Universal scaling of spontaneous imbibition for arbitrary petrophysical properties: Water-wet and mixed-wet states and Handy's conjecture

Journal of Petroleum Science and Engineering

Volumn 101, Issue , 2013, Pages 44-61

  Schmid, K S ^a   Geiger, S ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Analytical solution; Formation evaluation; Imbibition; Scaling group; Time scales; Wettability

Indexed keywords

BUCKLEY-LEVERETT SOLUTIONS; DARCY'S EQUATIONS; EXPONENTIAL MODELS; FORMATION EVALUATION; FRACTURED RESERVOIR; GENERAL CORRELATIONS; GENERAL SOLUTIONS; GEOTHERMAL RESERVOIR; IMBIBITION; INITIAL WATER CONTENTS; KEY PROCESS; LABORATORY DATUM; MASTER EQUATIONS; PETROPHYSICAL; PETROPHYSICAL PROPERTIES; ROCK SAMPLE; ROCK TYPES; SCALING GROUP; SPONTANEOUS IMBIBITION; TIME-SCALES; UNIVERSAL SCALING; UPSCALING; VISCOSITY RATIOS; WATER FLOOD; WATER-WET SYSTEMS; WETTING FRONTS; WETTING PHASE;

GEOTHERMAL FIELDS; MASS TRANSFER; WETTING;

GROUP THEORY;

BOUNDARY CONDITION; CAPILLARITY; DARCY LAW; HYDROCARBON RESERVOIR; IMBIBITION; MASS TRANSFER; VISCOSITY; VISCOUS FLOW; WATER CONTENT; WETTABILITY;

EID: 84873749402     PISSN: 09204105     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.petrol.2012.11.015     Document Type: Article

References (115)

1. Abushaikha, A., Gosselin, O., 2008. Matrix-fracture transfer function in dual-media flow simulation: review, comparison and validation. In: Europec/EAGE Conference and Exhibition.
2. Anderson W.G. Wettability literature survey-part 4. effects of wettability on capillary pressure. J. Pet. Technol. 1987, 39(10):1283-1300.
3. Anderson W.G. Wettability literature survey part 5. the effects of wettability on relative permeability. J. Pet. Technol. 1987, 39(11):1453-1468.
4. Anderson R., Tohidi B., Webber J.B.W. Gas hydrate growth and dissociation in narrow pore networks. capillary inhibition and hysteresis phenomena. Geol. Soc. London Spec. Publ. 2009, 319(1):145.
5. Anton L., Hilfer R. Trapping and mobilization of residual fluid during capillary desaturation in porous media. Phys. Rev. E 1999, 59(6):6819.
6. Aronofsky, J.S., Masse, L., Natanson, S.G., 1958. A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoirs. Petroleum Transactions, AIME 213, 17-19.
7. Babadagli T., Hatiboglu C.U. Analysis of counter-current gas-water capillary imbibition transfer at different temperatures. J. Pet. Sci. Eng. 2007, 55(3-4):277-293.
8. Babadagli, T., Zeidani, K., 2004. Evaluation of matrix-fracture imbibition transfer functions for different types of oil, rock and aqueous phase. In: SPE/DOE Symposium on Improved Oil Recovery.
9. Barenblatt G.I., Zheltov I.P., Kochina I.N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. 1960, 24(5):1286-1303.
10. Barenblatt, G.I., Entov, V.M., Ryzhik, V.M., 1990. Theory of Fluid Flows through Natural Rocks.
11. Barenblatt G.I., Patzek T.W., Silin D.B. The mathematical model of nonequilibrium effects in water-oil displacement. SPE J. 2003, 8(4):409-416. ISSN 1086-055X.
12. Bear J. Dynamics of Fluids in Porous Media 1972, Dover, New York, NY.
13. Behbahani H.S., Blunt M.J. Analysis of imbibition in mixed-wet rocks using pore-scale modeling. SPE J. 2005, 10(4):466-474.
14. Behbahani H.S., Di Donato G., Blunt M.J. Simulation of counter-current imbibition in water-wet fractured reservoirs. J. Pet. Sci. Eng. 2006, 50(1):21-39.
15. Benavente D., Lock P., Angeles Garcia Del Cura M., Ordóñez S. Predicting the capillary imbibition of porous rocks from microstructure. Transp. Porous Media 2002, 49(1):59-76.
16. Beydoun Z.R. Arabian plate oil and gas. why so rich and so prolific?. Episodes Newsmagazine Int. Union Geol. Sci. 1998, 21(2):74-81.
17. Bottero S., Hassanizadeh S.M., Kleingeld P.J., Heimovaara T.J. Nonequilibrium capillarity effects in two-phase flow through porous media at different scales. Water Resour. Res. 2011, 47(10):W10505.
18. Bourbiaux B., Kalaydjian F. Experimental study of cocurrent and countercurrent flows in natural porous media. SPE Res. Eng. 1990, 5(3):361-368. ISSN 0885-9248.
19. Buckley S.E., Leverett M.C. Mechanisms of fluid displacement in sands. Trans. Am. Inst. Min. Metall. Eng. AIME 1942, 146:107-116.
20. Chaturvedi T., Schembre J.M., Kovscek A.R. Spontaneous imbibition and wettability characteristics of powder river basin coal. Int. J. Coal Geol. 2009, 77(1-2):34-42.
21. Chen Z.X. Some invariant solutions to two-phase fluid displacement problems including capillary effect. SPE Reservoir Eng. 1988, 3(2):691-700.
22. Chen, J., Miller, M.A., Sepehrnoori, K., 1995. Theoretical investigation of countercurrent imbibition in fractured reservoir matrix blocks. In: SPE Reservoir Simulation Symposium.
23. Cil M., Reis J.C. A multi-dimensional, analytical model for counter-current water imbibition into gas-saturated matrix blocks. J. Pet. Sci. Eng. 1996, 16(1-3):61-69.
24. Cil, M., Reis, J., Miller, M., Misra, D., 1998. An examination of countercurrent capillary imbibition recovery from single matrix blocks and recovery predictions by analytical matrix/fracture transfer functions. In: SPE Annual Technical Conference and Exhibition.
25. Civan F., Rasmussen M. Asymptotic analytical solutions for imbibition waterfloods in fractured reservoirs. SPE J. 2001, 6(2):171-181.
26. Clennell M.B., Hovland M., Booth J.S., Henry P., Winters W.J. Formation of natural gas hydrates in marine sediments 1. conceptual model of gas hydrate growth conditioned by host sediment properties. J. Geophys. Res. 1999, 104(B10). 22985-23.
27. Cueto-Felgueroso L., Juanes R. Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media. Phys. Rev. Lett. 2008, 101(December (24)):244504. 10.1103/PhysRevLett.101.244504.
28. Delijani E.B., Pishvaie M.R. Green element solution of one-dimensional counter-current spontaneous imbibition in water wet porous media. J. Pet. Sci. Eng. 2010, 70(3-4):302-307.
29. Di Donato G., Lu H., Tavassoli Z., Blunt M. Multirate-transfer dual-porosity modeling of gravity drainage and imbibition. SPE J. 2007, 12(1):77-88.
30. Fernø M.A., Haugen Å., Graue A. Wettability effects on the matrix-fracture fluid transfer in fractured carbonate rocks. J. Pet. Sci. Eng. 2011.
31. Finch-Savage W.E., Leubner-Metzger G. Seed dormancy and the control of germination. New Phytol. 2006, 171(3):501-523. ISSN 1469-8137.
32. Finch-Savage W.E., Rowse H.R., Dent K.C. Development of combined imbibition and hydrothermal threshold models to simulate maize (Zea mays) and chickpea (Cicer arietinum) seed germination in variable environments. New Phytol. 2005, 165(3):825-838. ISSN 1469-8137.
33. Fischer H., Morrow N.R. Scaling of oil recovery by spontaneous imbibition for wide variation in aqueous phase viscosity with glycerol as the viscosifying agent. J. Pet. Sci. Eng. 2006, 52(1-4):35-53.
34. Fischer H., Wo S., Morrow N.R. Modeling the effect of viscosity ratio on spontaneous imbibition. SPE Reservoir Eval. Eng. 2006, 102641:577-589.
35. s x occurring in two-phase flow in porous media. SIAM J. Appl. Math. 1982, 42(2):318-332. 10.1137/0142025.
36. Graue A., Viksund B.G., Baldwin B.A. Reproducible wettability alteration of low-permeable outcrop chalk. SPE Reservoir Eval. Eng. 1999, 2(2):134-140.
37. Gruener S., Sadjadi Z., Hermes H.E., Kityk A.V., Knorr K., Egelhaaf S.U., Rieger H., Huber P. Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores. Proc. Nat. Acad. Sci. 2012, 109(26):10245-10250.
38. Gummerson R.J., Hall C., Hoff W.D., Hawkes R., Holland G.N., Moore W.S. Unsaturated water flow within porous materials observed by NMR imaging. Nature 1979, 281:56-57.
39. Gupta A., Civan F. An improved model for laboratory measurement of matrix to fracture transfer function parameters in immiscible displacement. Pap. SPE 1994, 28929:25-28.
40. Hall C. Anomalous diffusion in unsaturated flow. fact or fiction. Cem. Concr. Res. 2007, 37(3):378-385. ISSN 0008-8846.
41. Hamon, G., Vidal, J., 1986. Scaling-up the capillary imbibition process from laboratory experiments on homogeneous and heterogeneous samples. In: SPE 15852, Proceedings of the European Petroleum Conference, vol. 15852, London, October 20-22, pp. 37-49.
42. Handy, L.L., 1960. Determination of effective capillary pressures for porous media from imbibition data.Petroleum Transactions, AIME 219, 75-80.
43. Hassanizadeh S.M. Derivation of basic equations of mass transport in porous media, part 2. Generalized Darcy's and Fick's laws. Adv. Water Resour. 1986, 9(4):207-222.
44. Hassanizadeh S.M., Gray W.G. Toward an improved description of the physics of two-phase flow. Adv. Water Resour. 1993, 16(1):53-67.
45. Hazlett R.D. Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks. Transp. Porous Media 1995, 20(1):21-35.
46. Høgnesen E.J., Standnes D.C., Austad T. Scaling spontaneous imbibition of aqueous surfactant solution into preferential oil-wet carbonates. Energy Fuels 2004, 18(6):1665-1675.
47. Jackson M.D., Valvatne P.H., Blunt M.J. Prediction of wettability variation and its impact on flow using pore-to reservoir-scale simulations. J. Pet. Sci. Eng. 2003, 39(3-4):231-246.
48. Jadhunandan P.P., Morrow N.R. Spontaneous imbibition of water by crude oil/brine/rock systems. In Situ 1991, 15(4):319-345.
49. Kashchiev D., Firoozabadi A. Analytical solutions for 1-D countercurrent imbibition in water-wet media. SPE J. 2002, 8(4):401-408.
50. Kazemi H., S Merrill L., Porterfield K.L., Zeman P.R. Numerical simulation of water-oil flow in naturally fractured reservoirs. SPE J. 1976, 16:317-326.
51. Kazemi H., Gilman J.R., Eisharkawy A.M. Analytical and numerical solution of oil recovery from fractured reservoirs with empirical transfer functions. SPE (Soc. Pet. Eng.) Reservoir Eng. (United States) 1992, 7(2):219-227.
52. Lake, L.W., 1989. Enhanced Oil Recovery.
53. Lavi B., Marmur A., Bachmann J. Porous media characterization by the two-liquid method. effect of dynamic contact angle and inertia. Langmuir 2008, 24(5):1918-1923.
54. Lee C.H., Karpyn Z.T. Numerical analysis of imbibition front evolution in fractured sandstone under capillary-dominated conditions. Transp. Porous Media 2012, 94(1):359-383,. 10.1007/s11242-012-0009-x.
55. Li K., Horne R.N. Generalized scaling approach for spontaneous imbibition. an analytical model. SPE Reservoir Eval. Eng. 2006, 9(3):251-258.
56. Li K., Horne R.N. Method to evaluate the potential of water injection in naturally fractured reservoirs. Transp. Porous Media 2009, 83:699-709.
57. Li, K., Chow, K., Horne, R.N., 2002. Effect of initial water saturation on spontaneous water imbibition. In: SPE Western Regional/AAPG Pacific Section Joint Meeting.
58. Li Y., Morrow N.R., Ruth D. Similarity solution for linear counter-current spontaneous imbibition. J. Pet. Sci. Eng. 2003, 39(3-4):309-326.
59. Lucas R. Über das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten. Colloid Polym. Sci. 1918, 23(1):15-22.
60. Ma S., Morrow N.R., Zhang X. Generalized scaling of spontaneous imbibition data for strongly water-wet systems. J. Pet. Sci. Eng. 1997, 18(3-4):165-178. ISSN 0920-4105.
61. Marmur A. Kinetics of penetration into uniform porous media. testing the equivalent-capillary concept. Langmuir 2003, 19(14):5956-5959.
62. Martic G., Gentner F., Seveno D., Coulon D., DeConinck J., Blake T.D. A molecular dynamics simulation of capillary imbibition. Langmuir 2002, 18(21):7971-7976.
63. Mason G., Fischer H., Morrow N.R., Ruth D.W. Correlation for the effect of fluid viscosities on counter-current spontaneous imbibition. J. Pet. Sci. Eng. 2010, 72(1-2):195-205. ISSN 0920-4105.
64. Mattax C.C., Kyte J.R. Imbibition oil recovery from fractured, water-drive reservoir. SPE J. 1962, 2(2):177-184.
65. McWhorter D.B., Sunada D.K. Exact integral solutions for two-phase flow. Water Resour. Res. 1990, 26(3):399-413.
66. Mirzaei M., Das D.B. Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3d porous media. implications of micro-heterogeneities. Chem. Eng. Sci. 2007, 62(7):1927-1947.
67. Mirzaei-Paiaman A., Masihi M., Standnes D.C. An analytic solution for the frontal flow period in 1d counter-current spontaneous imbibition into fractured porous media including gravity and wettability effects. Transp. Porous Media 2011, 89:1-14. 10.1007/s11242-011-9751-8.
68. Morrow N.R., Mason G. Recovery of oil by spontaneous imbibition. Curr. Opin. Colloid Interface Sci. 2001, 6(4):321-337. ISSN 1359-0294. 10.1016/S1359-0294(01)00100-5.
69. Morrow, N.R., Ma, S., Zhou, X., Zhang, X., 1994. Characterization of wettability from spontaneous imbibition measurements. In: Annual Technical Meeting, Calgary, Alberta, Canada.
70. Muskat M. Physical Principles of Oil Production 1949, McGraw-Hill, New York.
71. Narahara G.M., Pozzi A.L., Blackshear T.H. Effect of connate water on gas/oil relative permeabilities for water-wet and mixed-wet Berea rock. SPE Adv. Technol. Ser. 1993, 1(2):114-122.
72. O'Carroll D.M., Mumford K.G., Abriola L.M., Gerhard J.I. Influence of wettability variations on dynamic effects in capillary pressure. Water Resour. Res. 2010, 46. 10.1029/2009WR008712.
73. Philip J.R. A very general class of exact solutions in concentration-dependent diffusion. Nature 1960, 4708:233.
74. Pooladi-Darvish M., Firoozabadi A. Cocurrent and countercurrent imbibition in a water-wet matrix block. SPE J. 2000, 5(1):3-11.
75. Pordel Shahri M., Jamialahmadi M., Shadizadeh S.R. New normalization index for spontaneous imbibition. J. Pet. Sci. Eng. 2012, 82:130-139.
76. Rangel-German E.R., Kovscek A.R. Experimental and analytical study of multidimensional imbibition in fractured porous media. J. Pet. Sci. Eng. 2002, 36(1-2):45-60.
77. Rangel-German E.R., Kovscek A.R. Time-dependent matrix-fracture shape factors for partially and completely immersed fractures. J. Pet. Sci. Eng. 2006, 54(3-4):149-163.
78. Rapoport L.A. Scaling laws for use in design and operation of water-oil flow models. Trans. AIME 1955, 204(1955):143-150.
79. Rasmussen M.L., Civan F. Analytical solutions for waterfloods in fractured reservoirs obtained by an asymptotic approximation. SPE J. 1998, 3(3):249-252.
80. Reis J.C., Cil M. A model for oil expulsion by counter-current water imbibition in rocks. one-dimensional geometry. J. Pet. Sci. Eng. 1993, 10(2):97-107.
81. Rezaveisi M., Ayatollahi S., Rostami B. Experimental investigation of matrix wettability effects on water imbibition in fractured artificial porous media. J. Pet. Sci. Eng. 2012, 10.1016/j.petrol.2012.03.004.
82. Ruth D.W., Arthur J.K. A revised analytic solution to the linear displacement problem including capillary pressure effects. Transp. Porous Media 2011, 86:881-894.
83. Ruth, D.W., Morrow, N.R., Yu, L., Buckley, J., 2000. Simulation study of spontaneous imbibition. In: International Society of Core Analysts Annual Meeting, Abu Dhabi, UAE, October.
84. Ruth, D.W., Mason, G., Morrow, N.R., Li, Y., 2004. The effect of fluid viscosities on counter-current spontaneous imbibition. In: Proceedings of the Society of Core Analysts Symposium, Abu Dhabi, SCA2004-11, pp. 1-13.
85. Ruth D.W., Li Y., Mason G., Morrow N.R. An approximate analytical solution for counter-current spontaneous imbibition. Transp. Porous Media 2007, 66(3):373-390.
86. Salathiel R.A. Oil recovery by surface film drainage in mixed-wettability rocks. J. Pet. Technol. 1973, 25(10):1216-1224.
87. Sanchez Bujanos, J.L., Miller, M.A., Sephernoori, K., 1998. Scaling parameters for characterizing waterflood recovery from anisotropic matrix blocks in naturally fractured reservoirs. In: SPE International Petroleum Conference, pp. 61-69.
88. Schechter D.S., Zhou D., Orr F.M., et al. Low ift drainage and imbibition. J. Pet. Sci. Eng. 1994, 11(4):283-300.
89. Schembre J.M., Kovscek A.R. Estimation of dynamic relative permeability and capillary pressure from countercurrent imbibition experiments. Transp. Porous Media 2006, 65(1):31-51. ISSN 0169-3913.
90. Schembre, J.M., Akin, S., Castanier, L.M., Kovscek, A.R., 1998. Spontaneous water imbibition into diatomite. In: SPE Western Regional Meeting.
91. Schmid K.S., Geiger S. Universal scaling of spontaneous imbibition for water-wet systems. Water Resour. Res. 2012, 48. 10.1029/2011WR011566.
92. Schmid K.S., Geiger S., Sorbie K.S. Semianalytical solutions for co- and countercurrent imbibition and dispersion of solutes in immiscible two-phase flow. Water Resour. Res. 2011, 47(2). 10.1029/2010WR009686.
93. Schmid K.S., Geiger S., Sorbie K.S. Analytical solutions for co- and countercurrent imbibition of sorbing, dispersive solutes in immiscible two-phase flow. Comput. Geoscience 2012, 16. 10.1007/s10596-012-9282-6.
94. Shikhmurzaev Y.D., Sprittles J.E. Wetting front dynamics in an isotropic porous medium. J. Fluid Mech. 2012, 694:399-407.
95. Standnes D.C. Spontaneous imbibition of water into cylindrical cores with high aspect ratio: numerical and experimental results. J. Pet. Sci. Eng. 2006, 50(2):151-160.
96. Standnes D.C. Scaling group for spontaneous imbibition including gravity. Energy Fuels 2010, 24(5):2980-2984.
97. Standnes D.C. Scaling spontaneous imbibition of water data accounting for fluid viscosities. J. Pet. Sci. Eng. 2010, 73:214-219.
98. Tavassoli Z., Zimmerman R.W., Blunt M.J. Analytic analysis for oil recovery during counter-current imbibition in strongly water-wet systems. Transp. Porous Media 2005, 58(1):173-189.
99. Tavassoli Z., Zimmerman R.W., Blunt M.J. Analysis of counter-current imbibition with gravity in weakly water-wet systems. J. Pet. Sci. Eng. 2005, 48(1-2):94-104.
100. Tong Z., Xie X., Morrow N.R. Scaling of viscosity ratio for oil recovery by imbibition from mixed-wet rocks. Petrophysics 2002, 43(4):338-346.
101. Unsal E., Matthäi S.K., Blunt M.J. Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions. Comput. Geosciences 2010, 14:1-12.
102. Valvatne P.H., Blunt M.J. Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 2004, 40(7). ISSN 0043-1397. 10.1029/2003WR002627.
103. Van Dijke M.I.J., Sorbie K.S. Pore-scale network model for three-phase flow in mixed-wet porous media. Phys. Rev. E 2002, 66(4):046302.
104. Van Dijke M.I.J., Sorbie K.S. Pore-scale modelling of three-phase flow in mixed-wet porous media: multiple displacement chains. J. Pet. Sci. Eng. 2003, 39(3-4):201-216.
105. Warren J.E., Root P.J. The behavior of naturally fractured reservoirs. SPE J. 1963, 3(3):245-255.
106. Washburn E.W. The dynamics of capillary flow. Phys. Rev. 1921, 17(3):273-283.
107. Welge H.J. A simplified method for computing oil recovery by gas or water drive. Trans. AIME 1952, 195:91-98.
108. Wu Y.S., Pan L. Special relative permeability functions with analytical solutions for transient flow into unsaturated rock matrix. Water Resour. Res. 2003, 39(4):1-3.
109. Xie X., Morrow N.R. Oil recovery by spontaneous imbibition from weakly water-wet rocks. Petrophysics 2001, 42(4):313-322.
110. Yortsos Y.C., Fokas A.S. An analytical solution for linear waterflood including the effects of capillary pressure. SPE J. 1983, 23(1):115-124.
111. Zhang X., Morrow N., Ma S. Experimental verification of a modified scaling group for spontaneous imbibition. SPE Res. Eng. 1996, 11(4):280-285. ISSN 0885-9248.
112. Zhou X., Morrow N.R., Ma S. Interrelationship of wettability, initial water saturation, aging time, and oil recovery by spontaneous imbibition and waterflooding. SPE J. 2000, 5(2):199-207.
113. Zhou D., Jia L., Kamath J., Kovscek A.R. Scaling of counter-current imbibition processes in low-permeability porous media. J. Pet. Sci. Eng. 2002, 33(1-3):61-74. ISSN 0920-4105.
114. Zimmerman R.W., Bodvarsson G.S. An approximate solution for one-dimensional absorption in unsaturated porous media. Water Resour. Res. 1989, 25(6):1422-1428.
115. Zimmerman R.W., Bodvarsson G.S. A simple approximate solution for horizontal infiltration in a Brooks-Corey medium. Transp. Porous Media 1991, 6(2):195-205.