Two-phase flow: Structure, UP scaling, and consequences for macroscopic transport properties

Vadose Zone Journal

Volumn 11, Issue 3, 2012, Pages

  Toussaint, R ^a,e   Maloy K J ^b,e   Meheust Y ^c   Lovoll G ^b,d   Jankov, M ^b   Schafer G ^a   Schmittbuhl, J ^a  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b UNIVERSITY OF OSLO   (Norway)

^c UNIVERSITÉ DE RENNES 1   (France)

^d DNV GL   (Norway)

^e CENTRE FOR ADVANCED STUDY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

BIPHASIC FLOW; CAPILLARY FORCE; CASE EXPRESSION; DISPLACEMENT VELOCITY; EXPERIMENTAL STUDIES; FLUID-PHASE; FRACTAL GEOMETRY; HELE-SHAW CELLS; IMMISCIBLE FLUIDS; LENGTH SCALE; MACROSCOPIC SCALE; MACROSCOPIC TRANSPORT; PRESSURE DIFFERENCES; UNSTABLE FLOWS; UPSCALING; VISCOUS FORCES;

AIR; CAPILLARITY; FRACTAL DIMENSION; IMAGING TECHNIQUES; MONOLAYERS; POROUS MATERIALS; TWO PHASE FLOW;

TRANSPORT PROPERTIES;

BOUNDARY CONDITION; DISPLACEMENT; DRAINAGE; EXPERIMENTAL STUDY; FLOW STRUCTURE; FRACTURE; GEOMETRY; POROUS MEDIUM; SATURATION; TWO PHASE FLOW; TWO-DIMENSIONAL MODELING; VISCOSITY;

EID: 84869453680     PISSN: None     EISSN: 15391663     Source Type: Journal    
DOI: 10.2136/vzj2011.0123     Document Type: Article

References (76)

1. Auradou, H., K.J. Måløy, J. Schmittbuhl, A. Hansen, and D. Bideau. 1999. Competition between correlated buoyancy and uncorrelated capillary effects during drainage. Phys. Rev. E 60:7224-7234. doi:10.1103/PhysRevE.60.7224
2. Benremita, H., and G. Schäfer. 2003. Transfert du trichloréthylène en milieu poreux à partir d'un panache de vapeurs. C. R. Mec. 331:835-842. doi:10.1016/j.crme.2003.08.006
3. Birovljev, A., L. Furuberg, J. Feder, T. Jøssang, K.J. Måløy, and A. Aharony. 1991. Gravity invasion percolation in two dimensions: Experiment and simulation. Phys. Rev. Lett. 67:584-587. doi:10.1103/PhysRevLett.67.584
4. Birovljev, A., G. Wagner, P. Meakin, J. Feder, and T. Jøssang. 1995. Migration and fragmentation of invasion percolation clusters in two-dimensional porous media. Phys. Rev. E 51:5911-5915. doi:10.1103/PhysRevE.51.5911
5. Blunt, M.J. 2001. Flow in porous media: Pore-network model and multiphase flow. Curr. Opin. Colloid Interface Sci. 6:197-207. doi:10.1016/S1359-0294(01)00084-X
6. Brown, S.R. 1987. Fluid flow through rock joints: The effect of surface roughness. J. Geophys. Res. 92(B2):1337-1347. doi:10.1029/JB092iB02p01337
7. Brown, S.R. 1995. Simple mathematical model of a rough fracture. J. Geophys. Res. 100(B4):5941-5952. doi:10.1029/94JB03262
8. Chandler, R., J. Koplik, K. Lerman, and J.F. Willemsen. 1982. Capillary displacement and percolation in porous media. J. Fluid Mech. 119:249-267. doi:10.1017/S0022112082001335
9. Chen, S., K.H. Kim, F. Qin, and A.T. Watson. 1992. Quantitative NMR imaging of multiphase flow in porous media. Magn. Reson. Imaging 10:815-826. doi:10.1016/0730-725X(92)90417-X
10. Cheng, X., L. Xu, A. Patterson, H.M. Jaeger, and S.R. Nagel. 2008. Towards the zero-surface-tension limit in granular fingering instability. Nat. Phys. 4:234-237. doi:10.1038/nphys834
11. Chevalier, C., A. Lindner, M. Leroux, and E. Clément. 2009. Morphodynamics during air injection into a confined granular suspension. J. Non-Newtonian Fluid Mech. 158:63-72. doi:10.1016/j.jnnfm.2008.07.007
12. Chuoke, R.L., P. van Meurs, and C. van der Poel. 1959. The instability of slow, immiscible, viscous liquid-liquid displacement in permeable media. Trans. Am. Inst. Min. Metall. Pet. Eng. 216:188-194.
13. de Gennes, P.G., and E. Guyon. 1978. Lois generales pour l'injection d'un fluide dans un milieu poreux aléatoire. J. Mec. 17:403-432.
14. Domb, C. 1996. The critical point: A historical introduction to the modern theory of critical phenomena. Taylor and Francis, London.
15. Drazer, G., and J. Koplik. 2002. Transport in rough self-affine fractures. Phys. Rev. E 66:026303. doi:10.1103/PhysRevE.66.026303
16. Dridi, L., I. Pollet, O. Razakarisoa, and G. Schäfer. 2009. Characterisation of a DNAPL source zone in a porous aquifer using the Partitioning Interwell Tracer Test and an inverse modelling approach. J. Contam. Hydrol. 107:22-44.
17. Feder, J. 1988. Fractals. Plenum Press, New York.
18. Frette, O.I., K.J. Måløy, J. Schmittbuhl, and A. Hansen. 1997. Immiscible displacement of viscosity-matched fluids in two-dimensional porous media. Phys. Rev. E 55:2969-2975. doi:10.1103/PhysRevE.55.2969
19. Frette, V., J. Feder, T. Jøssang, and P. Meakin. 1992. Buoyancy-driven fluid migra tion in porous media. Phys. Rev. Lett. 68:3164-3167. doi:10.1103/Phys-RevLett.68.3164
20. Frette, V., J. Feder, T. Jøssang, P. Meakin, and K.J. Måløy. 1994. Fast, immiscible fluid-fluid displacement in three-dimensional porous media at finite viscosity contrast. Phys. Rev. E 50:2881-2890. doi:10.1103/PhysRevE.50.2881
21. Furuberg, L., K.J. Måløy, and J. Feder. 1996. Intermittent behavior in slow drainage. Phys. Rev. E 53:966-977. doi:10.1103/PhysRevE.53.966
22. Goren, L., E. Aharonov, D. Sparks, and R. Toussaint. 2010. Pore pressure evolution in deforming granular material: A general formulation and the infinitely stiff approximation. J. Geophys. Res. 115(B09216). doi:10.1029/2009JB007191
23. Goren, L., E. Aharonov, D. Sparks, and R. Toussaint. 2011. The mechanical coupling of fluid-filled granular material under shear. Pure Appl. Geophys. 168:2289-2323. doi:10.1007/s00024-011-0320-4
24. Haines, W.B. 1930. Studies in the physical properties of soil: V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith. J. Agric. Sci. 20:97-116. doi:10.1017/S002185960008864X
25. Hassanizadeh, S.M., M.A. Celia, and H.K. Dahle. 2002. Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow. Vadose Zone J. 1:38-57.
26. Holtzman, R., and R. Juanes. 2010. Crossover from fingering to fracturing in deformable disordered media. Phys. Rev. E 82:046305. doi:10.1103/Phys-RevE.82.046305
27. Hou, J., Z.Q. Li, S.K. Zhang, X.L. Cao, Q.J. Du, and X.W. Song. 2009. Computerized tomography study of the microscopic flow mechanism of polymer flooding. Transp. Porous Media 79:407-418. doi:10.1007/s11242-008-9330-9
28. Johnsen, Ø., C. Chevalier, A. Lindner, R. Toussaint, E. Clément, K.J. Måløy, et al. 2008a. Decompaction and fluidization of a saturated and confined granular medium by injection of a viscous liquid or a gas. Phys. Rev. E 78:051302. doi:10.1103/PhysRevE.78.051302
29. Johnsen, Ø., R. Toussaint, K.J. Måløy, and E.G. Flekkøy. 2006. Pattern formation during central air injection into granular materials confined in a circular Hele-Shaw cell. Phys. Rev. E 74:011301. doi:10.1103/PhysRevE.74.011301
30. Johnsen, Ø., R. Toussaint, K.J. Måløy, E.G. Flekkøy, and J. Schmittbuhl. 2008b. Coupled air/granular flow in a linear Hele-Shaw cell. Phys. Rev. E 77:011301. doi:10.1103/PhysRevE.77.011301
31. Kong, X.-Z., M. Holzner, F. Stauffer, and W. Kinzelbach. 2011. Time-resolved 3D visualization of air injection in a liquid-saturated refractive-index-matched porous medium. Exp. Fluids 50:1659-1670. doi:10.1007/s00348-010-1018-6
32. Lemaire, E., Y.O.M. Abdelhaye, J. Larue, R. Benoit, P. Levitz, and H. van Damme. 1993. Pattern formation in noncohesive and cohesive granular media. Fractals 1:968-976. doi:10.1142/S0218348X93001040
33. Lenormand, R. 1989. Flow through porous media: Limits of fractal patterns. Proc. R. Soc. London Ser. A 423:159-168. doi:10.1098/rspa.1989.0048
34. Lenormand, R., E. Touboul, and C. Zarcone. 1988. Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189:165-187. doi:10.1017/S0022112088000953
35. Løvoll, G., M. Jankov, K.J. Måløy, R. Toussaint, J. Schmittbuhl, G. Schäfer, and Y. Méheust. 2010. Influence of viscous fingering on dynamic saturation-pressure curves in porous media. Transp. Porous Media 86:305-324. doi:10.1007/s11242-010-9622-8
36. Løvoll, G., Y. Méheust, K.J. Måløy, E. Aker, and J. Schmittbuhl. 2005. Competition of gravity, capillary and viscous forces during drainage in a two-dimensional porous medium, a pore scale study. Energy 30:861-872. doi:10.1016/j.energy. 2004.03.100
37. Løvoll, G., Y. Méheust, R. Toussaint, J. Schmittbuhl, and K.J. Måløy. 2004. Growth activity during fingering in a porous Hele-Shaw cell. Phys. Rev. E 70:026301. doi:10.1103/PhysRevE.70.026301
38. Måløy, K.J., J. Feder, and T. Jøssang. 1985. Vicous fingering fractals in porous media. Phys. Rev. Lett. 55:2688-2691. doi:10.1103/PhysRevLett.55.2688
39. Måløy, K.J., L. Furuberg, J. Feder, and T. Jøssang. 1992. Dynamics of slow drainage in porous media. Phys. Rev. Lett. 68:2161-2164. doi:10.1103/PhysRev-Lett.68.2161
40. Mandava, S.S., A.T. Watson, and M.E. Carl. 1990. NMR imaging of saturation during immiscible displacements. AIChE J. 36:1680-1686. doi:10.1002/aic.690361108
41. Méheust, Y., G. Løvoll, K.J. Måløy, and J. Schmittbuhl. 2002. Interface scaling in a two-dimensional porous medium under combined viscous, gravity, and capillary effects. Phys. Rev. E 66:051603. doi:10.1103/PhysRevE.66.051603
42. Méheust, Y., and J. Schmittbuhl. 2000. Flow enhancement of a rough fracture. Geophys. Res. Lett. 27:2989-2992. doi:10.1029/1999GL008464
43. Méheust, Y., and J. Schmittbuhl. 2001. Geometrical heterogeneities and permeability anisotropy of rough fractures. J. Geophys. Res. 106(B2):2089-2102. doi:10.1029/2000JB900306
44. Méheust, Y., and J. Schmittbuhl. 2003. Scale effects related to flow in rough fractures. Pure Appl. Geophys. 160:1023-1050. doi:10.1007/PL00012559
45. Moebius, F., and D. Or. 2012. Interfacial jumps and pressure bursts during fluid displacement in interacting irregular capillaries. J. Colloid Interface Sci. 377:406-415
46. Neuville, A., R. Toussaint, and J. Schmittbuhl. 2010a. Fracture roughness and thermal exchange: A case study at Soultz-sous-forêts. C. R. Geosci. 342:616-625. doi:10.1016/j.crte.2009.03.006
47. Neuville, A., R. Toussaint, and J. Schmittbuhl. 2010b. Hydro-thermal coupling in a self-affine rough fracture. Phys. Rev. E 82:036317. doi:10.1103/Phys-RevE.82.036317
48. Neuville, A., R. Toussaint, and J. Schmittbuhl. 2011. Hydraulic transmissivity and heat exchange efficiency of open fractures: A model based on lowpass filtered apertures. Geophys. J. Int. 186:1064-1072. doi:10.1111/j.1365-246X.2011.05126.x
49. Neuville, A., R. Toussaint, and J. Schmittbuhl. 2012a. Fracture aperture reconstruct tion and determination of hydrological properties: A case study at Draix (French Alps). Hydrol. Processes 26:2095-2105. doi:10.1002/hyp.7985
50. Neuville, A., R. Toussaint, J. Schmittbuhl, D. Koehn, and J. Schwarz. 2012b. Characterization of major discontinuities from borehole cores of the black consolidated marl formation of Draix (French Alps). Hydrol. Processes 26: 2085-2094. doi:10.1002/hyp.7984
51. Niebling, M.J., E.G. Flekkøy, K.J. Måløy, and R. Toussaint. 2010a. Mixing of a granular layer falling through a fluid. Phys. Rev. E 82:011301. doi:10.1103/PhysRevE.82.011301
52. Niebling, M.J., E.G. Flekkøy, K.J. Måløy, and R. Toussaint. 2010b. Sedimentation instabilities: Impact of the fluid compressibility and viscosity. Phys. Rev. E 82:051302. doi:10.1103/PhysRevE.82.051302
53. Niemeyer, L., L. Pietronero, and H.J. Wiesmann. 1984. Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52:1033. doi:10.1103/PhysRev-Lett.52.1033
54. Nsir, K., G. Schäfer, R. di Chiara Roupert, O. Razakarisoa, and R. Toussaint. 2012. Laboratory experiments on DNAPL gravity fingering in water-saturated porous media. Int. J. Multiphase Flow 40:83-92. doi:10.1016/j.ijmultiphaseflow.2011.12.003
55. Paterson, L., V. Hornof, and G. Neale. 1984a. Visualization of a surfactant flood of an oil-saturated porous medium. SPE J. 24:325-327. doi:10.2118/11598-PA
56. Paterson, L., V. Hornof, and G. Neale. 1984b. Water fingering into an oil-wet porous medium saturated with oil at connate water saturation. Rev. Inst. Fr. Pet. 39:517-522.
57. Sandnes, B., E.G. Flekkøy, H.A. Knudsen, K.J. Måløy, and H. See. 2011. Patterns and flow in frictional fluid dynamics. Nat. Commun. 2:288. doi:10.1038/ncomms1289
58. Stokes, J.P., D.A. Weitz, J.P. Gollub, A. Dougherty, M.O. Robbins, P.M. Chaikin, and H.M. Lindsay. 1986. Interfacial stability of immiscible displacement in a porous medium. Phys. Rev. Lett. 57:1718. doi:10.1103/PhysRev-Lett.57.1718
59. Szymczak, P., and A.J.C. Ladd. 2011. Instabilities in the dissolution of a porous matrix. Geophys. Res. Lett. 38:L07403. doi:10.1029/2011GL046720
60. Tallakstad, K.T., H.A. Knudsen, T. Ramstad, G. Løvoll, K.J. Måløy, R. Toussaint, and E.G. Flekkøy. 2009a. Steady-state two-phase flow in porous media: Statistics and transport properties. Phys. Rev. Lett. 102:074502. doi:10.1103/PhysRevLett.102.074502
61. Tallakstad, K.T., G. Løvoll, H.A. Knudsen, T. Ramstad, E.G. Flekkøy, and K.J. Måløy. 2009b. Steady-state, simultaneous two-phase flow in porous media: An experimental study. Phys. Rev. E 80:036308. doi:10.1103/Phys-RevE.80.036308
62. Toussaint, R., G. Løvoll, Y. Méheust, K.J. Måløy, and J. Schmittbuhl. 2005. Influence of pore-scale disorder on viscous fingering during drainage. Europhys. Lett. 71:583. doi:10.1209/epl/i2005-10136-9
63. Varas, G., V. Vidal, and J.C. Geminard. 2011. Morphology of air invasion in an immersed granular layer. Phys. Rev. E 83(6):061302. doi:10.1103/Phys-RevE.83.061302
64. Vinningland, J.L., Ø. Johnsen, E.G. Flekkøy, R. Toussaint, and K.J. Måløy. 2007a. A granular Rayleigh-Taylor instability: Experiments and simulations. Phys. Rev. Lett. 99:048001. doi:10.1103/PhysRevLett.99.048001
65. Vinningland, J.L., Ø. Johnsen, E.G. Flekkøy, R. Toussaint, and K.J. Måløy. 2007b. Experiments and simulations of a gravitational granular flow instability. Phys. Rev. E 76:051306. doi:10.1103/PhysRevE.76.051306
66. Vinningland, J.L., Ø. Johnsen, E.G. Flekkøy, R. Toussaint, and K.J. Måløy. 2010. Size invariance of the granular Rayleigh-Taylor instability. Phys. Rev. E 81:041308. doi:10.1103/PhysRevE.81.041308
67. Vinningland, J.L., R. Toussaint, M. Niebling, E.G. Flekkøy, and K.J. Måløy. 2012. Family-Viscek scaling of detachment fronts in granular Rayleigh-Taylor instabili ties during sedimentating granular/fluid flows. Eur. Phys. J. Spec. Topics 204:27-40.
68. Wagner, G., A. Birovljev, J. Feder, and T. Jøssang. 1997. Fragmentation and migra tion of invasion percolation clusters: Experiments and simulations. Phys. Rev. E 55:7015-7029. doi:10.1103/PhysRevE.55.7015
69. Weitz, D.A., J.P. Stokes, R.C. Ball, and A.P. Kushnick. 1987. Dynamic capillary pressure in porous media: Origin of the viscous-fingering length scale. Phys. Rev. Lett. 59:2967. doi:10.1103/PhysRevLett.59.2967
70. Wilkinson, D. 1984. Percolation model of immiscible displacement in the presence of buoyancy forces. Phys. Rev. A 30:520-531. doi:10.1103/PhysRevA.30.520
71. Wilkinson, D. 1986. Percolation effects in immiscible displacement. Phys. Rev. A 34:1380-1391. doi:10.1103/PhysRevA.34.1380
72. Wilkinson, D., and J.F. Willemsen. 1983. Invasion percolation: A new form of percolation theory. J. Phys. A 16:3365-3376. doi:10.1088/0305-4470/16/14/028
73. Xu, B., Y.C. Yortsos, and D. Salin. 1998. Invasion percolation with viscous forces. Phys. Rev. E 57:739-751. doi:10.1103/PhysRevE.57.739
74. Yan, J., X. Luo, W. Wang, F. Chen, R. Toussaint, J. Schmittbuhl, et al. 2012a. An experimental study of oil secondary migration in a three-dimensional tilted porous medium. AAPG Bull. 96(5):773-788. doi:10.1306/09091110140.
75. Yan, J., X. Luo, W. Wang, F. Chen, R. Toussaint, et al. 2012b. Testing oil saturation in migration paths using NMRI. J. Petrol. Sci. Petrol. Eng. 86-87:237-245. doi:10.1016/j.petrol.2012.03.027
76. Zimmerman, R., and G. Bodvarsson. 1996. Hydraulic conductivity of rock fractures. Transp. Porous Media 23:1-30. doi:10.1007/BF00145263