Relative permeability

Absolute, effective, and relative permeability

Reservoirs contain water and oil or gas in varying amounts. Each interferes with and impedes the flow of the others. The aquifer portion of a reservoir system by definition contains water as a single phase (100% S_w). The permeability of that rock to water is absolute permeability (K_ab). The permeability of a reservoir rock to any one fluid in the presence of others is its effective permeability to that fluid. It depends on the values of fluid saturations. Relative permeability to oil (K_ro), gas (K_rg), or water (K_rw) is the ratio of effective permeability of oil, gas, or water to absolute permeability. Relative permeability can be expressed as a number between 0 and 1.0 or as a percent. Pore type and formation wettability affect relative permeability.

Why k_ro or k_rg is less than k_ab

Figure 1 See text for explanation.

A pore system saturated 100% with any fluid transmits that fluid at a rate relative to the pore throat size and the pressure differential. In the drawing in Figure 1, the absolute pore throat size (A) is noted as the distance between grain surfaces. When a sample contains oil or gas and water (where water wets the grain surface), the pore throat size (B) for oil or gas flow is less than the absolute pore throat size (A). The thickness of the water layer coating the grains is proportional to the S_w of the rock. In other words, as buoyancy pressure increases, S_w decreases and the effective size of the pore throat for oil or gas flow (B) increases.

Interpreting a relative permeability curve

The diagram below shows relationships between relative permeability curves (drainage and imbibition), capillary pressure, and fluid distribution in a homogeneous section of a reservoir system. The reservoir system rock has a porosity of 30% and a permeability of 10 md (r₃₅ = 1.1μ). Laboratory single-phase air permeability is typically used to represent absolute permeability (K_a when determining relative permeability to oil or water at a specific S_w.

The figure below depicts three relative permeability curves:

• Water (K_rw)—similar for both drainage and imbibition tests
• Oil drainage (K_ro-D)—reflects migrating oil displacing water (decreasing S_w) with increasing buoyancy pressure (P_b)
• Oil imbibition (K_ro-I)—reflects reduction in oil saturation (S₀) as a water front moves through a rock sample, resaturating it with water (S_xo)

The curve labeled K_ro represents the relative permeability of a formation to oil in the presence of varying water saturation (S_w). The curve labeled K_rw represents the relative permeability of the formation to water.

Consider points A–D below. Point A, at S_w = 100%, is the original condition of the sample. Here K_rw ≈ K_a (10 md). At point B (S_w ≈ 90%, S₀ = 10%), oil breaks through the sample, representing the migration saturation of the sample; K_ro = 1.0. At point C (S_w ≈ 50%, S_o ≈ 10%), K_rw is less than 1% of K_a and water, now confined to only the smallest ports, ceases to flow while oil flow approaches its maximum. At point D on the K_ro-D curve (S_w ≈ 20%, S_o ≈ 80%), relative permeability is approaching 1.0 (~ 10 md).

Figure 9-27 is an example of “drainage” relative permeability of a water-wet reservoir. It shows changes in K_ro and K_rw as S_w decreases, as in a water-drive reservoir during hydrocarbon fill-up. “Imbibition” K_ro and K_rw have a different aspect, being measured while S_w increases, as it does during production in a reservoir with a water drive.

Figure 9-27 Modified.

Drainage vs. imbibition curves

The drainage curve determines from computed S_w whether a zone is representative of lower transitional (K_rw> K_ro - D), upper transitional (K_rwro - D), or free oil (K_rw ≈ 0). The imbibition curve relates to performance due to filtrate invasion from water injection or flushing from natural water drive.

Pore throat size and k_r

Every pore type has a unique relative permeability signature. Consider the hypothetical drainage relative permeability type curves shown below. Curves A, B, and C represent the relative permeability relationships for rocks with different port types: macro, meso, and micro, respectively. Curve A represents a rock with greater performance capability than B or C. Note how critical water saturation decreases as pore throat size increases. Also note the changing position of K_ro–K_rw crossover with changes in pore throat size.

Critical water saturation

Critical S_w is the point where water saturation is so low that no significant water cut can be measured; only hydrocarbon flows from the reservoir. At S_w higher than critical S_w, water flows with hydrocarbon. Where S_w becomes great enough, only water flows.

Critical water saturation

The critical S_w value is different for each port type. Curve A in Figure 9-28 represents rocks with macroporosity. It has a critical S_w less than 20%. Curve B represents a rock (continued) with mesoporosity. Mesoporous rocks have a critical S_w of 20–60%. Curve C represents rocks with microporosity. They have a critical S_w of 60–80%.

Figure 9-28 See text for explanation.

The table below summarizes representative critical S_w values for macro-, meso-, and micropore types that correspond to A, B, and C, respectively, in Figure 9-28.

Pore type	Micro	Meso	Macro
Critical Sw	60–80%	20–60%
Length of transition zone	>30 m	2–30 m	0–2 m

See also

• Pore–fluid interaction
• Hydrocarbon expulsion, migration, and accumulation
• Characterizing rock quality
• Pc curves and saturation profiles
• Converting Pc curves to buoyancy, height, and pore throat radius
• What is permeability?

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