Abstract
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.
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Abbreviations
- k :
-
absolute permeability, m2
- k i :
-
effective permeability of phasei; i=1, 2, m2
- k ij :
-
generalized effective permeability of phasei; i, j=1, 2, m2
- k ri :
-
relative permeability of phasei(i.e. (k i /k));i=1, 2
- M r :
-
end point mobility ratio (i.e.k 1r Μ 2/k 2r Μ 1)
- R 12 :
-
function relating the flow potential in phase 1 to that in phase 2
- U i :
-
Darcy velocity of phasei;i=1, 2, m/s
- λ ij :
-
generalized effective mobility of phase i (i.e. kij/Μ j );i j=1, 2, m2/Pa·s
- λ i :
-
effective mobility of phasei (i.e.k i /Μ i );i=1, 2, m2/Pa·s
- Μ i :
-
viscosity of phasei, Pa·s
- ψ i :
-
flow potential of phasei, J/m3
- i:
-
irreducible
- r:
-
residual
- 1:
-
wetting phase
- 2:
-
nonwetting phase
- *:
-
countercurrent flow
- ':
-
pure countercurrent flow
References
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Bentsen, R.G. An investigation into whether the nondiagonal mobility coefficients which arise in coupled, two phase flow are equal. Transp Porous Med 14, 23–32 (1994). https://doi.org/10.1007/BF00617026
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DOI: https://doi.org/10.1007/BF00617026