Resour. Res. 45, W07406 (2009). doi: 10. 1029/2008WR007315.
49. Pyrak-Nolte, L. J., Helgeston, D., Haley, G. M., Morris, J. W.: Immiscible fluid flow. In: Tillersson and Wawersik, Balkema A. A. (eds) Fracture, Proceeding of the 33rd U. S. Rock mechanics symposium, pp. 571-578, Rotterdam (1992).
50. Raats, D. A. C., Klute, A.: Transport in soils: the balance of momentum. Soil Sci. Soc. Am. J. 32(4), 161-166 (1968). doi: 10. 2136/sssaj1968. 03615995003200040013x.
51. Rasoloarijaona, M., Auriault, J. L.: Nonlinear seepage flow through a rigid porous medium. Eur. J. Mech. B/Fluids 13(2), 177-195 (1994).
52. Rocha, R. P. A., Cruz, M. E.: Calculation of the permeability and apparent permeability of three-dimensional porous media. Transp. Porous Media 83(2), 349-373 (2010). doi: 10. 1007/s11242-009-9445-7.
53. Romm, E. S.: Fluid flow in fractured rocks. Translated from the Russian, English translation: Blake, W. R., Bartlesville, O. K., 1972, Nedra Publishing House, Moscow (1966).
54. Rose, W.: Petroleum reservoir engineering at the crossroads (ways of thinking and doing). Iran Petroleum Inst. Bull. 46, 23-27 (1972).
55. Rossen, W. R., Kumar, A. T. A.: Single and two-phase flow in natural fractures. Paper SPE 24195 presented at the 67th SPE annual technical conference and exhibition, Washington, DC, 4-7 Oct 1992. doi: 10. 2118/24915-MS.
56. Saez, A. E., Carbonell, R. G.: Hydrodynamic parameters for gas-liquid co-current flow in packed beds. AIChE J. 31(1), 52-62 (1985). doi: 10. 1002/aic. 690310105.
57. Sanchez-Palencia, E.: Non homogeneous media and vibration theory. Lecture Notes in Physics, Springer, New York (1980). doi: 10. 1007/3-540-10000-8.
58. Schneebeli, G.: Expériences sur la limite de validité de la loi de Darcy et l'apparition de la turbulence dans un écoulement de filtration. La Houille Blanche 2, 141-149 (1955). doi: 10. 1051/lhb/1955030.
59. Scheidegger, A. E.: The physics of flow through porous media. Macmillan, New York (1960).
60. Schulenberg, T., Muller, U.: A refined model for the coolability of core debris with flow entry from bottom. 6th Information Exchange Meanding on Debris Coolability, EPRI NP-4455, 108-113 Los Angeles (1984).
61. Turland, B. D., Moore, K. A.: One-dimensional models of boiling and dryout. Post accident debris cooling. Paper presented at 5th Post Accident Heat Removal Information Exchange Mtg., Karlsruhe (1983).
62. Whitaker, S.: Flow in porous media I: a theoretical derivation of Darcy's law. Transp. Porous Media 1(1), 3-25 (1986). doi: 10. 1007/BF01036523.
63. 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. 16(6), 1016-1024 (1980). doi: 10. 1029/WR016i006p01016.
64. Zarcone, C., Lenormand, R.: Détermination expérimentale du couplage visqueux dans les écoulements diphasiques en milieu poreux. C. R. Acad. Sci. Paris 318(série II), 1429-1435 (1994).
65. Zimmerman, R. W., Yeo, I. W.: Fluid flow in rock fractures: From the Navier-Stokes equations to the cubic law. In: Faybishenko, B., Witherspoon, P. A., Benton, S. M. (eds.) Dynamics of Fluids in Fractured Rock, Geophys. Monogr. (122), pp. 213-224. AGU, Washington, DC (2000).
66. Zimmerman, R. W., Al-Yaarubi, A. H., Pain, C. S., Grattoni, C. A.: Nonlinear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 41, 163 (2004).