Fundamentals of Fluid Flow in Porous Media


Chapter 2

Relative Permeability

Three Phase Relative Permeability: Relative Permeability in Three-Phase Systems

In three-phase systems, there is no obvious distinction in relative permeability of water wet and oil wet systems.  Most researchers can identify the characteristics of the wetting phase and the nonwetting phase.  However, the pattern for the intermediate wetting phase is not fully identified yet.  For fractionally wet, intermediate and mixed wet system, special characteristics of relative permeability are not known at all.

Most researchers agree that the relative permeability of the wetting phase depends on its saturation only.  Anderson mentioned that many researchers found that in a water wet system, there was a good agreement between the wetting phase relative permeability of two-phase systems ( water in the water oil tests and oil in gas-oil tests )

[1].  However, there have been some experiments which show that the wetting phase relative permeability depends on saturations of the other phases.  Some researchers even found that the trapped gas saturation could affect both the water and oil relative permeabilities.  There are other experiments which show that the wetting phase relative permeability was affected by the nonwetting phase saturation in water wet systems.  Most researchers still insist however that the relative permeability of the wetting phase should be a function of its saturation only.  They suggest that some of these systems that showed significant difference in the relative permeability of the wetting phase were not strongly water wet.

Three-phase relative permeability data for water wet sandpacks have been reported by several people.  However, there is very limited three-phase data for oil wet cores.  The data for water wet cores and sandpacks show generally consistent behavior; gas and water primarily depend on the gas or water saturation respectively, and are weak functions of the saturations of other fluids present.  These data indicate that a strongly wetting phase ( water ) and a nonwetting phase ( gas ) are not affected by the other phases.  However, Schneider et al. reported that the three-phase relative permeability of gas ( krg ) values are smaller than the two-phase krg in drainage[2].  This is because of flow interference between the gas ( nonwetting ) phase and the oil (intermediate wetting) phase in a water wet system containing three phases.  Corey et al., however, saw from their experiments that gas relative permeability was essentially the same in two-phase and three-phase systems[3].  The intermediate wetting phase ( oil ) appears to be influenced by interactions with the other phases, but the nature of the interaction is not very distinctive.  In some cases the dependence of oil relative permeability on the saturations of the other phases is apparent and in some cases it is not.  The experimental data often shows so much scattering that no conclusion can be reached.  Even though the evidence is not as overwhelming as for the wetting phase, many researchers agree that the relative permeability of the nonwetting phase is a function of its own saturation only.

In water wet systems with trapped gas present, Schneider et al. found that the maximum value of kro is larger than the value in the case without gas[2].  They explained that this is because gas is the nonwetting phase with respect to oil.  Also, the trapped gas saturation resulted in lower krw.  This is not consistent with the general belief that for water wet system; water relative permeability is a function of water saturation only.

DiCarlo et al. performed three-phase experiments and they have seen other characteristics[4]:

  • The permeabilities of the most wetting fluid are always similar. In both cases of water wet and oil wet media, krw and kro can be described by a power law, kr ~Sα, where α = 5.  However, a lower saturation is reached in the oil-wet medium than in the water-wet medium.  This is consistent with Craig’s generalization that for oil wet systems Swi is lower than Swi in water wet system.  For the strongly and uniformly water wet and oil wet media, it is expected that the configuration of the most wetting fluid should be similar in both systems at the same saturation, thus they should have the same relative permeability characteristics.
  • At high saturations, the permeabilities of oil ( nonwetting phase ) in water wet media and water ( nonwetting phase ) in oil wet media are similar. Both can be described by a power law, kr ~Sα, where α = 4. DiCarlo et al. believed that at high saturations the arrangement of oil filled pores in a water-wet medium and the water filled pores in oil wet medium are quite similar.
  • At low saturations, the permeabilities of oil in water wet media and water in oil wet media are very different. The oil relative permeability remains finite at low saturations while the water relative permeability drops off quickly and approaches zero.  At low saturation phases may remain connected through wetting layers in crevices in the pore space.  It is this connectivity which controls relative permeability at low saturation.  It is possible that the pore scale configuration and connectivity of oil and water is very different for water wet and oil wet media.
  • The gas relative permeability for the oil-wet medium is approximately half its value in a water wet medium. In water wet media, the water phase will occupy the smallest pores and crevices while the gas phase occupies the large pore spaces since gas is more nonwetting than oil.  In oil wet media, the water and gas phases compete for the largest pores.  It is possible that at a specific gas saturations in the oil wet system, the gas is in smaller pathways leading to a lower permeability.
  • For the fractionally wet sand, the oil, water and gas relative permeabilities are between the oil, water and gas relative permeabilities in the water wet and oil wet sands.

Schneider et al. mentioned that for systems having no strong wetting preference, characteristics of three-phase flow can be very different than for two-phase flow[2].  This suggests that the relative permeability might be a function of other phases as well.


[1] Anderson, W.G., “Wettability Literature Survey – Part 5: The Effects of Wettability on Relative Permeability”, SPE 16323.

[2] Schneider, F.N. and Owens, W.W., “Sandstone and Carbonate Two- and Three-Phase Relative Permeability Characteristics”, Trans., AIME (1970) 249, 75-84.

[3] Corey, A.T., Rathjens, C.H., Henderson, J.H., “Three-Phase Relative Permeability”, Trans., AIME (1956) 207, 349-351.

[4] DiCarlo, D.A., Sagni, A. And Blunt, M.J., “The Effect of Wettability on Three-Phase Relative Permeability”, SPE 49317.


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