Fundamentals of Fluid Flow in Porous Media


Chapter 2

Relative Permeability

Three Phase Relative Permeability

Three-phase flow situations occur when gas is injected into a reservoir or when a reservoir is produced at a pressure below its bubble point.  The flow of one phase relative to the other phases is represented by the relative permeability of that phase.  Therefore, relative permeability is an essential variable in the prediction of reservoir performance in reservoir simulation studies.

Relative permeability is a direct measure of the ability of the porous medium to conduct flow of one fluid when two or more fluids are present.  The flow of the fluids in the medium is controlled by the pore geometry, wettability, fluid distribution, and saturation history. Wettability is a controlling factor in determining three-phase relative permeability characteristics through its effect on the fluids distribution and flow of the three phases.

The fluids distribution in water wet and oil wet systems is quite different.  When a system is water wet, water fills all the small pores and exists as a film in the larger pores.  When the medium is oil wet, the reverse is true; oil will occupy the small pores and exists as a film in the larger pores.  It is very rare for a reservoir to be gas wet, so gas wet systems will not be discussed.

It is generally believed that reservoirs are originally water wet.  As oil migrates into the reservoir, crude oils come in contact with the rock surface and adsorption can occur which alters the wettability of the rock

[1].  This can lead to many different forms of wettability.  The wettability of a system can range from strongly water wet to strongly oil wet.  When the rock has equal preference for both oil and water, the system has neutral or intermediate wettability.  Fractional wettability is a condition when different areas of the core have different wetting preferences.  There is also a special case of fractional wettability, called mixed wettability, where the small pores are water wet and the large pores are oil wet.

There are two methods of evaluating the relative permeability of each phase: steady state and unsteady state.  Each method has its own advantages and disadvantages, however most researchers say that the unsteady state method should not be used.  The experimental procedure to evaluate relative permeability of two-phase flow is easy, so a lot of relative permeability data were collected.  However, for three-phase flow, the procedure is quite complicated so not many experiments were carried out.  Therefore, relative permeability characteristics of three-phase system are not fully understood.

Generally, the relative permeability can be obtained for imbibition (wetting phase displacing nonwetting phase) or drainage (nonwetting phase displacing wetting phase).  At the same wetting phase saturation, the fluid distribution in the pores will be different, thus it is expected that relative permeability in drainage and imbibition will also be different.  Many researchers published contradictory findings, so hysteresis between drainage and imbibition in three-phase flow is still being studied.  Most researchers have seen that in strongly wetted mediums, the wetting phase and nonwetting phase show very little hysteresis.  However, for the intermediate wetting phase significant hysteresis was seen.

Due to the complex nature of three-phase relative permeability experiments and the lack of agreement between the limited data, many models were developed to generate three-phase relative permeability values.  These models have often not compared with all the available experimental data.

There were many experiments performed with two-phase flow to study the effects of interfacial tension, temperature, flow rate, and viscosity on the relative permeability characteristics.  Some researchers found that these parameters affect relative permeability while some reported otherwise.  Experiments on three-phase flow to study the effects of these parameters are very rare to non-existent.  The effects of these parameters on two-phase relative permeability are included in the discussion, since it is likely that these parameters will affect three-phase flow in a similar manner.

The flow of fluid in carbonates is also investigated.  Most carbonates are usually oil wet, this means that relative permeability should be different than that of sandstones, which are usually water wet.Relative permeability in heavy oil systems is also being studied.


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


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