Interfacial viscous coupling: A myth or reality?

Journal of Petroleum Science and Engineering

Volumn 23, Issue 1, 1999, Pages 13-26

  Ayub, Muhammad ^a   Bentsen, Ramon G ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Coupled processes; Flow mechanism; Multiphase flow; Permeability; Permeability coefficients

Indexed keywords

COUPLED PROCESSES; DARCY FORMULATION; INTERFACIAL VISCOUS COUPLING;

HYDRAULIC CONDUCTIVITY; INTERFACES (MATERIALS); MATHEMATICAL MODELS; MULTIPHASE FLOW; THERMODYNAMICS; VISCOUS FLOW;

PETROLEUM ENGINEERING;

FLUID FLOW; MULTIPHASE FLOW; PERMEABILITY; POROUS MEDIUM;

EID: 0032821302     PISSN: 09204105     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0920-4105(99)00003-0     Document Type: Article

References (121)

1. Auriault J.-L., Lebaigue O. Dynamics of two immiscible fluids flowing through deformable porous media. Transport in Porous Media. 4:1989;105-128.
2. Auriault J.-L., Lewandowska J. On the cross-effects of coupled macroscopic transport equations in porous media. Transport in Porous Media. 16:1994;31-52.
3. Avraam D.G., Payatakes A.C. Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms. Transport in Porous Media. 20:1995;135-168.
4. Bachmat Y., Bear J. Macroscopic modeling of transport phenomena in porous media: 1. The continuum approach. Transport in Porous Media. 1:1986;213-240.
5. Bacri J., Chaouche M., Salin D. Modele simple de permeabilities croisees. C.R. Acad. Sci., Paris. 311:1990;591-596. Series II.
6. Bear, J., 1972. Dynamics of Fluids in Porous Media. Elsevier, New York.
7. Bear J., Bachmat Y. Macroscopic modeling of transport phenomena in porous media: 2. Application to mass, momentum and energy transport. Transport in Porous Media. 1:1986;241-269.
8. Bedford A., Drumheller D.S. Recent advances - theories of immiscible and structured mixtures. Int. J. Eng. Sci. 21(8):1983;863-960.
9. Bentsen R.G. Construction and experimental testing of a new pressure difference equation. AOSTRA J. Res. 8:1992;159-168.
10. Bentsen, R.G., 1992b. Effect of neglecting viscous coupling and dynamic capillary pressure on the one-dimensional flow of two immiscible phases through a porous medium. SPE unsolicited paper No. SPE-26016.
11. Bentsen R.G. An investigation into whether the nondiagonal mobility coefficients which arise in coupled, two-phase flow are equal. Transport in Porous Media. 14(1):1994;23-32.
12. Bentsen R.G. Impact of model error on the measurement of flow properties needed to described flow through porous media. Revue de Linstitut Francais du Petrole. 52(3):1997;299-315.
13. Bentsen R.G. Influence of hydrodynamic forces and interfacial momentum transfer on the flow of two immiscible phases. J. Petrol. Sci. Eng. 19:1998;177-190.
14. Bentsen R.G. Effect of momentum transfer between fluid phases on effective mobility. J. Petrol. Sci. Eng. 21:1997;27-42.
15. Bentsen R.G., Manai A.A. Measurement of cocurrent and countercurrent relative permeability curves using the steady-state method. AOSTRA J. Res. 7:1991;169-181.
16. Bentsen R.G., Manai A.A. On the use of conventional cocurrent and countercurrent effective permeabilities to estimate the four generalized permeability coefficients which arise in coupled, two-phase flow. Transport in Porous Media. 11:1993;243-262.
17. Berge H.F.M.T., Bolt G.H. Coupling between liquid flow and heat flow in porous media: a connection between two classical approaches. Transport in Porous Media. 3:1988;35-49.
18. Bolt G.H., Groenevelt Coupling phenomenon as a possible cause for non-Darcian behavior of water in soil. Bull. I.A.S.H. 14(2):1969;17-26.
19. Bourbiaux, B.J., Kalaydjian, F.J., 1990. Experimental study of cocurrent and countercurrent flows in natural porous media. SPE Reservoir Eng., Aug. 5, pp. 361-368.
20. Bowen R.M. Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18:1980;1129-1148.
21. Bowen R.M. Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 20(6):1982;697-735.
22. Buckley S.E., Leverett M.C. Mechanism of fluid displacement in sands. Trans. AIME. 146:1942;107-116.
23. Chatenever A., Calhoun J.C. Jr. Visual examinations of fluid behavior in porous media - Part 1. Trans. AIME. 195:1952;149-156.
24. Chavent, G., 1976. A new formulation of diphasic incompressible flow in porous media. Lecture Notes in Mathematics, Vol. 503, Springer, New York.
25. Cheng P., Wang C.Y. A multiphase mixture model for multiphase, multicomponent transport in capillary porous media: II. Numerical simulation of the transport of organic compounds in the subsurface. Int. J. Heat Mass Transfer. 39(17):1996;3619-3632.
26. Child E.C. The water table, equipotentials, and streamlines in drained land: III. Soil Sci. 59:1945;405-415.
27. Cloud W.F. Variation of pressure gradient with distance of rectilinear flow of gas-saturated oil and unsaturated oil through unconsolidated sands. Trans. AIME. 86:1930;337-350.
28. Collins, R.E., 1961. Flow of Fluids Through Porous Materials. McGraw Hill, New York.
29. Darcy, H., 1856. La Fontaine de la Ville de Dijon. Victor Dalmont, Paris.
30. de Groot, S.R., 1963. Thermodynamics of Irreversible Processes. North-Holland Publishing, Amsterdam.
31. de Groot, S.R., Mazur, P., 1963. Non-Equilibrium Thermodynamics. North-Holland Publishing, Amsterdam.
32. de la Cruz V., Spanos T.J.T. Mobilization of oil ganglia. AIChE J. 29(5):1983;854-858.
33. Del Riop J.A., de Harro M.L. Extended irreversible thermodynamics as a framework for transport phenomena in porous media. Transport in Porous Media. 9:1992;207-221.
34. Doolen, G.D., Frisch, U., Hasslacher, B., Orszag, S., Wolfram, S., 1990. Lattice Gas Methods for Partial Differential Equations. Addison-Wesley.
35. Drumheller D.S. The theoretical treatment of a porous solid using a mixture theory. Int. J. Solids Structures. 14:1978;441-456.
36. Dullien F.A.L., Dong M. Experimental determination of the flow transport coefficients in the coupled equations of two-phase flow in porous media. Transport in Porous Media. 25:1996;97-120.
37. Ehrlich R. Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities. Transport in Porous Media. 11(3):1993;201-218.
38. Fatt, I., 1953. The Effect of Overburdon Pressure on Relative Permeability. JPT, October, pp. 15-16.
39. Ferreol B., Rothman D.H. Lattice-Boltzmann simulation of flow through fontainebleau sandstone. Transport in Porous Media. 20:1995;3-20.
40. Fletcher J.E. Some properties of water solutions that influence infiltration. Trans. Am. Geophys. Union. 30(4):1949;548-554.
41. Frisch U., Hasslacher B., Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56(14):1986;1505-1508.
42. Gao Y., Sharma M.M. A LGA model for dispersion in heterogeneous porous media. Transport in Porous Media. 17:1994;19-32.
43. Gao Y., Sharma M.M. A LGA model for fluid flow in heterogeneous porous media. Transport in Porous Media. 17:1994;1-17.
44. Goode, P.A., 1991. Momentum Transfer Across Fluid-Fluid Interfaces in Porous Media. PhD Thesis, Heriot-Watt University, UK.
45. Goode P.A., Ramakrishnan T.S. Momentum transfer across fluid-fluid interfaces in porous media: a network model. AIChE J. 39(7):1993;1124-1134.
46. Gray W.G. A derivation of the equations for multi-phase transport. Chem. Eng. Sci. 30:1975;229-233.
47. Gray W.G., Lee P.C.Y. On the theorems for local volume averaging of multiphase systems. Int. J. Multiphase Flow. 3:1977;333-340.
48. Greenkorn, R.A., 1983. Flow Phenomena in Porous Media. Marcel Dekker, New York.
49. Gutman, S., 1990. Lattice gas methods in porous media computations. Annual AIChE Meeting, Rock/Fluid Interaction in Petroleum Reservoirs I, Chicago, IL, USA, Nov. 11-16.
50. Hassanizadeh M., Gray W.G. General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations. Advances in Water Resources. 2:1979;191-203.
51. Hassanizadeh M., Gray W.G. General conservation equations for multi-phase systems: 1. Averaging procedure. Advances in Water Resources. 2:1979;131-144.
52. Hassanizadeh M., Gray W.G. General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. Advances in Water Resources. 3:1980;25-40.
53. Hassanizadeh S.M., Gray W.G. High velocity flow in porous media. Transport in Porous Media. 2:1987;521-531.
54. Hessler G.L., Rice R.R., Leeman E.H. Investigations on the recovery of oil from sandstones by gas drive. Trans. AIME. 118:1936;116-137.
55. Hubbert M.K. Review and discussion, physical principles of oil production by Morris Muskat. J. Geol. 58(6):1950;655-660.
56. Islam M.R., Bentsen R.G. Effect of different parameters on two-phase relative permeability. AOSTRA J. Res. 3:1987;69-90.
57. Kadanoff L.P., McNamara G.R., Zanetti G. From automata to fluid flow: comparisons of simulation and theory. Phys. Rev. A. 40(8):1989;4527-4541.
58. Kalaydjian F. A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface. Transport in Porous Media. 2:1987;537-552.
59. Kalaydjian F. Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media. Transport in Porous Media. 5(3):1990;215-229.
60. Kalaydjian, F., Marle, C.M., 1987. Thermodynamic aspects of multiphase flow in porous media. 2nd Inst. Francais Du Petrole Explor. Res. Conf., Migration of Hydrocarbons in Sedimentary Basins, June 15-19, Carcans, France, pp. 513-531.
61. Katchalsky, A., Curran, P.F., 1967. Nonequilibrium Thermodynamics in Biophysics. Harvard Univ. Press, Cambridge, MA.
62. Kinny J.H., Breunig T.M., Starr T.L., Haupt D., Nichols M.C., Stock S.R., Butts M.D., Saroyan R.A. X-ray tomographic study of chemical vapor infiltration processing of ceramic composite. Science. 26:1993;789-792.
63. Klute, A., 1967. Notes on flow water in unsaturated soils. Presented at the M.I.T. Summer Session on Ground Water Hydrology and Flow Through Porous Media.
64. Leverett M.C. Capillary behavior in porous solids. Trans. AIME. 142:1941;152-169.
65. Liang, Q., 1993. Interaction Between Immiscible Phases Flowing at Different Velocities in Porous Media. DE Thesis, Louisiana Tech. University, USA.
66. Liang Q., Lohrenz J. Dynamic method of measuring coupling coefficients of transport equations of two-phase flow in porous media. Transport in Porous Media. 15:1994;71-79.
67. Longeron, D., 1987. Study of the influence of thermodynamic parameters on two-phase flow in porous media. 2nd Inst. Francais Du Petrole Explor. Res. Conf., Migration of Hydrocarbons in Sedimentary Basins, June 15-19, Carcans, France, pp. 257-279.
68. Manai, A.A., 1991. The measurement of cocurrent and countercurrent relative permeabilities and their use to estimate generalized relative permeabilities. MS Thesis, University of Alberta, Canada.
69. Mannseth T. Commentary on 'Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media' by F. Kalaydjian. Transport in Porous Media. 6:1991;469-471.
70. Monaco, R., 1989. Discrete Kinetic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics. World Scientific, Singapore.
71. Moore T.V. Behavior of fluids in oil reservoirs. Bull. Am. Assoc. Pet. Geol. 22(9):1938;1237-1249.
72. Murdoch A.I., Kowalski S.J. On fluid-fluid coupling within porous media: a mixture theoretical approach based upon molecular considerations. Transport in Porous Media. 8:1992;47-70.
73. Muskat, M., 1949. The Physical Principles of Oil Production. McGraw Hill, New York.
74. Muskat, M., 1982. The Flow of Homogeneous Fluids through Porous Media. International Human Resources Development, Boston.
75. Muskat M., Meres M.W. The flow of heterogeneous fluids through porous media. Physics. 7:1936;346-363.
76. Muskat M., Wyckoff R.D., Botset H.G., Meres M.W. Flow of gas-liquid mixtures through sands. Trans. AIME. 123:1937;69-96.
77. Narasimhan T.N. A note on volume-averaging. Advances in Water Resources. 3:1980;135-139.
78. Olson J.F., Rothman D.H. Two-fluid flow in sedimentary rock: simulation, transport, and complexity. J. Fluid Mech. 341:1997;343-370.
79. Onsager L. Reciprocal relations in irreversible processes: I. Phys. Rev. 37:1931;405-426.
80. Onsager L. Reciprocal relations in irreversible processes: II. Phys. Rev. 38:1931;2265-2279.
81. Philip, J.R., 1972. Flow in porous media. Proceedings of the XIII International Congress of Theoretical and Applied Mechanics, Moscow University, August 21-26, pp. 279-294.
82. Plummer, F.B., Hunter, J.C., Jr., Timmerman, E.H., 1937. Flow of mixtures of oil and water through sand. API Drill. Prod. Pract., pp. 417-421.
83. Rakotomalala N., Salin D.D. Viscous coupling in a model porous medium geometry: effect of fluid contact area. Appl. Scientific Res. 55:1995;155-169.
84. Rapoport L.A., Leas W.J. Relative permeability to a liquid in a liquid-gas system. Trans. AIME. 192:1951;83-98.
85. Richardson J.G., Kerver J.K., Hafford J.A., Osoba J.S. Laboratory determination of relative permeability. Trans. AIME. 195:1952;187-196.
86. Rose, W., 1951. Some problems of relative permeability measurement. World Petroleum Cong. Proc., Section II, The Hague, pp. 446-459.
87. Rose W. Problems of relative permeability. Petrol. Eng. 26(4):1954;B58-B72.
88. Rose W. Transport through interstitial paths of porous solids. METU J. Pure Appl. Sci. 2(2):1969;117-132.
89. Rose W. Attaching new meaning to the equations of Buckley and Leverett. J. Petrol. Sci. Eng. 1(3):1988;223-228.
90. Rose W. Measuring transport coefficients necessary for the description of coupled two-phase flow of immiscible fluids in porous media. Transport in Porous Media. 3(2):1988;163-171.
91. Rose W. Data interpretation problems to be expected in the study of coupled two-phase flow of immiscible fluid flows in porous media. Transport in Porous Media. 4:1989;185-198.
92. Rose W. Coupling coefficients for two-phase flow in pore spaces of simple geometry. Transport in Porous Media. 5(1):1990;97-102.
93. Rose W. Lagrangian simulation of coupled two-phase flows. Math. Geol. 22(6):1990;641-654.
94. Rose W. Critical questions about the coupling hypothesis. J. Petrol. Sci. Eng. 5(4):1991;299-307.
95. Rose W. Richard's assumptions and Hassler's presumptions. Transport in Porous Media. 6(1):1991;91-99.
96. Rose W. Coupling coefficients for two-phase flow in pore spaces of simple geometry. Transport in Porous Media. 10:1993;293-296.
97. Rose W. Ideas about viscous coupling in anisotropic media. Transport in Porous Media. 18:1995;87-93.
98. Rose W. An upgraded viscous coupling measurement methodology. Transport in Porous Media. 28:1997;221-231.
99. Rothman D.H. Celluar-automation fluids: a model for flow in porous media. Geophysics. 53(4):1988;509-518.
100. Rothman D.H. Macroscopic laws for immiscible two-phase flow in porous media: results from numerical experiments. J. Geophys. Res. 95(B6):1990;8663-8674.
101. Rothman D.H., Keller J.M. Immiscible celluar-automation fluids. J. Stat. Phys. 52(3/4):1988;1119-1127.
102. Scheidegger, A.E., 1960. The Physics of Flow Through Porous Media. University of Toronto Press, Toronto.
103. Scott, P.H., Rose, W., 1953. An Explanation of the Yuster Effect. JPT, Nov., pp. 19-20.
104. Slattery J.C. Single-phase flow through porous media. AIChE J. 15(6):1969;866-872.
105. Slattery J.C. Two-phase flow through porous media. AIChE J. 16(3):1970;345-352.
106. Spanos T.J.T., de la Cruz V., Hube J., Sharma R.C. An analysis of Buckley-Leverett theory. J. Can. Petrol. Tech. 25(1):1986;71-75.
107. Trapp J.A. On the relationship between continuum mixture theory and integral averaged equations for immiscible fluids. Int. J. Eng. Sci. 14:1976;991-998.
108. van Genabeek O., Rothman D.H. Macroscopic manifestations of microscopic flows through porous media: phenomenology from simulation. Annu. Rev. Earth Planet. Sci. 24:1996;63-87.
109. Wang C.Y. A alternative description of viscous coupling in two-phase flow through porous media. Transport in Porous Media. 28:1997;205-219.
110. Wang C.Y., Beckermann C. A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media: I. Formulation. Int. J. Heat Transfer. 36(11):1993;2747-2758.
111. Wang C.Y., Cheng P. A multiphase mixture model for multiphase, multicomponent transport in capillary porous media: I. Model development. Int. J. Heat Mass Transfer. 39(17):1996;3607-3618.
112. Whitaker, S., 1967. Diffusion and dispersion in porous media. AIChE J., May, pp. 420-427.
113. Whitaker S. The transport equations for multi-phase systems. Chem. Eng. Sci. 28:1973;139-147.
114. Whitaker S. Flow in porous media: II. The governing equations for immiscible, two-phase flow. Transport in Porous Media. 1:1986;105-125.
115. Wolfram S. Cellular automation fluids: 1. Basic theory. J. Stat. Phys. 45:1986;471-526.
116. Wolfram, S., 1986b. Theory and applications of cellular automata. World Scientific, Singapore.
117. Wyckoff R.D., Botset H.G. The flow of gas-liquid mixtures through unconsolidated sands. Physics. 7:1936;325-345.
118. Yortsos Y.C. The relationship between immiscible and miscible displacement in porous media. AIChE J. 33:1987;1912-1915.
119. Yuster, S.T., 1951. Theoretical considerations of multiphase flow in idealized capillary systems. World Petroleum Cong. Proc., Section II, The Hague, pp. 437-445.
120. Zanetti G. Hydrodynamics of lattice-gas automata. Phys. Rev. A. 40(3):1989;1539-1548.
121. Zarcone C., Lenormand R. Determination experimentale du couplage visqueux dans les ecoulements diphasiques en milieu poreux. C.R. Acad. Sci., Paris. 318:1994;1429-1438. Series II.