Effective and Relative Permeability

Porosity
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Mustafa AbdulSattar

          When there is only one type of fluid flowing through porous media, the permeability for this case is called “absolute permeability.” However, when there is more than one type of fluids present in a rock, a permeability of each fluid to flow is decreased because another fluid will be moving in the rock as well.  A new term of permeability called “effective permeability” is a permeability of a rock to a particular fluid when more than one type of fluid is in a rock

Reservoir consists of three fluids (gas, oil, and water) so these are commonly used abbreviations for effective permeability for each fluid.

  • kg = effective permeability to gas
  • ko = effective permeability to oil
  • kw = effective permeability to water

Normally, it is common to state effective permeability as a function of a rock’s absolute permeability. Relative permeability is defined as a ration of effective permeability to an absolute permeability of rock. The relative permeability is widely used in reservoir engineering. These functions below are the relative permeability of gas, oil, and water.

  • krg = kg ÷ k
  • kro = ko ÷ k
  • krw = kw ÷ k

k = absolute permeability

Oil-water relative permeability
Fig.1
relative permeability As water saturation (Sw) decreases
Fig.2

Relative permeability is normally plotted as a function of water saturation in a rock . Figure 1 demonstrates a plot of oil-water relative permeability curves.

As water saturation (Sw) decreases, relative permeability of oil (Kro) decreases and relative permeability of water increases (Krw). If water saturation is

below connate water saturation (Swc), only oil will flow, but water will not flow (Figure 2)

When water saturation (Sw) in a rock is equal to connate water saturation (Swc), water starts to flow (Figure 3) Water starts to flow at Swc

permeability when water saturation
Fig.3


Oil flow continues to decrease and water flow continues to decrease because the water saturation goes up. If water saturation (Sw) is between connate water saturation (Swc) and 1 minus Sor (irreducible oil saturation), both oil and water flow (Figure 4).

Once water saturation in a rock increases to 1 minus Sor (irreducible oil saturation), oil will not flow, but only water will flow. Beyond this point oil will not move at all but water will continue to increase as water saturation (Sw) in a rock increases (Figure 5).

permeability curve
Fig.4
permeabilty when there is no oil flow
Fig.5