Effective and Relative Permeability

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.

k_g = effective permeability to gas

k_o = effective permeability to oil

k_w = 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.

Relative permeability to gas – k_rg = k_g÷k

Relative permeability to oil – k_ro = k_o÷k

Relative permeability to water – k_rw = k_w÷k

Where;

k = absolute permeability

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

Figure 1 – Relative Permeability Plot

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).

Figure 2 – Oil flow only when Sw < Swc

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

Figure 3 – Water Starts to Flow

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 raturation), both oil and water flow (Figure 4).

Figure 4 – Both oil and water flow

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).

Figure 5 – Oil will not flow

Applications of Relative Permeability

Relative permeability of rock is used to predict the flow of each fluid phase, displacement efficiency and expected recoverable reserves.

References

Abhijit Y. Dandekar, 2013. Petroleum Reservoir Rock and Fluid Properties, Second Edition. 2 Edition. CRC Press.

L.P. Dake, 1983. Fundamentals of Reservoir Engineering, Volume 8 (Developments in Petroleum Science). New impression Edition. Elsevier Science.

Tarek Ahmed PhD PE, 2011. Advanced Reservoir Management and Engineering, Second Edition. 2 Edition. Gulf Professional Publishing.