Transport in Porous Media

, Volume 14, Issue 1, pp 23–32 | Cite as

An investigation into whether the nondiagonal mobility coefficients which arise in coupled, two phase flow are equal

  • Ramon G. Bentsen


Recent developments in two-phase flow through porous media show that four mobilities are required to define completely the flow characteristics of a particular porous medium. Because, in idealized porous media, it has been shown that two of these mobilities, the nondiagonal mobilities which represent the viscous coupling exerted between fluid phases, are equal, it has been suggested that they may be equal, as well, in real porous media. It is shown in this paper that these two interactive mobilities cannot be equal in real porous media. Moreover, it is demonstrated that the relative permeabilities which pertain to pure countercurrent flow differ from those which pertain to steady-state, countercurrent flow, and that the pure countercurrent-flow relative permeabilities depend strongly on viscosity ratio. Finally, it is suggested that, because three different experiments give rise to three different sets of relative permeability curves, the conventional description of two-phase flow is inadequate inasmuch as it does not account properly for the viscous coupling exerted between fluid phases.

Key words

Countercurrent flow effective permeability mobility viscous coupling immiscible flow 



absolute permeability, m2


effective permeability of phasei; i=1, 2, m2


generalized effective permeability of phasei; i, j=1, 2, m2


relative permeability of phasei(i.e. (k i /k));i=1, 2


end point mobility ratio (i.e.k1rΜ2/k2rΜ1)


function relating the flow potential in phase 1 to that in phase 2


Darcy velocity of phasei;i=1, 2, m/s

Greek Letters


generalized effective mobility of phase i (i.e. kij/Μ j );i j=1, 2, m2/Pa·s


effective mobility of phasei (i.e.k i /Μ i );i=1, 2, m2/Pa·s


viscosity of phasei, Pa·s


flow potential of phasei, J/m3

Subscripts and Superscripts






wetting phase


nonwetting phase


countercurrent flow


pure countercurrent flow


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Ramon G. Bentsen
    • 1
  1. 1.Department of Mining, Metallurgical and Petroleum Engineering EdmontonUniversity of AlbertaAlbertaCanada

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