Relative Permeability: Definition, Reservoir Rock Properties, and Fluid Flow
What Is Relative Permeability?
Relative permeability (kr) is the ratio of effective permeability of a phase (oil, water, or gas) in a multiphase system to the absolute permeability of the rock at 100% saturation of that phase. It is expressed as a dimensionless number between 0 and 1: kro is oil relative permeability, krw is water relative permeability, and krg is gas relative permeability. Relative permeability curves — kr plotted against water saturation Sw — are the most influential input to reservoir simulation models and waterflood predictions. They govern how easily each phase flows relative to the others at any given saturation state, directly controlling recovery factor, watercut development, mobility ratio, and the economic life of every conventional oil and gas field.
Key Takeaways
- Relative permeability is dimensionless (0–1): kr = 0 means the phase cannot flow at that saturation; kr = 1 means it flows as if the rock contains only that phase.
- kro at connate water saturation (Swi) is the starting point for primary production; krw at residual oil saturation (Sor) is the endpoint of a waterflood.
- Relative permeability is controlled by wettability — water-wet and oil-wet systems produce very different kr curves with dramatically different recovery implications.
- Corefloods (steady-state or unsteady-state displacement experiments) are the standard laboratory method to measure kr; centrifuge methods provide alternative endpoint data.
- kr curves are used directly in every reservoir simulator (Eclipse, CMG IMEX, tNavigator) — errors in kr are the most common source of mismatched history-match predictions.
Reading Relative Permeability Curves
A typical oil-water kr plot shows two curves on axes of Sw (x-axis) and kr (y-axis). The curves have four key endpoints: Swi (irreducible water saturation, the minimum water that remains even after maximum drainage — typically 10–30%); kro(Swi) (oil relative permeability at irreducible water, the starting point for a virgin reservoir — often 0.6–1.0); Sor (residual oil saturation, the minimum oil remaining after complete waterflood — typically 15–35%); and krw(Sor) (water relative permeability at residual oil — typically 0.1–0.6, controls waterflood economics).
In a water-wet system, the crossover of kro and krw occurs at Sw > 0.5 — water must reach high saturation before it begins to dominate flow. kro drops rapidly as water saturation increases; krw rises slowly. In an oil-wet system, the crossover occurs at low Sw (often 0.2–0.4), kro remains significant even at high water saturations, and krw rises rapidly. Oil-wet systems produce water early and copiously, but can leave large residual oil volumes on grain surfaces. Wettability determines which curve shape governs production — and it can change within a reservoir due to asphaltene deposition, OBM invasion, or acidic crude contact with carbonate minerals.
- Symbol: kro (oil), krw (water), krg (gas)
- Range: 0 to 1 (dimensionless)
- Governing factor: wettability, pore geometry, saturation history (drainage vs. imbibition)
- Laboratory measurement: steady-state coreflood, unsteady-state (JBN method), centrifuge
- Reservoir simulator input: kr tables vs Sw (and krg vs Sg for gas phases)
- Key endpoints: kro(Swi), krw(Sor), Swi, Sor
- Standard references: API RP 40; SCA recommended practices; SPE 10150 (Honarpour correlations)
- Imbibition vs drainage: direction of saturation change produces different kr curves (hysteresis)
Always measure relative permeability at reservoir conditions (net confining stress, reservoir temperature) using native or restored-state cores rather than cleaned, extracted plugs. Laboratory kr curves on cleaned cores systematically underestimate kro in the intermediate to high water saturation range — cleaning strips the asphaltene and wettability modifiers that determine the in-situ wetting state, producing artificially water-wet curves that overpredict waterflood performance. The gap between cleaned-core kr and native-state kr can represent 5–15 saturation units difference in Sor — which in a 500 MMbbl OOIP field means 25–75 million barrels of reserves difference. Request native-state cores from the wellsite, run kr within 60 days without cleaning, and use the Amott-Harvey index from the same plugs to verify the wetting state assumed in the simulation model.
Relative Permeability Synonyms and Related Terminology
Relative permeability is also referred to as:
- kr curves — the most common shorthand in reservoir engineering and simulation
- Effective permeability (ke) — absolute permeability × relative permeability; the actual phase mobility at a given saturation
- Phase mobility (λ) — effective permeability divided by viscosity (ke/μ); the combination that enters the mobility ratio calculation
- Rock curves — simulation engineer shorthand for the kr and capillary pressure tables that define rock multiphase flow behaviour
Related terms: Wettability, Waterflood, Capillary Pressure, Permeability
Frequently Asked Questions About Relative Permeability
Why do kr curves depend on saturation history (hysteresis)?
The path by which saturation changes matters: drainage (decreasing water saturation — oil moving in) produces different kr curves than imbibition (increasing water saturation — water moving in). A pore throat drained of water traps that water differently than a throat flooded with water after drainage. The capillary trapping mechanism creates kr hysteresis: after waterflooding, some residual oil is trapped in pore throats by snap-off (oil thread breakage); during re-drainage (gas injection after waterflood), some of this trapped oil is remobilised. In a WAG (water-alternating-gas) injection project, both imbibition (water cycles) and drainage (gas cycles) kr curves are needed in the simulator. Using only imbibition curves underestimates gas-phase mobility during gas slugs and overpredicts gas storage capacity.
How are kr curves validated against field data?
Laboratory kr curves are almost never directly usable in reservoir simulators without calibration to field behaviour. Lab curves represent core-plug scale (centimetres); reservoir simulation gridblocks represent meters to tens of metres. Upscaled (pseudo) kr functions are derived by history-matching field watercut data — adjusting curve shape, endpoint saturations, and kr exponents (Corey model parameters) until the simulation matches observed watercut rise, water breakthrough timing, and well-by-well rate performance. The Corey-Brooks model — kro = kro(Swi) × [(1 - Sw - Sor)/(1 - Swi - Sor)]^n₀, with exponents n₀ and nw — provides a mathematically tractable parameterisation for history-matching. A mismatch between lab kr and history-match kr should trigger investigation into rock typing, wettability, and structural geology rather than automatic adoption of the history-match curves as ground truth.
What is the practical difference between kro end-point and kro at initial conditions?
kro(Swi) — oil relative permeability at connate water saturation — is the maximum oil kr in a virgin reservoir. In a strong water-wet system it is close to 1.0; in mixed-wet or oil-wet systems it may be 0.6–0.8, meaning oil is never as mobile as it would be in an otherwise identical single-phase system. This endpoint directly sets the maximum deliverability of a new well — a well in a reservoir with kro(Swi) = 0.5 versus 1.0 will produce at half the rate from identical reservoir permeability. The endpoint matters enormously for initial production forecasts and facility design. Sensitivity to kro endpoint is one reason reservoir engineers request multiple core plugs spanning the full saturation range: a single kr measurement is insufficient to constrain the critical endpoints.
Why Relative Permeability Matters in Oil and Gas
Relative permeability is arguably the most consequential rock property in reservoir engineering — more influential than absolute permeability alone because it determines how oil, water, and gas share the available pore space and flow capacity. Every waterflood design, every gas injection scheme, every EOR project, and every reservoir simulation depends on kr inputs that are accurate at reservoir conditions. Errors in kr propagate through the entire production forecast: a 10-unit error in Sor misrepresents both the recovery target and the economic life of the field. Getting relative permeability right — through proper core handling, native-state preservation, and careful laboratory methodology — is one of the most valuable investments in any reservoir characterisation programme.