Abstract
Theoretical analysis is presented to quantify the viscous coupling effect in two-phase flow through porous media. The analysis is based on the principle of potential difference equations as well as on the interfacial contact area and partition concept. The analysis shows that viscous coupling effect is negligible throughout the normalized saturation range. The expression, Xϕ 2, was developed for the quantification of the parameter that controls the amount of viscous coupling, where X was theoretically found to have a maximum value of 2.
Similar content being viewed by others
References
Ayub, M.: 2000, Experimental testing of interfacial coupling phenomena in two-phase flow. A thesis submitted to the Department of Civil of and Environmental Engineering of the University of Alberta in partial fulfillment for the award of the degree of Doctor of Philosophy in Petroleum Engineering, Spring 2000.
Ayub, M. and Bentsen, R. G.: 2005, Experimental testing of interfacial coupling in two-phase flow in porous media, Petroleum Sci. & Tech. In press.
M. Ayub R.G. Bentsen (1999) ArticleTitleInterfacial viscous coupling: a myth or reality? J. Petrol. Sci. Eng. 23 13–26 Occurrence Handle10.1016/S0920-4105(99)00003-0
Ayodele, O. R.: 2004, Mathematical modeling, experimental testing and numerical simulation of interfacial coupling phenomena of two-phase flow in porous media. A thesis submitted to the Department of Civil of and Environmental Engineering of the University of Alberta in partial fulfillment for the award of the degree of Doctor of Philosophy in Petroleum Engineering, Spring 2004.
A. Babchin J. Yuan (1997) ArticleTitleOn the capillary coupling between two phases in a droplet train Transport Porous Media 26 225–228 Occurrence Handle10.1023/A:1006571425936
Bentsen, R. G.: 2005, Interfacial coupling in vertical, two-phase flow through porous media, Petroleum Sci. Tech. In press.
R.G. Bentsen (2003a) ArticleTitleComment on capillary coupling Transport Porous Media 50 371–371 Occurrence Handle10.1023/A:1021169214556
R.G. Bentsen (2003b) ArticleTitleThe role of capillarity in two-phase flow through porous media Transport Porous Media 51 103–112 Occurrence Handle10.1023/A:1021203705402
R.G. Bentsen (2001) ArticleTitleThe physical origin of interfacial coupling in two-phase flow through porous media Transport Porous Media 44 109–122 Occurrence Handle10.1023/A:1010791526239
R.G. Bentsen (1998a) ArticleTitleInfluence of hydrodynamic forces and interfacial momentum transfer on the flow of two immiscible phases J. Petrol. Sci. Eng. 19 177–190 Occurrence Handle10.1016/S0920-4105(97)00021-1
R.G. Bentsen (1998b) ArticleTitleEffect of momentum transfer between fluid phases on effective mobility J. Petrol. Sci. Eng. 21 27–42 Occurrence Handle10.1016/S0920-4105(98)00035-7
R.G. Bentsen (1997) ArticleTitleImpact of model error on the measurement of flow properties needed to describe flow through porous media Revue de l’institut francais du petrole 52 IssueID3 299–315
R.G. Bentsen (1994a) ArticleTitleEffect of hydrodynamic forces on capillary pressure and relative permeability Transport Porous Media 17 121–132 Occurrence Handle10.1007/BF00624728
R.G. Bentsen (1994b) ArticleTitleEffect of hydrodynamic forces on the pressure-difference equation Transport Porous Media 17 133–144 Occurrence Handle10.1007/BF00624729
R.G. Bentsen (1992) ArticleTitleConstruction and experimental testing of a new pressure-difference equation AOSTRA J. Res. 8 159–168
Bourbiaux, B. J. and Kalaydjian, F. J.: 1990, Experimental study of cocurrent and countercurrent flows in natural porous media, SPE Res. Eng. J. 361–368
E. Dana F. Skoczylas (2002) ArticleTitleExperimental study of two-phase flow in three sandstones. II. Measuring relative permeabilities during two-phase steady-state experiments Int. J. Multiphase Flow 28 1965–1981 Occurrence Handle10.1016/S0301-9322(02)00091-5
P.G. Gennes Particlede (1983) ArticleTitleTheory of slow biphasic flows in porous media Ph. Ch. Hydr. 4 175–185
Cruz Particlede la T.J.T. Spanos (1983) ArticleTitleMobilization of oil ganglia AIChE J. 29 IssueID5 854–858 Occurrence Handle10.1002/aic.690290522
F. Kalaydjian (1990) ArticleTitleOrigin and quantification of coupling between relative permeabilities for two-phase flows in porous media Transport Porous Media 5 IssueID3 215–229 Occurrence Handle10.1007/BF00140013
F. Kalaydjian (1987) ArticleTitleA macroscopic description of multiphase flow in porous media involving space-time evolution of fluid/fluid interface Transport Porous Media 2 537–552 Occurrence Handle10.1007/BF00192154
Kalaydjian F. and Legait B. (1987). Permeabilities relatives couplees dans des ecoulements en capillaires et en milieux poreux. C.R. Acad. Sci. Paris 304, series II, 1035–1038
Lelièvre, R. F.: 1966, Etude d’ écoulements disphasiques permanents à contre-courants en milieu poreux - Comparaison avec les écoulements de même sens (in French). Ph.D. Thesis, University of Toulouse, France.
K. Langaas P. Papatzacous (2001) ArticleTitleNumerical investigations of the steady state relative permeability of a simplified porous media Transport Porous Media 45 241–266 Occurrence Handle10.1023/A:1012002002804
M. Muskat M.W. Meres (1936) ArticleTitleThe flow of heterogeneous fluids through porous media Physics 7 346–363 Occurrence Handle10.1063/1.1745403
T.N. Nasr D.H.S. Law H. Golbeck G. Korpany (2000) ArticleTitleCounter-current aspect of the SAGD process JCPT 39 IssueID1 41–47
L. Onsager (1931a) ArticleTitleReciprocal relations in irreversible processes-I Phys. Rev. 37 405–426 Occurrence Handle10.1103/PhysRev.37.405
L. Onsager (1931b) ArticleTitleReciprocal relations in irreversible processes-II Phys. Rev. 38 2265–2279 Occurrence Handle10.1103/PhysRev.38.2265
N. Rakotomalala D. Salin C.Y. Yortsos (1995) ArticleTitleViscous coupling in a model porous medium geometry: Effect of fluid contact area App. Sci. Res. 55 155–169 Occurrence Handle10.1007/BF00868469
W. Rose (2000) ArticleTitleMyths about later-day extension of Darcy’s law J. Petrol. Sci. Eng. 26 187–198 Occurrence Handle10.1016/S0920-4105(00)00033-4
Rose, W.: 1999, Relative permeability ideas - Then and now (Richards to Leverett to Yuster, and Beyond). SPE paper number 57442 presented at the 1999 SPE regional meeting, Charleston, West Virginia, Oct. 1999.
T.J.T. Spanos V. Cruz Particlede la J. Hube (1988) ArticleTitleAn analysis of the theoretical foundations of relative permeability curves AOSTRA J. Res. 4 181–192
C.Y. Wang (1997) ArticleTitleAn alternative description of viscous coupling in two-phase flow through porous media Transport Porous Media 28 205–219 Occurrence Handle10.1023/A:1006514204336
S. Whitaker (1986) ArticleTitleFlow in porous media II: The governing equations for immiscible, two-phase flow Transport Porous Media 1 105–125 Occurrence Handle10.1007/BF00714688
Yuster S.T. (1951). Theoretical consideration of multiphase flow in idealized capillary systems, in: Proceeding of the Third World Petroleum Congress 2, 437–445
C. Zarcone R. Lenormand (1994) ArticleTitleDétermination expérimentale du couplage visqueux dans les écoulements diphasiques en milieu poreux C. R. Acad. Sci. Paris 318 1429–1438
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ayodele, O.R. Theoretical Analysis of Viscous Coupling in Two-phase Flow through Porous Media. Transp Porous Med 64, 171–184 (2006). https://doi.org/10.1007/s11242-005-2809-8
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11242-005-2809-8