Fundamentals of Fluid Flow in Porous Media


Chapter 2

Relative Permeability

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

The wetting fluid in a uniformly wetted system is located in the smaller pores and as a thin film in the larger pores, while the non wetting phase is located in the centers of the larger pores.  In general, at a given saturation, the relative permeability of a fluid is higher when it is the non wetting fluid

[1].  This means that the water relative permeability is larger in an oil wet system than it would be in a water wet system.  This occurs because the wetting fluid usually travels through the small pores, while the nonwetting fluid moves through the larger pores, which results in better flow of the nonwetting fluid.  Also, at low nonwetting phase saturation the nonwetting phase will be trapped as discontinuous blobs in the larger pores which block the flow of the wetting fluid, thus decreasing its relative permeability.  On the other hand, the relative permeability of the nonwetting phase at low wetting phase saturation is very high since it travels through the center of the larger pores.  This nonwetting phase relative permeability could be as high as the absolute permeability, which indicates that the wetting phase does not significantly restrict the flow of the nonwetting phase.

In a water-oil system, as the system becomes more oil wet, relative permeability of water ( krw ) increases, relative permeability of oil ( kro ) decreases, and the cross-over point occurs at a lower water saturation ( see Figure 2‑85 )[1].

Relative Permeability of Water Wet and Oil Wet Systems
Figure 2-85: Relative Permeability of Water Wet and Oil Wet Systems

These special characteristics allowed Craig to generalize a few rules of thumb[1], which indicate the differences in the relative permeability of strongly water wet and strongly wet oil cores.  These rules are presented in Table 1 below.

  Water wet Oil wet
Swc > 20-25 % of PV < 10-15% of PV
Sw when krw = kro > 50% < 50%
krw at max Sw < 30% > 50% ( can be 100% )


Exceptions have been found to these rules, therefore wettability experiments should be performed separately to evaluate the wettability of the reservoir instead of relying only on Craig’s rules of thumb.  Also, Craig’s rules of thumb can only distinguish water wet conditions from oil wet; they cannot identify the degree of wettability, or neutrally wet, fractionally wet or mixed wet conditions.

Pore geometry can also have a strong effect on the measured relative permeability curves, affecting the cross over point in two-phase flow and the irreducible water saturation1.  If the pore medium consists of a significant number of small pores, the irreducible water saturation is relatively large.  Anderson has also mentioned the significant differences in Swc found in rocks with large, well interconnected pores compared to rocks containing smaller and less well connected pores.  In the water wet cores, the smaller pores are filled with water, thus a larger number of small pores increases the irreducible water saturation, but if these pores are less well connected, the water flow is not better.  When comparing these two samples, the rock with many smaller pores has a larger irreducible water saturation and the cross-over point for the relative permeability occurs at higher water saturation.


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


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