Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Relative Permeability

The absolute permeability is a property of the porous medium and is a measure of the capacity of the medium to transmit fluids. The absolute permeability is referred to the rock condition where single phase saturation is considered in other words the rock is fully saturated with one homogeneous fluid.

Fluid flow in reservoirs typically involves more than one fluid, which means that the general ability of one fluid to flow is affected by the presence of other fluids in the reservoir. In order to develop estimates of fluid behavior in reservoirs, this phenomenon needs to be quantified in some way. The concept of describing this multiphase flow in reservoirs is known as relative permeability, which is defined as the ratio of the effective permeability of a fluid to the absolute permeability of the rock. The effective permeability is a relative measure of conductance of the porous medium for one fluid phase in the presence of other fluid phases.

Where,

• k_ro = relative permeability to oil
• k_rg = relative permeability to gas
• k_rw = relative permeability to water
• k = absolute permeability
• k_o = effective permeability to oil for a given oil saturation
• k_g = effective permeability to gas for a given gas saturation
• k_w = effective permeability to water for a given water saturation

In the definition of effective permeability each fluid phase is considered to be completely independent of the other fluids in the flow network. The fluids are considered immiscible, so that Darcy’s law can be applied to each individually:

Where, s is direction.

Since the fluid is not completely saturating the rock, other factors come into play other than the pore size distribution. According to experimental evidence, effective permeability is a function of dominant fluid saturation, saturation history, wettability characteristic and pore geometry. So to determine the relative permeability for one phase it is necessary to specify the fluid saturation. In contrast to absolute permeability, relative permeability for each phase is not a unique value and there is a special relative permeability value for each saturation amount.

Since the effective permeabilities may range from zero to k, the relative permeabilities may have any value between zero and one. It should be pointed out that when three phases are present the sum of the relative permeabilities ( k_ro + k_rg + k_rw ) is both variable and always less than or equal to unity.