Universal scaling of spontaneous imbibition for water-wet systems

Water Resources Research

Volumn 48, Issue 3, 2012, Pages

  Schmid, K S ^a   Geiger, S ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COUNTER CURRENT; COUNTER-CURRENT IMBIBITION; DARCY MODEL; DUAL POROSITY MODEL; DYNAMIC EFFECTS; EXACT ANALYTICAL SOLUTIONS; INITIAL WATER SATURATION; MASTER EQUATIONS; NONAQUEOUS PHASE LIQUIDS; PLANT SEEDS; PORE VOLUME; SCALING GROUP; SPONTANEOUS IMBIBITION; TRANSFER RATES; UNIVERSAL SCALING; UPSCALING; VISCOSITY RATIOS; WATER PHASE; WATER-WET SYSTEMS; WETTING PHASE;

BIOREMEDIATION; CARBON DIOXIDE; MULTIPHASE FLOW;

SEED;

BIOREMEDIATION; CAPILLARY PRESSURE; CARBON DIOXIDE; COUNTERCURRENT; DARCY LAW; DUAL POROSITY; FLOW PATTERN; GERMINATION; IMBIBITION; MODEL VALIDATION; NONAQUEOUS PHASE LIQUID; PORE SPACE; SCALE EFFECT; SEED;

EID: 84858692089     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR011566     Document Type: Article

References (78)

1. Alava, M., M. Dubé, and M. Rost (2004), Imbibition in disordered media, Adv. Phys., 53(2), 83-175.
2. Anderson, R., B. Tohidi, and J. B. W. Webber (2009), Gas hydrate growth and dissociation in narrow pore networks: Capillary inhibition and hysteresis phenomena, Geol. Soc. London Spec. Publ., 319(1), 145-159.
3. Anton, L., and R. Hilfer (1999), Trapping and mobilization of residual fluid during capillary desaturation in porous media, Phys. Rev. E, 59(6), 6819-6823. (Pubitemid 129691101)
4. Aronofsky, J. S., L. Masse, and S. G. Natanson (1958), A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoirs, Petrol. Trans. AIME, 213, 17-19.
5. Babadagli, T., and C. U. Hatiboglu (2007), Analysis of counter-current gaswater capillary imbibition transfer at different temperatures, J. Petrol. Sci. Eng., 55(3-4), 277-293. (Pubitemid 46112008)
6. Barenblatt, G. I., I. P. Zheltov, and I. N. Kochina (1960), Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24(5), 1286-1303.
7. Barenblatt, G. I., V. M. Entov, and V. M. Ryzhik (1990), Theory of Fluid Flows Through Natural Rocks, Springer, New York.
8. Barenblatt, G. I., T. W. Patzek, and D. B. Silin (2003), The mathematical model of nonequilibrium effects in water-oil displacement, SPE J., 8(4), 409-416.
9. Bear, J. (1972), Dynamics of Fluids in Porous Media, Dover, New York.
10. Bickle, M. J. (2009), Geological carbon storage, Nat. Geosci., 2(12), 815-818.
11. Bottero, S., S. M. Hassanizadeh, P. J. Kleingeld, and T. J. Heimovaara (2011), Nonequilibrium capillarity effects in two-phase flow through porous media at different scales, Water Resour. Res., 47, W10505, doi:10.1029/ 2011WR010887.
12. Bourbiaux, B., and F. Kalaydjian (1990), Experimental study of cocurrent and countercurrent flows in natural porous media, SPE Res. Eng., 5(3), 361-368. (Pubitemid 20732763)
13. Brusseau, M. L. (1992), Rate-limited mass transfer and transport of organic solutes in porous media that contain immobile immiscible organic liquid, Water Resour. Res., 28(1), 33-45, doi:10.1029/91WR02498.
14. Buckley, S. E., and M. C. Leverett (1942), Mechanisms of fluid displacement in sands, Trans. AIME, 146, 107116.
15. Cai, J., and B. Yu (2011), A discussion of the effect of tortuosity on the capillary imbibition in porous media, Transp. Porous Media, 89, 1-13, doi:10.1007/s11242-011-9767-0.
16. Chaturvedi, T., J. M. Schembre, and A. R. Kovscek (2009), Spontaneous imbibition and wettability characteristics of powder river basin coal, Int. J. Coal Geol., 77(1-2), 34-42.
17. Chen, J., M. A. Miller, and K. Sepehrnoori (1995), Theoretical investigation of countercurrent imbibition in fractured reservoir matrix blocks, Pap. 29141-MS, SPE Reservoir Simul. Symp., 12-15 Feb., Society of Petroleum Engineers, San Antonio, Tex.
18. Chen, Z. X. (1988), Some invariant solutions to two-phase fluid displacement problems including capillary effect, SPE Res. Eng., 3(2), 691-700.
19. Cil, M., and J. C. Reis (1996), A multi-dimensional, analytical model for counter-current water imbibition into gas-saturated matrix blocks, J. Petrol. Sci. Eng., 16(1-3), 61-69.
20. Civan, F., and M. Rasmussen (2001), Asymptotic analytical solutions for imbibition waterfloods in fractured reservoirs, SPE J., 6(2), 171-181. (Pubitemid 32697840)
21. Clennell, M. B., M. Hovland, J. S. Booth, P. Henry, and W. J. Winters (1999), Formation of natural gas hydrates in marine sediments 1. Conceptual model of gas hydrate growth conditioned by host sediment properties, J. Geophys. Res., 104(B10), 22,985-23,003.
22. Delker, T., D. B. Pengra, and P. Wong (1996), Interface pinning and the dynamics of capillary rise in porous media, Phys. Rev. Lett., 76(16), 2902-2905. (Pubitemid 126639027)
23. Di Donato, G., and M. J. Blunt (2004), Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs, Water Resour. Res., 40, W04203, doi:10.1029/2003WR002772.
24. Di Donato, G., H. Lu, Z. Tavassoli, and M. Blunt (2007), Multirate-transfer dual-porosity modeling of gravity drainage and imbibition, SPE J., 12(1), 77-88. (Pubitemid 46614264)
25. Dubé, M., S. Majaniemi, M. Rost, M. J. Alava, K. R. Elder, and T. Ala-Nissila (2001), Interface pinning in spontaneous imbibition, Phys. Rev. E, 64(5), 051605.
26. Finch-Savage, W. E., H. R. Rowse, and K. C. Dent (2005), Development of combined imbibition and hydrothermal threshold models to simulate maize (Zea mays) and chickpea (Cicer arietinum) seed germination in variable environments, New Phytol., 165(3), 825-838.
27. Fischer, H., S. Wo, and N. Morrow (2006), Modeling the effect of viscosity ratio on spontaneous imbibition, SPE Reservoir Eval. Eng., 102641, 577-589.
28. -2 sx occurring in two-phase flow in porous media, SIAM J. Appl. Math., 42(2), 318-332, doi:10.1137/ 0142025.
29. Goel, G., and D. M. O'Carroll (2011), Experimental investigation of nonequilibrium capillarity effects: Fluid viscosity effects, Water Resour. Res., 47(9), W09507, doi:10.1029/2010WR009861.
30. Gummerson, R. J., C. Hall, W. D. Hoff, R. Hawkes, G. N. Holland, and W. S. Moore (1979), Unsaturated water flow within porous materials observed by NMR imaging, Nature, 281, 56-57. (Pubitemid 10255558)
31. Haggerty, R., and S. M. Gorelick (1995), Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity, Water Resour. Res., 31(10), 2383-2400. (Pubitemid 26475182)
32. Hall, C. (2007), Anomalous diffusion in unsaturated flow: Fact or fiction-, Cem. Concr. Res., 37(3), 378-385. (Pubitemid 46275628)
33. Hamon, G., and J. Vidal (1986), Scaling-up the capillary imbibition process from laboratory experiments on homogeneous and heterogeneous samples, SPE 15852, Proceedings of the European Petroleum Conference, 20-22 Oct., pp. 37-49, Society of Petroleum Engineers, London.
34. Handy, L. L. (1960), Determination of effective capillary pressures for porous media from imbibition data, Petrol. Trans. AIME, 219, 75-80.
35. Hassanizadeh, S. M., and W. G. Gray (1990), Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Adv. Water Res., 13(4), 169-186.
36. Hulshof, J., and J. R. King (1998), Analysis of a darcy flow model with a dynamic pressure saturation relation, SIAM J. Appl. Math., 59, 318-346.
37. Jadhunandan, P. P., and N. R. Morrow (1991), Spontaneous imbibition of water by crude oil/brine/rock systems, In Situ, 15(4), 319-345.
38. Juanes, R., E. J. Spiteri, F. M. Orr Jr., and M. J. Blunt (2006), Impact of relative permeability hysteresis on geological CO2 storage Water Resour. Res., 42, W12418, doi:10.1029/2005WR004806. (Pubitemid 46188241)
39. Kalaydjian, F. J. M. (1992), Dynamic capillary pressure curve for water/ oil displacement in porous media: Theory vs. experiment, paper 24813, SPE Annu. Tech. Conf. and Exhibition, pp. 491-506, SPE, Allen, Tex.
40. Kashchiev, D., and A. Firoozabadi (2002), Analytical solutions for 1-D countercurrent imbibition in water-wet media, SPE J., 8(4), 401-408.
41. Le Guen, S. S., and A. R. Kovscek (2006), Nonequilibrium effects during spontaneous imbibition, Transp. Porous Media, 63(1), 127-146.
42. Li, K., and R. Horne (2006), Generalized scaling approach for spontaneous imbibition: An analytical model, SPE Reservoir Eval. Eng., 9(3), 251-258. (Pubitemid 43984851)
43. Li, K., and R. N. Horne (2009), Method to evaluate the potential of water injection in naturally fractured reservoirs, Transp. Porous Media, 83, 699-709.
44. Li, Y., N. R. Morrow, and D. Ruth (2003), Similarity solution for linear counter- current spontaneous imbibition, J. Petrol. Sci. Eng., 39(3-4), 309-326. (Pubitemid 36911105)
45. Lucas, R. (1918), Über das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten, Colloid Polymer Sci., 23(1), 15-22.
46. Ma, S., N. R. Morrow, and X. Zhang (1997), Generalized scaling of spontaneous imbibition data for strongly water-wet systems, J. Petrol. Sci. Eng., 18(3-4), 165-178.
47. Manthey, S., S. M. Hassanizadeh, R. Helmig, and R. Hilfer (2008), Dimensional analysis of two-phase flow including a rate-dependent capillary pressure-saturation relationship, Adv. Water Res., 31(9), 1137-1150.
48. Marmur, A. (2003), Kinetics of penetration into uniform porous media: Testing the equivalent-capillary concept, Langmuir, 19(14), 5956-5959.
49. Mason, G., H. Fischer, N. R. Morrow, and D. W. Ruth (2010), Correlation for the effect of fluid viscosities on counter-current spontaneous imbibition, J. Petrol. Sci. Eng., 72(1-2), 195-205.
50. Mattax, C. C., and J. R. Kyte (1962), Imbibition oil recovery from fractured, water-drive reservoir, SPE J., 2(2), 177-184.
51. McWhorter, D. B., and D. K. Sunada (1990), Exact integral solutions for two-phase flow, Water Resour. Res., 26(3), 399-413.
52. Mirzaei-Paiaman, A., M. Masihi, and D. C. Standnes (2011), An analytic solution for the frontal flow period in 1D counter-current spontaneous imbibition into fractured porous media including gravity and wettability effects, Transp. PorousMedia, 89, 1-14, doi:10.1007/s11242-011-9751-8.
53. Morrow, N. R., and G. Mason (2001), Recovery of oil by spontaneous imbibition, Curr. Opin. Colloid Interface Sci., 6(4), 321-337, doi:10.1016/ S1359-0294(01)00100-5. (Pubitemid 32878585)
54. Muskat, M. (1949), Physical Principles of Oil Production, McGraw Hill, New York.
55. Parrish, D. J., and A. C. Leopold (1977), Transient changes during soybean imbibition, Plant Physiol., 59(6), 1111-1115.
56. Pentland, C. H., R. El-Maghraby, S. Iglauer, and M. J. Blunt (2011), Measurements of the capillary trapping of super-critical carbon dioxide in berea sandstone, Geophys. Res. Lett., 38(6), L06401, doi:10.1029/ 2011GL046683.
57. Philip, J. R. (1960), A very general class of exact solutions in concentration- dependent diffusion, Nature, 4708, 233.
58. Rangel-German, E. R., and A. R. Kovscek (2002), Experimental and analytical study of multidimensional imbibition in fractured porous media, J. Petol. Sci. Eng., 36(1-2), 45-60. (Pubitemid 35212362)
59. Rapoport, L. A. (1955), Scaling laws for use in design and operation of water-oil flow models, Trans. AIME, 204, 143-150.
60. Rasmussen, M. L., and F. Civan (1998), Analytical solutions for waterfloods in fractured reservoirs obtained by an asymptotic approximation, SPE J., 3(3), 249-252. (Pubitemid 128444681)
61. Reis, J. C., and M. Cil (1993), A model for oil expulsion by counter-current water imbibition in rocks: One-dimensional geometry, J. Petrol. Sci. Eng., 10(2), 97-107.
62. Ruth, D. W., and J. K. Arthur (2011), A revised analytic solution to the linear displacement problem including capillary pressure effects, Transp. Porous Media, 86, 881-894.
63. Ruth, D. W., Y. Li, G. Mason, and N. R. Morrow (2007), An approximate analytical solution for counter-current spontaneous imbibition, Transp. Porous Media, 66(3), 373-390.
64. Sanchez Bujanos, J. L., M. A. Miller, and K. Sephernoori (1998), Scaling parameters for characterizing waterflood recovery from anisotropic matrix blocks in naturally fractured reservoirs, paper 39626, SPE Int. Petrol. Conf., 61-69, Society of Petroleum Engineers, Villahermosa, Mexico.
65. Schembre, J. M., and A. R. Kovscek (2006), Estimation of dynamic relative permeability and capillary pressure from countercurrent imbibition experiments, Transp. Porous Media, 65(1), 31-51. (Pubitemid 44445991)
66. Schmid, K. S., S. Geiger, and K. S. Sorbie (2011), Semianalytical solutions for co- and countercurrent imbibition and dispersion of solutes in immiscible two-phase flow, Water Resour. Res., 47(2), W02550, doi:10.1029/ 2010WR009686.
67. Spayd, K., and M. Shearer (2011), The Buckley-Leverett equation with dynamic capillary pressure, SIAM J. Appl. Math., 71, 1088-1108.
68. Tavassoli, Z., R. W. Zimmerman, and M. J. Blunt (2005a), Analytic analysis for oil recovery during counter-current imbibition in strongly waterwet systems, Transp. Porous Media, 58(1), 173-189.
69. Tavassoli, Z., R. W. Zimmerman, and M. J. Blunt (2005b), Analysis of counter-current imbibition with gravity in weakly water-wet systems, J. Petrol. Sci. Eng., 48(1-2), 94-104. (Pubitemid 40936365)
70. Valvatne, P. H., and M. J. Blunt (2004), Predictive pore-scale modeling of two-phase flow in mixed wet media, Water Resour. Res., 40,W07406, doi:10.1029/2003WR002627.
71. Warren, J. E., and P. J. Root (1963), The behavior of naturally fractured reservoirs, SPE J., 3(3), 245-255.
72. Washburn, E. W. (1921), The dynamics of capillary flow, Phys. Rev., 17(3), 273-283.
73. Wu, Y. S., and L. Pan (2003), Special relative permeability functions with analytical solutions for transient flow into unsaturated rock matrix, Water Resour. Res., 39(4), 1104, doi:10.1029/2002WR001495.
74. Yortsos, Y. C., and A. S. Fokas (1983), An analytical solution for linear waterflood including the effects of capillary pressure, SPE J., 23(1), 115-124. (Pubitemid 13510519)
75. Zhang, X., N. Morrow, and S. Ma (1996), Experimental verification of a modified scaling group for spontaneous imbibition, SPE Res. Eng., 11(4), 280-285. (Pubitemid 126431818)
76. Zhou, D., L. Jia, J. Kamath, and A. R. Kovscek (2002), Scaling of countercurrent imbibition processes in low-permeability porous media, J. Petrol. Sci. Eng., 33(1-3), 61-74. (Pubitemid 34527637)
77. Zimmerman, R. W., and G. S. Bodvarsson (1989), An approximate solution for one-dimensional absorption in unsaturated porous media, Water Resour. Res., 25(6), 1422-1428. (Pubitemid 20397949)
78. Zimmerman, R. W., and G. S. Bodvarsson (1991), A simple approximate solution for horizontal infiltration in a brooks-corey medium, Transp. Porous Media, 6(2), 195-205.